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Practice › LeetCode › LeetCode 36xx ›

LeetCode 3656 - Determine if a Simple Graph Exists

LeetCode Problem 3656 Difficulty: 🟡 Medium Topics: Array, Binary Search, Graph Theory, Sorting, Prefix Sum Solution Correctness The proposed solution explains in detail how Algorithm S computes subtraction in radix $b$ and how the complement-based correction works when a final borrow occurs. However, the exercise asks specifically to show that if $u_n = v_{n-1}$, then $q = b - 1$ or $b - 2$ , where $q$ is presumably the...

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LeetCode 3645 - Maximum Total from Optimal Activation Order

LeetCode Problem 3645 Difficulty: 🟡 Medium Topics: Array, Two Pointers, Greedy, Sorting, Heap (Priority Queue) Solution Problem Understanding This problem involves determining the maximum total value achievable by activating elements in an array under a set of constraints. We are given two arrays, value and limit , both of length n . Each element starts inactive, and activating an element adds its corresponding value[i] to the total. However, activation is...

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LeetCode 3631 - Sort Threats by Severity and Exploitability

LeetCode Problem 3631 Difficulty: 🟡 Medium Topics: Array, Sorting Solution Problem Understanding The problem gives a list of threats, where each threat is represented as a triplet [IDi, sevi, expi] . Each threat has a unique identifier, a severity value, and an exploitability value. From these two attributes, a derived metric called score is defined as score = 2 × severity + exploitability . The task is to reorder the...

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LeetCode 3920 - Maximize Fixed Points After Deletions

LeetCode Problem 3920 Difficulty: 🔴 Hard Topics: Array, Binary Search, Sorting Solution Problem Understanding The problem asks us to maximize the number of fixed points in an array after performing deletions. A fixed point is an index i such that nums[i] == i . We are allowed to delete any number of elements from the array, and after each deletion, all remaining elements shift left, which reassigns the indices starting...

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LeetCode 3913 - Sort Vowels by Frequency

LeetCode Problem 3913 Difficulty: 🟡 Medium Topics: String, Sorting, Counting Solution Problem Understanding The problem requires us to reorder the vowels in a given string s based on their frequency, while keeping all consonants in their original positions. Specifically, the vowels must appear in non-increasing order of frequency . If two vowels have the same frequency, the one that appeared first in the string should come first in the sorted...

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LeetCode 3886 - Sum of Sortable Integers

LeetCode Problem 3886 Difficulty: 🔴 Hard Topics: Array, Math, Sorting, Enumeration Solution Problem Understanding The problem asks us to find all integers k that divide the length of the input array nums and for which the array can be sorted into non-decreasing order using a very specific operation. The operation is to partition nums into consecutive subarrays of length k and then cyclically rotate each subarray independently any number of...

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LeetCode 3814 - Maximum Capacity Within Budget

LeetCode Problem 3814 Difficulty: 🟡 Medium Topics: Array, Two Pointers, Binary Search, Sorting Solution Corrected Solution for Exercise 4.3.1.9 Exercise 4.3.1.9 asks for a generalization of Algorithm A to add two $n$-place numbers in a mixed-radix system with bases $b_0, b_1, \dots, b_{n-1}$ from right to left. Algorithm A in TAOCP §4.3.1 describes standard addition with carry propagation in a single-radix positional system. Here we adapt it to mixed-radix arithmetic,...

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LeetCode 3776 - Minimum Moves to Balance Circular Array

LeetCode Problem 3776 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting Solution Corrected Solution for Exercise 4.3.1.7 Exercise 4.3.1.7 asks for the average number of times the algorithm of Exercise 5 finds that a carry propagates through exactly $k$ digits of the partial answer, for $k = 1, 2, \dots, n$, under the assumption that both inputs are independent and uniformly distributed integers in $[0, b^n - 1]$. We provide a...

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LeetCode 3752 - Lexicographically Smallest Negated Permutation that Sums to Target

LeetCode Problem 3752 Difficulty: 🟡 Medium Topics: Array, Math, Two Pointers, Greedy, Sorting Solution LeetCode 3752: Lexicographically Smallest Negated Permutation that Sums to Target Problem Understanding We are given two values: n , which determines the numbers 1, 2, ..., n target , which is the required sum of the final array We must construct an array of length n whose absolute values are exactly the numbers 1 through n...

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LeetCode 3732 - Maximum Product of Three Elements After One Replacement

LeetCode Problem 3732 Difficulty: 🟡 Medium Topics: Array, Math, Greedy, Sorting Solution Problem Understanding This problem asks us to maximize the product of any three distinct elements in an array, given that we are allowed to replace exactly one element in the array with any integer from -10^5 to 10^5 . The input is an integer array nums of length at least 3 and at most 10^5 . The goal...

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LeetCode 3649 - Number of Perfect Pairs

LeetCode Problem 3649 Difficulty: 🟡 Medium Topics: Array, Math, Two Pointers, Sorting Solution Problem Understanding This problem asks us to count the number of perfect pairs in an integer array nums . A pair (i, j) is perfect if i < j and the elements at these indices satisfy two conditions: the minimum of |a - b| and |a + b| is less than or equal to the smaller absolute...

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LeetCode 3627 - Maximum Median Sum of Subsequences of Size 3

LeetCode Problem 3627 Difficulty: 🟡 Medium Topics: Array, Math, Greedy, Sorting, Game Theory Solution LeetCode 3627 - Maximum Median Sum of Subsequences of Size 3 Problem Understanding We are given an array nums whose length is always divisible by 3 . The array must be emptied by repeatedly selecting exactly three elements. For each selected triple, we compute its median, add that median to our answer, and remove all three...

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LeetCode 3613 - Minimize Maximum Component Cost

LeetCode Problem 3613 Difficulty: 🟡 Medium Topics: Binary Search, Union-Find, Graph Theory, Sorting Solution Problem Understanding The problem asks us to minimize the maximum cost among components in a connected undirected graph after removing edges. Each edge has a weight, and the cost of a connected component is the largest weight of any edge in that component. You can remove edges freely, but the graph must end up with at...

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LeetCode 3608 - Minimum Time for K Connected Components

LeetCode Problem 3608 Difficulty: 🟡 Medium Topics: Binary Search, Union-Find, Graph Theory, Sorting Solution LeetCode 3608 - Minimum Time for K Connected Components Problem Understanding We are given an undirected graph with n vertices and a list of edges. Each edge has a removal time timei . The graph evolves over time. At time t , every edge whose removal time satisfies timei <= t has already been removed. All...

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LeetCode 3551 - Minimum Swaps to Sort by Digit Sum

LeetCode Problem 3551 Difficulty: 🟡 Medium Topics: Array, Hash Table, Sorting Solution Problem Understanding The problem asks us to sort an array of distinct positive integers not by their natural numeric value, but by the sum of their digits . If two numbers share the same digit sum, the smaller number must come first. After determining this sorted order, we must calculate the minimum number of swaps needed to transform...

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LeetCode 3555 - Smallest Subarray to Sort in Every Sliding Window

LeetCode Problem 3555 Difficulty: 🟡 Medium Topics: Array, Two Pointers, Stack, Greedy, Sorting, Monotonic Stack Solution Problem Understanding We are given an array nums and a window size k . For every contiguous subarray of length k , we must determine the minimum length of a continuous segment that needs to be sorted so that the entire window becomes non-decreasing. In other words, for each sliding window: nums[i : i...

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LeetCode 3531 - Count Covered Buildings

LeetCode Problem 3531 Difficulty: 🟡 Medium Topics: Array, Hash Table, Sorting Solution Solution A single-precision floating point number in MIX, as defined in Section 4.2.1, consists of a sign byte, an exponent field, and a normalized fraction stored in one word. A double-precision floating point number in format (1) consists of the same sign and exponent structure, but with an eight-byte fraction split across two words, the most significant five...

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LeetCode 3025 - Find the Number of Ways to Place People I

LeetCode Problem 3025 Difficulty: 🟡 Medium Topics: Array, Math, Geometry, Sorting, Enumeration Solution Correctness The proposed solution does not address the actual content of the TAOCP exercise. The exercise is about constructing and explaining numerical instability in floating point evaluation of algebraically equivalent expressions, but the “solution” instead discusses Python runtime errors, missing imports, and input parsing issues. These are unrelated to floating point arithmetic, polynomial rearrangement, or conditioning. A...

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LeetCode 2933 - High-Access Employees

LeetCode Problem 2933 Difficulty: 🟡 Medium Topics: Array, Hash Table, String, Sorting Solution LeetCode 2933 - High-Access Employees Problem Understanding This problem provides a list of employee access records. Each record contains two pieces of information: The employee's name. A timestamp in 24-hour "HHMM" format. All timestamps belong to the same day, so there is no need to handle dates or day transitions. An employee is considered high-access if they...

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LeetCode 3774 - Absolute Difference Between Maximum and Minimum K Elements

LeetCode Problem 3774 Difficulty: 🟢 Easy Topics: Array, Sorting Solution Problem Understanding The problem asks us to calculate the absolute difference between the sum of the k largest elements and the sum of the k smallest elements in a given array nums . In other words, we first need to identify the k smallest values, sum them up, then identify the k largest values, sum them, and finally compute the...

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LeetCode 3394 - Check if Grid can be Cut into Sections

LeetCode Problem 3394 Difficulty: 🟡 Medium Topics: Array, Sorting Solution

Practice › LeetCode › LeetCode 36xx ›

LeetCode 3633 - Earliest Finish Time for Land and Water Rides I

LeetCode Problem 3633 Difficulty: 🟢 Easy Topics: Array, Two Pointers, Binary Search, Greedy, Sorting Solution Problem Understanding The problem asks us to determine the earliest possible time a tourist can finish exactly one land ride and one water ride at a theme park, where rides may be taken in either order. Each ride has a start time , representing when it becomes available, and a duration , representing how long...

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LeetCode 3634 - Minimum Removals to Balance Array

LeetCode Problem 3634 Difficulty: 🟡 Medium Topics: Array, Binary Search, Sliding Window, Sorting Solution Problem Understanding The problem asks us to transform a given integer array nums into a balanced array with the minimum number of removals . An array is defined as balanced if its maximum element does not exceed k times its minimum element. Formally, for array A , it must satisfy: $$\max(A) \le k \cdot \min(A)$$ We...

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LeetCode 3890 - Integers With Multiple Sum of Two Cubes

LeetCode Problem 3890 Difficulty: 🟡 Medium Topics: Hash Table, Sorting, Counting, Enumeration Solution Problem Understanding The problem asks us to find all integers x less than or equal to a given integer n such that x can be expressed as the sum of cubes of two positive integers in at least two distinct ways . A “distinct way” means that the pairs (a, b) used to form x are different,...

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LeetCode 3780 - Maximum Sum of Three Numbers Divisible by Three

LeetCode Problem 3780 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting, Heap (Priority Queue) Solution Here is a comprehensive, detailed solution guide for LeetCode 3780 - Maximum Sum of Three Numbers Divisible by Three, following your requested format: Problem Understanding The problem asks us to select exactly three integers from the given integer array nums such that the sum of those three integers is divisible by 3 . Among all possible...

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LeetCode 3769 - Sort Integers by Binary Reflection

LeetCode Problem 3769 Difficulty: 🟢 Easy Topics: Array, Sorting Solution Problem Understanding This problem asks us to sort an array of positive integers based on a transformation called binary reflection . The binary reflection of a number is obtained by converting the number to its binary representation, reversing the order of the bits (ignoring leading zeros), and then interpreting the resulting binary string as a decimal integer. For example, the...

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LeetCode 3767 - Maximize Points After Choosing K Tasks

LeetCode Problem 3767 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting, Heap (Priority Queue) Solution Problem Understanding The problem gives two integer arrays, technique1 and technique2 , each of length n , representing two ways to complete n tasks. Completing the i th task with technique1 yields technique1[i] points, while using technique2 yields technique2[i] points. You are also given an integer k , which specifies the minimum number of tasks that...

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LeetCode 3763 - Maximum Total Sum with Threshold Constraints

LeetCode Problem 3763 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting, Heap (Priority Queue) Solution Problem Understanding The problem gives you two integer arrays, nums and threshold , each of length n . Each index i represents a value nums[i] you can add to a running total, but you can only choose that index when the current step is at least threshold[i] . You start at step = 1 and increment...

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LeetCode 3759 - Count Elements With at Least K Greater Values

LeetCode Problem 3759 Difficulty: 🟡 Medium Topics: Array, Binary Search, Divide and Conquer, Sorting, Quickselect Solution Problem Understanding The problem asks us to count how many elements in an array have at least k values that are strictly greater than them. More concretely, for every element nums[i] , we need to determine how many numbers in the array are larger than nums[i] . If that count is at least k...

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LeetCode 3851 - Maximum Requests Without Violating the Limit

LeetCode Problem 3851 Difficulty: 🟡 Medium Topics: Array, Hash Table, Greedy, Sliding Window, Sorting Solution LeetCode 3851 - Maximum Requests Without Violating the Limit Problem Understanding We are given a list of requests, where each request consists of a user ID and a timestamp. Multiple users can appear in the input, and a user may have multiple requests at different times. For a particular user, the rate limit rule states...

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LeetCode 3842 - Toggle Light Bulbs

LeetCode Problem 3842 Difficulty: 🟢 Easy Topics: Array, Hash Table, Sorting, Simulation Solution LeetCode 3842 - Toggle Light Bulbs Problem Understanding The problem gives us an array bulbs , where each value represents a light bulb number between 1 and 100 . Initially, there are exactly 100 light bulbs, and every bulb is turned off. We process the array from left to right. For each value bulbs[i] : If that...

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LeetCode 3731 - Find Missing Elements

LeetCode Problem 3731 Difficulty: 🟢 Easy Topics: Array, Hash Table, Sorting Solution Problem Understanding This problem asks us to reconstruct a missing sequence of integers from a partially incomplete array. We are given an integer array nums containing unique values , and we know an important fact: the array originally contained every integer in a continuous range , but some numbers were removed. Even though some values are missing, the...

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LeetCode 3730 - Maximum Calories Burnt from Jumps

LeetCode Problem 3730 Difficulty: 🟡 Medium Topics: Array, Two Pointers, Greedy, Sorting Solution Problem Understanding The problem asks us to determine the maximum total calories that can be burned while visiting every block exactly once in an arbitrary order. We are given an integer array heights , where heights[i] represents the height of a block. We begin on the ground at height 0 , and our first jump must go...

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LeetCode 3812 - Minimum Edge Toggles on a Tree

LeetCode Problem 3812 Difficulty: 🔴 Hard Topics: Tree, Depth-First Search, Graph Theory, Topological Sort, Sorting Solution LeetCode 3812 - Minimum Edge Toggles on a Tree Problem Understanding We are given a tree with n nodes and n - 1 edges. Every node has a binary color represented by the strings start and target . An operation consists of selecting an edge and toggling both of its endpoints. If a node...

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LeetCode 3806 - Maximum Bitwise AND After Increment Operations

LeetCode Problem 3806 Difficulty: 🔴 Hard Topics: Array, Greedy, Bit Manipulation, Sorting Solution Problem Understanding The problem asks us to find the maximum possible bitwise AND of any subset of size m from an array nums after performing up to k increment operations . Each operation allows us to increase any element in the array by 1. The output is the largest integer that can be obtained as the bitwise...

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LeetCode 3799 - Word Squares II

LeetCode Problem 3799 Difficulty: 🟡 Medium Topics: Array, String, Backtracking, Sorting, Enumeration Solution LeetCode 3799 - Word Squares II Problem Understanding We are given an array of distinct 4-letter words. Our goal is to construct every valid word square consisting of exactly four different words: top forms the top row. bottom forms the bottom row. left forms the left column. right forms the right column. Since each word has length...

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LeetCode 3685 - Subsequence Sum After Capping Elements

LeetCode Problem 3685 Difficulty: 🟡 Medium Topics: Array, Two Pointers, Dynamic Programming, Sorting Solution Here is a complete, rigorous study companion-style solution guide for LeetCode 3685 - Subsequence Sum After Capping Elements , following your requested format and voice. Problem Understanding We are given an integer array nums of size n and a positive integer k . For any integer x from 1 to n , we define the capped...

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LeetCode 3661 - Maximum Walls Destroyed by Robots

LeetCode Problem 3661 Difficulty: 🔴 Hard Topics: Array, Binary Search, Dynamic Programming, Sorting Solution LeetCode 3661 - Maximum Walls Destroyed by Robots Problem Understanding This problem takes place on a one dimensional number line. We are given positions of robots and positions of walls. Every robot owns exactly one bullet, and that bullet can be fired either to the left or to the right. A robot located at position robots[i]...

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LeetCode 3635 - Earliest Finish Time for Land and Water Rides II

LeetCode Problem 3635 Difficulty: 🟡 Medium Topics: Array, Two Pointers, Binary Search, Greedy, Sorting Solution Great! We will cover LeetCode 3627 - Maximum Median Sum of Subsequences of Size 3 in a full, comprehensive technical guide following your formatting requirements. Problem Understanding The problem gives us an integer array nums with a length divisible by 3. We are asked to remove the array in steps by selecting any three elements...

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LeetCode 3572 - Maximize Y‑Sum by Picking a Triplet of Distinct X‑Values

LeetCode Problem 3572 Difficulty: 🟡 Medium Topics: Array, Hash Table, Greedy, Sorting, Heap (Priority Queue) Solution LeetCode 3572 - Maximize Y-Sum by Picking a Triplet of Distinct X-Values Problem Understanding The problem gives us two arrays, x and y , both of length n . Each position i represents a pair (x[i], y[i]) . We need to select exactly three distinct indices i , j , and k such that...

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LeetCode 3556 - Sum of Largest Prime Substrings

LeetCode Problem 3556 Difficulty: 🟡 Medium Topics: Hash Table, Math, String, Sorting, Number Theory Solution Problem Understanding The problem requires identifying prime numbers from all possible substrings of a given string of digits and summing the three largest unique primes. In simpler terms, given a string s of length up to 10, we must consider every contiguous sequence of digits, convert it to an integer (ignoring any leading zeros), and...

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LeetCode 3534 - Path Existence Queries in a Graph II

LeetCode Problem 3534 Difficulty: 🔴 Hard Topics: Array, Two Pointers, Binary Search, Dynamic Programming, Greedy, Bit Manipulation, Graph Theory, Sorting Solution Problem Understanding This problem asks us to compute the shortest path between nodes in an implicit undirected graph defined by a nums array and a maxDiff . Each node i corresponds to nums[i] . There is an edge between nodes i and j if the absolute difference of their...

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LeetCode 3464 - Maximize the Distance Between Points on a Square

LeetCode Problem 3464 Difficulty: 🔴 Hard Topics: Array, Math, Binary Search, Geometry, Sorting Solution LeetCode 3464 - Maximize the Distance Between Points on a Square Problem Understanding We are given a square of side length side . Every point in the input lies somewhere on the boundary of this square. We must choose exactly k points from the given set. For any two selected points, we can compute their Manhattan...

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LeetCode 3414 - Maximum Score of Non-overlapping Intervals

LeetCode Problem 3414 Difficulty: 🔴 Hard Topics: Array, Binary Search, Dynamic Programming, Sorting Solution Problem Understanding This problem combines weighted interval scheduling with an additional constraint: we may select at most 4 intervals, and if multiple selections achieve the same maximum total weight, we must return the lexicographically smallest list of original indices. Each interval is represented as: [left, right, weight] where: left is the starting position right is the...

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LeetCode 3745 - Maximize Expression of Three Elements

LeetCode Problem 3745 Difficulty: 🟢 Easy Topics: Array, Greedy, Sorting, Enumeration Solution LeetCode 3745 - Maximize Expression of Three Elements Problem Understanding The problem gives us an integer array nums and asks us to choose three elements a , b , and c from distinct indices such that the expression: $$a + b - c$$ is as large as possible. The important detail is that the three elements must come...

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LeetCode 3727 - Maximum Alternating Sum of Squares

LeetCode Problem 3727 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting Solution LeetCode 3727 - Maximum Alternating Sum of Squares Problem Understanding We are given an integer array nums , and we are allowed to rearrange its elements in any order before computing a score. The score of a rearranged array arr is defined as: $$arr[0]^2 - arr[1]^2 + arr[2]^2 - arr[3]^2 + \cdots$$ The sign alternates between positive and negative...

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LeetCode 3695 - Maximize Alternating Sum Using Swaps

LeetCode Problem 3695 Difficulty: 🔴 Hard Topics: Array, Greedy, Union-Find, Sorting Solution LeetCode 3695 - Maximize Alternating Sum Using Swaps Problem Understanding We are given an array nums and a list of allowed swap operations. The alternating sum of an array is defined as: $$nums[0] - nums[1] + nums[2] - nums[3] + \cdots$$ Elements at even indices contribute positively, while elements at odd indices contribute negatively. The important detail is...

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LeetCode 3684 - Maximize Sum of At Most K Distinct Elements

LeetCode Problem 3684 Difficulty: 🟢 Easy Topics: Array, Hash Table, Greedy, Sorting Solution Problem Understanding This problem requires selecting at most k distinct elements from a given array of positive integers nums such that their sum is maximized. The result must be returned as a list sorted in strictly descending order . The input nums represents a collection of numbers from which we can pick a subset. Each number can...

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LeetCode 3667 - Sort Array By Absolute Value

LeetCode Problem 3667 Difficulty: 🟢 Easy Topics: Array, Math, Two Pointers, Sorting Solution Problem Understanding The problem asks us to reorder an integer array such that the elements are sorted in non-decreasing order of their absolute values . This means we are not sorting based on the actual numeric value, but rather based on how far each number is from zero on the number line, regardless of sign. In simpler...

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LeetCode 3606 - Coupon Code Validator

LeetCode Problem 3606 Difficulty: 🟢 Easy Topics: Array, Hash Table, String, Sorting Solution Problem Understanding The problem is asking us to validate a set of coupons based on three criteria: the coupon code must be a non-empty string containing only alphanumeric characters or underscores, the business line must belong to a set of four predefined categories, and the coupon must be active. We are given three arrays of equal length,...

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LeetCode 3567 - Minimum Absolute Difference in Sliding Submatrix

LeetCode Problem 3567 Difficulty: 🟡 Medium Topics: Array, Sorting, Matrix Solution Problem Understanding The problem requires computing a specific statistic for every contiguous k x k submatrix of a given m x n integer matrix grid . For each submatrix, we must find the minimum absolute difference between any two distinct elements. The final result is a 2D array ans of size (m - k + 1) x (n -...

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LeetCode 3545 - Minimum Deletions for At Most K Distinct Characters

LeetCode Problem 3545 Difficulty: 🟢 Easy Topics: Hash Table, String, Greedy, Sorting, Counting Solution LeetCode 3545 - Minimum Deletions for At Most K Distinct Characters Problem Understanding The problem gives us a string s containing lowercase English letters and an integer k . We are allowed to delete any characters from the string, including multiple occurrences of the same character. After performing the deletions, the resulting string must contain at...

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LeetCode 3536 - Maximum Product of Two Digits

LeetCode Problem 3536 Difficulty: 🟢 Easy Topics: Math, Sorting Solution LeetCode 3536 - Maximum Product of Two Digits Problem Understanding The problem gives us a positive integer n and asks us to find the maximum product that can be formed by multiplying any two digits that appear in the number. The input is a single integer. We must examine all of its digits and determine which pair of digits produces...

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LeetCode 3517 - Smallest Palindromic Rearrangement I

LeetCode Problem 3517 Difficulty: 🟡 Medium Topics: String, Sorting, Counting Sort Solution Problem Understanding The problem asks us to take a palindromic string s and return its lexicographically smallest palindromic permutation . In other words, we need to rearrange the characters of s into a palindrome that is the smallest possible if you were to compare it alphabetically with all other palindromic arrangements. The input string s is guaranteed to...

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LeetCode 3491 - Phone Number Prefix

LeetCode Problem 3491 Difficulty: 🟢 Easy Topics: Array, String, Trie, Sorting Solution Problem Understanding The problem is asking us to determine whether any phone number in a given list is a prefix of another phone number. In simpler terms, if you have a list of strings representing numbers, you need to check that no string starts with another string from the list. If all numbers are independent prefixes, the output...

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LeetCode 3476 - Maximize Profit from Task Assignment

LeetCode Problem 3476 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting, Heap (Priority Queue) Solution Problem Understanding This problem asks us to assign tasks to workers in order to maximize total profit, under strict skill constraints. Each worker has a skill level, and each task has a required skill and an associated profit. A worker can only complete a task if their skill exactly matches the task's required skill. Additionally, there...

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LeetCode 3478 - Choose K Elements With Maximum Sum

LeetCode Problem 3478 Difficulty: 🟡 Medium Topics: Array, Sorting, Heap (Priority Queue) Solution Problem Understanding This problem asks us to compute a "maximum sum" for each index in an array based on a relationship with other elements. Specifically, for each index i in nums1 , we must consider all previous or other indices j where nums1[j] < nums1[i] , and then select up to k values from nums2[j] to maximize...

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LeetCode 3467 - Transform Array by Parity

LeetCode Problem 3467 Difficulty: 🟢 Easy Topics: Array, Sorting, Counting Solution LeetCode 3467 - Transform Array by Parity Problem Understanding The problem gives us an integer array nums and asks us to transform it using three operations that must be performed in a specific order. First, every even number must be replaced with 0 . Second, every odd number must be replaced with 1 . After this transformation, the array...

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LeetCode 3462 - Maximum Sum With at Most K Elements

LeetCode Problem 3462 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting, Heap (Priority Queue), Matrix Solution Problem Understanding We are given a matrix grid , where each row contains a collection of values that can potentially be selected. We are also given an array limits , where limits[i] specifies the maximum number of elements that may be chosen from row i . The goal is to select at most k elements...

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LeetCode 3458 - Select K Disjoint Special Substrings

LeetCode Problem 3458 Difficulty: 🟡 Medium Topics: Hash Table, String, Dynamic Programming, Greedy, Sorting Solution Problem Understanding The problem asks us to determine whether we can select k disjoint special substrings from a given string s . A special substring is defined as a substring where every character in it does not appear anywhere else in the string. Additionally, the substring cannot be the entire string itself. The input consists...

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LeetCode 3457 - Eat Pizzas!

LeetCode Problem 3457 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting Solution Problem Understanding The problem presents an array pizzas of size n where each element represents the weight of a pizza. Every day, you must eat exactly 4 pizzas , and the total weight you gain from these 4 pizzas depends on whether the day is odd or even. On odd-numbered days, your weight gain is equal to the heaviest...

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LeetCode 3446 - Sort Matrix by Diagonals

LeetCode Problem 3446 Difficulty: 🟡 Medium Topics: Array, Sorting, Matrix Solution Problem Understanding We are given an n x n square matrix grid . Every cell belongs to exactly one top-left to bottom-right diagonal. Two cells (r1, c1) and (r2, c2) are on the same diagonal if r1 - c1 == r2 - c2 . The problem asks us to independently sort each diagonal, but the required sorting order depends...

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LeetCode 3433 - Count Mentions Per User

LeetCode Problem 3433 Difficulty: 🟡 Medium Topics: Array, Math, Sorting, Simulation Solution LeetCode 3433 - Count Mentions Per User Problem Understanding This problem asks us to simulate a sequence of user activity events and count how many times each user is mentioned across all message events. We are given: numberOfUsers , the total number of users with IDs from 0 to numberOfUsers - 1 events , where each event is...

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LeetCode 3428 - Maximum and Minimum Sums of at Most Size K Subsequences

LeetCode Problem 3428 Difficulty: 🟡 Medium Topics: Array, Math, Dynamic Programming, Sorting, Combinatorics Solution Problem Understanding We are given an array nums and an integer k . For every subsequence whose size is at most k , we look at two values: The minimum element in that subsequence. The maximum element in that subsequence. We add minimum + maximum for every valid subsequence, then return the total modulo 10^9 +...

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LeetCode 3424 - Minimum Cost to Make Arrays Identical

LeetCode Problem 3424 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting Solution Problem Understanding The problem asks us to transform one integer array arr into another integer array brr with the minimum cost using two types of operations. The first operation allows splitting arr into contiguous subarrays and rearranging them at a fixed cost k per operation. The second operation allows adjusting any element by adding or subtracting a positive integer...

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LeetCode 3413 - Maximum Coins From K Consecutive Bags

LeetCode Problem 3413 Difficulty: 🟡 Medium Topics: Array, Binary Search, Greedy, Sliding Window, Sorting, Prefix Sum Solution LeetCode 3413 - Maximum Coins From K Consecutive Bags Problem Understanding We are given several non-overlapping segments on a number line. Each segment [l, r, c] means that every bag at positions l, l+1, ..., r contains exactly c coins. All positions not covered by any segment contain 0 coins. The goal is...

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LeetCode 1847 - Closest Room

LeetCode Problem 1847 Difficulty: 🔴 Hard Topics: Array, Binary Search, Sorting, Ordered Set Solution LeetCode 1847: Closest Room Problem Understanding We are given a list of hotel rooms, where each room has: Problem Understanding The problem gives us a collection of hotel rooms, where each room has two attributes: A unique room ID A room size We are also given several queries. Each query contains: preferred : the room ID...

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LeetCode 3119 - Maximum Number of Potholes That Can Be Fixed

LeetCode Problem 3119 Difficulty: 🟡 Medium Topics: String, Greedy, Sorting Solution LeetCode 3119 - Maximum Number of Potholes That Can Be Fixed Problem Understanding We are given a road represented as a string containing only two characters: 'x' represents a pothole. '.' represents a smooth section of road. We are also given a repair budget. A repair operation can only be applied to a contiguous group of potholes. If we...

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LeetCode 3074 - Apple Redistribution into Boxes

LeetCode Problem 3074 Difficulty: 🟢 Easy Topics: Array, Greedy, Sorting Solution Problem Understanding The problem asks us to redistribute a collection of apple packs into boxes while using the minimum number of boxes . Each pack apple[i] contains a certain number of apples, and each box capacity[j] can hold up to a certain number of apples. Apples from a single pack can be split across multiple boxes, so we are...

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LeetCode 2740 - Find the Value of the Partition

LeetCode Problem 2740 Difficulty: 🟡 Medium Topics: Array, Sorting Solution LeetCode 2740: Find the Value of the Partition Problem Understanding We are given an array nums containing positive integers. Our task is to divide all elements into two non-empty groups, nums1 and nums2 . Every element must belong to exactly one of the two groups, and neither group may be empty. For a particular partition, the value is defined as:...

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LeetCode 1913 - Maximum Product Difference Between Two Pairs

LeetCode Problem 1913 Difficulty: 🟢 Easy Topics: Array, Sorting Solution Problem Understanding This problem asks us to find the maximum product difference between two pairs of numbers from a given array. Specifically, given an array nums , we need to select four distinct indices w, x, y, z to form two pairs (nums[w], nums[x]) and (nums[y], nums[z]) . The goal is to maximize the expression (nums[w] * nums[x]) - (nums[y]...

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LeetCode 1782 - Count Pairs Of Nodes

LeetCode Problem 1782 Difficulty: 🔴 Hard Topics: Array, Hash Table, Two Pointers, Binary Search, Graph Theory, Sorting, Counting Solution LeetCode 1782 - Count Pairs Of Nodes Problem Understanding We are given an undirected graph with n nodes and a list of edges. Multiple edges between the same pair of nodes are allowed. For any pair of nodes (a, b) , define incident(a, b) as the number of edges connected to...

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LeetCode 1851 - Minimum Interval to Include Each Query

LeetCode Problem 1851 Difficulty: 🔴 Hard Topics: Array, Binary Search, Sweep Line, Sorting, Heap (Priority Queue) Solution Problem Understanding The problem gives us a collection of inclusive integer intervals and a list of query values. For every query, we must determine the size of the smallest interval that contains that query value. An interval [left, right] contains a query q if: left <= q <= right The size of an...

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LeetCode 1921 - Eliminate Maximum Number of Monsters

LeetCode Problem 1921 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting Solution Problem Understanding This problem asks us to determine how many monsters we can eliminate before any one of them reaches the city. Each monster starts at some distance from the city and moves toward it at a constant speed. We are also given a weapon that can eliminate exactly one monster every minute. The weapon starts fully charged at...

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LeetCode 3169 - Count Days Without Meetings

LeetCode Problem 3169 Difficulty: 🟡 Medium Topics: Array, Sorting Solution LeetCode 3169 - Count Days Without Meetings Problem Understanding The problem gives us a total number of working days, numbered from 1 to days , along with a list of meeting intervals. Each interval [start, end] represents a meeting that occupies every day from start through end , inclusive. Our task is to determine how many days remain completely free,...

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LeetCode 2294 - Partition Array Such That Maximum Difference Is K

LeetCode Problem 2294 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting Solution Problem Understanding The problem gives us an integer array nums and an integer k . We must divide the array into one or more subsequences such that every number belongs to exactly one subsequence, and for every subsequence, the difference between its maximum value and minimum value is at most k . The goal is to minimize the number...

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LeetCode 2681 - Power of Heroes

LeetCode Problem 2681 Difficulty: 🔴 Hard Topics: Array, Math, Dynamic Programming, Sorting, Prefix Sum Solution Problem Understanding The problem asks us to compute the total "power" across every possible non-empty subset of heroes. For any selected group of heroes, its power is defined as: $$(\text{maximum strength in the group})^2 \times (\text{minimum strength in the group})$$ We are given an array nums , where each value represents the strength of one...

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LeetCode 2713 - Maximum Strictly Increasing Cells in a Matrix

LeetCode Problem 2713 Difficulty: 🔴 Hard Topics: Array, Hash Table, Binary Search, Dynamic Programming, Memoization, Sorting, Matrix, Ordered Set Solution Problem Understanding The problem gives us an m x n matrix where each cell contains an integer value. We may start from any cell, and from the current cell we are allowed to move only within the same row or the same column. However, there is an important restriction: we...

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LeetCode 2974 - Minimum Number Game

LeetCode Problem 2974 Difficulty: 🟢 Easy Topics: Array, Sorting, Heap (Priority Queue), Simulation Solution Problem Understanding The problem gives us an integer array nums with an even number of elements. We repeatedly simulate a game between Alice and Bob until the array becomes empty. In each round, the following sequence happens: Alice removes the smallest remaining number. Bob removes the next smallest remaining number. Bob appends his removed number to...

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LeetCode 2860 - Happy Students

LeetCode Problem 2860 Difficulty: 🟡 Medium Topics: Array, Sorting, Enumeration Solution Problem Understanding The problem asks us to determine the number of ways to select a subset of students from a class such that every student is happy according to the given rules. Each student has a number nums[i] that represents a threshold. A student is happy if they are selected and the total number of selected students is strictly...

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LeetCode 2973 - Find Number of Coins to Place in Tree Nodes

LeetCode Problem 2973 Difficulty: 🔴 Hard Topics: Dynamic Programming, Tree, Depth-First Search, Sorting, Heap (Priority Queue) Solution Problem Understanding The problem gives us a tree with n nodes labeled from 0 to n - 1 . The tree is undirected and rooted at node 0 . The tree structure is described by the edges array, where each edge [a, b] connects nodes a and b . Each node also has...

Practice › LeetCode › LeetCode 26xx ›

LeetCode 2616 - Minimize the Maximum Difference of Pairs

LeetCode Problem 2616 Difficulty: 🟡 Medium Topics: Array, Binary Search, Dynamic Programming, Greedy, Sorting Solution Problem Understanding The problem asks us to select exactly p disjoint pairs from the array nums such that the largest difference among all chosen pairs is as small as possible. For every pair (i, j) , the pair difference is defined as: $$|nums[i] - nums[j]|$$ The goal is not to minimize the sum of differences,...

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LeetCode 3132 - Find the Integer Added to Array II

LeetCode Problem 3132 Difficulty: 🟡 Medium Topics: Array, Two Pointers, Sorting, Enumeration Solution Problem Understanding We are given two integer arrays, nums1 and nums2 . The array nums2 was created from nums1 using two operations: Remove exactly two elements from nums1 . Add the same integer x to every remaining element. After these operations, the resulting multiset of values becomes exactly equal to nums2 . The order of elements does...

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LeetCode 2567 - Minimum Score by Changing Two Elements

LeetCode Problem 2567 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting Solution Problem Understanding The problem asks us to manipulate an array of integers, nums , in a very specific way to minimize a metric called the "score." The score is defined as the sum of two quantities: the high score , which is the maximum absolute difference between any two elements in the array, and the low score , which...

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LeetCode 2344 - Minimum Deletions to Make Array Divisible

LeetCode Problem 2344 Difficulty: 🔴 Hard Topics: Array, Math, Sorting, Heap (Priority Queue), Number Theory Solution Problem Understanding The problem gives us two arrays of positive integers, nums and numsDivide . We are allowed to delete any number of elements from nums , and our goal is to make the smallest remaining element in nums divide every number in numsDivide . The key phrase here is smallest remaining element ....

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LeetCode 2840 - Check if Strings Can be Made Equal With Operations II

LeetCode Problem 2840 Difficulty: 🟡 Medium Topics: Hash Table, String, Sorting Solution Problem Understanding The problem asks us to determine whether two strings s1 and s2 of equal length can be made identical using a specific type of swap operation. The operation allows us to choose any two indices i and j such that i < j and j - i is even , and then swap the characters at...

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LeetCode 2966 - Divide Array Into Arrays With Max Difference

LeetCode Problem 2966 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting Solution Problem Understanding The problem asks us to divide an integer array nums of size n (where n is guaranteed to be a multiple of 3) into smaller arrays of exactly size 3, such that within each array, the difference between the largest and smallest element does not exceed a given integer k . The goal is to return a...

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LeetCode 2242 - Maximum Score of a Node Sequence

LeetCode Problem 2242 Difficulty: 🔴 Hard Topics: Array, Graph Theory, Sorting, Enumeration Solution Problem Understanding The problem gives us an undirected graph with n nodes. Each node has a score, and the graph edges define which nodes are directly connected. We must find a valid sequence of exactly four distinct nodes such that every adjacent pair in the sequence has an edge between them. A valid sequence looks like this:...

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LeetCode 2148 - Count Elements With Strictly Smaller and Greater Elements

LeetCode Problem 2148 Difficulty: 🟢 Easy Topics: Array, Sorting, Counting Solution Problem Understanding The problem gives us an integer array nums and asks us to count how many elements satisfy a very specific condition. For an element nums[i] to be counted, there must exist: at least one element in the array that is strictly smaller than nums[i] at least one element in the array that is strictly greater than nums[i]...

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LeetCode 1889 - Minimum Space Wasted From Packaging

LeetCode Problem 1889 Difficulty: 🔴 Hard Topics: Array, Binary Search, Sorting, Prefix Sum Solution Problem Understanding The problem gives us a list of package sizes and several suppliers. Each supplier offers an unlimited number of boxes, but only in certain fixed sizes. We must choose exactly one supplier and pack every package using only the box sizes that supplier provides. Each package must go into a single box whose size...

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LeetCode 2996 - Smallest Missing Integer Greater Than Sequential Prefix Sum

LeetCode Problem 2996 Difficulty: 🟢 Easy Topics: Array, Hash Table, Sorting Solution Problem Understanding The problem asks us to find the smallest missing integer in the array that is greater than or equal to the sum of the longest sequential prefix . A sequential prefix means the beginning part of the array where every number increases by exactly 1 compared to the previous number. Formally, for a prefix nums[0..i] ,...

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LeetCode 3010 - Divide an Array Into Subarrays With Minimum Cost I

LeetCode Problem 3010 Difficulty: 🟢 Easy Topics: Array, Sorting, Enumeration Solution Problem Understanding The problem asks us to split a given array nums into exactly three disjoint contiguous subarrays and minimize the sum of their costs . The important detail is how cost is defined. The cost of a subarray is simply its first element . For example: [1,2,3] has cost 1 [10,5] has cost 10 Since we must divide...

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LeetCode 2345 - Finding the Number of Visible Mountains

LeetCode Problem 2345 Difficulty: 🟡 Medium Topics: Array, Stack, Sorting, Monotonic Stack Solution LeetCode 2345 - Finding the Number of Visible Mountains Problem Understanding Each mountain is represented by a peak point (x, y) . Because the mountain is a right-angled isosceles triangle with slopes +1 and -1 , its shape is completely determined by its peak. For a mountain with peak (x, y) : The left boundary touches the...

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LeetCode 2503 - Maximum Number of Points From Grid Queries

LeetCode Problem 2503 Difficulty: 🔴 Hard Topics: Array, Two Pointers, Breadth-First Search, Union-Find, Sorting, Heap (Priority Queue), Matrix Solution Problem Understanding The problem asks us to calculate the maximum number of points that can be collected in a grid for a series of queries. The grid is represented by an m x n matrix of integers, where each cell has a value. For each query value q , we start...

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LeetCode 2008 - Maximum Earnings From Taxi

LeetCode Problem 2008 Difficulty: 🟡 Medium Topics: Array, Hash Table, Binary Search, Dynamic Programming, Sorting Solution Problem Understanding The problem describes a taxi traveling along a one directional road from point 1 to point n . Along the way, passengers request rides. Each ride is represented as [start, end, tip] , meaning the passenger wants to travel from start to end and will additionally pay a tip. If we accept...

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LeetCode 2824 - Count Pairs Whose Sum is Less than Target

LeetCode Problem 2824 Difficulty: 🟢 Easy Topics: Array, Two Pointers, Binary Search, Sorting Solution Problem Understanding This problem asks us to count the number of unique pairs of indices (i, j) in a given integer array nums such that the sum of the two numbers at those indices is strictly less than a given target . The array is 0-indexed, so valid pairs satisfy 0 <= i < j <...

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LeetCode 2146 - K Highest Ranked Items Within a Price Range

LeetCode Problem 2146 Difficulty: 🟡 Medium Topics: Array, Breadth-First Search, Sorting, Heap (Priority Queue), Matrix Solution Problem Understanding This problem gives us a 2D grid representing a shop layout. Every cell in the grid has one of three meanings: 0 means the cell is blocked by a wall and cannot be traversed. 1 means the cell is empty space and can be walked through. Any value greater than 1 represents...

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LeetCode 1996 - The Number of Weak Characters in the Game

LeetCode Problem 1996 Difficulty: 🟡 Medium Topics: Array, Stack, Greedy, Sorting, Monotonic Stack Solution Problem Understanding In this problem, every character in the game has two attributes: attack defense The input is a 2D array called properties , where: properties[i] = [attacki, defensei] represents the stats of the i-th character. A character is considered weak if there exists another character with: strictly greater attack strictly greater defense Both conditions must...

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LeetCode 2731 - Movement of Robots

LeetCode Problem 2731 Difficulty: 🟡 Medium Topics: Array, Brainteaser, Sorting, Prefix Sum Solution LeetCode 2731 - Movement of Robots Problem Understanding The problem gives us a list of robots positioned on an infinite number line. Each robot starts at a unique coordinate from the array nums , and each robot has an associated movement direction from the string s . A robot moves exactly one unit per second. If the...

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LeetCode 2790 - Maximum Number of Groups With Increasing Length

LeetCode Problem 2790 Difficulty: 🔴 Hard Topics: Array, Math, Binary Search, Greedy, Sorting Solution LeetCode 2790 - Maximum Number of Groups With Increasing Length Problem Understanding We are given an array usageLimits where usageLimits[i] tells us how many times the number i can be used across all groups. The numbers available are exactly 0 through n - 1 , where n is the length of the array. We want to...

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LeetCode 2602 - Minimum Operations to Make All Array Elements Equal

LeetCode Problem 2602 Difficulty: 🟡 Medium Topics: Array, Binary Search, Sorting, Prefix Sum Solution Problem Understanding The problem gives us an integer array nums and another array queries . For every query value q , we must calculate the minimum number of operations required to make every element in nums equal to q . One operation consists of increasing or decreasing a single element by exactly 1 . Since each...

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LeetCode 2779 - Maximum Beauty of an Array After Applying Operation

LeetCode Problem 2779 Difficulty: 🟡 Medium Topics: Array, Binary Search, Sliding Window, Sorting Solution Problem Understanding This problem asks us to determine the maximum "beauty" of an array after performing a set of allowed operations. Specifically, the beauty is defined as the length of the longest subsequence consisting of equal elements. The operation lets us pick an element at index i (only once per index) and change it to any...

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LeetCode 2171 - Removing Minimum Number of Magic Beans

LeetCode Problem 2171 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting, Enumeration, Prefix Sum Solution Problem Understanding The problem asks us to remove beans from bags in such a way that all non-empty bags have the same number of beans while minimizing the total number of beans removed. Each element in the input array beans represents a bag with a positive number of beans. We are allowed to remove any number...

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LeetCode 2098 - Subsequence of Size K With the Largest Even Sum

LeetCode Problem 2098 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting Solution Problem Understanding The problem asks us to find the largest possible even sum of a subsequence of length k from a given integer array nums . A subsequence is a sequence that can be obtained by deleting some elements from the array without changing the relative order of the remaining elements. The input consists of an array of integers...

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LeetCode 1984 - Minimum Difference Between Highest and Lowest of K Scores

LeetCode Problem 1984 Difficulty: 🟢 Easy Topics: Array, Sliding Window, Sorting Solution Problem Understanding The problem asks us to find the minimum possible difference between the highest and lowest scores when selecting exactly k scores from an array of student scores. The input is a 0-indexed integer array nums where each element represents a student's score, and an integer k which is the number of scores to pick. The expected...

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LeetCode 2144 - Minimum Cost of Buying Candies With Discount

LeetCode Problem 2144 Difficulty: 🟢 Easy Topics: Array, Greedy, Sorting Solution Problem Understanding This problem asks us to minimize the total amount of money spent when buying candies under a special discount rule. For every two candies that are purchased, we may take one additional candy for free. However, the free candy must have a cost less than or equal to the cheaper of the two purchased candies. The input...

Practice › LeetCode › LeetCode 33xx ›

LeetCode 3301 - Maximize the Total Height of Unique Towers

LeetCode Problem 3301 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting Solution Problem Understanding We are given an array maximumHeight where maximumHeight[i] represents the largest height that tower i is allowed to have. Our goal is to assign an actual height to every tower such that: Every assigned height is a positive integer. The assigned height of tower i is at most maximumHeight[i] . All assigned heights are distinct. Among all...

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LeetCode 3365 - Rearrange K Substrings to Form Target String

LeetCode Problem 3365 Difficulty: 🟡 Medium Topics: Hash Table, String, Sorting Solution Problem Understanding This problem asks whether it is possible to rearrange k contiguous equal-length substrings of a string s to form another string t , given that s and t are anagrams. In simpler terms, we are splitting s into k pieces of the same size, then permuting these pieces in any order to see if we can...

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LeetCode 3035 - Maximum Palindromes After Operations

LeetCode Problem 3035 Difficulty: 🟡 Medium Topics: Array, Hash Table, String, Greedy, Sorting, Counting Solution LeetCode 3035 - Maximum Palindromes After Operations Problem Understanding This problem gives us an array of strings, words , and allows us to swap any character with any other character across the entire collection of strings. The swaps are completely unrestricted. We may swap characters between different strings, within the same string, or perform no...

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LeetCode 2968 - Apply Operations to Maximize Frequency Score

LeetCode Problem 2968 Difficulty: 🔴 Hard Topics: Array, Binary Search, Sliding Window, Sorting, Prefix Sum Solution LeetCode 2968 - Apply Operations to Maximize Frequency Score Problem Understanding This problem asks us to maximize the frequency of the most common value in an array after performing at most k operations. Each operation allows us to choose any element and either increase or decrease it by exactly 1 . Since we can...

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LeetCode 3167 - Better Compression of String

LeetCode Problem 3167 Difficulty: 🟡 Medium Topics: Hash Table, String, Sorting, Counting Solution Problem Understanding The problem gives us a compressed string where every character is immediately followed by its frequency. For example, the string "a3b2" represents the original expanded string "aaabb" . However, the input compression is not guaranteed to be optimal. The same character may appear multiple times in different parts of the compressed string. For example: "a3c9b2c1"...

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LeetCode 3088 - Make String Anti-palindrome

LeetCode Problem 3088 Difficulty: 🔴 Hard Topics: String, Greedy, Sorting, Counting Sort Solution Problem Understanding We are given a string s of even length, and we may swap any two characters any number of times. Since unrestricted swapping allows us to rearrange the string arbitrarily, the real task is to determine whether some permutation of the characters can form an anti-palindrome. A string is an anti-palindrome if every character differs...

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LeetCode 2597 - The Number of Beautiful Subsets

LeetCode Problem 2597 Difficulty: 🟡 Medium Topics: Array, Hash Table, Math, Dynamic Programming, Backtracking, Sorting, Combinatorics Solution Problem Understanding The problem asks us to count how many non-empty subsets of the array nums are considered "beautiful". A subset is beautiful if there are no two numbers inside the subset whose absolute difference equals k . For example, if k = 2 , then the subset cannot contain both 2 and...

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LeetCode 2948 - Make Lexicographically Smallest Array by Swapping Elements

LeetCode Problem 2948 Difficulty: 🟡 Medium Topics: Array, Union-Find, Sorting Solution Problem Understanding The problem asks us to transform a given array of positive integers nums into its lexicographically smallest form by performing a specific swap operation any number of times. The operation allows swapping any two elements nums[i] and nums[j] only if the absolute difference between them is at most limit . The lexicographically smallest array is one where,...

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LeetCode 2449 - Minimum Number of Operations to Make Arrays Similar

LeetCode Problem 2449 Difficulty: 🔴 Hard Topics: Array, Greedy, Sorting Solution LeetCode 2449 - Minimum Number of Operations to Make Arrays Similar Problem Understanding We are given two arrays, nums and target , of equal length. In a single operation, we choose two different indices and add 2 to one element while subtracting 2 from another element. This operation preserves the total sum of the array because every +2 is...

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LeetCode 2280 - Minimum Lines to Represent a Line Chart

LeetCode Problem 2280 Difficulty: 🟡 Medium Topics: Array, Math, Geometry, Sorting, Number Theory Solution Problem Understanding In this problem, we are given a list of stock prices over different days. Each element in stockPrices is a pair: [day, price] This represents a point on a 2D graph where: The X-axis is the day The Y-axis is the stock price on that day The line chart is formed by connecting consecutive...

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LeetCode 3186 - Maximum Total Damage With Spell Casting

LeetCode Problem 3186 Difficulty: 🟡 Medium Topics: Array, Hash Table, Two Pointers, Binary Search, Dynamic Programming, Sorting, Counting Solution Problem Understanding The problem gives us an array power , where each element represents the damage value of a spell. Every spell can be used at most once, and multiple spells may share the same damage value. The restriction is the important part of the problem. If we decide to cast...

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LeetCode 2273 - Find Resultant Array After Removing Anagrams

LeetCode Problem 2273 Difficulty: 🟢 Easy Topics: Array, Hash Table, String, Sorting Solution Problem Understanding This problem asks us to repeatedly remove words from an array when two adjacent words are anagrams of each other . We are given a 0-indexed string array words , where every string contains only lowercase English letters. During each operation, we may choose an index i such that the word at words[i] is an...

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LeetCode 2271 - Maximum White Tiles Covered by a Carpet

LeetCode Problem 2271 Difficulty: 🟡 Medium Topics: Array, Binary Search, Greedy, Sliding Window, Sorting, Prefix Sum Solution That is a long-form reference guide request. To avoid truncation and keep the formatting exact, I will provide the complete solution guide for LeetCode 2271 in a single structured response. Problem Understanding The problem gives us a collection of disjoint white tile intervals and a carpet of fixed length. Each interval [li, ri]...

Practice › LeetCode › LeetCode 25xx ›

LeetCode 2542 - Maximum Subsequence Score

LeetCode Problem 2542 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting, Heap (Priority Queue) Solution LeetCode 2542 - Maximum Subsequence Score Problem Understanding The problem gives us two integer arrays, nums1 and nums2 , both of the same length n , along with an integer k . We must choose exactly k indices from the arrays. The chosen indices form a subsequence, meaning the selected positions come from the original arrays...

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LeetCode 2607 - Make K-Subarray Sums Equal

LeetCode Problem 2607 Difficulty: 🟡 Medium Topics: Array, Math, Greedy, Sorting, Number Theory Solution Problem Understanding The problem asks us to transform a circular integer array so that every subarray of length k has the same sum. A circular array means the end wraps around to the beginning, so subarrays can cross the boundary of the array. The allowed operation is increasing or decreasing any element by 1, and the...

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LeetCode 2406 - Divide Intervals Into Minimum Number of Groups

LeetCode Problem 2406 Difficulty: 🟡 Medium Topics: Array, Two Pointers, Greedy, Sorting, Heap (Priority Queue), Prefix Sum Solution Problem Understanding The problem gives us a list of inclusive intervals, where each interval is represented as [left, right] . We must divide all intervals into groups such that no two intervals inside the same group intersect. The important detail is that the intervals are inclusive. This means two intervals overlap even...

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LeetCode 2070 - Most Beautiful Item for Each Query

LeetCode Problem 2070 Difficulty: 🟡 Medium Topics: Array, Binary Search, Sorting Solution Problem Understanding The problem gives us a list of items, where each item has two properties: price beauty Each entry looks like: items[i] = [pricei, beautyi] We are also given a list of queries. For every query value queries[j] , we must determine: Among all items whose price is less than or equal to the query value, what...

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LeetCode 1985 - Find the Kth Largest Integer in the Array

LeetCode Problem 1985 Difficulty: 🟡 Medium Topics: Array, String, Divide and Conquer, Sorting, Heap (Priority Queue), Quickselect Solution Problem Understanding This problem asks us to find the kth largest value among a list of integers that are represented as strings. Each element in nums is a non-negative integer encoded as a string with no leading zeros, and we are required to return the kth largest value according to numeric order,...

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LeetCode 3219 - Minimum Cost for Cutting Cake II

LeetCode Problem 3219 Difficulty: 🔴 Hard Topics: Array, Greedy, Sorting Solution Problem Understanding We are given an m x n rectangular cake and need to divide it completely into 1 x 1 pieces. The cake can be cut along predefined horizontal and vertical lines. There are m - 1 possible horizontal cuts and n - 1 possible vertical cuts: horizontalCut[i] is the cost of cutting across horizontal line i verticalCut[j]...

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LeetCode 2343 - Query Kth Smallest Trimmed Number

LeetCode Problem 2343 Difficulty: 🟡 Medium Topics: Array, String, Divide and Conquer, Sorting, Heap (Priority Queue), Radix Sort, Quickselect Solution Problem Understanding This problem provides a list of numbers represented as strings, all of equal length. The task is to answer multiple queries, where each query asks for the index of the k-th smallest number after trimming every number in the list to its last trimi digits. Importantly, if two...

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LeetCode 2706 - Buy Two Chocolates

LeetCode Problem 2706 Difficulty: 🟢 Easy Topics: Array, Greedy, Sorting Solution Problem Understanding The problem is asking us to purchase exactly two chocolates from a store given their individual prices, while ensuring that after buying them we do not end up in debt. The input consists of an array prices , where each element represents the cost of one chocolate, and an integer money , which is the total money...

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LeetCode 3319 - K-th Largest Perfect Subtree Size in Binary Tree

LeetCode Problem 3319 Difficulty: 🟡 Medium Topics: Tree, Depth-First Search, Sorting, Binary Tree Solution LeetCode 3319 - K-th Largest Perfect Subtree Size in Binary Tree Problem Understanding We are given the root of a binary tree and an integer k . Our goal is to find the size of the k -th largest perfect binary subtree contained anywhere within the tree. A perfect binary tree has two defining properties: Every...

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LeetCode 2071 - Maximum Number of Tasks You Can Assign

LeetCode Problem 2071 Difficulty: 🔴 Hard Topics: Array, Two Pointers, Binary Search, Greedy, Queue, Sorting, Monotonic Queue Solution Problem Understanding This problem asks us to maximize the number of tasks that can be completed using a group of workers, where each worker can perform at most one task. Each task has a required strength value, and each worker has a current strength value. A worker can complete a task if...

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LeetCode 2195 - Append K Integers With Minimal Sum

LeetCode Problem 2195 Difficulty: 🟡 Medium Topics: Array, Math, Greedy, Sorting Solution Problem Understanding The problem asks us to append k unique positive integers to an existing array nums such that none of the integers we add are already in nums , and the sum of the numbers we append is minimized. In other words, we want to pick the smallest k positive integers that are missing from nums ....

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LeetCode 2389 - Longest Subsequence With Limited Sum

LeetCode Problem 2389 Difficulty: 🟢 Easy Topics: Array, Binary Search, Greedy, Sorting, Prefix Sum Solution Problem Understanding This problem asks us to determine, for each query, the maximum number of elements we can select from an array nums such that their sum does not exceed a given value. We are not required to maintain consecutive elements, only the relative order for subsequences, but in this problem the relative order does...

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LeetCode 2563 - Count the Number of Fair Pairs

LeetCode Problem 2563 Difficulty: 🟡 Medium Topics: Array, Two Pointers, Binary Search, Sorting Solution Problem Understanding The problem asks us to count how many pairs of indices (i, j) satisfy two conditions: i < j The sum nums[i] + nums[j] lies within the inclusive range [lower, upper] We are given an integer array nums and two bounds, lower and upper . The goal is to return the total number of...

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LeetCode 3111 - Minimum Rectangles to Cover Points

LeetCode Problem 3111 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting Solution Problem Understanding The problem gives us a collection of 2D points, where each point is represented as (xi, yi) . We must cover every point using a set of rectangles. Each rectangle has a very special form: Its bottom edge always lies on the x-axis, meaning the rectangle starts at y = 0 . The rectangle spans horizontally from...

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LeetCode 2784 - Check if Array is Good

LeetCode Problem 2784 Difficulty: 🟢 Easy Topics: Array, Hash Table, Sorting Solution Problem Understanding The problem defines a special type of array called a "good" array. A good array must be a permutation of: $$base[n] = [1, 2, 3, ..., n-1, n, n]$$ This means the array must contain: Every integer from 1 to n - 1 exactly once The integer n exactly twice No other numbers Total length equal...

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LeetCode 3104 - Find Longest Self-Contained Substring

LeetCode Problem 3104 Difficulty: 🔴 Hard Topics: Hash Table, String, Sorting Solution Problem Understanding The problem asks us to find the longest self-contained substring in a given string s . A substring is self-contained if it does not share any characters with the rest of the string . More formally, for a substring t of s , every character in t must appear only inside t and not elsewhere in...

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LeetCode 1968 - Array With Elements Not Equal to Average of Neighbors

LeetCode Problem 1968 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting Solution Problem Understanding The problem asks us to rearrange a distinct integer array so that no element is equal to the average of its neighbors . The input is a zero-indexed array nums of length at least 3, and all elements are guaranteed to be distinct. The output should be any valid rearrangement of nums that satisfies the condition for...

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LeetCode 3011 - Find if Array Can Be Sorted

LeetCode Problem 3011 Difficulty: 🟡 Medium Topics: Array, Bit Manipulation, Sorting Solution Here’s the complete, detailed technical solution guide for LeetCode 3011 - Find if Array Can Be Sorted , following your requested formatting and style: Problem Understanding The problem provides a 0-indexed array of positive integers nums . The task is to determine if the array can be sorted in ascending order by performing a series of adjacent swaps...

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LeetCode 2592 - Maximize Greatness of an Array

LeetCode Problem 2592 Difficulty: 🟡 Medium Topics: Array, Two Pointers, Greedy, Sorting Solution Here is the complete, detailed technical solution guide for LeetCode 2592 - Maximize Greatness of an Array following your formatting requirements. Problem Understanding The problem gives us an integer array nums and asks us to permute it into a new array perm such that the number of indices i for which perm[i] > nums[i] is maximized. This...

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LeetCode 3024 - Type of Triangle

LeetCode Problem 3024 Difficulty: 🟢 Easy Topics: Array, Math, Sorting Solution Problem Understanding The problem gives an integer array nums of length 3 , where each value represents the length of a side of a possible triangle. Our task is to determine what kind of triangle these three sides can form. There are four possible outputs: "equilateral" if all three sides are equal "isosceles" if exactly two sides are equal...

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LeetCode 2971 - Find Polygon With the Largest Perimeter

LeetCode Problem 2971 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting, Prefix Sum Solution LeetCode 2971 - Find Polygon With the Largest Perimeter Problem Understanding The problem gives us an array nums containing positive integers. Each integer represents a potential side length that we may use when constructing a polygon. A polygon must have at least three sides. The key geometric property we are given is that if the side lengths...

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LeetCode 2551 - Put Marbles in Bags

LeetCode Problem 2551 Difficulty: 🔴 Hard Topics: Array, Greedy, Sorting, Heap (Priority Queue) Solution Problem Understanding The problem asks us to distribute weights.length marbles into k contiguous bags, where the cost of a bag is defined as the sum of the first and last marble in that bag. We are to calculate the difference between the maximum and minimum possible total scores across all valid distributions. The input weights is...

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LeetCode 2590 - Design a Todo List

LeetCode Problem 2590 Difficulty: 🟡 Medium Topics: Array, Hash Table, String, Design, Sorting Solution Problem Understanding This problem asks us to design a small task management system, similar to a lightweight todo application. We need to implement a TodoList class that supports adding tasks, marking tasks as completed, retrieving all pending tasks for a user, and filtering pending tasks by tag. Each task belongs to a specific user and contains...

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LeetCode 2459 - Sort Array by Moving Items to Empty Space

LeetCode Problem 2459 Difficulty: 🔴 Hard Topics: Array, Hash Table, Sorting Solution Problem Understanding The array contains every integer from 0 to n - 1 exactly once. The value 0 represents the empty space, while every other number represents an item that should eventually appear in sorted order. The operation is unusual compared to normal array sorting problems. In one move, we may take any item and place it into...

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LeetCode 3125 - Maximum Number That Makes Result of Bitwise AND Zero

LeetCode Problem 3125 Difficulty: 🟡 Medium Topics: String, Greedy, Sorting Solution Problem Understanding The problem asks us to find the largest integer x such that: x <= n The bitwise AND of every integer in the inclusive range [x, n] equals 0 In other words, we want the widest possible suffix ending at n whose cumulative bitwise AND becomes zero, while keeping x as large as possible. For example, if...

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LeetCode 1943 - Describe the Painting

LeetCode Problem 1943 Difficulty: 🟡 Medium Topics: Array, Hash Table, Sorting, Prefix Sum Solution Problem Understanding The problem describes a painting laid out on a number line. Each segment of the painting is represented as a half-closed interval [start, end) and is painted with a unique color value. Since multiple segments may overlap, different colors can exist simultaneously over the same region. Instead of returning the actual set of colors...

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LeetCode 1982 - Find Array Given Subset Sums

LeetCode Problem 1982 Difficulty: 🔴 Hard Topics: Array, Hash Table, Sorting, Counting Solution Problem Understanding The problem gives us an integer n and an array sums of length 2^n , which contains every possible subset sum of an unknown array of length n . Our task is to reconstruct any one valid array ans of size n such that the multiset of all subset sums of ans exactly matches the...

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LeetCode 3027 - Find the Number of Ways to Place People II

LeetCode Problem 3027 Difficulty: 🔴 Hard Topics: Array, Math, Geometry, Sorting, Enumeration Solution Problem Understanding The problem asks us to determine how many valid placements of Alice and Bob exist on a 2D grid of points such that Alice can build a rectangular fence with her position as the upper left corner and Bob’s position as the lower right corner . A placement is only valid if no other person...

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LeetCode 2363 - Merge Similar Items

LeetCode Problem 2363 Difficulty: 🟢 Easy Topics: Array, Hash Table, Sorting, Ordered Set Solution Problem Understanding The problem gives us two collections of items, items1 and items2 , where every item is represented as a pair: [value, weight] The value acts like a unique identifier for an item, while weight represents that item's associated weight. Within each individual array, values are guaranteed to be unique, meaning no value appears twice...

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LeetCode 3218 - Minimum Cost for Cutting Cake I

LeetCode Problem 3218 Difficulty: 🟡 Medium Topics: Array, Two Pointers, Dynamic Programming, Greedy, Sorting Solution Problem Understanding The problem gives us an m x n rectangular cake and asks us to cut it into individual 1 x 1 pieces. We are allowed to cut along predefined horizontal and vertical lines. Each line has a fixed cost associated with it. The important detail is that the same cut may need to...

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LeetCode 3347 - Maximum Frequency of an Element After Performing Operations II

LeetCode Problem 3347 Difficulty: 🔴 Hard Topics: Array, Binary Search, Sliding Window, Sorting, Prefix Sum Solution LeetCode 3347 - Maximum Frequency of an Element After Performing Operations II Problem Understanding The problem gives us an integer array nums , along with two integers, k and numOperations . We are allowed to perform exactly numOperations operations. In each operation: We must choose an index that has not been used before. We...

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LeetCode 2164 - Sort Even and Odd Indices Independently

LeetCode Problem 2164 Difficulty: 🟢 Easy Topics: Array, Sorting Solution Problem Understanding The problem asks us to take an integer array nums and sort its elements based on their indices in two separate ways: the elements at even indices should be sorted in non-decreasing order, and the elements at odd indices should be sorted in non-increasing order. The array is 0-indexed , so index 0 is considered even, index 1...

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LeetCode 2300 - Successful Pairs of Spells and Potions

LeetCode Problem 2300 Difficulty: 🟡 Medium Topics: Array, Two Pointers, Binary Search, Sorting Solution Problem Understanding The problem asks us to determine, for each spell, how many potions it can pair with to achieve a product of at least success . The arrays spells and potions represent the strengths of spells and potions, respectively. The output is an array of integers where each element corresponds to the number of successful...

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LeetCode 2766 - Relocate Marbles

LeetCode Problem 2766 Difficulty: 🟡 Medium Topics: Array, Hash Table, Sorting, Simulation Solution Problem Understanding The problem gives us an array nums representing the positions of marbles on a number line. Multiple marbles may exist at the same position, so nums can contain duplicates. We are also given two arrays, moveFrom and moveTo , which describe a sequence of move operations. For each index i , we must move every...

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LeetCode 2412 - Minimum Money Required Before Transactions

LeetCode Problem 2412 Difficulty: 🔴 Hard Topics: Array, Greedy, Sorting Solution Problem Understanding The problem asks us to determine the minimum initial money required to complete all transactions in any order . Each transaction is defined by [costi, cashbacki] , meaning that performing the transaction requires at least costi money, and after completing it, we receive cashbacki back. In other words, we must choose a starting amount of money such...

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LeetCode 2576 - Find the Maximum Number of Marked Indices

LeetCode Problem 2576 Difficulty: 🟡 Medium Topics: Array, Two Pointers, Binary Search, Greedy, Sorting Solution Problem Understanding This problem asks us to maximize the number of indices in an array that can be "marked" using a specific operation. You are given an integer array nums and can repeatedly pick two different unmarked indices i and j such that 2 * nums[i] <= nums[j] . Once selected, both indices i and...

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LeetCode 2089 - Find Target Indices After Sorting Array

LeetCode Problem 2089 Difficulty: 🟢 Easy Topics: Array, Binary Search, Sorting Solution LeetCode 2089, Find Target Indices After Sorting Array Problem Understanding The problem gives us an integer array nums and an integer target . We must sort the array in non-decreasing order and then return every index where the value equals target . A target index is simply an index i such that: $nums[i] = target$ The important detail...

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LeetCode 3380 - Maximum Area Rectangle With Point Constraints I

LeetCode Problem 3380 Difficulty: 🟡 Medium Topics: Array, Math, Binary Indexed Tree, Segment Tree, Geometry, Sorting, Enumeration Solution LeetCode 3380 - Maximum Area Rectangle With Point Constraints I Problem Understanding The problem gives us a set of unique points on a 2D plane. We need to determine the largest possible axis-aligned rectangle that can be formed using exactly four of those points as its corners. An axis-aligned rectangle means: The...

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LeetCode 2333 - Minimum Sum of Squared Difference

LeetCode Problem 2333 Difficulty: 🟡 Medium Topics: Array, Binary Search, Greedy, Sorting, Heap (Priority Queue) Solution I can do that, but the complete guide with all requested sections and the level of detail you specified will exceed a single message limit. I will split it cleanly into multiple parts while preserving your exact formatting requirements. Planned structure: Part 1 Problem Understanding Approaches Algorithm Walkthrough Why the greedy + binary search...

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LeetCode 2809 - Minimum Time to Make Array Sum At Most x

LeetCode Problem 2809 Difficulty: 🔴 Hard Topics: Array, Dynamic Programming, Sorting Solution Problem Understanding The problem provides two integer arrays nums1 and nums2 of equal length, along with a target integer x . Each second, every element in nums1 increases by the corresponding element in nums2 . After the increment, you can choose one index and set its value in nums1 to zero. The task is to determine the minimum...

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LeetCode 2418 - Sort the People

LeetCode Problem 2418 Difficulty: 🟢 Easy Topics: Array, Hash Table, String, Sorting Solution LeetCode 2418, Sort the People Problem Understanding This problem gives us two arrays of equal length: names[i] represents the name of a person heights[i] represents the height of that same person The two arrays are aligned by index, meaning the person at index i has both the name names[i] and the height heights[i] . The goal is...

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LeetCode 2813 - Maximum Elegance of a K-Length Subsequence

LeetCode Problem 2813 Difficulty: 🔴 Hard Topics: Array, Hash Table, Stack, Greedy, Sorting, Heap (Priority Queue) Solution Problem Understanding The problem presents a 0-indexed 2D array items of length n , where each element represents an item with two values: a profit and a category. You are asked to select exactly k items to form a subsequence . A subsequence preserves the original order of items but can skip elements....

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LeetCode 3080 - Mark Elements on Array by Performing Queries

LeetCode Problem 3080 Difficulty: 🟡 Medium Topics: Array, Hash Table, Sorting, Heap (Priority Queue), Simulation Solution Here’s a fully detailed technical solution guide for LeetCode 3080 following your requested format. Problem Understanding The problem gives a zero-indexed array nums of size n consisting of positive integers and a 2D array queries of size m where each query is [indexi, ki] . All elements of nums are initially unmarked. Each query...

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LeetCode 2580 - Count Ways to Group Overlapping Ranges

LeetCode Problem 2580 Difficulty: 🟡 Medium Topics: Array, Sorting Solution Problem Understanding The problem gives us a list of integer ranges, where each range represents all integers between start and end , inclusive. We must divide all ranges into exactly two groups. Either group may be empty. The important restriction is that overlapping ranges cannot be separated. If two ranges share at least one common integer, they must belong to...

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LeetCode 2587 - Rearrange Array to Maximize Prefix Score

LeetCode Problem 2587 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting, Prefix Sum Solution Problem Understanding The problem gives us a 0-indexed array of integers , nums , which can include negative numbers, zero, and positive numbers. We are allowed to reorder the elements in any way we choose. After reordering, we compute the prefix sum array , prefix , where prefix[i] is the sum of all elements from index 0...

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LeetCode 2126 - Destroying Asteroids

LeetCode Problem 2126 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting Solution Problem Understanding In this problem, we are given the starting mass of a planet and a list of asteroid masses. The planet can collide with the asteroids in any order we choose. Every time the planet collides with an asteroid, one of two things happens: If the planet's current mass is greater than or equal to the asteroid's mass,...

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LeetCode 1834 - Single-Threaded CPU

LeetCode Problem 1834 Difficulty: 🟡 Medium Topics: Array, Sorting, Heap (Priority Queue) Solution Problem Understanding The problem asks us to simulate the execution of tasks on a single-threaded CPU . Each task has an enqueue time and a processing time . The CPU can process one task at a time and must select the next task according to two rules: first by shortest processing time , and then by smallest...

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LeetCode 2475 - Number of Unequal Triplets in Array

LeetCode Problem 2475 Difficulty: 🟢 Easy Topics: Array, Hash Table, Sorting Solution Problem Understanding The problem gives us a 0-indexed integer array nums , and we must count how many triplets (i, j, k) satisfy two conditions. First, the indices must be strictly increasing: 0 <= i < j < k < nums.length Second, the values at those indices must all be different from each other: nums[i] != nums[j] nums[i]...

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LeetCode 2751 - Robot Collisions

LeetCode Problem 2751 Difficulty: 🔴 Hard Topics: Array, Stack, Sorting, Simulation Solution Problem Understanding This problem describes a simulation of robots moving on a one-dimensional line, each with a given starting position, health, and direction. Every robot moves at the same speed, and collisions occur when two robots meet at the same position. The key rules are: if two robots collide, the one with lower health is removed, the one...

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LeetCode 3362 - Zero Array Transformation III

LeetCode Problem 3362 Difficulty: 🟡 Medium Topics: Array, Two Pointers, Greedy, Sorting, Heap (Priority Queue), Prefix Sum Solution Problem Understanding We are given an integer array nums and a list of interval queries. Each query [l, r] allows us to reduce every element inside that range by at most 1 . The important detail is that the decrement is optional and independent for every index in the range. This means...

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LeetCode 2583 - Kth Largest Sum in a Binary Tree

LeetCode Problem 2583 Difficulty: 🟡 Medium Topics: Tree, Breadth-First Search, Sorting, Binary Tree Solution Problem Understanding The problem gives us the root of a binary tree and an integer k . For every level in the tree, we calculate the sum of all node values that appear on that level. After computing all level sums, we must return the kth largest level sum. A binary tree level is determined by...

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LeetCode 2500 - Delete Greatest Value in Each Row

LeetCode Problem 2500 Difficulty: 🟢 Easy Topics: Array, Sorting, Heap (Priority Queue), Matrix, Simulation Solution Problem Understanding The problem presents an m x n matrix grid of positive integers and asks us to simulate a repeated deletion process on it. In each operation, for every row in the matrix, we remove the greatest element. After deleting these elements, we take the largest of the removed elements from all rows and...

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LeetCode 2135 - Count Words Obtained After Adding a Letter

LeetCode Problem 2135 Difficulty: 🟡 Medium Topics: Array, Hash Table, String, Bit Manipulation, Sorting Solution Problem Understanding The problem requires us to determine how many strings in targetWords can be formed from strings in startWords through a specific transformation. The transformation involves two operations: appending a single letter not already present in the string, and then rearranging all letters arbitrarily. Essentially, we are checking whether, by adding one new character...

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LeetCode 2943 - Maximize Area of Square Hole in Grid

LeetCode Problem 2943 Difficulty: 🟡 Medium Topics: Array, Sorting Solution LeetCode 2943 - Maximize Area of Square Hole in Grid Problem Understanding The grid is formed by n + 2 horizontal bars and m + 2 vertical bars. These bars divide the plane into unit squares. The bars are numbered starting from 1 . Some horizontal bars listed in hBars may be removed, and some vertical bars listed in vBars...

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LeetCode 3265 - Count Almost Equal Pairs I

LeetCode Problem 3265 Difficulty: 🟡 Medium Topics: Array, Hash Table, Sorting, Counting, Enumeration Solution Problem Understanding The problem asks us to find the number of index pairs (i, j) in an array nums such that i < j and the integers nums[i] and nums[j] are almost equal . Two integers are considered almost equal if you can make them equal by swapping any two digits at most once in either...

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LeetCode 2659 - Make Array Empty

LeetCode Problem 2659 Difficulty: 🔴 Hard Topics: Array, Binary Search, Greedy, Binary Indexed Tree, Segment Tree, Sorting, Ordered Set Solution LeetCode 2659 - Make Array Empty Problem Understanding The problem gives us an array of distinct integers and defines two possible operations: If the first element is currently the smallest value in the array, we remove it. Otherwise, we move the first element to the end of the array. We...

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LeetCode 2491 - Divide Players Into Teams of Equal Skill

LeetCode Problem 2491 Difficulty: 🟡 Medium Topics: Array, Hash Table, Two Pointers, Sorting Solution Problem Understanding This problem asks us to divide a given list of player skill levels into teams of exactly two players such that every team has the same total skill . The chemistry of a team is defined as the product of the skills of the two players, and we are asked to return the sum...

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LeetCode 2895 - Minimum Processing Time

LeetCode Problem 2895 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting Solution Problem Understanding This problem gives us two arrays: processorTime , where each value represents the time when a processor becomes available tasks , where each value represents how long a task takes to execute Each processor has exactly 4 cores, and each core can execute exactly one task. Since there are n processors and each processor has 4 cores,...

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LeetCode 2454 - Next Greater Element IV

LeetCode Problem 2454 Difficulty: 🔴 Hard Topics: Array, Binary Search, Stack, Sorting, Heap (Priority Queue), Monotonic Stack Solution Problem Understanding The problem asks us to compute, for every element in the array, its "second greater element" to the right. For an index i , we are interested in elements positioned after i . Among those elements, we only care about values strictly greater than nums[i] . The second greater element...

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LeetCode 2250 - Count Number of Rectangles Containing Each Point

LeetCode Problem 2250 Difficulty: 🟡 Medium Topics: Array, Hash Table, Binary Search, Binary Indexed Tree, Sorting Solution Here is the complete, detailed technical solution guide for LeetCode 2250 - Count Number of Rectangles Containing Each Point in a single, comprehensive response. Problem Understanding The problem provides two arrays: rectangles and points . Each element of rectangles is [li, hi] , representing a rectangle with its bottom-left corner at (0, 0)...

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LeetCode 1887 - Reduction Operations to Make the Array Elements Equal

LeetCode Problem 1887 Difficulty: 🟡 Medium Topics: Array, Sorting Solution Problem Understanding This problem asks us to make all elements in an integer array equal by repeatedly reducing the largest elements to the next largest element in the array. The input is an array nums of integers, where each operation requires identifying the current largest element and reducing it to the value of the next largest element strictly smaller than...

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LeetCode 3068 - Find the Maximum Sum of Node Values

LeetCode Problem 3068 Difficulty: 🔴 Hard Topics: Array, Dynamic Programming, Greedy, Bit Manipulation, Tree, Sorting Solution Problem Understanding You are given a tree with n nodes. Every node has a value stored in the array nums , and every edge connects two nodes in an undirected manner. You may repeatedly perform the following operation on any edge [u, v] : Replace nums[u] with nums[u] XOR k Replace nums[v] with nums[v]...

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LeetCode 2733 - Neither Minimum nor Maximum

LeetCode Problem 2733 Difficulty: 🟢 Easy Topics: Array, Sorting Solution Problem Understanding The problem asks us to select a number from an array of distinct positive integers such that the chosen number is neither the minimum nor the maximum in the array. In other words, we must return a number that lies strictly between the smallest and largest elements. If all numbers are either the minimum or maximum (for example,...

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LeetCode 2154 - Keep Multiplying Found Values by Two

LeetCode Problem 2154 Difficulty: 🟢 Easy Topics: Array, Hash Table, Sorting, Simulation Solution LeetCode 2154 - Keep Multiplying Found Values by Two Problem Understanding This problem asks us to repeatedly search for a value inside an integer array and double that value whenever it is found. We begin with the integer original . If that number exists anywhere in the array nums , we multiply it by two and repeat...

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LeetCode 2863 - Maximum Length of Semi-Decreasing Subarrays

LeetCode Problem 2863 Difficulty: 🟡 Medium Topics: Array, Stack, Sorting, Monotonic Stack Solution LeetCode 2863 - Maximum Length of Semi-Decreasing Subarrays Problem Understanding The problem gives us an integer array nums and asks for the length of the longest contiguous subarray whose first element is strictly greater than its last element. A subarray is any contiguous segment of the array. For a subarray nums[i...j] to be considered semi-decreasing, the following...

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LeetCode 2274 - Maximum Consecutive Floors Without Special Floors

LeetCode Problem 2274 Difficulty: 🟡 Medium Topics: Array, Sorting Solution LeetCode 2274 - Maximum Consecutive Floors Without Special Floors Problem Understanding The problem gives us a range of rented floors in a building, from bottom to top , inclusive. Within this range, some floors are marked as special floors and cannot be counted as regular office floors. Our task is to determine the largest number of consecutive floors that do...

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LeetCode 2517 - Maximum Tastiness of Candy Basket

LeetCode Problem 2517 Difficulty: 🟡 Medium Topics: Array, Binary Search, Greedy, Sorting Solution LeetCode 2517 - Maximum Tastiness of Candy Basket Problem Understanding The problem gives us an array price where each element represents the price of a candy. We must choose exactly k distinct candies and maximize the basket's "tastiness". The tastiness of a basket is defined as the minimum absolute difference between the prices of any two candies...

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LeetCode 3102 - Minimize Manhattan Distances

LeetCode Problem 3102 Difficulty: 🔴 Hard Topics: Array, Math, Geometry, Sorting, Ordered Set Solution Problem Understanding The problem asks us to minimize the maximum Manhattan distance between any two points on a 2D plane after removing exactly one point from the input list. The input points is an array of integer coordinates [[x1, y1], [x2, y2], ..., [xn, yn]] . The Manhattan distance between two points (x1, y1) and (x2,...

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LeetCode 3288 - Length of the Longest Increasing Path

LeetCode Problem 3288 Difficulty: 🔴 Hard Topics: Array, Binary Search, Sorting Solution Problem Understanding We are given a collection of distinct points on a 2D plane. Each point is represented as (x, y) . An increasing path is a sequence of points where both coordinates strictly increase from one point to the next. If we move from point A = (x1, y1) to point B = (x2, y2) , then...

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LeetCode 1998 - GCD Sort of an Array

LeetCode Problem 1998 Difficulty: 🔴 Hard Topics: Array, Math, Union-Find, Sorting, Number Theory Solution Problem Understanding The problem asks whether it is possible to sort an integer array nums into non-decreasing order using a very specific type of swap. You can swap any two elements nums[i] and nums[j] if and only if their greatest common divisor (GCD) is greater than 1. The input is an array of integers ranging from...

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LeetCode 2165 - Smallest Value of the Rearranged Number

LeetCode Problem 2165 Difficulty: 🟡 Medium Topics: Math, Sorting Solution Problem Understanding In this problem, we are given an integer num , which may be positive, negative, or zero. Our goal is to rearrange its digits so that the resulting number is as small as possible while preserving the original sign. The important detail is that the sign cannot change. If the number is positive, the rearranged number must also...

Practice › LeetCode › LeetCode 27xx ›

LeetCode 2780 - Minimum Index of a Valid Split

LeetCode Problem 2780 Difficulty: 🟡 Medium Topics: Array, Hash Table, Sorting Solution Problem Understanding The problem asks us to find a minimum index at which a given integer array nums can be split into two non-empty contiguous subarrays, such that both subarrays share the same dominant element as the original array. A dominant element is one that occurs in more than half of the elements of an array. The input...

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LeetCode 2136 - Earliest Possible Day of Full Bloom

LeetCode Problem 2136 Difficulty: 🔴 Hard Topics: Array, Greedy, Sorting Solution Problem Understanding The problem presents a scenario where we have n flower seeds, each of which requires two phases to bloom: a planting phase and a growth phase. Each seed i takes plantTime[i] full days to plant, which can be spread across non-consecutive days. After planting, the seed requires growTime[i] full days to grow, and only after this period...

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LeetCode 3016 - Minimum Number of Pushes to Type Word II

LeetCode Problem 3016 Difficulty: 🟡 Medium Topics: Hash Table, String, Greedy, Sorting, Counting Solution LeetCode 3016 - Minimum Number of Pushes to Type Word II Problem Understanding This problem asks us to redesign a telephone keypad so that typing a given word requires the fewest total key presses possible. A traditional telephone keypad contains keys 2 through 9 , giving us exactly 8 available keys . Each lowercase English letter...

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LeetCode 3107 - Minimum Operations to Make Median of Array Equal to K

LeetCode Problem 3107 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting Solution Problem Understanding The problem asks us to transform an integer array so that its median becomes exactly k , using the minimum number of operations. In one operation, we may either increase or decrease any single element by 1 . The median is defined after sorting the array in non-decreasing order. For arrays with odd length, the median is...

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LeetCode 2679 - Sum in a Matrix

LeetCode Problem 2679 Difficulty: 🟡 Medium Topics: Array, Sorting, Heap (Priority Queue), Matrix, Simulation Solution Problem Understanding The problem gives us a 2D integer matrix nums . Each row contains several integers, and we repeatedly perform a special removal process until every element has been removed. During each operation, we do two things: From every row, remove the largest remaining element. Among all removed elements from this round, take the...

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LeetCode 3382 - Maximum Area Rectangle With Point Constraints II

LeetCode Problem 3382 Difficulty: 🔴 Hard Topics: Array, Math, Binary Indexed Tree, Segment Tree, Geometry, Sorting Solution Problem Understanding The problem asks us to find the maximum area rectangle that can be formed from a given set of points on a 2D plane, under strict constraints. Each rectangle must have its edges parallel to the x and y axes, must use exactly four points from the input as corners, and...

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LeetCode 1885 - Count Pairs in Two Arrays

LeetCode Problem 1885 Difficulty: 🟡 Medium Topics: Array, Two Pointers, Binary Search, Sorting Solution Problem Understanding The problem asks us to count the number of index pairs (i, j) such that i < j and the sum of elements at these indices in nums1 is greater than the sum of elements at the same indices in nums2 . Formally, we want the number of pairs (i, j) where nums1[i] +...

Practice › LeetCode › LeetCode 25xx ›

LeetCode 2578 - Split With Minimum Sum

LeetCode Problem 2578 Difficulty: 🟢 Easy Topics: Math, Greedy, Sorting Solution Problem Understanding The problem asks us to take a positive integer num and split its digits into two non-negative integers num1 and num2 such that the sum num1 + num2 is minimized. Importantly, the digits of num must be entirely used between num1 and num2 , but their order can be rearranged, and leading zeros are allowed in both...

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LeetCode 2931 - Maximum Spending After Buying Items

LeetCode Problem 2931 Difficulty: 🔴 Hard Topics: Array, Greedy, Sorting, Heap (Priority Queue), Matrix Solution LeetCode 2931 - Maximum Spending After Buying Items Problem Understanding We are given an m × n matrix values where each row represents a shop and each column represents an item in that shop. The important property is that every row is sorted in non-increasing order: values[i][0] >= values[i][1] >= ... >= values[i][n-1] When buying...

Practice › LeetCode › LeetCode 24xx ›

LeetCode 2402 - Meeting Rooms III

LeetCode Problem 2402 Difficulty: 🔴 Hard Topics: Array, Hash Table, Sorting, Heap (Priority Queue), Simulation Solution Problem Understanding The problem is about scheduling meetings into a fixed number of rooms, where each meeting has a unique start time and a defined duration. We have n rooms numbered from 0 to n - 1 , and we are given a list of meetings represented as [start, end) intervals. The task is...

Practice › LeetCode › LeetCode 23xx ›

LeetCode 2332 - The Latest Time to Catch a Bus

LeetCode Problem 2332 Difficulty: 🟡 Medium Topics: Array, Two Pointers, Binary Search, Sorting Solution Problem Understanding The problem asks us to determine the latest time we can arrive at a bus station to catch a bus , given the departure times of buses, arrival times of other passengers, and the maximum capacity of each bus. The buses and passengers are both represented as integer arrays with unique values, and passengers...

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LeetCode 2323 - Find Minimum Time to Finish All Jobs II

LeetCode Problem 2323 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting Solution Problem Understanding This problem asks us to assign jobs to workers in a way that minimizes the total number of days needed to finish all jobs. We are given two integer arrays of equal length: jobs[i] represents the amount of work required for the i-th job. workers[j] represents how much work the j-th worker can complete in one day....

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LeetCode 2268 - Minimum Number of Keypresses

LeetCode Problem 2268 Difficulty: 🟡 Medium Topics: Hash Table, String, Greedy, Sorting, Counting Solution Problem Understanding The problem asks us to determine the minimum number of keypresses required to type a given string s using a keypad with 9 buttons. Each button can map to at most 3 letters , and each letter must be mapped to exactly one button. When typing a character, the number of presses depends on...

Practice › LeetCode › LeetCode 24xx ›

LeetCode 2497 - Maximum Star Sum of a Graph

LeetCode Problem 2497 Difficulty: 🟡 Medium Topics: Array, Greedy, Graph Theory, Sorting, Heap (Priority Queue) Solution Problem Understanding The problem gives us an undirected graph where each node has an associated integer value. We are asked to form a star graph and compute the maximum possible star sum. A star graph is defined by choosing one node as the center and selecting up to k of its neighbors. The resulting...

Practice › LeetCode › LeetCode 30xx ›

LeetCode 3075 - Maximize Happiness of Selected Children

LeetCode Problem 3075 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting Solution Problem Understanding The problem gives us an array happiness representing the happiness values of n children standing in a queue and asks us to select exactly k children to maximize the sum of their happiness. The twist is that each time we select a child, all unselected children have their happiness decreased by 1, but their happiness cannot go...

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LeetCode 2410 - Maximum Matching of Players With Trainers

LeetCode Problem 2410 Difficulty: 🟡 Medium Topics: Array, Two Pointers, Greedy, Sorting Solution Problem Understanding This problem requires us to maximize the number of matchings between players and trainers under the condition that a player's ability cannot exceed the trainer's training capacity. In other words, a player i can only be assigned to trainer j if players[i] <= trainers[j] . Additionally, each player and each trainer can participate in at...

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LeetCode 2099 - Find Subsequence of Length K With the Largest Sum

LeetCode Problem 2099 Difficulty: 🟢 Easy Topics: Array, Hash Table, Sorting, Heap (Priority Queue) Solution Problem Understanding The problem asks us to find a subsequence of length k from a given integer array nums such that the sum of the elements in the subsequence is maximized. A subsequence is defined as a sequence that can be obtained from the original array by deleting zero or more elements without changing the...

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LeetCode 2160 - Minimum Sum of Four Digit Number After Splitting Digits

LeetCode Problem 2160 Difficulty: 🟢 Easy Topics: Math, Greedy, Sorting Solution Problem Understanding The problem asks us to take a four-digit integer num and split its digits into two new integers such that the sum of these two integers is minimized. We are allowed to use all digits exactly once, and the new integers can have leading zeros . For instance, if the number is 2932 , the digits are...

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LeetCode 2545 - Sort the Students by Their Kth Score

LeetCode Problem 2545 Difficulty: 🟡 Medium Topics: Array, Sorting, Matrix Solution Problem Understanding In this problem, we are given a matrix named score with dimensions m x n . Each row represents a student, and each column represents an exam. The value score[i][j] is the score obtained by the i th student on the j th exam. The task is to sort the rows of the matrix according to the...

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LeetCode 3143 - Maximum Points Inside the Square

LeetCode Problem 3143 Difficulty: 🟡 Medium Topics: Array, Hash Table, String, Binary Search, Sorting Solution Problem Understanding The problem asks us to find the maximum number of points that can be contained in a square centered at the origin (0, 0) such that no two points inside the square share the same tag. The square's edges are parallel to the axes, and points on the edges are considered inside. The...

Practice › LeetCode › LeetCode 24xx ›

LeetCode 2456 - Most Popular Video Creator

LeetCode Problem 2456 Difficulty: 🟡 Medium Topics: Array, Hash Table, String, Sorting, Heap (Priority Queue) Solution Problem Understanding The problem gives us three parallel arrays: creators[i] represents the creator of the i th video ids[i] represents the video ID of the i th video views[i] represents the number of views for the i th video Each index corresponds to one video. Multiple videos can belong to the same creator, and...

Practice › LeetCode › LeetCode 25xx ›

LeetCode 2512 - Reward Top K Students

LeetCode Problem 2512 Difficulty: 🟡 Medium Topics: Array, Hash Table, String, Sorting, Heap (Priority Queue) Solution Problem Understanding The problem asks us to compute a ranking of students based on textual feedback they receive. We are given two lists of words: positive_feedback and negative_feedback . Every time a student receives a report, we score that report by adding 3 points for each word that appears in positive_feedback and subtracting 1...

Practice › LeetCode › LeetCode 27xx ›

LeetCode 2747 - Count Zero Request Servers

LeetCode Problem 2747 Difficulty: 🟡 Medium Topics: Array, Hash Table, Sliding Window, Sorting Solution Problem Understanding This problem asks us to count servers that did not receive any requests within a certain time window for multiple queries. You are given n servers, each with a unique ID from 1 to n . The logs array records requests, where each entry [server_id, time] indicates that server_id received a request at time...

Practice › LeetCode › LeetCode 26xx ›

LeetCode 2604 - Minimum Time to Eat All Grains

LeetCode Problem 2604 Difficulty: 🔴 Hard Topics: Array, Two Pointers, Binary Search, Sorting Solution Problem Understanding The problem asks us to determine the minimum time needed for all hens to eat all grains when both hens and grains are located on a one-dimensional line. Each hen can move left or right by 1 unit per second and can eat multiple grains, but only when occupying the same position as the...

Practice › LeetCode › LeetCode 23xx ›

LeetCode 2357 - Make Array Zero by Subtracting Equal Amounts

LeetCode Problem 2357 Difficulty: 🟢 Easy Topics: Array, Hash Table, Greedy, Sorting, Heap (Priority Queue), Simulation Solution LeetCode 2357 - Make Array Zero by Subtracting Equal Amounts Problem Understanding This problem gives us an array nums containing non-negative integers. We want to transform the entire array into zeros using a specific operation. In a single operation, we must choose a positive integer x that is less than or equal to...

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LeetCode 2421 - Number of Good Paths

LeetCode Problem 2421 Difficulty: 🔴 Hard Topics: Array, Hash Table, Tree, Union-Find, Graph Theory, Sorting Solution Problem Understanding The problem is asking us to count the number of good paths in a tree. A tree is a connected acyclic graph with n nodes and n - 1 edges. Each node has an integer value assigned by the array vals . A good path is defined as a simple path (no...

Practice › LeetCode › LeetCode 26xx ›

LeetCode 2613 - Beautiful Pairs

LeetCode Problem 2613 Difficulty: 🔴 Hard Topics: Array, Math, Divide and Conquer, Geometry, Sorting, Ordered Set Solution Problem Understanding The problem asks us to find a beautiful pair of indices (i, j) in two integer arrays nums1 and nums2 of equal length. A pair (i, j) is beautiful if it minimizes the sum of the absolute differences between the corresponding elements: |nums1[i] - nums1[j]| + |nums2[i] - nums2[j]| among all...

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LeetCode 2285 - Maximum Total Importance of Roads

LeetCode Problem 2285 Difficulty: 🟡 Medium Topics: Greedy, Graph Theory, Sorting, Heap (Priority Queue) Solution Here is the complete technical solution guide for LeetCode 2285 following your requested format and level of detail: Problem Understanding The problem gives you n cities, numbered from 0 to n - 1 , and a list of bidirectional roads connecting pairs of cities. Each city must be assigned a unique integer value from 1...

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LeetCode 2819 - Minimum Relative Loss After Buying Chocolates

LeetCode Problem 2819 Difficulty: 🔴 Hard Topics: Array, Binary Search, Sorting, Prefix Sum Solution LeetCode 2819 - Minimum Relative Loss After Buying Chocolates Problem Understanding We are given an array prices , where each value represents the price of a chocolate. For every query [k, m] , Bob wants to choose exactly m chocolates. The payment rule depends on the threshold k : If a chocolate costs at most k...

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LeetCode 3039 - Apply Operations to Make String Empty

LeetCode Problem 3039 Difficulty: 🟡 Medium Topics: Array, Hash Table, Sorting, Counting Solution LeetCode 3039 - Apply Operations to Make String Empty Problem Understanding The problem gives us a lowercase string s and defines a repeated operation. During one operation, we scan through all letters from 'a' to 'z' . For each letter, if that letter appears in the current string, we remove its first occurrence. This process continues until...

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LeetCode 2251 - Number of Flowers in Full Bloom

LeetCode Problem 2251 Difficulty: 🔴 Hard Topics: Array, Hash Table, Binary Search, Sorting, Prefix Sum, Ordered Set Solution Problem Understanding The problem asks us to determine, for a list of people arriving at certain times, how many flowers are in full bloom at the time of their arrival. Each flower has a start and end time representing the period it is in full bloom, inclusive of both endpoints. The input...

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LeetCode 2589 - Minimum Time to Complete All Tasks

LeetCode Problem 2589 Difficulty: 🔴 Hard Topics: Array, Binary Search, Stack, Greedy, Sorting Solution Problem Understanding This problem is asking us to determine the minimum amount of time that a computer must be turned on to execute a set of tasks, given that each task has a specified time window [starti, endi] and requires a total duration durationi that does not need to be continuous. In other words, the computer...

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LeetCode 2655 - Find Maximal Uncovered Ranges

LeetCode Problem 2655 Difficulty: 🟡 Medium Topics: Array, Sorting Solution LeetCode 2655 - Find Maximal Uncovered Ranges Problem Understanding The problem gives us an integer n , representing a conceptual array nums of length n , indexed from 0 to n - 1 . We are also given a list of inclusive ranges, where each range marks positions in the array as covered. Our task is to determine every maximal...

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LeetCode 2054 - Two Best Non-Overlapping Events

LeetCode Problem 2054 Difficulty: 🟡 Medium Topics: Array, Binary Search, Dynamic Programming, Sorting, Heap (Priority Queue) Solution Problem Understanding The problem gives us a list of events, where each event is represented as: [startTime, endTime, value] Each event occupies an inclusive time interval from startTime to endTime . If we attend that event, we earn value points. We are allowed to attend at most two events, but the chosen events...

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LeetCode 2141 - Maximum Running Time of N Computers

LeetCode Problem 2141 Difficulty: 🔴 Hard Topics: Array, Binary Search, Greedy, Sorting Solution Problem Understanding The problem is asking us to determine the maximum number of minutes n computers can run simultaneously using a given set of batteries. Each battery has a fixed amount of energy in minutes, and you can initially assign at most one battery per computer . After that, you can swap batteries freely between computers at...

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LeetCode 3009 - Maximum Number of Intersections on the Chart

LeetCode Problem 3009 Difficulty: 🔴 Hard Topics: Array, Hash Table, Math, Binary Indexed Tree, Geometry, Sweep Line, Sorting Solution I can provide the full guide, but I want to avoid giving you a technically incorrect reference document. For LeetCode 3009 , there are two subtly different interpretations that materially change the optimal algorithm and correctness proof: whether intersections at a chart vertex (k, y[k]) count once or twice when both...

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LeetCode 2234 - Maximum Total Beauty of the Gardens

LeetCode Problem 2234 Difficulty: 🔴 Hard Topics: Array, Two Pointers, Binary Search, Greedy, Sorting, Enumeration, Prefix Sum Solution Problem Understanding In this problem, we are given several gardens, where flowers[i] represents how many flowers are already planted in the i-th garden. We are also given a limited number of additional flowers, newFlowers , that we may distribute among the gardens. The goal is to maximize the total beauty score after...

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LeetCode 3081 - Replace Question Marks in String to Minimize Its Value

LeetCode Problem 3081 Difficulty: 🟡 Medium Topics: Hash Table, String, Greedy, Sorting, Heap (Priority Queue), Counting Solution Problem Understanding The problem gives us a string s containing lowercase English letters and the character '?' . Every '?' must be replaced with a lowercase letter so that the resulting string has the minimum possible value. The value of a string is determined by counting repeated occurrences of letters. For every position...

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LeetCode 3267 - Count Almost Equal Pairs II

LeetCode Problem 3267 Difficulty: 🔴 Hard Topics: Array, Hash Table, Sorting, Counting, Enumeration Solution LeetCode 3267 - Count Almost Equal Pairs II Problem Understanding We are given an array nums containing positive integers. We need to count how many pairs of indices (i, j) with i < j satisfy a special condition called almost equal . Two numbers x and y are considered almost equal if we can make them...

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LeetCode 2248 - Intersection of Multiple Arrays

LeetCode Problem 2248 Difficulty: 🟢 Easy Topics: Array, Hash Table, Sorting, Counting Solution Problem Understanding The problem is asking us to find the intersection of multiple arrays. Specifically, given a 2D array nums , where each nums[i] is a non-empty array of distinct positive integers , we want to identify which integers appear in every array in nums . The result should be sorted in ascending order. In simpler terms,...

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LeetCode 2342 - Max Sum of a Pair With Equal Sum of Digits

LeetCode Problem 2342 Difficulty: 🟡 Medium Topics: Array, Hash Table, Sorting, Heap (Priority Queue) Solution Problem Understanding The problem requires finding the maximum sum of a pair of numbers in an array such that the sum of the digits of both numbers is equal. Specifically, you are given a 0-indexed array nums containing positive integers. You can choose two distinct indices i and j such that i != j ,...

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LeetCode 2554 - Maximum Number of Integers to Choose From a Range I

LeetCode Problem 2554 Difficulty: 🟡 Medium Topics: Array, Hash Table, Binary Search, Greedy, Sorting Solution Problem Understanding The problem gives us three inputs: banned , an array of integers that are not allowed to be selected n , which defines the valid integer range [1, n] maxSum , the maximum total sum allowed for all chosen integers We must choose as many distinct integers as possible while satisfying four conditions:...

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LeetCode 2371 - Minimize Maximum Value in a Grid

LeetCode Problem 2371 Difficulty: 🔴 Hard Topics: Array, Union-Find, Graph Theory, Topological Sort, Sorting, Matrix Solution Problem Understanding The problem presents a matrix grid of size m x n with distinct positive integers . The goal is to transform this matrix so that every element is replaced with another positive integer while maintaining the relative order in each row and column . This means that if an element was larger...

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LeetCode 3098 - Find the Sum of Subsequence Powers

LeetCode Problem 3098 Difficulty: 🔴 Hard Topics: Array, Dynamic Programming, Sorting Solution Problem Understanding The problem asks us to compute the sum of powers of all subsequences of length k from an array nums . A subsequence is any subset of elements taken in order from the array without reordering. The power of a subsequence is defined as the minimum absolute difference between any two elements in that subsequence. We...

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LeetCode 2638 - Count the Number of K-Free Subsets

LeetCode Problem 2638 Difficulty: 🟡 Medium Topics: Array, Math, Dynamic Programming, Sorting, Combinatorics Solution That is a detailed, long-form solution guide request. Before I generate it, I need one missing detail: do you want the solution centered on the optimal DP + graph/component approach (grouping numbers by modulo k and solving independent chains with house-robber style DP), or should I also include an alternative bitmask/backtracking approach for educational comparison? I...

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LeetCode 2448 - Minimum Cost to Make Array Equal

LeetCode Problem 2448 Difficulty: 🔴 Hard Topics: Array, Binary Search, Greedy, Sorting, Prefix Sum Solution This guide will use the weighted median optimization approach, which is the key insight behind solving this problem efficiently within the constraints. Problem Understanding The problem gives us two arrays, nums and cost , each of length n . The nums[i] value represents the current number at index i , and cost[i] represents how expensive...

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LeetCode 3367 - Maximize Sum of Weights after Edge Removals

LeetCode Problem 3367 Difficulty: 🔴 Hard Topics: Dynamic Programming, Tree, Depth-First Search, Sorting Solution Problem Understanding We are given an undirected weighted tree with n nodes and n - 1 edges. Since the graph is a tree, there is exactly one simple path between any pair of nodes, and there are no cycles. Each edge has a weight, and we may remove any number of edges. After removals, every node...

Practice › LeetCode › LeetCode 25xx ›

LeetCode 2548 - Maximum Price to Fill a Bag

LeetCode Problem 2548 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting Solution Problem Understanding The problem is asking us to maximize the total price of items placed in a bag with a fixed capacity. Each item is defined by a price and a weight, but unlike traditional knapsack problems, items can be divided proportionally , meaning we can take fractions of an item. Specifically, if we take a fraction f of...

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LeetCode 2386 - Find the K-Sum of an Array

LeetCode Problem 2386 Difficulty: 🔴 Hard Topics: Array, Sorting, Heap (Priority Queue) Solution That is a long, structured reference document with multiple sections, full prose explanations, worked examples, two complete implementations, test suites, and edge case analysis. To make sure I match your formatting exactly and avoid truncation, I will prepare it as a complete technical guide in one response. Before I generate it, I want to confirm one detail...

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LeetCode 3323 - Minimize Connected Groups by Inserting Interval

LeetCode Problem 3323 Difficulty: 🟡 Medium Topics: Array, Binary Search, Sliding Window, Sorting Solution Problem Understanding The problem asks us to minimize the number of connected groups in a set of intervals by adding exactly one interval of length at most k . Each interval [start, end] represents a continuous range on the number line. A connected group is a set of intervals that, taken together, form a continuous segment...

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LeetCode 3273 - Minimum Amount of Damage Dealt to Bob

LeetCode Problem 3273 Difficulty: 🔴 Hard Topics: Array, Greedy, Sorting Solution LeetCode 3273 - Minimum Amount of Damage Dealt to Bob Problem Understanding This problem asks us to determine the minimum total damage Bob will receive while fighting a group of enemies. Each enemy has two attributes: damage[i] , the amount of damage they inflict on Bob every second while alive. health[i] , the amount of health they start with....

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LeetCode 2225 - Find Players With Zero or One Losses

LeetCode Problem 2225 Difficulty: 🟡 Medium Topics: Array, Hash Table, Sorting, Counting Solution Problem Understanding The problem gives us a list of match results. Each match is represented as a pair: [winner, loser] This means the player winner defeated the player loser . Our goal is to return two separate lists: All players who never lost any match. All players who lost exactly one match. Both lists must be sorted...

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LeetCode 2463 - Minimum Total Distance Traveled

LeetCode Problem 2463 Difficulty: 🔴 Hard Topics: Array, Dynamic Programming, Sorting Solution Here is a comprehensive, reference-quality solution guide for LeetCode 2463 - Minimum Total Distance Traveled following your formatting requirements. Problem Understanding The problem gives us a set of robots on an X-axis, each at a unique position, and a set of factories, each at a unique position with a maximum capacity of robots it can repair. Robots are...

Practice › LeetCode › LeetCode 18xx ›

LeetCode 1878 - Get Biggest Three Rhombus Sums in a Grid

LeetCode Problem 1878 Difficulty: 🟡 Medium Topics: Array, Math, Sorting, Heap (Priority Queue), Matrix, Prefix Sum Solution Problem Understanding The problem asks us to compute the largest three distinct rhombus sums in a given m x n integer grid. A rhombus in this context is a square rotated 45 degrees, whose corners align with grid cells. The rhombus sum includes only the border cells of this shape, not the interior....

Practice › LeetCode › LeetCode 29xx ›

LeetCode 2952 - Minimum Number of Coins to be Added

LeetCode Problem 2952 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting Solution Problem Understanding The problem asks us to determine the minimum number of coins we need to add to an existing list of coins so that every integer from 1 to a given target can be formed as the sum of some subsequence of the coins. Here, a subsequence is a selection of coins in their original order, but we...

Practice › LeetCode › LeetCode 21xx ›

LeetCode 2191 - Sort the Jumbled Numbers

LeetCode Problem 2191 Difficulty: 🟡 Medium Topics: Array, Sorting Solution Problem Understanding The problem asks us to sort an array of integers based on a custom digit mapping rather than their natural numeric value. Each digit from 0 to 9 has a mapped value given in the mapping array, and every number in nums can be "transformed" by replacing each digit according to this mapping. The key point is that...

Practice › LeetCode › LeetCode 24xx ›

LeetCode 2465 - Number of Distinct Averages

LeetCode Problem 2465 Difficulty: 🟢 Easy Topics: Array, Hash Table, Two Pointers, Sorting Solution Problem Understanding The problem requires calculating the number of distinct averages generated from a sequence of numbers using a specific process. The input is an integer array nums of even length. The process repeatedly removes the smallest and largest numbers from the array, calculates their average, and continues until the array is empty. The output is...

Practice › LeetCode › LeetCode 28xx ›

LeetCode 2830 - Maximize the Profit as the Salesman

LeetCode Problem 2830 Difficulty: 🟡 Medium Topics: Array, Hash Table, Binary Search, Dynamic Programming, Sorting Solution LeetCode 2830 - Maximize the Profit as the Salesman Problem Understanding This problem gives us n houses arranged on a number line and a collection of purchase offers. Each offer is represented as [start, end, gold] , meaning a buyer wants to purchase every house in the inclusive range [start, end] and is willing...

Practice › LeetCode › LeetCode 30xx ›

LeetCode 3085 - Minimum Deletions to Make String K-Special

LeetCode Problem 3085 Difficulty: 🟡 Medium Topics: Hash Table, String, Greedy, Sorting, Counting Solution Problem Understanding The problem asks us to transform a given string word into a k-special string using the minimum number of deletions. A string is considered k-special if, for every pair of characters in the string, the difference in their frequencies does not exceed k . In simpler terms, all characters' counts must be roughly balanced,...

Practice › LeetCode › LeetCode 27xx ›

LeetCode 2785 - Sort Vowels in a String

LeetCode Problem 2785 Difficulty: 🟡 Medium Topics: String, Sorting Solution Problem Understanding This problem requires us to reorder the vowels in a string while keeping all consonants in their original positions. In simpler terms, we are asked to extract all vowels from a string, sort them by their ASCII values, and then put them back in their original positions, leaving consonants untouched. The input s is a string containing only...

Practice › LeetCode › LeetCode 24xx ›

LeetCode 2441 - Largest Positive Integer That Exists With Its Negative

LeetCode Problem 2441 Difficulty: 🟢 Easy Topics: Array, Hash Table, Two Pointers, Sorting Solution Problem Understanding The problem asks us to find the largest positive integer k in a given array nums such that its negative counterpart -k also exists in the array. In other words, for each positive integer in the array, we need to check whether its negative exists. If multiple positive integers satisfy this property, we return...

Practice › LeetCode › LeetCode 33xx ›

LeetCode 3346 - Maximum Frequency of an Element After Performing Operations I

LeetCode Problem 3346 Difficulty: 🟡 Medium Topics: Array, Binary Search, Sliding Window, Sorting, Prefix Sum Solution Problem Understanding The problem gives us an integer array nums , along with two integers, k and numOperations . We are allowed to perform exactly numOperations operations. In each operation, we must choose a unique index that has not been used before, and modify that element by adding any integer value in the range...

Practice › LeetCode › LeetCode 26xx ›

LeetCode 2611 - Mice and Cheese

LeetCode Problem 2611 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting, Heap (Priority Queue) Solution Problem Understanding The problem gives us two arrays, reward1 and reward2 , where each index represents a specific type of cheese. Every cheese must be eaten by exactly one of the two mice. If cheese i is eaten by the first mouse, we gain reward1[i] points. If it is eaten by the second mouse, we gain...

Practice › LeetCode › LeetCode 33xx ›

LeetCode 3397 - Maximum Number of Distinct Elements After Operations

LeetCode Problem 3397 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting Solution Problem Understanding The problem asks us to maximize the number of distinct elements in an integer array nums by performing a limited set of operations. Each element can be modified at most once by adding an integer in the range [-k, k] . The goal is to determine the largest possible count of unique numbers after applying these operations...

Practice › LeetCode › LeetCode 25xx ›

LeetCode 2501 - Longest Square Streak in an Array

LeetCode Problem 2501 Difficulty: 🟡 Medium Topics: Array, Hash Table, Binary Search, Dynamic Programming, Sorting Solution Problem Understanding The problem asks us to identify the longest square streak in an array of integers nums . A square streak is a subsequence of at least length 2 where, after sorting, every element is the square of the previous element. In other words, if the sorted subsequence is [x1, x2, ..., xk]...

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LeetCode 2557 - Maximum Number of Integers to Choose From a Range II

LeetCode Problem 2557 Difficulty: 🟡 Medium Topics: Array, Binary Search, Greedy, Sorting Solution Problem Understanding The problem is asking to select the maximum number of integers from the range [1, n] under several constraints. First, integers in the banned array cannot be chosen. Second, each integer can be chosen at most once. Third, the sum of all chosen integers must not exceed maxSum . The goal is to determine the...

Practice › LeetCode › LeetCode 27xx ›

LeetCode 2736 - Maximum Sum Queries

LeetCode Problem 2736 Difficulty: 🔴 Hard Topics: Array, Binary Search, Stack, Binary Indexed Tree, Segment Tree, Sorting, Monotonic Stack Solution LeetCode 2736 - Maximum Sum Queries Problem Understanding We are given two arrays, nums1 and nums2 , both of length n . Each index j represents a point: $$(nums1[j], nums2[j])$$ and has an associated value: $$nums1[j] + nums2[j]$$ For every query [xi, yi] , we must find an index j...

Practice › LeetCode › LeetCode 27xx ›

LeetCode 2708 - Maximum Strength of a Group

LeetCode Problem 2708 Difficulty: 🟡 Medium Topics: Array, Dynamic Programming, Backtracking, Greedy, Bit Manipulation, Sorting, Enumeration Solution Problem Understanding The problem asks us to select a non-empty subset of integers from a given array nums such that the product of the numbers in the subset is maximized. Each number represents a student’s exam score, and the subset represents a group of students. The "strength" of a group is the product...

Practice › LeetCode › LeetCode 18xx ›

LeetCode 1874 - Minimize Product Sum of Two Arrays

LeetCode Problem 1874 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting Solution Problem Understanding The problem defines the product sum of two arrays as the sum of the products of corresponding elements at the same indices. If we have arrays a and b , then the product sum is: $$\sum_{i=0}^{n-1} a[i] \times b[i]$$ We are given two arrays, nums1 and nums2 , both of the same length n . We are...

Practice › LeetCode › LeetCode 25xx ›

LeetCode 2593 - Find Score of an Array After Marking All Elements

LeetCode Problem 2593 Difficulty: 🟡 Medium Topics: Array, Hash Table, Sorting, Heap (Priority Queue), Simulation Solution Here is a comprehensive, detailed technical solution guide for LeetCode 2593 - Find Score of an Array After Marking All Elements , following your requested format precisely. Problem Understanding The problem provides an array of positive integers, nums . We are asked to simulate a scoring process where at each step we select the...

Practice › LeetCode › LeetCode 29xx ›

LeetCode 2967 - Minimum Cost to Make Array Equalindromic

LeetCode Problem 2967 Difficulty: 🟡 Medium Topics: Array, Math, Binary Search, Greedy, Sorting Solution LeetCode 2967 - Minimum Cost to Make Array Equalindromic Problem Understanding We are given an integer array nums . We may repeatedly choose any element and replace it with any positive integer x . Replacing a value nums[i] with x costs |nums[i] - x| . The goal is to transform the array so that every element...

Practice › LeetCode › LeetCode 30xx ›

LeetCode 3041 - Maximize Consecutive Elements in an Array After Modification

LeetCode Problem 3041 Difficulty: 🔴 Hard Topics: Array, Dynamic Programming, Sorting Solution Problem Understanding The problem is asking us to maximize the number of consecutive integers we can select from an array after we are allowed to increase any element by at most 1 . The input array nums contains positive integers and can have up to 10^5 elements, with each element ranging from 1 to 10^6 . The output...

Practice › LeetCode › LeetCode 18xx ›

LeetCode 1859 - Sorting the Sentence

LeetCode Problem 1859 Difficulty: 🟢 Easy Topics: String, Sorting Solution Problem Understanding The problem gives us a shuffled sentence , where every word has a number appended to its end. That number represents the word's original position in the sentence, using 1-indexed ordering . For example, the word "This1" means "This" originally appeared in position 1 , while "sentence4" means "sentence" originally appeared in position 4 . The words in...

Practice › LeetCode › LeetCode 23xx ›

LeetCode 2335 - Minimum Amount of Time to Fill Cups

LeetCode Problem 2335 Difficulty: 🟢 Easy Topics: Array, Greedy, Sorting, Heap (Priority Queue) Solution Problem Understanding The problem gives us an array amount of length 3 . Each index represents the number of cups that need to be filled for a specific water type: amount[0] represents cold water cups amount[1] represents warm water cups amount[2] represents hot water cups Every second, the machine can perform exactly one of these operations:...

Practice › LeetCode › LeetCode 20xx ›

LeetCode 2046 - Sort Linked List Already Sorted Using Absolute Values

LeetCode Problem 2046 Difficulty: 🟡 Medium Topics: Linked List, Two Pointers, Sorting Solution Problem Understanding The problem provides a singly linked list where the nodes are sorted in non-decreasing order by their absolute values , rather than their actual values. The task is to rearrange this list so that the nodes are sorted in non-decreasing order according to their actual values . For example, consider the input [0, 2, -5,...

Practice › LeetCode › LeetCode 28xx ›

LeetCode 2842 - Count K-Subsequences of a String With Maximum Beauty

LeetCode Problem 2842 Difficulty: 🔴 Hard Topics: Hash Table, Math, String, Greedy, Sorting, Combinatorics Solution Problem Understanding The problem requires us to count k-subsequences of a string s that have the maximum beauty , where beauty is defined as the sum of the frequency of each character in the subsequence. A k-subsequence is a subsequence of length k where all characters are unique. The input string can be up to...

Practice › LeetCode › LeetCode 20xx ›

LeetCode 2094 - Finding 3-Digit Even Numbers

LeetCode Problem 2094 Difficulty: 🟢 Easy Topics: Array, Hash Table, Recursion, Sorting, Enumeration Solution Problem Understanding The problem gives us an array named digits , where every element is a single decimal digit from 0 to 9 . We must use exactly three elements from this array to build valid three digit integers. The important detail is that each digit can only be used as many times as it appears...

Practice › LeetCode › LeetCode 22xx ›

LeetCode 2279 - Maximum Bags With Full Capacity of Rocks

LeetCode Problem 2279 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting Solution Problem Understanding The problem presents n bags, each with a defined maximum capacity and a current number of rocks. The input consists of two arrays: capacity and rocks , where capacity[i] is the maximum number of rocks bag i can hold, and rocks[i] is how many rocks are currently in that bag. Additionally, you are given an integer additionalRocks...

Practice › LeetCode › LeetCode 32xx ›

LeetCode 3281 - Maximize Score of Numbers in Ranges

LeetCode Problem 3281 Difficulty: 🟡 Medium Topics: Array, Binary Search, Greedy, Sorting Solution Problem Understanding The problem presents a list of intervals derived from the start array and a fixed d . Specifically, each interval is [start[i], start[i] + d] . The goal is to select exactly one integer from each interval such that the minimum absolute difference between any two chosen integers is maximized . In other words, you...

Practice › LeetCode › LeetCode 31xx ›

LeetCode 3189 - Minimum Moves to Get a Peaceful Board

LeetCode Problem 3189 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting, Counting Sort Solution Problem Understanding In this problem, we are given the positions of n rooks placed on an n x n chessboard. Each rook is represented as a pair [xi, yi] , where xi is the row index and yi is the column index. A peaceful board is defined as a board where: Every row contains exactly one rook...

Practice › LeetCode › LeetCode 21xx ›

LeetCode 2122 - Recover the Original Array

LeetCode Problem 2122 Difficulty: 🔴 Hard Topics: Array, Hash Table, Two Pointers, Sorting, Enumeration Solution Problem Understanding The problem presents a scenario in which Alice has an original array arr of length n consisting of positive integers. She chooses a positive integer k and generates two new arrays: lower and higher . The array lower is formed by subtracting k from each element of arr , while higher is formed...

Practice › LeetCode › LeetCode 28xx ›

LeetCode 2838 - Maximum Coins Heroes Can Collect

LeetCode Problem 2838 Difficulty: 🟡 Medium Topics: Array, Two Pointers, Binary Search, Sorting, Prefix Sum Solution LeetCode 2838 - Maximum Coins Heroes Can Collect Problem Understanding This problem gives us three arrays: heroes , where heroes[i] represents the power of the i th hero. monsters , where monsters[j] represents the power of the j th monster. coins , where coins[j] represents the reward obtained for defeating the j th monster....

Practice › LeetCode › LeetCode 31xx ›

LeetCode 3194 - Minimum Average of Smallest and Largest Elements

LeetCode Problem 3194 Difficulty: 🟢 Easy Topics: Array, Two Pointers, Sorting Solution LeetCode 3194 - Minimum Average of Smallest and Largest Elements Problem Understanding The problem gives us an even-length integer array nums . We repeatedly perform the following operation until the array becomes empty: Remove the smallest element. Remove the largest element. Compute their average. Store that average in another array called averages . After all pairs have been...

Practice › LeetCode › LeetCode 28xx ›

LeetCode 2818 - Apply Operations to Maximize Score

LeetCode Problem 2818 Difficulty: 🔴 Hard Topics: Array, Math, Stack, Greedy, Sorting, Monotonic Stack, Number Theory Solution Problem Understanding The problem gives us an array nums and an integer k . We begin with a score of 1 , and we are allowed to perform at most k operations. In each operation, we choose a subarray that has not been chosen before. From that subarray, we select the element with...

Practice › LeetCode › LeetCode 18xx ›

LeetCode 1877 - Minimize Maximum Pair Sum in Array

LeetCode Problem 1877 Difficulty: 🟡 Medium Topics: Array, Two Pointers, Greedy, Sorting Solution Problem Understanding The problem asks us to pair elements in an array of even length such that the largest sum among all pairs is minimized. In simpler terms, imagine we have a collection of numbers and we want to form pairs of two numbers each. Each number can only belong to one pair. Once we pair them,...

Practice › LeetCode › LeetCode 10xx ›

LeetCode 1048 - Longest String Chain

LeetCode Problem 1048 Difficulty: 🟡 Medium Topics: Array, Hash Table, Two Pointers, String, Dynamic Programming, Sorting Solution That is a long, structured technical guide that will exceed a practical single-message limit if done comprehensively with all requested sections, detailed walkthroughs, Python and Go solutions, worked examples, full test suite, and edge case analysis. I can provide it in full, following your exact formatting rules. I will include: Problem Understanding Brute...

Practice › LeetCode › LeetCode 13xx ›

LeetCode 1363 - Largest Multiple of Three

LeetCode Problem 1363 Difficulty: 🔴 Hard Topics: Array, Math, Dynamic Programming, Greedy, Sorting Solution I can do that, but the guide will be very long and may get truncated in a single message because of the required depth and sections. To preserve quality and include everything comprehensively, I recommend splitting it into 2 parts : Part 1 Problem Understanding Approaches Algorithm Walkthrough Python Solution Go Solution Part 2 Worked Examples...

Practice › LeetCode › LeetCode 12xx ›

LeetCode 1296 - Divide Array in Sets of K Consecutive Numbers

LeetCode Problem 1296 Difficulty: 🟡 Medium Topics: Array, Hash Table, Greedy, Sorting Solution Problem Understanding The problem gives us an integer array nums and an integer k . We need to determine whether it is possible to divide all numbers in the array into groups where: Each group contains exactly k numbers The numbers inside each group are consecutive integers Every element in the array must belong to exactly one...

Practice › LeetCode › LeetCode 03xx ›

LeetCode 354 - Russian Doll Envelopes

LeetCode Problem 354 Difficulty: 🔴 Hard Topics: Array, Binary Search, Dynamic Programming, Sorting Solution LeetCode 354, Russian Doll Envelopes Problem Understanding The problem gives a list of envelopes, where each envelope is represented as a pair [w, h] . The value w is the width and h is the height. An envelope can fit inside another envelope only if both dimensions are strictly smaller. That means envelope A can go...

Practice › LeetCode › LeetCode 03xx ›

LeetCode 358 - Rearrange String k Distance Apart

LeetCode Problem 358 Difficulty: 🔴 Hard Topics: Hash Table, String, Greedy, Sorting, Heap (Priority Queue), Counting Solution LeetCode 358 - Rearrange String k Distance Apart Problem Understanding The problem gives us a string s and an integer k . We must rearrange the characters in the string so that identical characters are separated by at least k positions. The phrase "at least distance k " means that if the same...

Practice › LeetCode › LeetCode 14xx ›

LeetCode 1498 - Number of Subsequences That Satisfy the Given Sum Condition

LeetCode Problem 1498 Difficulty: 🟡 Medium Topics: Array, Two Pointers, Binary Search, Sorting Solution Problem Understanding The problem asks us to find the number of non-empty subsequences of a given array nums such that for each subsequence, the sum of the minimum and maximum elements is less than or equal to a given target . A subsequence can be obtained by deleting zero or more elements from the array without...

Practice › LeetCode › LeetCode 06xx ›

LeetCode 642 - Design Search Autocomplete System

LeetCode Problem 642 Difficulty: 🔴 Hard Topics: String, Depth-First Search, Design, Trie, Sorting, Heap (Priority Queue), Data Stream Solution Problem Understanding The problem asks us to design an autocomplete system that behaves similarly to a search engine suggestion feature. The system starts with a collection of historical sentences and the number of times each sentence has been typed before. As the user types characters one by one, the system must...

Practice › LeetCode › LeetCode 08xx ›

LeetCode 893 - Groups of Special-Equivalent Strings

LeetCode Problem 893 Difficulty: 🟡 Medium Topics: Array, Hash Table, String, Sorting Solution Problem Understanding The problem asks us to group strings based on a special equivalence property. Specifically, two strings are special-equivalent if you can swap characters at even indices among themselves and characters at odd indices among themselves any number of times to make the two strings identical. The input is an array of strings words , all...

Practice › LeetCode › LeetCode 11xx ›

LeetCode 1170 - Compare Strings by Frequency of the Smallest Character

LeetCode Problem 1170 Difficulty: 🟡 Medium Topics: Array, Hash Table, String, Binary Search, Sorting Solution Problem Understanding The problem defines a function f(s) for a non-empty string s . This function returns the frequency of the lexicographically smallest character in the string. For example: f("dcce") = 2 The smallest character is 'c' 'c' appears 2 times We are given two arrays: queries , containing query strings words , containing reference...

Practice › LeetCode › LeetCode 06xx ›

LeetCode 658 - Find K Closest Elements

LeetCode Problem 658 Difficulty: 🟡 Medium Topics: Array, Two Pointers, Binary Search, Sliding Window, Sorting, Heap (Priority Queue) Solution Problem Understanding The problem gives us a sorted integer array arr , along with two integers, k and x . We need to return exactly k elements from the array that are closest to x . The definition of "closest" is important: An element a is closer than b if |a...

Practice › LeetCode › LeetCode 12xx ›

LeetCode 1200 - Minimum Absolute Difference

LeetCode Problem 1200 Difficulty: 🟢 Easy Topics: Array, Sorting Solution Problem Understanding The problem asks us to find all pairs of numbers in an array that have the smallest absolute difference. In other words, given a list of distinct integers, we want to identify every pair [a, b] such that the difference b - a is minimized across all possible pairs in the array, and we always list the smaller...

Practice › LeetCode › LeetCode 01xx ›

LeetCode 148 - Sort List

LeetCode Problem 148 Difficulty: 🟡 Medium Topics: Linked List, Two Pointers, Divide and Conquer, Sorting, Merge Sort Solution Problem Understanding The problem asks us to sort a singly linked list in ascending order and return the head of the sorted list. The input is the head node of a linked list. Each node contains an integer value and a pointer to the next node. Unlike arrays, linked lists do not...

Practice › LeetCode › LeetCode 11xx ›

LeetCode 1181 - Before and After Puzzle

LeetCode Problem 1181 Difficulty: 🟡 Medium Topics: Array, Hash Table, String, Sorting Solution Problem Understanding The problem gives us an array of phrases, where each phrase is a string made of lowercase English letters and spaces. Every phrase is well-formed, meaning there are no leading or trailing spaces and no consecutive spaces. We must generate all possible "Before and After" puzzles by combining two different phrases. A valid merge happens...

Practice › LeetCode › LeetCode 07xx ›

LeetCode 792 - Number of Matching Subsequences

LeetCode Problem 792 Difficulty: 🟡 Medium Topics: Array, Hash Table, String, Binary Search, Dynamic Programming, Trie, Sorting Solution Problem Understanding The problem asks us to count how many words in a given list are subsequences of a string s . A subsequence is formed by deleting zero or more characters from the string without changing the order of the remaining characters. For instance, "ace" is a subsequence of "abcde" because...

Practice › LeetCode › LeetCode 15xx ›

LeetCode 1580 - Put Boxes Into the Warehouse II

LeetCode Problem 1580 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting Solution Problem Understanding In this problem, we are given two arrays: boxes , where each value represents the height of a box warehouse , where each value represents the height of a room in the warehouse Every box has width 1 , and every warehouse room also has width 1 . Boxes cannot be stacked, meaning each room can contain...

Practice › LeetCode › LeetCode 15xx ›

LeetCode 1564 - Put Boxes Into the Warehouse I

LeetCode Problem 1564 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting Solution Problem Understanding The problem gives us two arrays: boxes , where each value represents the height of a box warehouse , where each value represents the height of a room in the warehouse Every box has width 1 , and every warehouse room also has width 1 . Boxes cannot be stacked, so each room can hold at most...

Practice › LeetCode › LeetCode 18xx ›

LeetCode 1833 - Maximum Ice Cream Bars

LeetCode Problem 1833 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting, Counting Sort Solution Problem Understanding This problem asks us to determine the maximum number of ice cream bars a boy can buy with a limited number of coins. The input consists of an array costs , where costs[i] represents the price of the i-th ice cream bar, and an integer coins representing the total coins available. The boy can purchase...

Practice › LeetCode › LeetCode 13xx ›

LeetCode 1340 - Jump Game V

LeetCode Problem 1340 Difficulty: 🔴 Hard Topics: Array, Dynamic Programming, Sorting Solution Here is a comprehensive solution guide for LeetCode 1340 following your requested format. Problem Understanding The problem presents an array arr of integers and a maximum jump distance d . You can jump from an index i to another index j within d steps to the left or right, but only if the height at the destination arr[j]...

Practice › LeetCode › LeetCode 06xx ›

LeetCode 645 - Set Mismatch

LeetCode Problem 645 Difficulty: 🟢 Easy Topics: Array, Hash Table, Bit Manipulation, Sorting Solution Problem Understanding The problem describes a corrupted set of integers. Originally, the set contained every number from 1 through n exactly once. Because of an error, one number was duplicated, which means one other number disappeared. The input array nums represents this corrupted version of the set. Since one number appears twice and another is missing,...

Practice › LeetCode › LeetCode 09xx ›

LeetCode 950 - Reveal Cards In Increasing Order

LeetCode Problem 950 Difficulty: 🟡 Medium Topics: Array, Queue, Sorting, Simulation Solution Problem Understanding The problem gives us a deck of unique integer cards and asks us to arrange the deck so that a very specific reveal process produces the cards in increasing order. The reveal process works like this: Reveal the top card and remove it from the deck. Move the next top card to the bottom of the...

Practice › LeetCode › LeetCode 04xx ›

LeetCode 442 - Find All Duplicates in an Array

LeetCode Problem 442 Difficulty: 🟡 Medium Topics: Array, Hash Table, Sorting Solution Problem Understanding The problem gives us an integer array nums of length n , where every value is guaranteed to be in the range [1, n] . Each number appears either once or twice. Our task is to return all numbers that appear exactly twice. The important requirement is not just correctness, but efficiency. The solution must run...

Practice › LeetCode › LeetCode 20xx ›

LeetCode 2037 - Minimum Number of Moves to Seat Everyone

LeetCode Problem 2037 Difficulty: 🟢 Easy Topics: Array, Greedy, Sorting, Counting Sort Solution Problem Understanding This problem asks us to assign students to seats such that every student occupies exactly one seat and no two students share the same seat. Each student can move left or right on a number line, and every movement by one position costs exactly one move. The goal is to minimize the total number of...

Practice › LeetCode › LeetCode 05xx ›

LeetCode 524 - Longest Word in Dictionary through Deleting

LeetCode Problem 524 Difficulty: 🟡 Medium Topics: Array, Two Pointers, String, Sorting Solution Problem Understanding The problem gives us a source string s and a list of candidate words called dictionary . We must determine which dictionary word can be formed by deleting characters from s without changing the relative order of the remaining characters. This means we are looking for a subsequence relationship. A word is valid if we...

Practice › LeetCode › LeetCode 16xx ›

LeetCode 1610 - Maximum Number of Visible Points

LeetCode Problem 1610 Difficulty: 🔴 Hard Topics: Array, Math, Geometry, Sliding Window, Sorting Solution Problem Understanding In this problem, we are standing at a fixed position on a 2D plane, represented by location = [posx, posy] . Around us, there are multiple points, each with integer coordinates. We are allowed to rotate in place, but we cannot move. Our vision works like a camera with a limited viewing angle. The...

Practice › LeetCode › LeetCode 17xx ›

LeetCode 1738 - Find Kth Largest XOR Coordinate Value

LeetCode Problem 1738 Difficulty: 🟡 Medium Topics: Array, Divide and Conquer, Bit Manipulation, Sorting, Heap (Priority Queue), Matrix, Prefix Sum, Quickselect Solution Problem Understanding The problem asks us to compute the XOR coordinate value for each element in a given 2D matrix and then find the kth largest among them. Specifically, for a coordinate (a, b) , the value is defined as the XOR of all elements in the submatrix...

Practice › LeetCode › LeetCode 12xx ›

LeetCode 1235 - Maximum Profit in Job Scheduling

LeetCode Problem 1235 Difficulty: 🔴 Hard Topics: Array, Binary Search, Dynamic Programming, Sorting Solution Problem Understanding The problem gives us three arrays of equal length: startTime[i] represents when the i-th job starts endTime[i] represents when the i-th job finishes profit[i] represents the money earned if we complete that job Our goal is to select a subset of jobs that do not overlap in time while maximizing the total profit. Two...

Practice › LeetCode › LeetCode 12xx ›

LeetCode 1262 - Greatest Sum Divisible by Three

LeetCode Problem 1262 Difficulty: 🟡 Medium Topics: Array, Dynamic Programming, Greedy, Sorting Solution Problem Understanding The problem asks us to find the maximum sum of elements from an integer array nums such that the sum is divisible by three. In other words, we are allowed to pick any subset of numbers from the array, and our goal is to maximize the sum of that subset under the condition that the...

Practice › LeetCode › LeetCode 11xx ›

LeetCode 1152 - Analyze User Website Visit Pattern

LeetCode Problem 1152 Difficulty: 🟡 Medium Topics: Array, Hash Table, String, Sorting Solution Here is a comprehensive, detailed technical solution guide for LeetCode 1152 - Analyze User Website Visit Pattern following your requested format exactly. Problem Understanding The problem asks us to analyze user website visit sequences to determine the most common pattern of length three. We are given three arrays of equal length: username , timestamp , and website...

Practice › LeetCode › LeetCode 13xx ›

LeetCode 1300 - Sum of Mutated Array Closest to Target

LeetCode Problem 1300 Difficulty: 🟡 Medium Topics: Array, Binary Search, Sorting Solution Problem Understanding The problem gives us an integer array arr and an integer target . We are allowed to choose a value x , then modify the array so that every element larger than x becomes exactly x . Smaller elements remain unchanged. After this mutation, we compute the sum of the modified array. Our goal is to...

Practice › LeetCode › LeetCode 03xx ›

LeetCode 347 - Top K Frequent Elements

LeetCode Problem 347 Difficulty: 🟡 Medium Topics: Array, Hash Table, Divide and Conquer, Sorting, Heap (Priority Queue), Bucket Sort, Counting, Quickselect Solution Problem Understanding The problem asks us to return the k most frequently occurring elements from an integer array. We are given an array nums , which may contain duplicates, and an integer k . Our task is to identify which values appear most often and return exactly k...

Practice › LeetCode › LeetCode 10xx ›

LeetCode 1090 - Largest Values From Labels

LeetCode Problem 1090 Difficulty: 🟡 Medium Topics: Array, Hash Table, Greedy, Sorting, Counting Solution Problem Understanding The problem gives us two arrays, values and labels , where each index represents a single item. The item at index i has a value values[i] and a category or group identifier labels[i] . We want to choose a subset of these items such that two constraints are satisfied: We can select at most...

Practice › LeetCode › LeetCode 11xx ›

LeetCode 1122 - Relative Sort Array

LeetCode Problem 1122 Difficulty: 🟢 Easy Topics: Array, Hash Table, Sorting, Counting Sort Solution Problem Understanding This problem asks us to sort arr1 , but not in ordinary ascending or descending order. Instead, the sorting order is partially dictated by another array, arr2 . The key requirement is that every number appearing in arr2 must appear in arr1 in exactly the same relative order. If a number appears multiple times...

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LeetCode 252 - Meeting Rooms

LeetCode Problem 252 Difficulty: 🟢 Easy Topics: Array, Sorting Solution Problem Understanding The problem provides a list of meeting intervals, where each interval is represented as [start, end] . Each pair describes the start time and end time of a meeting. The task is to determine whether a single person can attend every meeting without any scheduling conflicts. In simpler terms, we need to check whether any two meetings overlap...

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LeetCode 1798 - Maximum Number of Consecutive Values You Can Make

LeetCode Problem 1798 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting Solution LeetCode 1798 - Maximum Number of Consecutive Values You Can Make Problem Understanding The problem gives us an array of coin values, where each coin can be used at most once. We are asked to determine the maximum number of consecutive integer values that can be formed starting from 0 . More specifically, if the answer is k ,...

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LeetCode 1169 - Invalid Transactions

LeetCode Problem 1169 Difficulty: 🟡 Medium Topics: Array, Hash Table, String, Sorting Solution Problem Understanding The problem asks us to identify transactions that are potentially invalid based on two rules. First, any transaction with an amount greater than $1000 is invalid. Second, any transaction is invalid if there exists another transaction with the same name that occurs within 60 minutes but in a different city. The input is a list...

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LeetCode 1636 - Sort Array by Increasing Frequency

LeetCode Problem 1636 Difficulty: 🟢 Easy Topics: Array, Hash Table, Sorting Solution Problem Understanding The problem asks us to reorder an array of integers based on the frequency of each value. Specifically, elements with lower frequency should appear before elements with higher frequency. If two elements have the same frequency, the one with the larger value should appear first. In other words, the sort is primary by increasing frequency and...

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LeetCode 1608 - Special Array With X Elements Greater Than or Equal X

LeetCode Problem 1608 Difficulty: 🟢 Easy Topics: Array, Binary Search, Sorting Solution Problem Understanding The problem gives us an array nums containing non-negative integers. We need to determine whether there exists an integer x such that exactly x elements in the array are greater than or equal to x . The important detail is that x does not need to appear inside the array itself. We are only concerned with...

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LeetCode 2229 - Check if an Array Is Consecutive

LeetCode Problem 2229 Difficulty: 🟢 Easy Topics: Array, Hash Table, Sorting Solution Problem Understanding The problem asks us to determine whether an integer array forms a perfect sequence of consecutive numbers without gaps or duplicates. More formally, if the array has length n and its minimum value is x , then the array is considered consecutive if it contains every integer in the range: $$[x, x + n - 1]$$...

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LeetCode 1305 - All Elements in Two Binary Search Trees

LeetCode Problem 1305 Difficulty: 🟡 Medium Topics: Tree, Depth-First Search, Binary Search Tree, Sorting, Binary Tree Solution Problem Understanding The problem gives us two binary search trees, root1 and root2 . A binary search tree, commonly abbreviated as BST, has the important property that for every node: All values in the left subtree are smaller than the node's value All values in the right subtree are larger than the node's...

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LeetCode 1329 - Sort the Matrix Diagonally

LeetCode Problem 1329 Difficulty: 🟡 Medium Topics: Array, Sorting, Matrix Solution Problem Understanding The problem asks us to sort every diagonal of a matrix independently in ascending order. A diagonal is defined as a sequence of cells that begins either from the first row or the first column, then continues by repeatedly moving one row down and one column to the right. For example, in a matrix: 1 2 34...

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LeetCode 1331 - Rank Transform of an Array

LeetCode Problem 1331 Difficulty: 🟢 Easy Topics: Array, Hash Table, Sorting Solution Problem Understanding The problem asks us to replace every number in the input array with its rank when the array is sorted in ascending order. A rank is defined by the relative ordering of the values: The smallest unique value gets rank 1 The second smallest unique value gets rank 2 Equal values must receive the same rank...

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LeetCode 1005 - Maximize Sum Of Array After K Negations

LeetCode Problem 1005 Difficulty: 🟢 Easy Topics: Array, Greedy, Sorting Solution Problem Understanding The problem is asking us to maximize the sum of an integer array after performing exactly k negations. A negation operation consists of picking an index i and replacing nums[i] with -nums[i] . This operation can be applied to the same element multiple times. The input consists of an array of integers nums and an integer k...

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LeetCode 1288 - Remove Covered Intervals

LeetCode Problem 1288 Difficulty: 🟡 Medium Topics: Array, Sorting Solution Problem Understanding The problem gives us a list of intervals, where each interval is represented as [li, ri] , corresponding to the half open interval [li, ri) . We need to remove every interval that is completely covered by another interval in the list. An interval [a, b) is considered covered by [c, d) if: c <= a b <=...

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LeetCode 1604 - Alert Using Same Key-Card Three or More Times in a One Hour Period

LeetCode Problem 1604 Difficulty: 🟡 Medium Topics: Array, Hash Table, String, Sorting Solution Problem Understanding The problem gives us two parallel arrays, keyName and keyTime . Each index represents a single key-card usage event. For example: keyName[i] = employee name keyTime[i] = time of usage Together, they describe when a specific employee used their key-card during a single day. Our task is to identify every employee who used their key-card...

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LeetCode 846 - Hand of Straights

LeetCode Problem 846 Difficulty: 🟡 Medium Topics: Array, Hash Table, Greedy, Sorting Solution Problem Understanding The problem asks us to determine whether a given collection of cards can be rearranged into groups of consecutive numbers, each of size groupSize . Each card is represented by an integer in the array hand , and Alice wants to form groups such that within each group, the card numbers are consecutive and the...

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LeetCode 2035 - Partition Array Into Two Arrays to Minimize Sum Difference

LeetCode Problem 2035 Difficulty: 🔴 Hard Topics: Array, Two Pointers, Binary Search, Dynamic Programming, Bit Manipulation, Sorting, Ordered Set, Bitmask Solution Problem Understanding The problem gives an array nums containing exactly 2 * n integers. We must divide these integers into two separate groups, each containing exactly n elements. After forming the two groups, we compute the sum of each group and measure the absolute difference between those sums. Our...

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LeetCode 1187 - Make Array Strictly Increasing

LeetCode Problem 1187 Difficulty: 🔴 Hard Topics: Array, Binary Search, Dynamic Programming, Sorting Solution Problem Understanding The problem is asking us to transform the array arr1 into a strictly increasing array using the minimum number of operations. Each operation allows replacing an element of arr1 with an element from arr2 . The final array must satisfy the strictly increasing condition, meaning each element is strictly greater than the previous one....

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LeetCode 532 - K-diff Pairs in an Array

LeetCode Problem 532 Difficulty: 🟡 Medium Topics: Array, Hash Table, Two Pointers, Binary Search, Sorting Solution Problem Understanding The problem asks us to count how many unique pairs of integers in the array have an absolute difference equal to k . A pair is considered valid if: The two elements come from different indices. The absolute difference between the two values is exactly k . The important detail is that...

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LeetCode 15 - 3Sum

LeetCode Problem 15 Difficulty: 🟡 Medium Topics: Array, Two Pointers, Sorting Solution LeetCode 15 - 3Sum Problem Understanding The problem gives us an integer array nums , and we need to find every unique triplet of numbers whose sum is exactly 0 . A triplet consists of three different indices: i != j i != k j != k The values themselves may be equal, but the indices must be...

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LeetCode 259 - 3Sum Smaller

LeetCode Problem 259 Difficulty: 🟡 Medium Topics: Array, Two Pointers, Binary Search, Sorting Solution Problem Understanding The problem asks us to count how many distinct index triplets (i, j, k) satisfy two conditions: The indices are ordered such that 0 <= i < j < k < n The sum of the corresponding values is strictly smaller than the given target In other words, we must examine combinations of three...

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LeetCode 1337 - The K Weakest Rows in a Matrix

LeetCode Problem 1337 Difficulty: 🟢 Easy Topics: Array, Binary Search, Sorting, Heap (Priority Queue), Matrix Solution Here is a comprehensive, detailed solution guide for LeetCode 1337 following your exact instructions. Problem Understanding The problem provides a binary m x n matrix mat , where each element is either 1 (representing a soldier) or 0 (representing a civilian). In each row, soldiers are always positioned before civilians, meaning all 1 s...

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LeetCode 1647 - Minimum Deletions to Make Character Frequencies Unique

LeetCode Problem 1647 Difficulty: 🟡 Medium Topics: Hash Table, String, Greedy, Sorting Solution Problem Understanding The problem asks us to make a string good , which means no two distinct characters in the string have the same frequency. The input is a string s consisting of lowercase English letters, and the output is the minimum number of character deletions required to achieve a good string. The frequency of a character...

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LeetCode 1383 - Maximum Performance of a Team

LeetCode Problem 1383 Difficulty: 🔴 Hard Topics: Array, Greedy, Sorting, Heap (Priority Queue) Solution Problem Understanding This problem asks us to build a team of at most k engineers such that the team's performance is maximized. Each engineer has two attributes: speed[i] , representing how fast the engineer is efficiency[i] , representing how efficient the engineer is The performance of a team is defined as: $$\text{performance} = (\text{sum of team...

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LeetCode 594 - Longest Harmonious Subsequence

LeetCode Problem 594 Difficulty: 🟢 Easy Topics: Array, Hash Table, Sliding Window, Sorting, Counting Solution Problem Understanding The problem asks us to find the length of the longest harmonious subsequence in an integer array. A harmonious array is defined as one where the difference between the maximum and minimum values is exactly 1 . In simpler terms, given an array nums , we are searching for the longest collection of...

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LeetCode 350 - Intersection of Two Arrays II

LeetCode Problem 350 Difficulty: 🟢 Easy Topics: Array, Hash Table, Two Pointers, Binary Search, Sorting Solution Problem Understanding The problem asks us to find the intersection of two integer arrays, but with an important detail: duplicates matter. If a number appears multiple times in both arrays, it must appear in the result as many times as it appears in both. For example, if 2 appears twice in nums1 and three...

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LeetCode 1094 - Car Pooling

LeetCode Problem 1094 Difficulty: 🟡 Medium Topics: Array, Sorting, Heap (Priority Queue), Simulation, Prefix Sum Solution Problem Understanding This problem asks us to determine whether a car can successfully complete a series of passenger trips without ever exceeding its seating capacity. Each trip is represented as: [numPassengers, from, to] This means: numPassengers passengers enter the car at location from Those same passengers leave the car at location to The important...

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LeetCode 360 - Sort Transformed Array

LeetCode Problem 360 Difficulty: 🟡 Medium Topics: Array, Math, Two Pointers, Sorting Solution Problem Understanding The problem gives us a sorted integer array nums and a quadratic transformation function: $$f(x) = ax^2 + bx + c$$ We must apply this function to every element in the array and return the transformed values in sorted order. The important detail is that the original array is already sorted in ascending order, but...

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LeetCode 47 - Permutations II

LeetCode Problem 47 Difficulty: 🟡 Medium Topics: Array, Backtracking, Sorting Solution Problem Understanding The problem asks us to generate every possible permutation of the given array nums , while ensuring that duplicate permutations are not included in the final result. A permutation is an arrangement of all elements in a particular order. For example, the permutations of [1,2,3] are all six possible orderings of those three numbers. The complication in...

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LeetCode 1244 - Design A Leaderboard

LeetCode Problem 1244 Difficulty: 🟡 Medium Topics: Hash Table, Design, Sorting Solution LeetCode 1244 - Design A Leaderboard Problem Understanding This problem asks us to design a leaderboard system that supports three operations efficiently. Each player has a unique playerId and an associated score. The leaderboard begins empty, and players can be added dynamically as operations are performed. The addScore(playerId, score) operation either creates a new player with the given...

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LeetCode 1471 - The k Strongest Values in an Array

LeetCode Problem 1471 Difficulty: 🟡 Medium Topics: Array, Two Pointers, Sorting Solution Problem Understanding This problem asks us to find the k strongest values in an array according to a custom definition of "strength". The first important detail is the definition of the array's centre. We do not use the average or median in the mathematical sense. Instead, we first sort the array, then select the element at index: $$\frac{n...

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LeetCode 646 - Maximum Length of Pair Chain

LeetCode Problem 646 Difficulty: 🟡 Medium Topics: Array, Dynamic Programming, Greedy, Sorting Solution Problem Understanding The problem gives us an array of integer pairs, where each pair represents an interval-like relationship of the form [left, right] . Every pair satisfies the condition left < right . We want to build the longest possible chain of pairs. A pair [c, d] can follow another pair [a, b] only if: b <...

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LeetCode 1724 - Checking Existence of Edge Length Limited Paths II

LeetCode Problem 1724 Difficulty: 🔴 Hard Topics: Depth-First Search, Union-Find, Graph Theory, Design, Sorting, Heap (Priority Queue), Minimum Spanning Tree Solution LeetCode 1724 - Checking Existence of Edge Length Limited Paths II Problem Understanding This problem gives us an undirected weighted graph with n nodes and a list of edges. Each edge connects two nodes and has an associated distance value. The graph may contain multiple edges between the same...

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LeetCode 769 - Max Chunks To Make Sorted

LeetCode Problem 769 Difficulty: 🟡 Medium Topics: Array, Stack, Greedy, Sorting, Monotonic Stack Solution Problem Understanding This problem is asking us to determine the maximum number of contiguous chunks into which we can split an array such that sorting each chunk individually and concatenating them results in a fully sorted array. The input array arr is a permutation of integers from 0 to n-1 , meaning it contains each integer...

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LeetCode 472 - Concatenated Words

LeetCode Problem 472 Difficulty: 🔴 Hard Topics: Array, String, Dynamic Programming, Depth-First Search, Trie, Sorting Solution Problem Understanding The problem asks us to identify all words in a given list that can be formed by concatenating at least two other words from the same list. In other words, each concatenated word must be fully composed of smaller words that exist in the input array. The input is a list of...

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LeetCode 1424 - Diagonal Traverse II

LeetCode Problem 1424 Difficulty: 🟡 Medium Topics: Array, Sorting, Heap (Priority Queue) Solution Problem Understanding The problem asks us to traverse a jagged 2D integer array nums diagonally. Specifically, elements are accessed by their "diagonal level," where each diagonal contains elements with the same sum of row and column indices. Within each diagonal, elements should appear in reverse order of their rows, meaning we start from the bottom-most row of...

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LeetCode 954 - Array of Doubled Pairs

LeetCode Problem 954 Difficulty: 🟡 Medium Topics: Array, Hash Table, Greedy, Sorting Solution Problem Understanding The problem asks whether it is possible to reorder an even-length array arr of integers such that every element can be paired with another element that is exactly double its value. In other words, after reordering, for every index i in the first half of the array, arr[2 * i + 1] should equal 2...

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LeetCode 869 - Reordered Power of 2

LeetCode Problem 869 Difficulty: 🟡 Medium Topics: Hash Table, Math, Sorting, Counting, Enumeration Solution Problem Understanding The problem gives us a positive integer n and asks whether its digits can be rearranged to form a power of two. The rearrangement may keep the digits in their original order or place them in any other order, but the resulting number cannot contain a leading zero. A power of two is any...

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LeetCode 1268 - Search Suggestions System

LeetCode Problem 1268 Difficulty: 🟡 Medium Topics: Array, String, Binary Search, Trie, Sorting, Heap (Priority Queue) Solution LeetCode 1268 - Search Suggestions System Problem Understanding This problem asks us to build a product suggestion system similar to what appears in e commerce search bars. We are given two inputs: products , an array of unique product names searchWord , the word the user types character by character After each character...

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LeetCode 1333 - Filter Restaurants by Vegan-Friendly, Price and Distance

LeetCode Problem 1333 Difficulty: 🟡 Medium Topics: Array, Sorting Solution Problem Understanding The problem is asking us to filter and sort a list of restaurants based on multiple criteria. Each restaurant is represented as an array [id, rating, veganFriendly, price, distance] . We are given three filters: veganFriendly , maxPrice , and maxDistance . The veganFriendly filter is either 1 or 0, where 1 means we only include restaurants that...

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LeetCode 16 - 3Sum Closest

LeetCode Problem 16 Difficulty: 🟡 Medium Topics: Array, Two Pointers, Sorting Solution Problem Understanding The problem gives us an integer array nums and a target integer target . We must select exactly three elements from the array, using distinct indices, and compute their sum. Among all possible three-number sums, we want the one whose value is closest to the target. The important detail is that we are not trying to...

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LeetCode 1387 - Sort Integers by The Power Value

LeetCode Problem 1387 Difficulty: 🟡 Medium Topics: Dynamic Programming, Memoization, Sorting Solution Problem Understanding This problem asks us to rank integers according to a special metric called the "power value". The power value of a number is determined by repeatedly applying the Collatz transformation rules until the number becomes 1 . The rules are: If the number is even, divide it by 2 If the number is odd, replace it...

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LeetCode 977 - Squares of a Sorted Array

LeetCode Problem 977 Difficulty: 🟢 Easy Topics: Array, Two Pointers, Sorting Solution Problem Understanding The problem asks us to take an array of integers nums that is already sorted in non-decreasing order and return a new array containing the squares of each number , also sorted in non-decreasing order. In simpler terms, we first transform every number x in the array to x * x , and then we produce...

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LeetCode 891 - Sum of Subsequence Widths

LeetCode Problem 891 Difficulty: 🔴 Hard Topics: Array, Math, Sorting Solution Problem Understanding The problem asks us to calculate the sum of widths for all non-empty subsequences of a given integer array nums . A subsequence is any sequence derived by removing zero or more elements from the original array while maintaining the order. The width of a sequence is defined as the difference between its maximum and minimum elements....

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LeetCode 2033 - Minimum Operations to Make a Uni-Value Grid

LeetCode Problem 2033 Difficulty: 🟡 Medium Topics: Array, Math, Sorting, Matrix Solution Problem Understanding The problem gives us a 2D integer matrix called grid and an integer x . In one operation, we may either add x to a cell or subtract x from a cell. Our goal is to make every value in the grid equal using the minimum number of operations. A key detail is that every operation...

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LeetCode 1846 - Maximum Element After Decreasing and Rearranging

LeetCode Problem 1846 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting Solution Problem Understanding The problem provides an array of positive integers and asks us to perform operations to transform it so that two conditions are satisfied: the first element must be 1 , and the absolute difference between adjacent elements cannot exceed 1 . We are allowed to decrease elements and rearrange the array. The ultimate goal is to maximize...

Practice › LeetCode › LeetCode 09xx ›

LeetCode 910 - Smallest Range II

LeetCode Problem 910 Difficulty: 🟡 Medium Topics: Array, Math, Greedy, Sorting Solution LeetCode 910, Smallest Range II Problem Understanding The problem gives us an integer array nums and an integer k . For every element in the array, we must choose exactly one of two operations: add k subtract k After modifying every element, we calculate the score of the array, which is defined as: max(nums) - min(nums) Our goal...

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LeetCode 1356 - Sort Integers by The Number of 1 Bits

LeetCode Problem 1356 Difficulty: 🟢 Easy Topics: Array, Bit Manipulation, Sorting, Counting Solution Problem Understanding The problem asks us to sort an integer array arr based on the number of 1 bits in the binary representation of each element. This means that we are not sorting by the integer value itself but by the count of 1 s in its binary form. If two numbers have the same number of...

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LeetCode 1054 - Distant Barcodes

LeetCode Problem 1054 Difficulty: 🟡 Medium Topics: Array, Hash Table, Greedy, Sorting, Heap (Priority Queue), Counting Solution Problem Understanding The problem is asking us to rearrange a list of barcodes so that no two adjacent barcodes are the same. The input is an array barcodes of integers where each integer represents a type of barcode. The output should be a rearranged array that satisfies the adjacency constraint. The constraints specify...

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LeetCode 1086 - High Five

LeetCode Problem 1086 Difficulty: 🟢 Easy Topics: Array, Hash Table, Sorting, Heap (Priority Queue) Solution Problem Understanding The problem asks us to compute the top five average score for each student given a list of [ID, score] pairs. Each ID represents a unique student, and score represents a single score they received. The goal is to return a list of [ID, topFiveAverage] pairs, where topFiveAverage is calculated by taking the...

Practice › LeetCode › LeetCode 06xx ›

LeetCode 621 - Task Scheduler

LeetCode Problem 621 Difficulty: 🟡 Medium Topics: Array, Hash Table, Greedy, Sorting, Heap (Priority Queue), Counting Solution Problem Understanding The Task Scheduler problem asks us to determine the minimum number of CPU intervals required to complete a list of tasks with a cooling constraint. Each task is represented by an uppercase letter A-Z. The CPU can execute one task per interval or remain idle. After executing a task, the CPU...

Practice › LeetCode › LeetCode 16xx ›

LeetCode 1679 - Max Number of K-Sum Pairs

LeetCode Problem 1679 Difficulty: 🟡 Medium Topics: Array, Hash Table, Two Pointers, Sorting Solution Problem Understanding The problem asks us to repeatedly remove pairs of numbers from an array such that the sum of each selected pair equals a target value k . Every time we successfully remove one valid pair, it counts as one operation. Our goal is to determine the maximum number of operations that can be performed...

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LeetCode 1087 - Brace Expansion

LeetCode Problem 1087 Difficulty: 🟡 Medium Topics: String, Backtracking, Stack, Breadth-First Search, Sorting Solution Problem Understanding In this problem, we are given a string that represents multiple possible words. Each position in the word may contain either a single fixed character or a set of alternative characters enclosed in curly braces. For example: a{b,c}d means: The first character is always 'a' The second character can be either 'b' or 'c'...

Practice › LeetCode › LeetCode 15xx ›

LeetCode 1547 - Minimum Cost to Cut a Stick

LeetCode Problem 1547 Difficulty: 🔴 Hard Topics: Array, Dynamic Programming, Sorting Solution Problem Understanding The problem asks us to determine the minimum total cost of cutting a wooden stick into pieces at specified positions. The stick has a length n , and we are given an array cuts representing the positions where cuts should be made. Importantly, the order of cuts is not fixed, and the cost of each cut...

Practice › LeetCode › LeetCode 13xx ›

LeetCode 1366 - Rank Teams by Votes

LeetCode Problem 1366 Difficulty: 🟡 Medium Topics: Array, Hash Table, String, Sorting, Counting Solution Problem Understanding The problem describes a voting based ranking system where every voter ranks all teams from best to worst. Each vote is represented as a string, where the character at index 0 is the top ranked team, the character at index 1 is the second ranked team, and so on. The final ranking is determined...

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LeetCode 823 - Binary Trees With Factors

LeetCode Problem 823 Difficulty: 🟡 Medium Topics: Array, Hash Table, Dynamic Programming, Sorting Solution Problem Understanding The problem asks us to determine the number of distinct binary trees that can be constructed from a given array of unique integers, where each integer is strictly greater than 1. The key constraint is that for every non-leaf node in the tree, its value must equal the product of its two children. Leaf...

Practice › LeetCode › LeetCode 09xx ›

LeetCode 975 - Odd Even Jump

LeetCode Problem 975 Difficulty: 🔴 Hard Topics: Array, Dynamic Programming, Stack, Sorting, Monotonic Stack, Ordered Set Solution Problem Understanding The problem asks us to determine how many starting indices in an array allow reaching the last element by performing a series of jumps defined as either odd-numbered or even-numbered. The distinction between odd and even jumps is crucial: odd-numbered jumps must move to the smallest value greater than or equal...

Practice › LeetCode › LeetCode 20xx ›

LeetCode 2015 - Average Height of Buildings in Each Segment

LeetCode Problem 2015 Difficulty: 🟡 Medium Topics: Array, Sorting, Heap (Priority Queue), Prefix Sum Solution Problem Understanding The problem describes a street as a number line, and each building occupies a half-closed interval [start, end) with a fixed height. Multiple buildings may overlap, and for every point on the street covered by at least one building, we want to compute the average height of all active buildings. The result must...

Practice › LeetCode › LeetCode 06xx ›

LeetCode 692 - Top K Frequent Words

LeetCode Problem 692 Difficulty: 🟡 Medium Topics: Array, Hash Table, String, Trie, Sorting, Heap (Priority Queue), Bucket Sort, Counting Solution Problem Understanding The problem gives us an array of strings called words and an integer k . Each string represents a word, and words may appear multiple times in the array. Our task is to return the k most frequent words. The result must follow two ordering rules. First, words...

Practice › LeetCode › LeetCode 01xx ›

LeetCode 169 - Majority Element

LeetCode Problem 169 Difficulty: 🟢 Easy Topics: Array, Hash Table, Divide and Conquer, Sorting, Counting Solution Problem Understanding The problem asks us to identify the majority element in a given array of integers nums . The majority element is defined as the number that appears more than half of the times in the array, i.e., more than ⌊n / 2⌋ times where n is the length of the array. The...

Practice › LeetCode › LeetCode 08xx ›

LeetCode 826 - Most Profit Assigning Work

LeetCode Problem 826 Difficulty: 🟡 Medium Topics: Array, Two Pointers, Binary Search, Greedy, Sorting Solution Problem Understanding This problem asks us to maximize the total profit earned by assigning jobs to workers, under a specific rule: each worker can only perform jobs whose difficulty is less than or equal to their ability. We are given three arrays: difficulty[i] represents how difficult the i-th job is. profit[i] represents how much money...

Practice › LeetCode › LeetCode 10xx ›

LeetCode 1099 - Two Sum Less Than K

LeetCode Problem 1099 Difficulty: 🟢 Easy Topics: Array, Two Pointers, Binary Search, Sorting Solution Problem Understanding This problem asks us to find the maximum sum of any two distinct numbers in an integer array nums such that their sum is strictly less than a given integer k . In other words, we are looking for two indices i and j with i < j where nums[i] + nums[j] is less...

Practice › LeetCode › LeetCode 04xx ›

LeetCode 455 - Assign Cookies

LeetCode Problem 455 Difficulty: 🟢 Easy Topics: Array, Two Pointers, Greedy, Sorting Solution LeetCode 455, Assign Cookies Problem Understanding This problem asks us to maximize the number of children who can be satisfied with the available cookies. Each child has a greed factor, and each cookie has a size. A child becomes content only if they receive a cookie whose size is greater than or equal to their greed factor....

Practice › LeetCode › LeetCode 06xx ›

LeetCode 694 - Number of Distinct Islands

LeetCode Problem 694 Difficulty: 🟡 Medium Topics: Array, Hash Table, Depth-First Search, Breadth-First Search, Union-Find, Sorting, Matrix, Hash Function Solution Problem Understanding The problem gives us a binary matrix called grid , where each cell contains either 0 or 1 . A value of 1 represents land, and a value of 0 represents water. An island is formed by connecting adjacent land cells in the four cardinal directions: up, down,...

Practice › LeetCode › LeetCode 02xx ›

LeetCode 253 - Meeting Rooms II

LeetCode Problem 253 Difficulty: 🟡 Medium Topics: Array, Two Pointers, Greedy, Sorting, Heap (Priority Queue), Prefix Sum Solution Problem Understanding The problem gives us a list of meeting intervals where each interval is represented as [start, end] . Each interval describes the time range during which a meeting occupies a conference room. The goal is to determine the minimum number of conference rooms needed so that all meetings can take...

Practice › LeetCode › LeetCode 02xx ›

LeetCode 295 - Find Median from Data Stream

LeetCode Problem 295 Difficulty: 🔴 Hard Topics: Two Pointers, Design, Sorting, Heap (Priority Queue), Data Stream Solution Problem Understanding The problem asks us to design a data structure that continuously receives integers from a stream and can efficiently return the median of all numbers seen so far. The median is defined as the middle element in a sorted list. If the number of elements is odd, the median is the...

Practice › LeetCode › LeetCode 13xx ›

LeetCode 1365 - How Many Numbers Are Smaller Than the Current Number

LeetCode Problem 1365 Difficulty: 🟢 Easy Topics: Array, Hash Table, Sorting, Counting Sort Solution Problem Understanding The problem asks us to determine, for each element in an array, how many elements in the same array are strictly smaller than it. In other words, for an element nums[i] , we count all elements nums[j] such that nums[j] < nums[i] and j != i . The input is a list of integers...

Practice › LeetCode › LeetCode 02xx ›

LeetCode 229 - Majority Element II

LeetCode Problem 229 Difficulty: 🟡 Medium Topics: Array, Hash Table, Sorting, Counting Solution Problem Understanding The problem asks us to find every element in an integer array that appears more than ⌊ n/3 ⌋ times, where n is the length of the array. The floor notation means we round down to the nearest integer. For example, if the array length is 8, then ⌊ 8/3 ⌋ = 2 , so...

Practice › LeetCode › LeetCode 05xx ›

LeetCode 522 - Longest Uncommon Subsequence II

LeetCode Problem 522 Difficulty: 🟡 Medium Topics: Array, Hash Table, Two Pointers, String, Sorting Solution Problem Understanding The problem asks us to find the length of the longest string in the array that is not a subsequence of any other string in the same array. A subsequence is formed by deleting zero or more characters from a string without changing the order of the remaining characters. For example, "abc" is...

Practice › LeetCode › LeetCode 05xx ›

LeetCode 581 - Shortest Unsorted Continuous Subarray

LeetCode Problem 581 Difficulty: 🟡 Medium Topics: Array, Two Pointers, Stack, Greedy, Sorting, Monotonic Stack Solution Problem Understanding The problem gives an integer array nums and asks for the length of the shortest continuous subarray such that, if only that subarray is sorted in non-decreasing order, the entire array becomes sorted. In other words, the array is "almost sorted", except for some misplaced elements. We need to identify the smallest...

Practice › LeetCode › LeetCode 02xx ›

LeetCode 220 - Contains Duplicate III

LeetCode Problem 220 Difficulty: 🔴 Hard Topics: Array, Sliding Window, Sorting, Bucket Sort, Ordered Set Solution Problem Understanding The problem asks whether there exists a pair of different indices (i, j) in the array such that two conditions are satisfied at the same time. The first condition is about index distance: $$|i - j| \leq indexDiff$$ This means the two elements must be relatively close together in the array. The...

Practice › LeetCode › LeetCode 07xx ›

LeetCode 768 - Max Chunks To Make Sorted II

LeetCode Problem 768 Difficulty: 🔴 Hard Topics: Array, Stack, Greedy, Sorting, Monotonic Stack Solution Problem Understanding The problem asks us to partition an array into the maximum possible number of contiguous chunks such that, after sorting each chunk independently and concatenating the results, the entire array becomes globally sorted. The key detail is that each chunk must remain contiguous. We cannot rearrange elements across chunk boundaries after splitting. Once the...

Practice › LeetCode › LeetCode 09xx ›

LeetCode 939 - Minimum Area Rectangle

LeetCode Problem 939 Difficulty: 🟡 Medium Topics: Array, Hash Table, Math, Geometry, Sorting Solution Problem Understanding The problem gives us a collection of distinct points on a 2D plane. Each point is represented as [x, y] , where x is the horizontal coordinate and y is the vertical coordinate. Our task is to determine the minimum possible area of an axis-aligned rectangle that can be formed using four of these...

Practice › LeetCode › LeetCode 08xx ›

LeetCode 888 - Fair Candy Swap

LeetCode Problem 888 Difficulty: 🟢 Easy Topics: Array, Hash Table, Binary Search, Sorting Solution LeetCode 888 - Fair Candy Swap Problem Understanding The problem gives us two arrays, aliceSizes and bobSizes , representing the candy boxes owned by Alice and Bob. Each element in the arrays is the number of candies in a particular box. Alice and Bob want to exchange exactly one box each so that, after the swap,...

Practice › LeetCode › LeetCode 02xx ›

LeetCode 218 - The Skyline Problem

LeetCode Problem 218 Difficulty: 🔴 Hard Topics: Array, Divide and Conquer, Binary Indexed Tree, Segment Tree, Sweep Line, Sorting, Heap (Priority Queue), Ordered Set Solution Problem Understanding The Skyline Problem asks us to compute the visible outer contour formed by a collection of rectangular buildings when viewed from far away. Each building is represented by three integers: a left x-coordinate, a right x-coordinate, and a height. The buildings sit on...

Practice › LeetCode › LeetCode 04xx ›

LeetCode 451 - Sort Characters By Frequency

LeetCode Problem 451 Difficulty: 🟡 Medium Topics: Hash Table, String, Sorting, Heap (Priority Queue), Bucket Sort, Counting Solution Problem Understanding The problem asks us to rearrange the characters of a string so that characters with higher frequency appear before characters with lower frequency. The output string must group identical characters together, and those groups must appear in descending order of occurrence count. For example, if the input is "tree" ,...

Practice › LeetCode › LeetCode 09xx ›

LeetCode 905 - Sort Array By Parity

LeetCode Problem 905 Difficulty: 🟢 Easy Topics: Array, Two Pointers, Sorting Solution Problem Understanding The problem asks us to rearrange an array so that all even numbers appear before all odd numbers. The relative ordering among even numbers does not matter, and the relative ordering among odd numbers also does not matter. The problem explicitly states that any valid arrangement is acceptable. We are given an integer array nums ....

Practice › LeetCode › LeetCode 13xx ›

LeetCode 1346 - Check If N and Its Double Exist

LeetCode Problem 1346 Difficulty: 🟢 Easy Topics: Array, Hash Table, Two Pointers, Binary Search, Sorting Solution Problem Understanding The problem gives an integer array arr and asks whether there exist two different indices i and j such that: arr[i] == 2 * arr[j] In simpler terms, we need to determine whether one number in the array is exactly double another number in the same array. The indices must be different,...

Practice › LeetCode › LeetCode 09xx ›

LeetCode 976 - Largest Perimeter Triangle

LeetCode Problem 976 Difficulty: 🟢 Easy Topics: Array, Math, Greedy, Sorting Solution Problem Understanding The problem gives us an array of integers called nums , where each integer represents a possible side length. Our goal is to select exactly three lengths that can form a valid triangle with a non-zero area, and among all valid triangles, return the maximum possible perimeter. A triangle is only valid if the sum of...

Practice › LeetCode › LeetCode 09xx ›

LeetCode 948 - Bag of Tokens

LeetCode Problem 948 Difficulty: 🟡 Medium Topics: Array, Two Pointers, Greedy, Sorting Solution Problem Understanding The problem gives us a collection of tokens, where each token has a numeric value. We also start with an initial amount of power and an initial score of 0 . Every token can be used at most once, and each token can be played in exactly one of two ways. If we play a...

Practice › LeetCode › LeetCode 00xx ›

LeetCode 88 - Merge Sorted Array

LeetCode Problem 88 Difficulty: 🟢 Easy Topics: Array, Two Pointers, Sorting Solution LeetCode 88 - Merge Sorted Array Problem Understanding This problem gives us two arrays, nums1 and nums2 , where both arrays are already sorted in non-decreasing order. We are also given two integers, m and n , which tell us how many valid elements exist in each array. The important detail is that nums1 has extra space at...

Practice › LeetCode › LeetCode 06xx ›

LeetCode 611 - Valid Triangle Number

LeetCode Problem 611 Difficulty: 🟡 Medium Topics: Array, Two Pointers, Binary Search, Greedy, Sorting Solution Problem Understanding The problem asks us to determine how many triplets from a given integer array nums can form a valid triangle. In geometric terms, a triangle is valid if the sum of any two sides is greater than the third side. Because we are only concerned with side lengths from an array, the key...

Practice › LeetCode › LeetCode 06xx ›

LeetCode 628 - Maximum Product of Three Numbers

LeetCode Problem 628 Difficulty: 🟢 Easy Topics: Array, Math, Sorting Solution Problem Understanding The problem gives an integer array nums and asks us to select exactly three numbers whose product is as large as possible. We must return that maximum product value. In simpler terms, among all possible combinations of three elements in the array, we need to determine which combination produces the greatest multiplication result. The input is an...

Practice › LeetCode › LeetCode 09xx ›

LeetCode 923 - 3Sum With Multiplicity

LeetCode Problem 923 Difficulty: 🟡 Medium Topics: Array, Hash Table, Two Pointers, Sorting, Counting Solution Problem Understanding The problem asks us to count how many index triplets (i, j, k) satisfy two conditions: The indices must follow the order i < j < k The values at those indices must sum to the given target Formally, we want: arr[i] + arr[j] + arr[k] == target The important detail is that...

Practice › LeetCode › LeetCode 05xx ›

LeetCode 506 - Relative Ranks

LeetCode Problem 506 Difficulty: 🟢 Easy Topics: Array, Sorting, Heap (Priority Queue) Solution LeetCode 506 - Relative Ranks Problem Understanding The problem gives us an array named score , where each element represents the score earned by an athlete in a competition. Every athlete has a unique score, which means there are no ties to worry about when determining rankings. We need to determine each athlete's placement based on score...

Practice › LeetCode › LeetCode 15xx ›

LeetCode 1585 - Check If String Is Transformable With Substring Sort Operations

LeetCode Problem 1585 Difficulty: 🔴 Hard Topics: String, Greedy, Sorting Solution Problem Understanding This problem asks whether we can transform one digit string, s , into another digit string, t , using a special operation. In one operation, we choose any non-empty contiguous substring of s and sort that substring in ascending order. The important detail is that sorting a substring only moves smaller digits toward the left and larger...

Practice › LeetCode › LeetCode 17xx ›

LeetCode 1772 - Sort Features by Popularity

LeetCode Problem 1772 Difficulty: 🟡 Medium Topics: Array, Hash Table, String, Sorting Solution Problem Understanding This problem asks us to determine the popularity of product features based on user survey responses. We are given a list of features where each element is a single-word feature name, and a list of responses where each element is a string of space-separated words that users reported liking. The popularity of a feature is...

Practice › LeetCode › LeetCode 02xx ›

LeetCode 268 - Missing Number

LeetCode Problem 268 Difficulty: 🟢 Easy Topics: Array, Hash Table, Math, Binary Search, Bit Manipulation, Sorting Solution Problem Understanding The problem gives an array nums containing n distinct integers. Every number is supposed to come from the range [0, n] , which means there are actually n + 1 possible values in total. Since the array only contains n numbers, exactly one value from that range is missing. The task...

Practice › LeetCode › LeetCode 03xx ›

LeetCode 314 - Binary Tree Vertical Order Traversal

LeetCode Problem 314 Difficulty: 🟡 Medium Topics: Hash Table, Tree, Depth-First Search, Breadth-First Search, Sorting, Binary Tree Solution Problem Understanding The problem asks us to group the nodes of a binary tree by their vertical columns and return those groups from left to right. Each node in the tree belongs to a conceptual coordinate system: The root starts at column 0 Moving to the left child decreases the column index...

Practice › LeetCode › LeetCode 14xx ›

LeetCode 1478 - Allocate Mailboxes

LeetCode Problem 1478 Difficulty: 🔴 Hard Topics: Array, Math, Dynamic Programming, Sorting Solution Here’s a complete, detailed technical solution guide for LeetCode 1478 following your requested format and requirements. Problem Understanding The problem provides a list houses , where each element represents the position of a house along a street. You are asked to allocate exactly k mailboxes to minimize the total distance from each house to its nearest mailbox....

Practice › LeetCode › LeetCode 08xx ›

LeetCode 853 - Car Fleet

LeetCode Problem 853 Difficulty: 🟡 Medium Topics: Array, Stack, Sorting, Monotonic Stack Solution Problem Understanding The problem describes a set of cars driving toward the same destination, represented by the integer target . Each car starts at a unique position and moves at a constant speed. Cars cannot overtake each other. If a faster car catches up to a slower car ahead of it, the faster car must slow down...

Practice › LeetCode › LeetCode 09xx ›

LeetCode 937 - Reorder Data in Log Files

LeetCode Problem 937 Difficulty: 🟡 Medium Topics: Array, String, Sorting Solution Problem Understanding In this problem, we are given a list of log strings. Each log contains an identifier followed by one or more words separated by spaces. The first token is always the identifier, and everything after it represents the content of the log. The logs are divided into two categories: Letter-logs, where every word after the identifier contains...

Practice › LeetCode › LeetCode 07xx ›

LeetCode 719 - Find K-th Smallest Pair Distance

LeetCode Problem 719 Difficulty: 🔴 Hard Topics: Array, Two Pointers, Binary Search, Sorting Solution Problem Understanding This problem asks us to find the k -th smallest distance among every possible pair of numbers in the array. For any pair (a, b) , the distance is defined as: $|a-b|$ We are given an array nums , and we must consider every pair (nums[i], nums[j]) where i < j . For each...

Practice › LeetCode › LeetCode 11xx ›

LeetCode 1101 - The Earliest Moment When Everyone Become Friends

LeetCode Problem 1101 Difficulty: 🟡 Medium Topics: Array, Union-Find, Sorting Solution Problem Understanding The problem is asking us to determine the earliest time at which a group of n people all become mutually acquainted, given a sequence of friendship formation events with timestamps. Each event [timestamp, xi, yi] indicates that person xi and person yi become friends at that exact moment. Friendship is symmetric, meaning if xi is friends with...

Practice › LeetCode › LeetCode 16xx ›

LeetCode 1630 - Arithmetic Subarrays

LeetCode Problem 1630 Difficulty: 🟡 Medium Topics: Array, Hash Table, Sorting Solution Problem Understanding The problem asks us to determine whether subarrays of a given array can be rearranged to form an arithmetic sequence. An arithmetic sequence is one where the difference between consecutive elements is constant. The input consists of an array nums of integers and two arrays l and r representing the start and end indices of multiple...

Practice › LeetCode › LeetCode 04xx ›

LeetCode 406 - Queue Reconstruction by Height

LeetCode Problem 406 Difficulty: 🟡 Medium Topics: Array, Binary Indexed Tree, Segment Tree, Sorting Solution LeetCode 406 - Queue Reconstruction by Height Problem Understanding This problem gives us a list of people where each person is represented as a pair [h, k] . The value h represents the person's height. The value k represents how many people standing in front of this person must have a height greater than or...

Practice › LeetCode › LeetCode 14xx ›

LeetCode 1465 - Maximum Area of a Piece of Cake After Horizontal and Vertical Cuts

LeetCode Problem 1465 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting Solution LeetCode 1465 - Maximum Area of a Piece of Cake After Horizontal and Vertical Cuts Problem Understanding This problem gives us a rectangular cake with height h and width w . We are also given two arrays: horizontalCuts , which contains the positions of horizontal cuts measured from the top edge verticalCuts , which contains the positions of vertical...

Practice › LeetCode › LeetCode 04xx ›

LeetCode 452 - Minimum Number of Arrows to Burst Balloons

LeetCode Problem 452 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting Solution Problem Understanding This problem is asking us to determine the minimum number of vertical arrows required to burst all balloons represented as intervals along the x-axis. Each balloon is defined by its start and end x-coordinates, [xstart, xend] . An arrow shot at position x bursts any balloon whose interval contains x . The arrows travel infinitely upward, so...

Practice › LeetCode › LeetCode 17xx ›

LeetCode 1710 - Maximum Units on a Truck

LeetCode Problem 1710 Difficulty: 🟢 Easy Topics: Array, Greedy, Sorting Solution LeetCode 1710 - Maximum Units on a Truck Problem Understanding The problem gives us several types of boxes, where each box type contains two values: The number of boxes available for that type The number of units inside each box of that type We also have a truck that can carry at most truckSize boxes total, regardless of type....

Practice › LeetCode › LeetCode 10xx ›

LeetCode 1040 - Moving Stones Until Consecutive II

LeetCode Problem 1040 Difficulty: 🟡 Medium Topics: Array, Math, Sliding Window, Sorting Solution Problem Understanding The problem gives an array stones representing positions of stones on the X-axis, where each position is unique. The goal is to move the endpoint stones -the stones at the smallest and largest positions-so that eventually all stones occupy consecutive positions on the X-axis. An endpoint stone can only be moved to a position that...

Practice › LeetCode › LeetCode 18xx ›

LeetCode 1840 - Maximum Building Height

LeetCode Problem 1840 Difficulty: 🔴 Hard Topics: Array, Math, Sorting Solution LeetCode 1840 - Maximum Building Height Problem Understanding This problem asks us to construct heights for n buildings arranged in a straight line while satisfying several constraints. Each building has a non-negative integer height. Building 1 must always have height 0 . Additionally, adjacent buildings cannot differ in height by more than 1 . This means that if one...

Practice › LeetCode › LeetCode 16xx ›

LeetCode 1637 - Widest Vertical Area Between Two Points Containing No Points

LeetCode Problem 1637 Difficulty: 🟢 Easy Topics: Array, Sorting Solution Problem Understanding This problem gives us a list of points on a 2D plane, where each point is represented as [x, y] . We need to find the widest vertical area that contains no points strictly inside it. A vertical area is defined by two vertical lines. Since the area extends infinitely along the y-axis, only the x-coordinates matter. The...

Practice › LeetCode › LeetCode 08xx ›

LeetCode 857 - Minimum Cost to Hire K Workers

LeetCode Problem 857 Difficulty: 🔴 Hard Topics: Array, Greedy, Sorting, Heap (Priority Queue) Solution Problem Understanding In this problem, we are given two arrays, quality and wage , where each index represents a worker. The value quality[i] describes how much work or contribution the i-th worker provides, while wage[i] describes the minimum amount that worker is willing to accept. We must hire exactly k workers, and the group must satisfy...

Practice › LeetCode › LeetCode 02xx ›

LeetCode 215 - Kth Largest Element in an Array

LeetCode Problem 215 Difficulty: 🟡 Medium Topics: Array, Divide and Conquer, Sorting, Heap (Priority Queue), Quickselect Solution Problem Understanding The problem asks us to find the kth largest element in an unsorted integer array. The important detail is that we are looking for the element that would appear in the kth position if the array were sorted in descending order. We are not looking for the kth distinct value. For...

Practice › LeetCode › LeetCode 13xx ›

LeetCode 1338 - Reduce Array Size to The Half

LeetCode Problem 1338 Difficulty: 🟡 Medium Topics: Array, Hash Table, Greedy, Sorting, Heap (Priority Queue) Solution Here is a complete, detailed technical solution guide for LeetCode 1338, following your requested formatting and structure. Problem Understanding The problem asks us to reduce the size of an integer array arr by removing all occurrences of a selected set of integers. Specifically, we want to find the minimum size of such a set...

Practice › LeetCode › LeetCode 12xx ›

LeetCode 1202 - Smallest String With Swaps

LeetCode Problem 1202 Difficulty: 🟡 Medium Topics: Array, Hash Table, String, Depth-First Search, Breadth-First Search, Union-Find, Sorting Solution Problem Understanding The problem gives us a string s and a list of index pairs called pairs . Each pair [a, b] means we are allowed to swap the characters at positions a and b . The important detail is that swaps can be performed any number of times. This changes the...

Practice › LeetCode › LeetCode 06xx ›

LeetCode 632 - Smallest Range Covering Elements from K Lists

LeetCode Problem 632 Difficulty: 🔴 Hard Topics: Array, Hash Table, Greedy, Sliding Window, Sorting, Heap (Priority Queue) Solution Problem Understanding The problem gives us k sorted integer lists, and we must find the smallest inclusive range [a, b] such that the range contains at least one element from every list. Each list is already sorted in non-decreasing order, which is a very important property. Instead of considering arbitrary combinations of...

Practice › LeetCode › LeetCode 10xx ›

LeetCode 1096 - Brace Expansion II

LeetCode Problem 1096 Difficulty: 🔴 Hard Topics: Hash Table, String, Backtracking, Stack, Breadth-First Search, Sorting Solution Problem Understanding The problem asks us to interpret a string expression representing a set of words generated according to a specific grammar and return all distinct words sorted in lexicographical order. The expression can contain lowercase letters, curly braces {} , and commas , . The rules of the grammar are: A single lowercase...

Practice › LeetCode › LeetCode 04xx ›

LeetCode 436 - Find Right Interval

LeetCode Problem 436 Difficulty: 🟡 Medium Topics: Array, Binary Search, Sorting Solution Problem Understanding This problem asks us to find, for each interval in a list, the "right interval" that starts at or after the end of the current interval and is the closest such interval in terms of starting time. Formally, given an array of intervals intervals[i] = [starti, endi] where each starti is unique, the right interval for...

Practice › LeetCode › LeetCode 05xx ›

LeetCode 502 - IPO

LeetCode Problem 502 Difficulty: 🔴 Hard Topics: Array, Greedy, Sorting, Heap (Priority Queue) Solution Problem Understanding The problem describes a scenario where we have a limited number of opportunities to invest in projects before an IPO. Each project has two properties: profits[i] , the amount of capital gained after completing the project capital[i] , the minimum amount of capital required to start the project We are also given: k ,...

Practice › LeetCode › LeetCode 07xx ›

LeetCode 710 - Random Pick with Blacklist

LeetCode Problem 710 Difficulty: 🔴 Hard Topics: Array, Hash Table, Math, Binary Search, Sorting, Randomized Solution Problem Understanding The problem asks us to design a data structure that can repeatedly return a random integer from the range [0, n - 1] , while excluding all integers that appear in a blacklist. Every valid number must have exactly the same probability of being chosen. The challenge is not simply filtering numbers....

Practice › LeetCode › LeetCode 07xx ›

LeetCode 726 - Number of Atoms

LeetCode Problem 726 Difficulty: 🔴 Hard Topics: Hash Table, String, Stack, Sorting Solution Problem Understanding This problem asks us to parse a chemical formula represented as a string and return a canonical string that counts the number of each atom in the formula. Each atom starts with an uppercase letter and may have lowercase letters following it. A number following an atom represents how many of that atom are present,...

Practice › LeetCode › LeetCode 08xx ›

LeetCode 833 - Find And Replace in String

LeetCode Problem 833 Difficulty: 🟡 Medium Topics: Array, Hash Table, String, Sorting Solution Problem Understanding The problem gives us a string s and three parallel arrays: indices[i] tells us where a replacement might happen sources[i] is the substring we expect to find at that index targets[i] is the string we should replace it with if the match is valid For each operation, we must check whether sources[i] actually appears in...

Practice › LeetCode › LeetCode 03xx ›

LeetCode 368 - Largest Divisible Subset

LeetCode Problem 368 Difficulty: 🟡 Medium Topics: Array, Math, Dynamic Programming, Sorting Solution Problem Understanding The problem gives us an array of distinct positive integers and asks us to find the largest subset where every pair of numbers satisfies a divisibility relationship. For any two elements a and b in the subset, either a % b == 0 or b % a == 0 must hold. In other words, every...

Practice › LeetCode › LeetCode 16xx ›

LeetCode 1632 - Rank Transform of a Matrix

LeetCode Problem 1632 Difficulty: 🔴 Hard Topics: Array, Union-Find, Graph Theory, Topological Sort, Sorting, Matrix Solution Problem Understanding The problem asks us to assign a rank to every element in a matrix while preserving ordering relationships inside rows and columns. For any two elements that share the same row or the same column: If one value is smaller, its rank must also be smaller. If two values are equal, their...

Practice › LeetCode › LeetCode 07xx ›

LeetCode 711 - Number of Distinct Islands II

LeetCode Problem 711 Difficulty: 🔴 Hard Topics: Array, Hash Table, Depth-First Search, Breadth-First Search, Union-Find, Sorting, Matrix, Hash Function Solution Problem Understanding In this problem, we are given a binary matrix where each cell contains either 0 or 1 . A value of 1 represents land, while 0 represents water. An island is formed by connecting adjacent land cells in the four cardinal directions: up, down, left, and right. The...

Practice › LeetCode › LeetCode 16xx ›

LeetCode 1657 - Determine if Two Strings Are Close

LeetCode Problem 1657 Difficulty: 🟡 Medium Topics: Hash Table, String, Sorting, Counting Solution Problem Understanding The problem asks whether two strings, word1 and word2 , are "close" according to two allowed operations. Operation 1 allows swapping any two existing characters in the string, which means the relative order of characters is flexible. Operation 2 allows transforming all occurrences of one character into another existing character, and vice versa, which effectively...

Practice › LeetCode › LeetCode 10xx ›

LeetCode 1065 - Index Pairs of a String

LeetCode Problem 1065 Difficulty: 🟢 Easy Topics: Array, String, Trie, Sorting Solution Problem Understanding The problem gives us a string called text and a list of dictionary words called words . We must find every substring inside text that exactly matches one of the words in the dictionary. For every valid match, we return the pair [i, j] , where: i is the starting index of the substring j is...

Practice › LeetCode › LeetCode 07xx ›

LeetCode 757 - Set Intersection Size At Least Two

LeetCode Problem 757 Difficulty: 🔴 Hard Topics: Array, Greedy, Sorting Solution Problem Understanding The problem asks us to find the minimum size of a set of integers, nums , such that each given interval [starti, endi] contains at least two integers from nums . Each interval is represented as a closed interval, meaning all integers between starti and endi inclusive belong to that interval. The goal is to construct nums...

Practice › LeetCode › LeetCode 07xx ›

LeetCode 767 - Reorganize String

LeetCode Problem 767 Difficulty: 🟡 Medium Topics: Hash Table, String, Greedy, Sorting, Heap (Priority Queue), Counting Solution Problem Understanding The problem asks us to rearrange the characters of a given string s such that no two adjacent characters are the same. The input is a string of lowercase English letters with a length between 1 and 500. The output should be either a valid rearrangement that satisfies the adjacency constraint...

Practice › LeetCode › LeetCode 09xx ›

LeetCode 945 - Minimum Increment to Make Array Unique

LeetCode Problem 945 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting, Counting Solution Problem Understanding This problem asks us to take an integer array nums and perform a series of increment operations so that every element in the array becomes unique. An increment operation increases an element by exactly 1. The goal is to compute the minimum number of such moves required. In simpler terms, we are asked: given an array...

Practice › LeetCode › LeetCode 14xx ›

LeetCode 1489 - Find Critical and Pseudo-Critical Edges in Minimum Spanning Tree

LeetCode Problem 1489 Difficulty: 🔴 Hard Topics: Union-Find, Graph Theory, Sorting, Minimum Spanning Tree, Strongly Connected Component Solution Problem Understanding The problem gives us a connected, weighted, undirected graph with n vertices and a list of edges. Each edge is represented as [u, v, weight] , meaning there is a bidirectional connection between vertices u and v with the given cost. The goal is not simply to compute one Minimum...

Practice › LeetCode › LeetCode 16xx ›

LeetCode 1648 - Sell Diminishing-Valued Colored Balls

LeetCode Problem 1648 Difficulty: 🟡 Medium Topics: Array, Math, Binary Search, Greedy, Sorting, Heap (Priority Queue) Solution Here is the complete, detailed technical solution guide for LeetCode 1648 - Sell Diminishing-Valued Colored Balls following your requested structure and formatting rules. Problem Understanding The problem asks us to sell orders number of balls from an inventory of different colored balls in a way that maximizes the total value obtained . Each...

Practice › LeetCode › LeetCode 16xx ›

LeetCode 1686 - Stone Game VI

LeetCode Problem 1686 Difficulty: 🟡 Medium Topics: Array, Math, Greedy, Sorting, Heap (Priority Queue), Game Theory Solution This is a long, structured technical guide with multiple substantial sections, worked examples, code, tables, and test coverage. To make sure it is complete and properly formatted according to your rules, I should generate it as a document/canvas rather than risk truncation in chat. I can produce the full guide for LeetCode 1686...

Practice › LeetCode › LeetCode 10xx ›

LeetCode 1029 - Two City Scheduling

LeetCode Problem 1029 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting Solution Problem Understanding In this problem, we are given an array called costs , where each element represents the travel cost for one person to two different cities. Specifically, costs[i] = [aCosti, bCosti] means: aCosti is the cost of flying person i to city A bCosti is the cost of flying person i to city B There are exactly 2n...

Practice › LeetCode › LeetCode 16xx ›

LeetCode 1691 - Maximum Height by Stacking Cuboids

LeetCode Problem 1691 Difficulty: 🔴 Hard Topics: Array, Dynamic Programming, Sorting Solution LeetCode 1691 - Maximum Height by Stacking Cuboids Problem Understanding This problem gives us a collection of 3D cuboids, where each cuboid is represented by three dimensions: width, length, and height. We may choose any subset of these cuboids and stack them vertically to maximize the total height. A cuboid can be placed on top of another cuboid...

Practice › LeetCode › LeetCode 00xx ›

LeetCode 75 - Sort Colors

LeetCode Problem 75 Difficulty: 🟡 Medium Topics: Array, Two Pointers, Sorting Solution Problem Understanding This problem asks us to sort an array that contains only three distinct values: 0 , 1 , and 2 . These values represent colors: 0 represents red 1 represents white 2 represents blue The goal is to rearrange the array so that all 0 s come first, followed by all 1 s, followed by all...

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LeetCode 1509 - Minimum Difference Between Largest and Smallest Value in Three Moves

LeetCode Problem 1509 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting Solution Problem Understanding The problem gives us an integer array nums , and we are allowed to perform at most three moves. In each move, we may select any element and change it to any value we want. After making up to three modifications, we must minimize the difference between the largest and smallest values remaining in the array. In...

Practice › LeetCode › LeetCode 03xx ›

LeetCode 324 - Wiggle Sort II

LeetCode Problem 324 Difficulty: 🟡 Medium Topics: Array, Divide and Conquer, Greedy, Sorting, Quickselect Solution Problem Understanding The problem asks us to rearrange an array so that it follows a strict alternating pattern: nums[0] < nums[1] nums[1] > nums[2] nums[2] < nums[3] and so on. This pattern is called a wiggle sequence because the values repeatedly go up and down. The input is an integer array nums , and we...

Practice › LeetCode › LeetCode 09xx ›

LeetCode 912 - Sort an Array

LeetCode Problem 912 Difficulty: 🟡 Medium Topics: Array, Divide and Conquer, Sorting, Heap (Priority Queue), Merge Sort, Bucket Sort, Radix Sort, Counting Sort Solution Problem Understanding The problem asks us to sort an integer array in ascending order without using any built in sorting functions. The result must contain the same elements as the input, but arranged from smallest to largest. The input is an array nums containing integers. These...

Practice › LeetCode › LeetCode 20xx ›

LeetCode 2021 - Brightest Position on Street

LeetCode Problem 2021 Difficulty: 🟡 Medium Topics: Array, Sorting, Prefix Sum, Ordered Set Solution Problem Understanding The problem asks us to find the position on a straight street that is illuminated by the largest number of street lamps, which is referred to as its brightness . The street is represented as a number line, and each street lamp is given as a pair [positioni, rangei] , which defines the interval...

Practice › LeetCode › LeetCode 08xx ›

LeetCode 825 - Friends Of Appropriate Ages

LeetCode Problem 825 Difficulty: 🟡 Medium Topics: Array, Two Pointers, Binary Search, Sorting Solution Problem Understanding The problem gives us an array ages , where each value represents the age of a person on a social media platform. We must determine how many friend requests are sent between people according to a specific set of rules. A person x can send a friend request to person y only if all...

Practice › LeetCode › LeetCode 07xx ›

LeetCode 759 - Employee Free Time

LeetCode Problem 759 Difficulty: 🔴 Hard Topics: Array, Sweep Line, Sorting, Heap (Priority Queue) Solution Problem Understanding The problem asks us to determine common free time intervals for a group of employees based on their schedules. Each employee has a list of non-overlapping intervals representing times when they are busy. Our goal is to find periods where all employees are simultaneously free , excluding any intervals of zero length. The...

Practice › LeetCode › LeetCode 17xx ›

LeetCode 1755 - Closest Subsequence Sum

LeetCode Problem 1755 Difficulty: 🔴 Hard Topics: Array, Two Pointers, Dynamic Programming, Bit Manipulation, Sorting, Bitmask Solution Problem Understanding The problem asks us to find a subsequence of a given integer array nums such that the sum of that subsequence is as close as possible to a given integer goal . A subsequence can include any subset of elements in their original order, including the possibility of selecting none (which...

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LeetCode 1727 - Largest Submatrix With Rearrangements

LeetCode Problem 1727 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting, Matrix Solution Problem Understanding The problem gives us a binary matrix, meaning every cell contains either 0 or 1 . We are allowed to rearrange the columns of the matrix in any order we want. The rearrangement is global for the row configuration being considered, meaning we are effectively free to permute the columns to maximize the size of a...

Practice › LeetCode › LeetCode 14xx ›

LeetCode 1418 - Display Table of Food Orders in a Restaurant

LeetCode Problem 1418 Difficulty: 🟡 Medium Topics: Array, Hash Table, String, Sorting, Ordered Set Solution Problem Understanding The problem gives a list of restaurant orders. Each order contains three pieces of information: Customer name Table number Food item An order looks like this: [customerName, tableNumber, foodItem] The goal is to build a display table that summarizes how many times each food item was ordered at every table. The output format...

Practice › LeetCode › LeetCode 13xx ›

LeetCode 1353 - Maximum Number of Events That Can Be Attended

LeetCode Problem 1353 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting, Heap (Priority Queue) Solution Problem Understanding The problem gives us a list of events, where each event is represented as a pair [startDay, endDay] . An event is available to attend on any single day within that inclusive range. The goal is to attend as many events as possible, with the restriction that only one event can be attended per...

Practice › LeetCode › LeetCode 15xx ›

LeetCode 1520 - Maximum Number of Non-Overlapping Substrings

LeetCode Problem 1520 Difficulty: 🔴 Hard Topics: Hash Table, String, Greedy, Sorting Solution LeetCode 1520 - Maximum Number of Non-Overlapping Substrings Problem Understanding This problem asks us to select as many non-overlapping substrings as possible from a given lowercase string s , while satisfying a strict containment rule. A substring is considered valid only if, whenever it contains a character c , it also contains every occurrence of c that...

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LeetCode 1030 - Matrix Cells in Distance Order

LeetCode Problem 1030 Difficulty: 🟢 Easy Topics: Array, Math, Geometry, Sorting, Matrix Solution Problem Understanding This problem asks us to return every cell in a matrix, ordered by its Manhattan distance from a given center cell. We are given four integers: rows , the number of rows in the matrix cols , the number of columns in the matrix rCenter , the row index of the reference cell cCenter ,...

Practice › LeetCode › LeetCode 13xx ›

LeetCode 1311 - Get Watched Videos by Your Friends

LeetCode Problem 1311 Difficulty: 🟡 Medium Topics: Array, Hash Table, Breadth-First Search, Graph Theory, Sorting Solution Problem Understanding This problem models a social network as an undirected graph. Each person is represented by an integer ID from 0 to n - 1 . The friends array describes the graph connections, while watchedVideos[i] contains the list of videos watched by person i . The goal is to find all videos watched...

Practice › LeetCode › LeetCode 07xx ›

LeetCode 747 - Largest Number At Least Twice of Others

LeetCode Problem 747 Difficulty: 🟢 Easy Topics: Array, Sorting Solution Problem Understanding The problem gives us an integer array nums in which the largest value is guaranteed to be unique. Our task is to determine whether this largest number is at least twice as large as every other number in the array. If that condition is satisfied, we return the index of the largest element. Otherwise, we return -1 ....

Practice › LeetCode › LeetCode 00xx ›

LeetCode 49 - Group Anagrams

LeetCode Problem 49 Difficulty: 🟡 Medium Topics: Array, Hash Table, String, Sorting Solution Problem Understanding The problem asks us to group together all strings that are anagrams of each other. Two strings are considered anagrams if they contain exactly the same characters with the same frequencies, but possibly in a different order. For example, "eat" , "tea" , and "ate" are all anagrams because each string contains one 'a' ,...

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LeetCode 242 - Valid Anagram

LeetCode Problem 242 Difficulty: 🟢 Easy Topics: Hash Table, String, Sorting Solution Problem Understanding The problem asks us to determine whether two strings are anagrams of each other. Two strings are considered anagrams if they contain exactly the same characters with exactly the same frequencies , but possibly in a different order. In other words, one string can be rearranged to form the other. For example, "anagram" and "nagaram" are...

Practice › LeetCode › LeetCode 10xx ›

LeetCode 1058 - Minimize Rounding Error to Meet Target

LeetCode Problem 1058 Difficulty: 🟡 Medium Topics: Array, Math, String, Greedy, Sorting Solution Problem Understanding The problem asks us to round an array of decimal prices to integers such that the sum of the rounded numbers equals a given target, while minimizing the total rounding error. Each price can be rounded either down ( Floor ) or up ( Ceil ). The rounding error for each price is defined as...

Practice › LeetCode › LeetCode 15xx ›

LeetCode 1508 - Range Sum of Sorted Subarray Sums

LeetCode Problem 1508 Difficulty: 🟡 Medium Topics: Array, Two Pointers, Binary Search, Sorting, Prefix Sum Solution Problem Understanding The problem requires calculating the sum of a subrange of all possible contiguous subarray sums of a given array nums . The first step is to generate every possible continuous subarray sum, sort them in non-decreasing order, and then extract the sum of elements between the left and right indices, inclusive, with...

Practice › LeetCode › LeetCode 14xx ›

LeetCode 1451 - Rearrange Words in a Sentence

LeetCode Problem 1451 Difficulty: 🟡 Medium Topics: String, Sorting Solution Problem Understanding The problem gives us a sentence where words are separated by single spaces, the very first character of the sentence is uppercase, and all remaining characters are lowercase. We must rearrange the words so that they appear in increasing order of word length. If two words have the same length, we must preserve their original relative order from...

Practice › LeetCode › LeetCode 18xx ›

LeetCode 1838 - Frequency of the Most Frequent Element

LeetCode Problem 1838 Difficulty: 🟡 Medium Topics: Array, Binary Search, Greedy, Sliding Window, Sorting, Prefix Sum Solution Problem Understanding This problem asks us to determine the maximum frequency of an element in an integer array nums after performing at most k increment operations. Each operation allows you to choose an element and increase it by 1 . The frequency of an element is the number of times it occurs in...

Practice › LeetCode › LeetCode 14xx ›

LeetCode 1491 - Average Salary Excluding the Minimum and Maximum Salary

LeetCode Problem 1491 Difficulty: 🟢 Easy Topics: Array, Sorting Solution Problem Understanding The problem gives us an array called salary , where each element represents the salary of an employee. Every salary value is unique, meaning no two employees have the same salary. Our task is to compute the average salary after excluding exactly one minimum salary and one maximum salary from the array. In other words, we must: Find...

Practice › LeetCode › LeetCode 12xx ›

LeetCode 1229 - Meeting Scheduler

LeetCode Problem 1229 Difficulty: 🟡 Medium Topics: Array, Two Pointers, Sorting Solution Problem Understanding This problem asks us to find the earliest overlapping time slot of a given duration between two people, given their individual availability schedules. Each person's availability is represented as an array of non-overlapping time slots [start, end] , where start and end are integers indicating the inclusive time range. The meeting duration is a single integer...

Practice › LeetCode › LeetCode 03xx ›

LeetCode 332 - Reconstruct Itinerary

LeetCode Problem 332 Difficulty: 🔴 Hard Topics: Array, String, Depth-First Search, Graph Theory, Sorting, Heap (Priority Queue), Eulerian Circuit Solution Problem Understanding The problem is asking us to reconstruct a flight itinerary given a list of tickets. Each ticket is a one-way flight represented as a pair of airport codes [from, to] . The traveler always starts at "JFK" , and the itinerary must use all tickets exactly once ....

Practice › LeetCode › LeetCode 02xx ›

LeetCode 217 - Contains Duplicate

LeetCode Problem 217 Difficulty: 🟢 Easy Topics: Array, Hash Table, Sorting Solution Problem Understanding The problem gives an integer array nums and asks whether any number appears more than once. If at least one value is repeated, we return true . If every value appears exactly once, we return false . The input is a list of integers. The output is a boolean value that answers a simple question: does...

Practice › LeetCode › LeetCode 11xx ›

LeetCode 1183 - Maximum Number of Ones

LeetCode Problem 1183 Difficulty: 🔴 Hard Topics: Math, Greedy, Sorting, Heap (Priority Queue) Solution LeetCode 1183, Maximum Number of Ones Problem Understanding The problem gives us a binary matrix M with dimensions height x width . Every cell in the matrix must contain either 0 or 1 . There is one important restriction: Every square submatrix of size sideLength x sideLength may contain at most maxOnes cells equal to 1...

Practice › LeetCode › LeetCode 04xx ›

LeetCode 414 - Third Maximum Number

LeetCode Problem 414 Difficulty: 🟢 Easy Topics: Array, Sorting Solution Problem Understanding The problem asks us to find the third distinct maximum number in an integer array. The key word is distinct. Duplicate values should only be counted once when determining rankings. For example, in the array [2,2,3,1] , the distinct values are {3,2,1} . Even though 2 appears twice, it only counts as one distinct number. The third distinct...

Practice › LeetCode › LeetCode 05xx ›

LeetCode 527 - Word Abbreviation

LeetCode Problem 527 Difficulty: 🔴 Hard Topics: Array, String, Greedy, Trie, Sorting Solution Problem Understanding The problem asks us to compute minimal unique abbreviations for an array of distinct strings. An abbreviation replaces the middle characters of a word with a count, keeping the first and last characters. For example, "internal" becomes "i6l" because there are six letters between i and l . The challenge arises when multiple words share...

Practice › LeetCode › LeetCode 09xx ›

LeetCode 922 - Sort Array By Parity II

LeetCode Problem 922 Difficulty: 🟢 Easy Topics: Array, Two Pointers, Sorting Solution Problem Understanding The problem gives an integer array nums where exactly half of the elements are even numbers and the other half are odd numbers. The task is to rearrange the array so that every even index contains an even number and every odd index contains an odd number. In other words: If an index i is even,...

Practice › LeetCode › LeetCode 05xx ›

LeetCode 539 - Minimum Time Difference

LeetCode Problem 539 Difficulty: 🟡 Medium Topics: Array, Math, String, Sorting Solution Problem Understanding The problem gives a list of time points in 24-hour clock format , where every time is represented as a string in the form "HH:MM" . Your task is to determine the smallest difference in minutes between any two time points in the list. A key detail is that time is cyclic , meaning the clock...

Practice › LeetCode › LeetCode 08xx ›

LeetCode 870 - Advantage Shuffle

LeetCode Problem 870 Difficulty: 🟡 Medium Topics: Array, Two Pointers, Greedy, Sorting Solution Problem Understanding The problem asks us to maximize the advantage of one array over another . Given two arrays nums1 and nums2 of equal length, the advantage is defined as the number of positions i where nums1[i] > nums2[i] . Our task is to rearrange nums1 to maximize this advantage. The input arrays represent two sets of...

Practice › LeetCode › LeetCode 16xx ›

LeetCode 1619 - Mean of Array After Removing Some Elements

LeetCode Problem 1619 Difficulty: 🟢 Easy Topics: Array, Sorting Solution LeetCode 1619, Mean of Array After Removing Some Elements Problem Understanding The problem gives us an integer array arr and asks us to compute the average value after removing the smallest 5% and the largest 5% of the elements. The important detail is that the removal is based on the sorted order of the array. We are not simply removing...

Practice › LeetCode › LeetCode 13xx ›

LeetCode 1348 - Tweet Counts Per Frequency

LeetCode Problem 1348 Difficulty: 🟡 Medium Topics: Hash Table, String, Binary Search, Design, Sorting, Ordered Set Solution Problem Understanding The problem is asking us to design a system that tracks tweets by their timestamp and allows querying the number of tweets in specific time intervals, split according to a frequency (minute, hour, or day). Specifically, we need to implement a TweetCounts class with two operations: recording a tweet and retrieving...

Practice › LeetCode › LeetCode 09xx ›

LeetCode 987 - Vertical Order Traversal of a Binary Tree

LeetCode Problem 987 Difficulty: 🔴 Hard Topics: Hash Table, Tree, Depth-First Search, Breadth-First Search, Sorting, Binary Tree Solution Problem Understanding The problem asks us to compute the vertical order traversal of a binary tree. In simpler terms, we are asked to “look at the tree from the side” and collect the nodes that align in the same vertical column. Each node has a position defined by (row, col) where row...

Practice › LeetCode › LeetCode 03xx ›

LeetCode 389 - Find the Difference

LeetCode Problem 389 Difficulty: 🟢 Easy Topics: Hash Table, String, Bit Manipulation, Sorting Solution Problem Understanding This problem gives us two strings, s and t . The string t is created by taking all characters from s , shuffling them into a different order, and then inserting exactly one additional character somewhere in the string. Our task is to identify and return that extra character. In other words, every character...

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LeetCode 2007 - Find Original Array From Doubled Array

LeetCode Problem 2007 Difficulty: 🟡 Medium Topics: Array, Hash Table, Greedy, Sorting Solution Problem Understanding The problem gives us an array called changed , which was supposedly created from another array called original . The transformation process works like this: Take every number in original . Append its doubled value, meaning 2 * x . Shuffle all the numbers together. For example, if: original = [1, 3, 4] then the...

Practice › LeetCode › LeetCode 10xx ›

LeetCode 1057 - Campus Bikes

LeetCode Problem 1057 Difficulty: 🟡 Medium Topics: Array, Sorting, Heap (Priority Queue) Solution LeetCode 1057 - Campus Bikes Problem Understanding This problem models a matching process between workers and bikes on a two dimensional grid. Each worker and each bike has a unique coordinate, and every worker must eventually receive exactly one bike. Since the number of bikes is at least the number of workers, a complete assignment is always...

Practice › LeetCode › LeetCode 05xx ›

LeetCode 588 - Design In-Memory File System

LeetCode Problem 588 Difficulty: 🔴 Hard Topics: Hash Table, String, Design, Trie, Sorting Solution Problem Understanding The problem asks us to design an in-memory file system that simulates basic file system operations without interacting with the real filesystem. We need to implement a FileSystem class that supports creating directories, adding and reading file content, and listing files or directories in a given path. The input consists of paths, which are...

Practice › LeetCode › LeetCode 08xx ›

LeetCode 881 - Boats to Save People

LeetCode Problem 881 Difficulty: 🟡 Medium Topics: Array, Two Pointers, Greedy, Sorting Solution LeetCode 881, Boats to Save People Problem Understanding This problem asks us to determine the minimum number of boats required to rescue all people, given two constraints. Each boat can carry at most two people, and the combined weight of the people in a boat cannot exceed the given weight limit. The input consists of: people ,...

Practice › LeetCode › LeetCode 14xx ›

LeetCode 1403 - Minimum Subsequence in Non-Increasing Order

LeetCode Problem 1403 Difficulty: 🟢 Easy Topics: Array, Greedy, Sorting Solution Problem Understanding The problem gives an integer array nums and asks us to build a subsequence whose sum is strictly greater than the sum of all elements that are not included in the subsequence. A subsequence means we are allowed to remove elements from the array while preserving the remaining elements. However, the final answer must be returned in...

Practice › LeetCode › LeetCode 04xx ›

LeetCode 462 - Minimum Moves to Equal Array Elements II

LeetCode Problem 462 Difficulty: 🟡 Medium Topics: Array, Math, Sorting Solution Problem Understanding This problem asks us to determine the minimum number of moves required to make all elements in an integer array equal, where a move consists of incrementing or decrementing a single element by 1 . In other words, we want to find a single target value that, when all elements are adjusted to it, requires the fewest...

Practice › LeetCode › LeetCode 07xx ›

LeetCode 761 - Special Binary String

LeetCode Problem 761 Difficulty: 🔴 Hard Topics: String, Divide and Conquer, Sorting Solution Problem Understanding The problem asks us to manipulate a special binary string to produce the lexicographically largest possible string. A special binary string has two properties: it contains equal numbers of 1 s and 0 s, and at every point in the string, the number of 1 s is at least as many as the number of...

Practice › LeetCode › LeetCode 00xx ›

LeetCode 18 - 4Sum

LeetCode Problem 18 Difficulty: 🟡 Medium Topics: Array, Two Pointers, Sorting Solution LeetCode 18 - 4Sum Problem Statement We are given an integer array nums and an integer target . The goal is to find every unique quadruplet of numbers in the array whose sum equals the target value. A quadruplet consists of four elements: nums[a], nums[b], nums[c], nums[d] where all four indices are distinct. The output should contain only...

Practice › LeetCode › LeetCode 07xx ›

LeetCode 720 - Longest Word in Dictionary

LeetCode Problem 720 Difficulty: 🟡 Medium Topics: Array, Hash Table, String, Trie, Sorting Solution LeetCode 720, Longest Word in Dictionary Problem Understanding This problem gives us an array of lowercase English words and asks us to find the longest word that can be constructed one character at a time using other words from the same dictionary. More specifically, suppose we have a candidate word like "world" . For this word...

Practice › LeetCode › LeetCode 01xx ›

LeetCode 147 - Insertion Sort List

LeetCode Problem 147 Difficulty: 🟡 Medium Topics: Linked List, Sorting Solution Problem Understanding The problem asks us to sort a singly linked list using the insertion sort algorithm. Unlike array sorting problems where elements can be accessed directly by index, linked lists require sequential traversal, so insertion operations behave differently and require careful pointer manipulation. The input is the head node of a singly linked list. Each node contains an...

Practice › LeetCode › LeetCode 04xx ›

LeetCode 475 - Heaters

LeetCode Problem 475 Difficulty: 🟡 Medium Topics: Array, Two Pointers, Binary Search, Sorting Solution Problem Understanding The problem gives two arrays, houses and heaters , where each value represents a position on a one dimensional horizontal line. Every heater has the same warming radius, and a house is considered covered if there exists at least one heater whose distance to the house is less than or equal to that radius....

Practice › LeetCode › LeetCode 16xx ›

LeetCode 1665 - Minimum Initial Energy to Finish Tasks

LeetCode Problem 1665 Difficulty: 🔴 Hard Topics: Array, Greedy, Sorting Solution Problem Understanding The problem gives us a list of tasks, where each task is represented as [actual, minimum] . For every task: minimum is the amount of energy we must currently have before we are allowed to start the task. actual is the amount of energy that gets consumed after finishing the task. Suppose a task is [4, 10]...

Practice › LeetCode › LeetCode 15xx ›

LeetCode 1500 - Design a File Sharing System

LeetCode Problem 1500 Difficulty: 🟡 Medium Topics: Hash Table, Design, Sorting, Heap (Priority Queue), Data Stream Solution Problem Understanding This problem asks us to design a miniature peer-to-peer file sharing system. The file is divided into m chunks, where every chunk has an ID from 1 to m . Users can join the system while already owning some chunks, leave the system entirely, and request chunks from other users. The...

Practice › LeetCode › LeetCode 13xx ›

LeetCode 1385 - Find the Distance Value Between Two Arrays

LeetCode Problem 1385 Difficulty: 🟢 Easy Topics: Array, Two Pointers, Binary Search, Sorting Solution Problem Understanding The problem is asking us to compute the distance value between two arrays arr1 and arr2 given a threshold d . Specifically, the distance value is defined as the count of elements in arr1 for which no element in arr2 is within a distance of d , i.e., there is no arr2[j] such that...

Practice › LeetCode › LeetCode 16xx ›

LeetCode 1626 - Best Team With No Conflicts

LeetCode Problem 1626 Difficulty: 🟡 Medium Topics: Array, Dynamic Programming, Sorting Solution Problem Understanding The problem asks us to build a basketball team with the maximum possible total score, while ensuring that the team does not contain any conflicts. Each player has two attributes: scores[i] , the player's skill score ages[i] , the player's age A conflict occurs when: a younger player has a strictly higher score than an older...

Practice › LeetCode › LeetCode 18xx ›

LeetCode 1818 - Minimum Absolute Sum Difference

LeetCode Problem 1818 Difficulty: 🟡 Medium Topics: Array, Binary Search, Sorting, Ordered Set Solution Problem Understanding The problem gives two arrays of positive integers, nums1 and nums2 , both of equal length n . The goal is to calculate the absolute sum difference between these arrays, which is the sum of the absolute differences at each index: |nums1[i] - nums2[i]| . You are allowed to replace at most one element...

Practice › LeetCode › LeetCode 02xx ›

LeetCode 280 - Wiggle Sort

LeetCode Problem 280 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting Solution Problem Understanding The problem asks us to rearrange an integer array so that it follows a specific alternating pattern called a wiggle sequence. The required relationship is: nums[0] <= nums[1] nums[1] >= nums[2] nums[2] <= nums[3] nums[3] >= nums[4] and so on. In other words, the values should alternate between valleys and peaks. Elements at odd indices should be...

Practice › LeetCode › LeetCode 01xx ›

LeetCode 179 - Largest Number

LeetCode Problem 179 Difficulty: 🟡 Medium Topics: Array, String, Greedy, Sorting Solution LeetCode 179 - Largest Number Problem Understanding This problem asks us to rearrange a list of non-negative integers so that, when concatenated together, they form the largest possible number. At first glance, this may look like a straightforward sorting problem where we simply sort the numbers in descending order. However, the challenge comes from the fact that the...

Practice › LeetCode › LeetCode 15xx ›

LeetCode 1589 - Maximum Sum Obtained of Any Permutation

LeetCode Problem 1589 Difficulty: 🟡 Medium Topics: Array, Greedy, Sorting, Prefix Sum Solution LeetCode 1589: Maximum Sum Obtained of Any Permutation Problem Understanding The problem gives us an integer array nums and a collection of range requests. Each request [start, end] asks for the sum of the subarray from index start to end , inclusive. The key twist is that we are allowed to rearrange the elements of nums in...

Practice › LeetCode › LeetCode 15xx ›

LeetCode 1552 - Magnetic Force Between Two Balls

LeetCode Problem 1552 Difficulty: 🟡 Medium Topics: Array, Binary Search, Sorting Solution Problem Understanding The problem asks us to distribute m balls into n baskets located at given positions along a line in such a way that the minimum distance between any two balls is maximized. The magnetic force between two balls is defined as the absolute difference of their positions. In simpler terms, we want to place the balls...

Practice › LeetCode › LeetCode 14xx ›

LeetCode 1481 - Least Number of Unique Integers after K Removals

LeetCode Problem 1481 Difficulty: 🟡 Medium Topics: Array, Hash Table, Greedy, Sorting, Counting Solution Problem Understanding This problem asks us to minimize the number of unique integers in an array after removing exactly k elements. In other words, we are given a list arr and a number k , and we need to strategically remove k elements so that the count of distinct integers left in the array is as...

Practice › LeetCode › LeetCode 16xx ›

LeetCode 1697 - Checking Existence of Edge Length Limited Paths

LeetCode Problem 1697 Difficulty: 🔴 Hard Topics: Array, Two Pointers, Union-Find, Graph Theory, Sorting Solution LeetCode 1697 - Checking Existence of Edge Length Limited Paths Problem Understanding This problem gives us an undirected weighted graph with n nodes. Each edge connects two nodes and has a distance value associated with it. We are also given multiple queries, where each query asks whether there exists a path between two nodes such...

Practice › LeetCode › LeetCode 15xx ›

LeetCode 1502 - Can Make Arithmetic Progression From Sequence

LeetCode Problem 1502 Difficulty: 🟢 Easy Topics: Array, Sorting Solution Problem Understanding The problem asks us to determine whether the elements of a given array can be rearranged so that they form an arithmetic progression. An arithmetic progression is a sequence where the difference between every pair of consecutive elements is the same. For example, [1, 3, 5, 7] is an arithmetic progression because every adjacent difference is 2 ....

Practice › LeetCode › LeetCode 06xx ›

LeetCode 630 - Course Schedule III

LeetCode Problem 630 Difficulty: 🔴 Hard Topics: Array, Greedy, Sorting, Heap (Priority Queue) Solution Problem Understanding The problem gives a list of online courses, where each course is represented as [duration, lastDay] . The duration tells us how many consecutive days are required to complete the course. The lastDay tells us the latest possible day by which the course must be finished. You begin on day 1 , and only...

Practice › LeetCode › LeetCode 14xx ›

LeetCode 1433 - Check If a String Can Break Another String

LeetCode Problem 1433 Difficulty: 🟡 Medium Topics: String, Greedy, Sorting Solution Problem Understanding The problem asks us to determine whether one string can "break" another string through some permutation. Given two strings s1 and s2 of equal length, a string x can break string y if, after arranging both strings in some order, every character in x is greater than or equal to the corresponding character in y when compared...

Practice › LeetCode › LeetCode 11xx ›

LeetCode 1196 - How Many Apples Can You Put into the Basket

LeetCode Problem 1196 Difficulty: 🟢 Easy Topics: Array, Greedy, Sorting Solution Problem Understanding This problem is asking us to determine how many apples we can fit into a basket with a maximum carrying capacity of 5000 units of weight. We are given an array weight where each element represents the weight of a single apple. The goal is to maximize the number of apples placed into the basket without exceeding...

Practice › LeetCode › LeetCode 03xx ›

LeetCode 378 - Kth Smallest Element in a Sorted Matrix

LeetCode Problem 378 Difficulty: 🟡 Medium Topics: Array, Binary Search, Sorting, Heap (Priority Queue), Matrix Solution Problem Understanding The problem gives us an n x n matrix where both rows and columns are sorted in ascending order. This means two ordering guarantees exist simultaneously: Every row is sorted from left to right. Every column is sorted from top to bottom. We are asked to return the kth smallest element across...

Practice › LeetCode › LeetCode 05xx ›

LeetCode 561 - Array Partition

LeetCode Problem 561 Difficulty: 🟢 Easy Topics: Array, Greedy, Sorting, Counting Sort Solution Problem Understanding The problem gives an array nums containing 2n integers. Our task is to divide these integers into exactly n pairs. For each pair (ai, bi) , we take the smaller value, min(ai, bi) . After computing the minimum value from every pair, we sum all of those minimums together. The goal is to arrange the...

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LeetCode 56 - Merge Intervals

LeetCode Problem 56 Difficulty: 🟡 Medium Topics: Array, Sorting Solution Problem Understanding The problem gives an array of intervals, where each interval is represented as [start, end] . Each interval describes a continuous range of values from start to end , inclusive. The goal is to combine all intervals that overlap into a single larger interval. After merging all overlapping intervals, we return a list of intervals where no two...

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LeetCode 786 - K-th Smallest Prime Fraction

LeetCode Problem 786 Difficulty: 🟡 Medium Topics: Array, Two Pointers, Binary Search, Sorting, Heap (Priority Queue) Solution Problem Understanding The problem asks us to find the k-th smallest fraction that can be formed by dividing one element of a sorted array arr by another element later in the array. The array arr is strictly increasing, starts with 1 , and all elements after the first are prime numbers. For every...

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LeetCode 274 - H-Index

LeetCode Problem 274 Difficulty: 🟡 Medium Topics: Array, Sorting, Counting Sort Solution LeetCode 274, H-Index Problem Understanding The problem gives an array called citations , where each element represents how many citations a research paper has received. Each index corresponds to one paper, and the value at that index is the number of times that paper has been cited. We must compute the researcher's h-index . The h-index is defined...

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LeetCode 973 - K Closest Points to Origin

LeetCode Problem 973 Difficulty: 🟡 Medium Topics: Array, Math, Divide and Conquer, Geometry, Sorting, Heap (Priority Queue), Quickselect Solution Problem Understanding This problem asks us to find the k points that are closest to the origin (0,0) from a list of 2D points. Each point is given as a pair [x, y] , and the distance is defined using the Euclidean formula, sqrt(x^2 + y^2) . The input consists of...

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LeetCode 1051 - Height Checker

LeetCode Problem 1051 Difficulty: 🟢 Easy Topics: Array, Sorting, Counting Sort Solution Problem Understanding The problem gives us an array called heights , where each value represents the height of a student standing in a line. The school wants the students arranged in non-decreasing order, meaning heights should appear from smallest to largest, allowing duplicates. We are asked to determine how many students are currently standing in the wrong position...

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LeetCode 2092 - Find All People With Secret

LeetCode Problem 2092 Difficulty: 🔴 Hard Topics: Depth-First Search, Breadth-First Search, Union-Find, Graph Theory, Sorting Solution Problem Understanding The problem describes a network of people who meet at different times. Whenever a person who already knows a secret participates in a meeting, they immediately share the secret with the other participant. The key detail is that sharing is instantaneous within the same timestamp. This means if someone learns the secret...

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LeetCode 721 - Accounts Merge

LeetCode Problem 721 Difficulty: 🟡 Medium Topics: Array, Hash Table, String, Depth-First Search, Breadth-First Search, Union-Find, Sorting Solution Problem Understanding This problem asks us to merge user accounts based on shared email addresses. Each account is represented as a list of strings. The first string is the user's name, and every remaining string is an email address associated with that account. The important detail is that two accounts belong to...

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LeetCode 1561 - Maximum Number of Coins You Can Get

LeetCode Problem 1561 Difficulty: 🟡 Medium Topics: Array, Math, Greedy, Sorting, Game Theory Solution LeetCode 1561 - Maximum Number of Coins You Can Get Problem Understanding The problem gives us an array called piles , where each element represents the number of coins in a pile. The length of the array is always divisible by 3 , meaning there are exactly 3n piles for some integer n . In every...

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LeetCode 791 - Custom Sort String

LeetCode Problem 791 Difficulty: 🟡 Medium Topics: Hash Table, String, Sorting Solution LeetCode 791, Custom Sort String Problem Understanding The problem gives us two strings, order and s . The string order defines a custom character ordering. Unlike normal alphabetical ordering, the characters in order specify exactly how characters should be prioritized relative to one another. Every character in order is unique, which means there are no conflicts or duplicate...

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LeetCode 349 - Intersection of Two Arrays

LeetCode Problem 349 Difficulty: 🟢 Easy Topics: Array, Hash Table, Two Pointers, Binary Search, Sorting Solution Problem Understanding The problem gives us two integer arrays, nums1 and nums2 , and asks us to return their intersection. The intersection consists of all values that appear in both arrays. However, the result must contain only unique elements, even if a number appears many times in either array. For example, if nums1 =...

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LeetCode 899 - Orderly Queue

LeetCode Problem 899 Difficulty: 🔴 Hard Topics: Math, String, Sorting Solution LeetCode 899 - Orderly Queue Problem Understanding This problem gives us a string s and an integer k . We are allowed to repeatedly perform one operation: Choose one of the first k characters of the string. Remove that character from its current position. Append it to the end of the string. Our goal is to determine the lexicographically...

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LeetCode 1133 - Largest Unique Number

LeetCode Problem 1133 Difficulty: 🟢 Easy Topics: Array, Hash Table, Sorting Solution Problem Understanding The problem is asking us to identify the largest integer in an array that occurs exactly once. In other words, among all integers that are unique (appear only one time), we need to find the maximum. If no such integer exists, the output should be -1 . The input nums is a list of integers, each...

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LeetCode 1460 - Make Two Arrays Equal by Reversing Subarrays

LeetCode Problem 1460 Difficulty: 🟢 Easy Topics: Array, Hash Table, Sorting Solution Problem Understanding This problem asks whether one integer array, arr , can be transformed into another array, target , by repeatedly reversing any non-empty contiguous subarray. A subarray reversal means choosing a continuous segment of the array and reversing the order of its elements. For example, reversing [2,4,1] changes it into [1,4,2] . The key detail is that...

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LeetCode 1402 - Reducing Dishes

LeetCode Problem 1402 Difficulty: 🔴 Hard Topics: Array, Dynamic Programming, Greedy, Sorting Solution Problem Understanding In this problem, we are given an integer array called satisfaction , where each element represents the satisfaction level of a dish prepared by a chef. The chef can cook dishes in any order, and each dish takes exactly one unit of time to prepare. The important detail is how the score is calculated. If...

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LeetCode 969 - Pancake Sorting

LeetCode Problem 969 Difficulty: 🟡 Medium Topics: Array, Two Pointers, Greedy, Sorting Solution Problem Understanding The problem is asking us to sort an array of unique integers using only pancake flips . A pancake flip is defined as reversing a prefix of the array from index 0 to index k-1 for some integer k between 1 and the length of the array. The input is a permutation of integers from...

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LeetCode 2231 - Largest Number After Digit Swaps by Parity

LeetCode Problem 2231 Difficulty: 🟢 Easy Topics: Sorting, Heap (Priority Queue) Solution Problem Understanding The problem gives us a positive integer num and allows us to swap digits only if the two digits have the same parity. In other words, an odd digit can only be swapped with another odd digit, and an even digit can only be swapped with another even digit. The goal is to return the largest...

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LeetCode 1751 - Maximum Number of Events That Can Be Attended II

LeetCode Problem 1751 Difficulty: 🔴 Hard Topics: Array, Binary Search, Dynamic Programming, Sorting Solution Problem Understanding You are given a list of events, where each event is represented as: startDay endDay value If you attend an event, you must attend the entire interval from startDay to endDay , inclusive. Because the interval is inclusive, two events conflict if one starts on the same day another ends. You may attend at...

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LeetCode 296 - Best Meeting Point

LeetCode Problem 296 Difficulty: 🔴 Hard Topics: Array, Math, Sorting, Matrix Solution Problem Understanding The problem gives us a two-dimensional binary grid where each cell contains either 0 or 1 . A value of 1 represents the home location of a friend, while 0 represents an empty cell. We must choose a single meeting point somewhere in the grid such that the sum of all Manhattan distances from every friend's...

Practice › LeetCode › LeetCode 04xx ›

LeetCode 435 - Non-overlapping Intervals

LeetCode Problem 435 Difficulty: 🟡 Medium Topics: Array, Dynamic Programming, Greedy, Sorting Solution Problem Understanding The problem gives an array of intervals where each interval is represented as [start, end] . Each interval describes a continuous range on a number line. The task is to remove the minimum number of intervals so that the remaining intervals no longer overlap. Two intervals overlap if one starts before the other finishes. However,...

Practice › LeetCode › LeetCode 14xx ›

LeetCode 1464 - Maximum Product of Two Elements in an Array

LeetCode Problem 1464 Difficulty: 🟢 Easy Topics: Array, Sorting, Heap (Priority Queue) Solution Problem Understanding The problem gives an integer array nums , and asks us to choose two different indices i and j . For those two elements, we compute the expression: $(nums[i]-1)(nums[j]-1)$ Our goal is to return the maximum possible value of this expression. In simpler terms, we need to find the two numbers in the array that...

Practice › LeetCode › LeetCode 01xx ›

LeetCode 164 - Maximum Gap

LeetCode Problem 164 Difficulty: 🟡 Medium Topics: Array, Sorting, Bucket Sort, Radix Sort Solution Problem Understanding The problem asks us to compute the largest difference between two consecutive elements after sorting the array . At first glance, this may seem straightforward: sort the array, then scan through adjacent pairs to find the maximum difference. However, there is an important constraint: the algorithm must run in linear time, O(n), and use...

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LeetCode 1086: High Five

Problem Restatement We are given a list of [id, score] pairs. For each student, compute the average of their top 5 scores (integer division). Return the result sorted by student ID. The official constraints state that each student has at least 5 scores. Input and Output Item Meaning Input List of [id, score] pairs Output [[id, top5avg], ...] sorted by id Function shape: def highFive(items: list[list[int]]) -> list[list[int]]: ... Examples...

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LeetCode 1051: Height Checker

Problem Restatement We are given an array heights representing the current order of students. The expected order is the students sorted by height in non-decreasing order. Return the number of indices where the current height does not match the expected height. The official constraints state that 1 <= heights.length <= 100 and 1 <= heights[i] <= 100 . Input and Output Item Meaning Input Array heights Output Number of positions...

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LeetCode 1040: Moving Stones Until Consecutive II

Problem Restatement We have n stones at distinct positions on an infinite line. In one move, we pick the leftmost or rightmost stone and move it to any unoccupied position between the leftmost and rightmost stones. We need to return [min_moves, max_moves] . The official constraints state that 3 <= stones.length <= 10^4 and 1 <= stones[i] <= 10^9 . Input and Output Item Meaning Input Array stones (distinct positions)...

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LeetCode 1099: Two Sum Less Than K

Problem Restatement We are given an integer array nums and an integer k . We need to find the maximum sum nums[i] + nums[j] where i < j and nums[i] + nums[j] < k . Return -1 if no such pair exists. The official constraints state that 1 <= nums.length <= 100 and 1 <= nums[i] <= 1000 . Input and Output Item Meaning Input Array nums and integer k...

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LeetCode 1029: Two City Scheduling

Problem Restatement We have 2n people who must each travel to one of two cities: city A or city B. Exactly n people must go to city A and exactly n must go to city B. The cost to send person i to city A is costs[i][0] and to city B is costs[i][1] . We need to return the minimum total cost. The official constraints state that 2 <= costs.length...

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LeetCode 1005: Maximize Sum Of Array After K Negations

Problem Restatement We are given an integer array nums and an integer k . In one operation, we choose an index and negate the value at that index. We must perform exactly k operations. We need to return the maximum possible sum of the array after exactly k negations. The official constraints state that 1 <= nums.length <= 10^4 , -100 <= nums[i] <= 100 , and 1 <= k...

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LeetCode 1058: Minimize Rounding Error to Meet Target

Problem Restatement We are given an array of price strings (floating-point) and an integer target . We must round each price either up ( ceil ) or down ( floor ). We need the rounded prices to sum exactly to target . Return the minimum total rounding error, or "-1" if it is impossible. The official constraints state that 1 <= prices.length <= 500 . Input and Output Item Meaning...

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LeetCode 1065: Index Pairs of a String

Problem Restatement We are given a string text and a list of strings words . Return all [i, j] pairs such that the substring text[i:j+1] is in words . The result must be sorted by i , then by j . The official constraints state that 1 <= text.length <= 100 and 1 <= words.length <= 20 . Input and Output Item Meaning Input String text and list words Output...

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LeetCode 1090: Largest Values From Labels

Problem Restatement We have n items, each with a value and a label . We want to choose a subset of items to maximize total value, subject to: At most numWanted items can be chosen. At most useLimit items with the same label can be chosen. The official constraints state that n == values.length == labels.length and 1 <= numWanted, useLimit <= n <= 2 * 10^4 . Input and...

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LeetCode 1054: Distant Barcodes

Problem Restatement We are given an array of barcodes. We need to rearrange the barcodes so that no two adjacent barcodes are equal. It is guaranteed that a valid rearrangement always exists. The official constraints state that 1 <= barcodes.length <= 10000 and 1 <= barcodes[i] <= 10000 . Input and Output Item Meaning Input Array barcodes Output Rearranged array with no two adjacent equal elements Function shape: def rearrangeBarcodes(barcodes:...

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LeetCode 1057: Campus Bikes

Problem Restatement We have a campus as a 2D grid. We are given the positions of n workers and m bikes. We need to assign one bike to each worker. We assign bikes greedily: Find the pair (worker, bike) with the smallest Manhattan distance. Assign that bike to that worker. Remove both from consideration. Repeat. If there are ties in distance, pick the smallest worker index, then smallest bike index....

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LeetCode 1094: Car Pooling

Problem Restatement We have a car with capacity seats. We are given a list of trips: each trip [numPassengers, from, to] means numPassengers passengers board at from and alight at to . We need to return true if it is possible to pick up all passengers without exceeding capacity at any point. The official constraints state that 1 <= trips.length <= 1000 , 1 <= numPassengers <= 100 , and...

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LeetCode 1030: Matrix Cells in Distance Order

Problem Restatement We are given an rows x cols matrix and a center cell (rCenter, cCenter) . We need to return all cells of the matrix sorted by their distance from the center, where distance is defined as: abs(r - rCenter) + abs(c - cCenter) (Manhattan distance). Ties can be broken in any order. The official constraints state that 1 <= rows, cols <= 100 and 0 <= rCenter <...

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LeetCode 975: Odd Even Jump

Problem Restatement We are given an integer array arr . From any starting index, we make jumps to the right. The jumps are numbered by jump count: Jump number Type 1st , 3rd , 5th , ... Odd jump 2nd , 4th , 6th , ... Even jump For an odd jump from index i , we must jump to an index j such that: i < j arr[i] <=...

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LeetCode 973: K Closest Points to Origin

Problem Restatement We are given an array points , where each item is a point on the 2D plane: [x, y] We are also given an integer k . Return the k points closest to the origin: (0, 0) The distance is Euclidean distance. The answer may be returned in any order, and the answer is guaranteed to be unique except for order. The official constraints are 1 <= k...

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LeetCode 846: Hand of Straights

Problem Restatement We are given an integer array hand , where each value is written on one card. We are also given an integer groupSize . We need to decide whether all cards can be rearranged into groups such that: Rule Meaning Group size Every group has exactly groupSize cards Consecutive values Cards in each group are consecutive Use all cards Every card must be used exactly once Return True...

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LeetCode 922: Sort Array By Parity II

Problem Restatement We are given an integer array nums . Exactly half of the numbers are even, and exactly half are odd. We need to rearrange the array so that: Index Required value Even index Even number Odd index Odd number Return any valid arrangement. For example: nums = [4, 2, 5, 7] One valid answer is: [4, 5, 2, 7] because indices 0 and 2 contain even numbers, and...

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LeetCode 899: Orderly Queue

Problem Restatement We are given a string s and an integer k . In one operation: Choose one of the first k characters of s . Remove it from its current position. Append it to the end of the string. Return the lexicographically smallest string we can get after any number of operations. Input and Output Item Meaning Input String s Input Integer k Output Lexicographically smallest reachable string Operation...

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LeetCode 969: Pancake Sorting

Problem Restatement We are given an integer array arr . A pancake flip chooses an integer k and reverses the first k elements of the array. We need to return a sequence of k values that sorts the array in increasing order. Any valid answer is accepted as long as it sorts the array using at most 10 * arr.length flips. The problem constraint gives 1 <= arr.length <= 100...

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LeetCode 950: Reveal Cards In Increasing Order

Problem Restatement We are given an array: deck Each card has a unique integer. We may reorder the deck however we want. The first element of the returned array is considered the top of the deck. Then the reveal process works like this: Reveal the top card and remove it. If cards remain, move the next top card to the bottom. Repeat until all cards are revealed. Return an initial...

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LeetCode 823: Binary Trees With Factors

Problem Restatement We are given an array arr of unique integers. Every value is greater than 1 . We need to count how many binary trees can be built using values from arr . Each value may be used any number of times. For every non-leaf node: node.val == node.left.val * node.right.val Return the number of possible binary trees modulo: 10**9 + 7 The left and right child order matters,...

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LeetCode 948: Bag of Tokens

Problem Restatement We are given an array of token values: tokens and an initial amount of power: power We start with score 0 . Each token may be played at most once, in one of two ways: Play type Requirement Effect Face-up power >= token Lose token power, gain 1 score Face-down score >= 1 Gain token power, lose 1 score We may play any number of tokens in any...

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LeetCode 870: Advantage Shuffle

Problem Restatement We are given two integer arrays: nums1 nums2 Both arrays have the same length. The advantage of nums1 over nums2 is the number of indices i where: nums1[i] > nums2[i] We may rearrange nums1 in any order. Return any permutation of nums1 that maximizes its advantage over nums2 . Input and Output Item Meaning Input nums1 , the array we may reorder Input nums2 , the fixed comparison...

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LeetCode 945: Minimum Increment to Make Array Unique

Problem Restatement We are given an integer array: nums In one move, we may choose any index and increment that value by 1 . We need to return the minimum number of moves required to make every value in nums unique. The problem guarantees that the answer fits in a 32-bit integer. The official examples include [1,2,2] -> 1 and [3,2,1,2,1,7] -> 6 . Input and Output Item Meaning Input...

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LeetCode 893: Groups of Special-Equivalent Strings

Problem Restatement We are given an array words . All strings have the same length. In one move, we can swap two characters only if their indices have the same parity: Swap type Allowed? Even index with even index Yes Odd index with odd index Yes Even index with odd index No Two strings are special-equivalent if one can be changed into the other using any number of these moves....

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LeetCode 891: Sum of Subsequence Widths

Problem Restatement We are given an integer array nums . For any non-empty subsequence, its width is: maximum value - minimum value Return the sum of widths of all non-empty subsequences. Because the answer can be very large, return it modulo: 10**9 + 7 A subsequence is formed by deleting zero or more elements without changing the order of the remaining elements. The problem asks for the sum of widths...

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LeetCode 720: Longest Word in Dictionary

Problem Restatement We are given an array of strings: words We need to find the longest word that can be built one character at a time by other words in the array. A word is valid if every prefix formed by removing the last character also exists in the array. For example: "world" is valid only if all these words exist: "w" "wo" "wor" "worl" "world" If there are multiple...

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LeetCode 49: Group Anagrams

Problem Restatement We are given an array of strings strs . We need to group strings that are anagrams of each other. Two strings are anagrams if they contain the same characters with the same frequencies, but possibly in a different order. The answer can be returned in any order. LeetCode states the input strings contain lowercase English letters, with 1 <= strs.length <= 10^4 and 0 <= strs[i].length <=...

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LeetCode 769: Max Chunks To Make Sorted

Problem Restatement We are given an array arr of length n . The array is a permutation of integers from 0 to n - 1 . We want to split arr into the maximum number of chunks. Then we sort each chunk individually and concatenate the chunks back in the same order. The final result must equal the fully sorted array. Return the largest number of chunks we can make....

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LeetCode 719: Find K-th Smallest Pair Distance

Problem Restatement We are given an integer array nums and an integer k . For every pair of indices: 0 <= i < j < len(nums) the distance between the pair is: abs(nums[i] - nums[j]) We need to return the kth smallest pair distance. The official problem defines the distance of two integers as their absolute difference and asks for the kth smallest distance among all pairs nums[i] and nums[j]...

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LeetCode 47: Permutations II

Problem Restatement We are given an array nums that may contain duplicate numbers. We need to return all possible unique permutations in any order. A permutation is an ordering that uses every element exactly once. Since nums may contain duplicates, different index choices can produce the same value ordering. We must return each unique ordering only once. The official problem states: given a collection of numbers that might contain duplicates,...

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LeetCode 768: Max Chunks To Make Sorted II

Problem Restatement We are given an integer array arr . We want to split it into some number of chunks. Then we sort each chunk individually and concatenate the sorted chunks back in the same order. The final result must equal the fully sorted version of arr . Return the maximum number of chunks we can make. The array may contain duplicate values. Input and Output Item Meaning Input An...

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LeetCode 624: Maximum Distance in Arrays

Problem Restatement We are given m arrays. Each array is sorted in ascending order. We must pick two integers from two different arrays and compute their distance. The distance between two integers a and b is: abs(a - b) Return the maximum possible distance. For example, from: arrays = [[1, 2, 3], [4, 5], [1, 2, 3]] we can pick 1 from the first array and 5 from the second...

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LeetCode 791: Custom Sort String

Problem Restatement We are given two strings: order s All characters in order are unique. The string order defines a custom ordering of characters. We need to rearrange the characters of s so that characters appearing in order follow that same relative order. Characters in s that do not appear in order may be placed anywhere in the result. Return any valid permutation of s . Input and Output Item...

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LeetCode 987: Vertical Order Traversal of a Binary Tree

Problem Restatement We are given the root of a binary tree. Each node has a coordinate: Node Position Root (row = 0, col = 0) Left child (row + 1, col - 1) Right child (row + 1, col + 1) We need to return the vertical order traversal of the tree. That means: Visit columns from left to right. Inside each column, visit nodes from top to bottom. If...

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LeetCode 937: Reorder Data in Log Files

Problem Restatement We are given a list of log strings. Each log has this structure: identifier content The first word is the identifier. The rest of the log is the content. There are two kinds of logs: Log type Meaning Letter-log Every word after the identifier contains lowercase letters Digit-log Every word after the identifier contains digits We need to reorder the logs using these rules: All letter-logs come before...

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LeetCode 912: Sort an Array

Problem Restatement We are given an integer array nums . Return the array sorted in ascending order. The problem requires solving this without using built-in sorting functions, in O(n log n) time, with as little extra space as possible. Input and Output Item Meaning Input An integer array nums Output The same values sorted in ascending order Restriction Do not use built-in sorting functions Target time O(n log n) Function...

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LeetCode 786: K-th Smallest Prime Fraction

Problem Restatement We are given a sorted array arr . The array contains 1 and some prime numbers. All values are unique. For every pair of indices i and j where: 0 <= i < j < len(arr) we form the fraction: arr[i] / arr[j] Return the k -th smallest fraction. The answer should be returned as: [numerator, denominator] Input and Output Item Meaning Input A sorted array arr and...

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LeetCode 675: Cut Off Trees for Golf Event

Problem Restatement We are given a forest represented as a 2D grid. Each cell has one of these meanings: Value Meaning 0 Obstacle, cannot be walked through 1 Empty ground, can be walked through > 1 Tree, can be walked through, value is the tree height We start at position (0, 0) . We must cut all trees in increasing order of height, from shortest to tallest. After a tree...

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LeetCode 646: Maximum Length of Pair Chain

Problem Restatement We are given a list of integer pairs. Each pair looks like: [left, right] A pair: [a, b] can be followed by: [c, d] if: b < c We need to build the longest possible chain of pairs. Return the maximum chain length. The constraints guarantee: left < right for every pair. Input and Output Item Meaning Input List of integer pairs Output Maximum valid chain length Chain...

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LeetCode 761: Special Binary String

Problem Restatement A special binary string is a binary string with two properties: It has the same number of 1 s and 0 s. Every prefix has at least as many 1 s as 0 s. We are given a special binary string s . One move lets us choose two consecutive non-empty special substrings and swap them. We need to return the lexicographically largest string possible after applying any...

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LeetCode 910: Smallest Range II

Problem Restatement We are given an integer array nums and an integer k . For every index i , we must either: nums[i] + k or: nums[i] - k Return the minimum possible difference between the maximum and minimum values after all choices are made. Unlike the previous problem, every number must choose exactly one of the two operations. Input and Output Item Meaning Input Integer array nums and integer...

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LeetCode 645: Set Mismatch

Problem Restatement We are given an array nums of length n . Originally, the array should contain every number from 1 to n exactly once. But an error happened: Error Meaning One number appears twice This is the duplicate number One number is missing This is the missing number We need to return: [duplicate, missing] in that exact order. The official examples include nums = [1, 2, 2, 4] ,...

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LeetCode 692: Top K Frequent Words

Problem Restatement We are given a list of words and an integer k . We need to return the k most frequent words. The ordering rules are: Rule Meaning Higher frequency first More common words come earlier Lexicographical tie-break If two words have the same frequency, the smaller alphabetical word comes first The official statement defines lexicographical order using normal alphabetical string comparison. Input and Output Item Meaning Input words...

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LeetCode 642: Design Search Autocomplete System

Problem Restatement We need to design an autocomplete system. The system starts with historical sentences and their usage counts. For every typed character except # , return up to three historical sentences that start with the current prefix. The result must be sorted by: Priority Rule First Higher frequency first Second ASCII order if frequencies are equal When the user types # , the current sentence is finished. The system...

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LeetCode 759: Employee Free Time

Problem Restatement We are given the working schedules of several employees. Each employee has a list of non-overlapping intervals, sorted by start time. Each interval represents a time when that employee is busy. We need to return all finite, positive-length intervals when every employee is free. We do not include infinite intervals before the earliest busy time or after the latest busy time. Input and Output Item Meaning Input schedule...

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LeetCode 757: Set Intersection Size At Least Two

Problem Restatement We are given a list of intervals. Each interval is: [start, end] We need to build a set S of integers such that every interval contains at least two numbers from S . Our goal is to make S as small as possible. Return the minimum possible size of S . Input and Output Item Meaning Input A list of intervals [start, end] Output The minimum size of...

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LeetCode 857: Minimum Cost to Hire K Workers

Problem Restatement We are given n workers. Each worker has: Data Meaning quality[i] The quality value of worker i wage[i] The minimum wage worker i must receive We need to hire exactly k workers. The payment must satisfy two rules: Every hired worker must be paid at least their minimum wage. In the hired group, pay must be proportional to quality. That means if one worker has twice the quality...

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LeetCode 881: Boats to Save People

Problem Restatement We are given an array people , where people[i] is the weight of the i th person. We also have an unlimited number of boats. Each boat has weight limit limit . Each boat can carry at most two people at the same time, and their total weight must be at most limit . Return the minimum number of boats needed to carry everyone. The official constraints allow...

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LeetCode 954: Array of Doubled Pairs

Problem Restatement We are given an integer array arr . We want to reorder the array so that for every pair: (arr[2 * i], arr[2 * i + 1]) the second number equals double the first number: arr[2 * i + 1] = 2 * arr[2 * i] Return true if such a reordering is possible. Otherwise, return false . The official constraints are: Constraint Value 2 <= arr.length <=...

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LeetCode 524: Longest Word in Dictionary through Deleting

Problem Restatement We are given: s dictionary We may delete some characters from s . We need to return the longest string in dictionary that can be formed as a subsequence of s . If multiple answers have the same length, return the lexicographically smallest one. If no dictionary word can be formed, return the empty string. The official problem asks us to find the longest dictionary word obtainable by...

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LeetCode 953: Verifying an Alien Dictionary

Problem Restatement We are given: A list of words called words A string called order The string order describes the alphabet order used in an alien language. We need to check whether the words are sorted lexicographically according to this alien alphabet. Return true if the list is correctly sorted. Otherwise, return false . The official constraints are: Constraint Value 1 <= words.length <= 100 Number of words 1 <=...

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LeetCode 611: Valid Triangle Number

Problem Restatement We are given an integer array nums . Each value can be treated as a side length. We need to count how many triplets can form a valid triangle. A triplet means choosing three different indices from the array. The official problem asks us to return the number of triplets chosen from nums that can make triangles if we take them as side lengths. The constraints are 1...

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LeetCode 522: Longest Uncommon Subsequence II

Problem Restatement We are given an array of strings strs . We need to return the length of the longest uncommon subsequence among them. An uncommon subsequence is a string that is a subsequence of one string but not a subsequence of any other string in the array. If no such subsequence exists, return -1 . The official problem asks for the length of the longest uncommon subsequence among an...

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LeetCode 630: Course Schedule III

Problem Restatement We are given a list of courses. Each course is represented as: [duration, lastDay] duration is how many days the course takes. lastDay is the latest day by which the course must be finished. We start on day 1 . We can take only one course at a time. We need to return the maximum number of courses we can finish before or on their deadlines. Input and...

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LeetCode 593: Valid Square

Problem Restatement We are given four points in 2D space: p1, p2, p3, p4 Each point is represented as: [x, y] We need to return True if these four points form a valid square. The points are not given in any particular order. A valid square has four equal sides with positive length and four right angles. The coordinates satisfy -10^4 <= x_i, y_i <= 10^4 . ( leetcode.com ,...

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LeetCode 853: Car Fleet

Problem Restatement There are n cars driving toward the same destination. The destination is at position target . For each car: Data Meaning position[i] Starting position of car i speed[i] Speed of car i A car cannot pass another car ahead of it. If a faster car catches up to a slower car before the destination, they become one fleet. The faster car slows down and follows the slower car....

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LeetCode 506: Relative Ranks

Problem Restatement We are given an integer array score . score[i] is the score of the i th athlete. All scores are unique. Athletes are ranked from highest score to lowest score: Place Rank string 1st "Gold Medal" 2nd "Silver Medal" 3rd "Bronze Medal" 4th and later The placement number as a string We need to return an array answer where: answer[i] is the rank of the i th athlete...

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LeetCode 539: Minimum Time Difference

Problem Restatement We are given a list of time points in 24-hour "HH:MM" format. We need to return the minimum difference in minutes between any two time points. The clock wraps around after midnight, so the difference between "23:59" and "00:00" is 1 , not 1439 . The input contains at least two time points. Each time point is formatted as "HH:MM" . Input and Output Item Meaning Input A...

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LeetCode 588: Design In-Memory File System

Problem Restatement We need to design an in-memory file system. The file system must support four operations: Operation Behavior ls(path) If path is a file, return only that file name. If path is a directory, return its direct children in lexicographic order. mkdir(path) Create the directory path. If middle directories do not exist, create them too. addContentToFile(filePath, content) Create the file if missing, otherwise append content to the existing file....

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LeetCode 628: Maximum Product of Three Numbers

Problem Restatement We are given an integer array nums . We need to choose three numbers from the array so that their product is as large as possible. Return that maximum product. The three numbers do not need to be next to each other. We only care about choosing any three different elements. Input and Output Item Meaning Input An integer array nums Output The maximum product of any three...

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LeetCode 977: Squares of a Sorted Array

Problem Restatement We are given an integer array nums sorted in non-decreasing order. We need to return a new array containing the square of each number, also sorted in non-decreasing order. The difficulty comes from negative numbers. For example: nums = [-4, -1, 0, 3, 10] If we square each value in the same order, we get: [16, 1, 0, 9, 100] This result is not sorted. The official constraints...

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LeetCode 976: Largest Perimeter Triangle

Problem Restatement We are given an integer array nums . Each number represents a possible side length of a triangle. We need to choose three lengths that can form a triangle with non-zero area. Among all valid choices, return the largest possible perimeter. If no three lengths can form a valid triangle, return 0 . A valid triangle with side lengths a , b , and c must satisfy the...

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LeetCode 826: Most Profit Assigning Work

Problem Restatement We are given three arrays: Array Meaning difficulty difficulty[i] is the difficulty of job i profit profit[i] is the profit from job i worker worker[j] is the maximum difficulty worker j can handle Each worker can do at most one job. A job can be used more than once. This is important. If three workers all choose the same job, we count that job's profit three times. If...

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LeetCode 726: Number of Atoms

Problem Restatement We are given a valid chemical formula string. The formula contains atom names, numbers, and parentheses. We need to count how many times each atom appears, then return the result as a string sorted by atom name. An atom name starts with one uppercase letter. It may be followed by lowercase letters. Examples: "H" "Mg" "Ca" A number after an atom means the atom appears that many times....

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LeetCode 502: IPO

Problem Restatement We are given n projects. Each project has: Array Meaning profits[i] The pure profit gained after finishing project i capital[i] The minimum capital needed to start project i We start with capital w . We can finish at most k distinct projects. After finishing a project, its profit is added to our capital. We need to return the maximum final capital possible after choosing at most k projects....

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LeetCode 561: Array Partition

Problem Restatement We are given an integer array nums containing 2n integers. We need to divide all numbers into n pairs: (a1, b1), (a2, b2), ..., (an, bn) For each pair, we take the smaller number: min(ai, bi) Return the maximum possible sum of these minimum values. The constraints are 1 <= n <= 10^4 , nums.length == 2 * n , and -10^4 <= nums[i] <= 10^4 . The...

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LeetCode 626: Exchange Seats

Problem Restatement We are given a table named Seat . Each row stores a student and their seat id . The id values start from 1 and increase continuously. We need to swap every two adjacent students: Original Seat New Seat 1 gets student from 2 2 gets student from 1 3 gets student from 4 4 gets student from 3 If the number of students is odd, the last...

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LeetCode 527: Word Abbreviation

Problem Restatement We are given an array of distinct lowercase words. For each word, we need to return its minimal unique abbreviation, while keeping the output in the same order as the input. The abbreviation starts with a prefix, then the number of abbreviated middle characters, then the last character. If the abbreviation is not shorter than the original word, we keep the original word. For example: "internal" -> "i6l"...

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LeetCode 475: Heaters

Problem Restatement We are given two arrays: houses heaters Each value is a position on a horizontal line. Every heater has the same warm radius r . A heater at position h warms every house whose position x satisfies: abs(x - h) <= r We need to return the minimum radius r so that every house is covered by at least one heater. The official problem states that all heaters...

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LeetCode 324: Wiggle Sort II

Problem Restatement We are given an integer array nums . Rearrange it in-place so that: nums[0] < nums[1] > nums[2] < nums[3] ... This alternating pattern is called wiggle order. The official problem guarantees that a valid answer exists. The follow-up asks for O(n) average time and O(1) extra space. Input and Output Item Meaning Input Integer array nums Output Rearrange nums in-place Wiggle rule nums[0] < nums[1] > nums[2]...

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LeetCode 350: Intersection of Two Arrays II

Problem Restatement We are given two integer arrays, nums1 and nums2 . Return their intersection. Unlike LeetCode 349, duplicates matter here. Each element in the result must appear as many times as it appears in both arrays. More precisely, if a value appears a times in nums1 and b times in nums2 , it should appear: min(a, b) times in the answer. The result may be returned in any order....

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LeetCode 349: Intersection of Two Arrays

Problem Restatement We are given two integer arrays, nums1 and nums2 . Return an array containing the intersection of the two arrays. The intersection means the values that appear in both arrays. Each value in the result must be unique, and the result can be returned in any order. The constraints allow values from 0 to 1000 , but a hash set solution works for general integers too. Input and...

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LeetCode 368: Largest Divisible Subset

Problem Restatement We are given a set of distinct positive integers nums . Return the largest subset answer such that for every pair of numbers in answer , one number divides the other. For any pair: answer[i], answer[j] at least one of these must be true: answer[i] % answer[j] == 0 or: answer[j] % answer[i] == 0 If there are multiple valid largest subsets, return any one of them. The...

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LeetCode 296: Best Meeting Point

Problem Restatement We are given a 2D grid containing only 0 and 1 . Each 1 marks the home of one person. A group of people wants to meet at one grid cell while minimizing the total travel distance. Distance is measured by Manhattan distance: distance = abs(r1 - r2) + abs(c1 - c2) We need to return the minimum possible total distance. The source statement says there are two...

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LeetCode 414: Third Maximum Number

Problem Restatement We are given an integer array nums . Return the third distinct maximum number in the array. If the array does not contain three distinct numbers, return the maximum number. Duplicates do not count as separate maximums. The problem statement says to return the third distinct maximum number, or the maximum number if the third maximum does not exist. The constraints include 1 <= nums.length <= 10^4 and...

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LeetCode 274: H-Index

Problem Restatement We are given an integer array citations . Each value: citations[i] is the number of citations received by the researcher's i th paper. Return the researcher's h-index. The h-index is the maximum value h such that the researcher has at least h papers with at least h citations each. The constraints are 1 <= citations.length <= 5000 and 0 <= citations[i] <= 1000 . The official examples include...

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LeetCode 217: Contains Duplicate

Problem Restatement We are given an integer array nums . We need to determine whether any value appears at least twice. Return: Return value Meaning True Some value appears more than once False Every value is distinct The official statement asks us to return true if any value appears at least twice in the array, and false if every element is distinct. Input and Output Item Meaning Input Integer array...

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LeetCode 75: Sort Colors

Problem Restatement We are given an array nums containing only three possible values: 0 1 2 These represent three colors: Value Color 0 Red 1 White 2 Blue We need to sort the array in place so that all 0 s come first, then all 1 s, then all 2 s. We cannot use the library sort function. The official constraints are 1 <= nums.length <= 300 , and every...

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LeetCode 147: Insertion Sort List

Problem Restatement We are given the head of a singly linked list. Sort the list using insertion sort and return the new head. Insertion sort builds a sorted output list one node at a time. At each step, it removes one node from the input, finds where it belongs in the sorted part, and inserts it there. LeetCode gives examples such as [4,2,1,3] -> [1,2,3,4] and [-1,5,3,4,0] -> [-1,0,3,4,5] ....

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LeetCode 169: Majority Element

Problem Restatement We are given an integer array nums of size n . We need to return the majority element. The majority element is the value that appears more than: n // 2 times. The problem guarantees that a majority element always exists. LeetCode also asks whether we can solve it in linear time and constant extra space. Input and Output Item Meaning Input Integer array nums Output The majority...

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LeetCode 88: Merge Sorted Array

Problem Restatement We are given two integer arrays: nums1 nums2 Both arrays are sorted in non-decreasing order. We are also given two integers: m n The first m elements of nums1 are valid sorted elements. The array nums2 contains n valid sorted elements. The total length of nums1 is m + n , so it has enough space to hold all elements from both arrays. We need to merge nums2...

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LeetCode 40: Combination Sum II

Problem Restatement We are given an array candidates and an integer target . We need to return all unique combinations where the chosen numbers sum to target . Each number in candidates may be used at most once. The input may contain duplicate values, but the answer must not contain duplicate combinations. The result may be returned in any order. The constraints are 1 <= candidates.length <= 100 , 1...

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LeetCode 164: Maximum Gap

Problem Restatement We are given an integer array nums . We need to imagine the array sorted in ascending order, then return the maximum difference between two successive elements. If the array has fewer than two elements, return 0 . The problem also requires an algorithm that runs in linear time and uses linear extra space. LeetCode states the constraints as 1 <= nums.length <= 10^5 and 0 <= nums[i]...

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LeetCode 462: Minimum Moves to Equal Array Elements II

Problem Restatement We are given an integer array nums . In one move, we can either increment or decrement one element by 1 . We need to return the minimum number of moves required to make all array elements equal. The official statement defines the move as incrementing or decrementing one array element by 1 . For example: nums = [1, 2, 3] We can make all values equal to...

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LeetCode 360: Sort Transformed Array

Problem Restatement We are given a sorted integer array nums and three integers a , b , and c . For every number x in nums , apply this function: f(x) = a * x * x + b * x + c Return all transformed values in sorted order. The input array is already sorted in ascending order. The follow-up asks for an O(n) solution, rather than transforming everything...

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LeetCode 436: Find Right Interval

Problem Restatement We are given a list of intervals. Each interval is: [start, end] For each interval i , we need to find another interval j such that: intervals[j][0] >= intervals[i][1] In words, interval j must start at or after interval i ends. Among all valid intervals, we need the one with the smallest start point. Return the original index of that interval. If no such interval exists, return -1...

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LeetCode 435: Non-overlapping Intervals

Problem Restatement We are given an array of intervals. Each interval has a start and an end: [start, end] We need to remove the minimum number of intervals so that the remaining intervals do not overlap. Two intervals that only touch at an endpoint do not overlap. For example: [1, 2] [2, 3] These can both remain, because the first interval ends exactly when the second interval starts. The official...

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LeetCode 259: 3Sum Smaller

Problem Restatement We are given: An integer array nums An integer target We need to count how many index triplets satisfy: i < j < k and: $$ nums[i] + nums[j] + nums[k] < target $$ Return the number of such triplets. The constraints are 0 <= nums.length <= 350 , -100 <= nums[i] <= 100 , and -100 <= target <= 100 . Input and Output Item Meaning Input...

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LeetCode 280: Wiggle Sort

Problem Restatement We are given an unsorted integer array nums . We need to reorder it in-place so that it follows this pattern: nums[0] <= nums[1] >= nums[2] <= nums[3] >= nums[4] ... So the values should alternate between low and high. The problem asks us to modify nums directly and return nothing. The input is guaranteed to have at least one valid answer. Input and Output Item Meaning Input...

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LeetCode 406: Queue Reconstruction by Height

Problem Restatement We are given a list of people. Each person is represented as: [h, k] where: Value Meaning h Person height k Number of people in front of this person whose height is greater than or equal to h We must reconstruct the original queue. Return the queue in any valid order. Input and Output Item Meaning Input A list of pairs [h, k] Output The reconstructed queue Height...

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LeetCode 56: Merge Intervals

Problem Restatement We are given an array of intervals. Each interval has a start and an end: [start, end] We need to merge all overlapping intervals and return a list of non-overlapping intervals that covers the same ranges as the original input. Two intervals overlap when the next interval starts before or exactly when the current interval ends. For example: [1, 4] and [4, 5] These overlap because they touch...

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LeetCode 18: 4Sum

Problem Restatement We are given an integer array nums and an integer target . We need to return all unique quadruplets: [nums[a], nums[b], nums[c], nums[d]] such that: 0 <= a, b, c, d < n the four indices are distinct, and: nums[a] + nums[b] + nums[c] + nums[d] == target The answer may be returned in any order, but duplicate quadruplets must not appear. The constraints are 1 <= nums.length...

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LeetCode 455: Assign Cookies

Problem Restatement We are given two arrays: g s The array g stores the greed factor of each child. The array s stores the size of each cookie. A child i is content if we give them one cookie j such that: s[j] >= g[i] Each child can get at most one cookie. Each cookie can be used at most once. We need to return the maximum number of content...

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LeetCode 354: Russian Doll Envelopes

Problem Restatement We are given a list of envelopes. Each envelope has: [width, height] One envelope can fit inside another only if both dimensions are strictly smaller. That means: w1 < w2 and h1 < h2 We want the maximum number of envelopes we can nest inside each other. This is called the Russian doll property. We may reorder the envelopes in any way. Input and Output Item Meaning Input...

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LeetCode 16: 3Sum Closest

Problem Restatement We are given an integer array nums and an integer target . We need to choose three integers from nums such that their sum is as close as possible to target . Return the sum of those three integers. The problem guarantees that each input has exactly one solution. The constraints are 3 <= nums.length <= 500 , -1000 <= nums[i] <= 1000 , and -10^4 <= target...

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LeetCode 179: Largest Number

Problem Restatement We are given a list of non-negative integers nums . We need to arrange the numbers so that, when they are joined together, they form the largest possible number. The answer may be very large, so we return it as a string instead of an integer. The official problem states this same requirement: arrange non-negative integers to form the largest number and return it as a string. Input...

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LeetCode 15: 3Sum

Problem Restatement We are given an integer array nums . We need to return all unique triplets: [nums[i], nums[j], nums[k]] such that: i != j i != k j != k and: nums[i] + nums[j] + nums[k] == 0 The solution set must not contain duplicate triplets. The order of the output and the order of values inside each triplet do not matter. The constraints are 3 <= nums.length <=...

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LeetCode 253: Meeting Rooms II

Problem Restatement We are given a list of meeting intervals. Each interval is: [start, end] A meeting room can host only one meeting at a time. We need to determine the minimum number of meeting rooms required so that all meetings can happen without overlap. Input and Output Item Meaning Input A list of meeting intervals Output Minimum number of rooms required Interval [start, end] Goal Schedule all meetings without...

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LeetCode 452: Minimum Number of Arrows to Burst Balloons

Problem Restatement We are given a list of balloons. Each balloon is represented by an interval: [xstart, xend] This means the balloon covers every horizontal position from xstart to xend , inclusive. An arrow is shot vertically upward from some x-coordinate x . The arrow bursts a balloon if: xstart <= x <= xend One arrow can burst many balloons if their intervals all contain the same x-coordinate. We need...

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LeetCode 252: Meeting Rooms

Problem Restatement We are given a list of meeting time intervals. Each interval contains: [start, end] A person can attend all meetings only if none of the meetings overlap. We need to return: True if all meetings can be attended False if at least two meetings overlap Two meetings overlap when one meeting starts before another meeting finishes. Input and Output Item Meaning Input A list of meeting intervals Output...

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LeetCode 451: Sort Characters By Frequency

Problem Restatement We are given a string s . We need to rearrange its characters so that characters with higher frequency appear before characters with lower frequency. The frequency of a character means how many times it appears in the string. If two characters have the same frequency, their relative order does not matter. Any valid order is accepted. For example: s = "tree" The character frequencies are: Character Frequency...

Wiki › Algorithms › 01. Searching and Sorting ›

11. Parallel, Distributed, and GPU Sorting

11. Parallel, distributed, and GPU sorting, 25 index slug name 311 parallel-merge-sort Parallel Merge Sort 312 parallel-quicksort Parallel Quicksort 313 parallel-sample-sort Parallel Sample Sort 314 parallel-radix-sort Parallel Radix Sort 315 parallel-bitonic-sort Parallel Bitonic Sort 316 parallel-odd-even-sort Parallel Odd Even Sort 317 parallel-counting-sort Parallel Counting Sort 318 gpu-bitonic-sort GPU Bitonic Sort 319 gpu-radix-sort GPU Radix Sort 320 gpu-merge-sort GPU Merge Sort 321 gpu-sample-sort GPU Sample Sort 322 cuda-warp-sort CUDA Warp Sort...

Wiki › Algorithms › 01. Searching and Sorting ›

7. Divide and Conquer Sorting

7. Divide and conquer sorting, 35 index slug name 181 merge-sort Merge Sort 182 top-down-merge-sort Top Down Merge Sort 183 bottom-up-merge-sort Bottom Up Merge Sort 184 natural-merge-sort Natural Merge Sort 185 in-place-merge-sort In Place Merge Sort 186 block-merge-sort Block Merge Sort 187 timsort Timsort 188 powersort Powersort 189 quicksort Quicksort 190 randomized-quicksort Randomized Quicksort 191 three-way-quicksort Three Way Quicksort 192 dual-pivot-quicksort Dual Pivot Quicksort 193 introsort Introsort 194 pdqsort Pattern...

Wiki › Algorithms › 01. Searching and Sorting ›

6. Elementary Sorting

6. Elementary sorting, 30 index slug name 151 bubble-sort Bubble Sort 152 optimized-bubble-sort Optimized Bubble Sort 153 cocktail-shaker-sort Cocktail Shaker Sort 154 odd-even-sort Odd Even Sort 155 gnome-sort Gnome Sort 156 selection-sort Selection Sort 157 stable-selection-sort Stable Selection Sort 158 double-selection-sort Double Selection Sort 159 insertion-sort Insertion Sort 160 binary-insertion-sort Binary Insertion Sort 161 shell-sort Shell Sort 162 shell-sort-shell-gaps Shell Sort with Shell Gaps 163 shell-sort-hibbard-gaps Shell Sort with Hibbard...

Wiki › Algorithms › 01. Searching and Sorting ›

9. Partial, Online, and Adaptive Sorting

9. Partial, online, and adaptive sorting, 30 index slug name 256 partial-sort Partial Sort 257 top-k-sort Top K Sort 258 incremental-sort Incremental Sort 259 online-insertion-sort Online Insertion Sort 260 adaptive-merge-sort Adaptive Merge Sort 261 natural-runs-sort Natural Runs Sort 262 patience-sorting-lis Patience Sorting for LIS 263 replacement-selection Replacement Selection 264 nearly-sorted-insertion-sort Nearly Sorted Insertion Sort 265 k-sorted-array-sort K Sorted Array Sort 266 min-heap-k-sorted-sort Min Heap K Sorted Sort 267 timsort-run-detection Timsort...

Wiki › Algorithms ›

01. Searching and Sorting

Searching and Sorting This 350 page list is usable as the final page inventory for Searching and Sorting . Total check: category count range Linear and sequential search 20 1-20 Binary search and ordered search 35 21-55 Hashing and table search 25 56-80 Tree and indexed search 35 81-115 Selection and order statistics 35 116-150 Elementary sorting 30 151-180 Divide and conquer sorting 35 181-215 Integer and distribution sorting 40...

Wiki › Algorithms › 01. Searching and Sorting ›

8. Integer and Distribution Sorting

8. Integer and distribution sorting, 40 index slug name 216 counting-sort Counting Sort 217 stable-counting-sort Stable Counting Sort 218 key-indexed-counting Key Indexed Counting 219 radix-sort Radix Sort 220 lsd-radix-sort LSD Radix Sort 221 msd-radix-sort MSD Radix Sort 222 american-flag-sort American Flag Sort 223 in-place-radix-sort In Place Radix Sort 224 binary-radix-sort Binary Radix Sort 225 burstsort Burstsort 226 bucket-sort Bucket Sort 227 uniform-bucket-sort Uniform Bucket Sort 228 histogram-sort Histogram Sort 229...

Wiki › Algorithms › 01. Searching and Sorting ›

10. External Memory, Cache, and Database Sorting

10. External memory, cache, and database sorting, 25 index slug name 286 external-merge-sort External Merge Sort 287 two-phase-multiway-merge-sort Two Phase Multiway Merge Sort 288 polyphase-merge-sort Polyphase Merge Sort 289 balanced-k-way-merge-sort Balanced K Way Merge Sort 290 cascade-merge-sort Cascade Merge Sort 291 distribution-sweeping-sort Distribution Sweeping Sort 292 cache-aware-sorting Cache Aware Sorting 293 cache-oblivious-sorting Cache Oblivious Sorting 294 funnel-sort Funnel Sort 295 buffer-tree-sort Buffer Tree Sort 296 b-tree-bulk-load-sort B Tree Bulk Load...

Programming › Algorithm Cookbook › Chapter 6. Sorting ›

6.23 Testing Sort Correctness

6.23 Testing Sort Correctness Sorting implementations are easy to get almost right and hard to get completely correct. Subtle bugs often appear only on edge cases, duplicate-heavy inputs, or adversarial patterns. A disciplined testing strategy verifies both the ordering and permutation properties under a wide range of inputs. Problem You have implemented a sorting algorithm. You want to verify that it is correct, stable when required, and robust across inputs....

Programming › Algorithm Cookbook › Chapter 6. Sorting ›

6.22 Parallel Sorting

6.22 Parallel Sorting Parallel sorting distributes work across multiple processing units. The goal is to reduce wall-clock time while preserving correctness and scalability. The cost model includes total work, parallel time (span), communication, and synchronization. Problem You have an array A[0..n-1] and p processors. You want to sort faster than a single-threaded algorithm by exploiting parallelism. Models Two common models guide design: Shared-memory model: threads access a common address space...

Programming › Algorithm Cookbook › Chapter 6. Sorting ›

6.25 Choosing the Right Sort

6.25 Choosing the Right Sort There is no single best sorting algorithm. The correct choice depends on input size, data characteristics, memory constraints, and required guarantees such as stability or worst-case bounds. Problem You need to select a sorting algorithm for a specific workload. The goal is to balance performance, memory usage, stability, and implementation complexity. Decision Factors Key dimensions that determine the choice: input size n data distribution key...

Programming › Algorithm Cookbook › Chapter 6. Sorting ›

6.21 Lower Bounds for Sorting

6.21 Lower Bounds for Sorting Lower bounds describe what no algorithm can beat under a given model. For sorting, the standard model is comparison-based sorting, where the algorithm learns order only by comparing elements. In this model, any algorithm must use at least on the order of ( n \log n ) comparisons in the worst case. Problem You want to understand the inherent cost of sorting and why many...

Programming › Algorithm Cookbook › Chapter 6. Sorting ›

6.20 Inversion Counting

6.20 Inversion Counting An inversion is a pair of positions that appears in the opposite order from the final sorted order. Inversion counting measures how far an array is from being sorted. It is useful for ranking distance, sorting analysis, permutation comparison, and adaptive algorithm design. Problem You have an array A[0..n-1] . You want to count the number of pairs (i, j) such that: i < j and A[i]...

Programming › Algorithm Cookbook › Chapter 6. Sorting ›

6.19 Coordinate Compression

6.19 Coordinate Compression Coordinate compression replaces large or sparse keys with small dense ranks. It preserves order while reducing the value range. This makes range-based algorithms, counting arrays, Fenwick trees, segment trees, and bucketed structures practical on data with large numeric keys. Problem You have values such as: [1000000000, -7, 42, 1000000000, 500000] The values are too large or too sparse to use directly as array indices. You want to...

Programming › Algorithm Cookbook › Chapter 6. Sorting ›

6.24 Common Bugs

6.24 Common Bugs Sorting bugs usually come from boundary errors, invalid invariants, or misunderstood comparison rules. Many implementations work on ordinary random inputs but fail on empty arrays, duplicate-heavy arrays, reverse sorted arrays, or arrays with custom records. Problem You have a sorting implementation that appears correct on common inputs. You want to identify the failure patterns that most often break sorting algorithms. Off-by-One Errors Sorting code frequently works with...

Programming › Algorithm Cookbook › Chapter 6. Sorting ›

6.15 External Sorting

6.15 External Sorting External sorting handles datasets that do not fit in main memory. The cost model changes from CPU time to I O. The goal is to minimize disk reads and writes by organizing the algorithm around sequential access and large transfers. Problem You have a dataset too large to fit into memory. You want to sort it using limited RAM and disk storage. Model Assume: N = number...

Programming › Algorithm Cookbook › Chapter 6. Sorting ›

6.18 Sorting Records

6.18 Sorting Records Sorting records means sorting structured values by one or more fields. The record itself usually contains more information than the key used for ordering. The sorting algorithm must move the whole record while comparing only the selected fields. Problem You have records such as: (name, department, salary, hired_at) You want to sort them by a rule such as: department ascending salary descending hired_at ascending Solution Define a...

Programming › Algorithm Cookbook › Chapter 6. Sorting ›

6.11 Partial Sorting

6.11 Partial Sorting Partial sorting orders only the part of the array that the caller needs. Instead of fully sorting all n elements, the algorithm produces the smallest k elements in sorted order, or arranges the array so that the first k elements are the desired subset. This is useful when a full order is wasteful. Search results, leaderboards, nearest-neighbor candidates, and reporting queries often need only the top few...

Programming › Algorithm Cookbook › Chapter 6. Sorting ›

6.16 Nearly Sorted Data

6.16 Nearly Sorted Data Nearly sorted inputs appear frequently in practice. Logs appended over time, incremental updates, and cached results often differ only slightly from sorted order. Algorithms that exploit this structure can run in linear or near-linear time. Problem You have an array A[0..n-1] that is close to sorted. You want to sort it faster than general-purpose O(n log n) algorithms. Measuring “Nearly Sorted” Several measures capture how far...

Programming › Algorithm Cookbook › Chapter 6. Sorting ›

6.17 Custom Comparators

6.17 Custom Comparators Sorting depends on a comparison relation. A custom comparator defines that relation for user-defined types and nontrivial ordering rules. The correctness of a sort relies on the comparator being consistent. When the comparator is inconsistent, the algorithm may produce incorrect output or fail to terminate. Problem You have elements that are not naturally ordered, or you need an order different from the default. You want to sort...

Programming › Algorithm Cookbook › Chapter 6. Sorting ›

6.14 Median Selection

6.14 Median Selection Median selection finds the middle value of a collection without fully sorting it. A full sort gives the median, but it also computes much more order information than the median requires. Selection algorithms avoid that extra work. Problem You have an array A[0..n-1] . You want the median value, or one of the median values, using less work than sorting the whole array. Median Definitions For an...

Programming › Algorithm Cookbook › Chapter 6. Sorting ›

6.12 Top k Selection

6.12 Top k Selection Top k selection finds the largest or smallest k elements without necessarily sorting the entire input. It is closely related to partial sorting, but the emphasis is selection rather than presentation. The caller may only need the set of best candidates, not their complete internal order. Problem You have an array A[0..n-1] and an integer k . You want the largest k elements, or the smallest...

Programming › Algorithm Cookbook › Chapter 6. Sorting ›

6.13 Quickselect

6.13 Quickselect Quickselect finds the element that would appear at a given index if the array were sorted. It uses the same partitioning idea as quick sort, but it recurses into only one side. This makes it useful for medians, percentiles, and top k boundaries. Problem You have an array A[0..n-1] and an index k . You want the element with rank k , using zero-based indexing, without fully sorting...

Programming › Algorithm Cookbook › Chapter 6. Sorting ›

6.8 Radix Sort

6.8 Radix Sort Radix sort sorts keys one digit at a time. It avoids direct comparisons between full keys by repeatedly applying a stable sort to smaller key components. For integers, those components are usually digits in base 10 , base 256 , or another fixed radix. Problem You have an array of nonnegative integers. You want to sort them in linear time relative to the number of elements and...

Programming › Algorithm Cookbook › Chapter 6. Sorting ›

6.5 Quick Sort

6.5 Quick Sort Quick sort is a divide and conquer sorting algorithm based on partitioning. It chooses a pivot, rearranges the array so that smaller elements go to one side and larger elements go to the other side, and then recursively sorts the two partitions. Unlike merge sort, quick sort does most of its work before the recursive calls. Problem You have an array A[0..n-1] . You want an in-place...

Programming › Algorithm Cookbook › Chapter 6. Sorting ›

6.9 Bucket Sort

6.9 Bucket Sort Bucket sort distributes elements into groups, sorts each group, and then concatenates the results. It relies on an assumption about the input distribution. When elements are spread roughly uniformly over a known range, bucket sort can run in linear time. Problem You have an array A[0..n-1] of real numbers in a known interval, typically [0, 1) . You want a sorting algorithm that exploits this range and...

Programming › Algorithm Cookbook › Chapter 6. Sorting ›

6.10 Stable Sorting

6.10 Stable Sorting A sorting algorithm is stable when equal keys keep their original relative order. Stability is not part of the basic sorting contract, because an unstable output may still be ordered and may still be a permutation of the input. Stability is an additional semantic guarantee about records, identities, and secondary fields. Problem You have records with keys, and two records may have equal keys but different attached...

Programming › Algorithm Cookbook › Chapter 6. Sorting ›

6.4 Merge Sort

6.4 Merge Sort Merge sort is the standard example of divide and conquer sorting. It divides the input into two smaller arrays, sorts each half, and then merges the two sorted halves into one sorted output. The central operation is not the division step. It is the merge step, because merging is where the algorithm combines local order into global order. Problem You have an array A[0..n-1] . You want...

Programming › Algorithm Cookbook › Chapter 6. Sorting ›

6.3 Insertion Sort

6.3 Insertion Sort Insertion sort builds a sorted prefix one element at a time. At step i , the prefix A[0..i-1] is already sorted, and the algorithm inserts A[i] into its correct position inside that prefix. This is the same operation used when sorting cards by hand: keep the left side ordered, take the next card, and slide it left until it belongs. Problem You have an array A[0..n-1] ....

Programming › Algorithm Cookbook › Chapter 6. Sorting ›

6.7 Counting Sort

6.7 Counting Sort Counting sort replaces comparisons with counting. It assumes keys come from a small integer range and uses that structure to achieve linear time. Instead of ordering elements directly, it counts how many times each key appears and reconstructs the sorted output from those counts. Problem You have an array A[0..n-1] where each element is an integer in a known range [0, k] . You want a stable...

Programming › Algorithm Cookbook › Chapter 6. Sorting ›

6.6 Heap Sort

6.6 Heap Sort Heap sort derives order from a heap structure. It first builds a max-heap from the input array, then repeatedly extracts the maximum element and places it at the end of the array. The array itself stores the heap, so the algorithm runs in place. Problem You have an array A[0..n-1] . You want a sorting algorithm with guaranteed $O(n \log n)$ time, constant extra space, and no...

Programming › Algorithm Cookbook › Chapter 6. Sorting ›

6.1 Sorting Contracts

6.1 Sorting Contracts Sorting begins with a contract. An algorithm is correct only if it satisfies two conditions: the output is ordered, and the output is a permutation of the input. Every implementation detail, optimization, and variation must preserve these two properties. Problem You are given a sequence A and a comparison relation ≤ . You need a procedure that returns a sequence B such that B is ordered under...

Programming › Algorithm Cookbook › Chapter 6. Sorting ›

6.2 Selection Sort

6.2 Selection Sort Selection sort is the simplest sorting algorithm built around a clear global choice. At each step, it finds the smallest element in the unsorted suffix and moves that element into the next output position. The sorted prefix grows by one element per pass. Problem You have an array A[0..n-1] . You want to sort it in nondecreasing order using only constant extra memory and a small number...

Programming › Algorithm Cookbook ›

Chapter 6. Sorting

Chapter 6. Sorting Sorting is treated here as a family of transformations with precise contracts, rather than as isolated algorithms. The input is a sequence together with a comparison relation. The output is a permutation of that sequence arranged so that the relation holds between consecutive elements. Two properties dominate every design: correctness of ordering and preservation of data through permutation. The chapter begins by fixing the contract. A sorting...

Programming › Algorithm Cookbook › Chapter 3. Linked Lists and Pointers ›

3.7 Merge Two Sorted Lists

Merging combines two sorted singly linked lists into one sorted list by relinking nodes. The operation does not create new nodes. It reuses existing nodes and preserves their order. Problem Given two lists l1 and l2 , both sorted in non-decreasing order, produce a single sorted list. l1: a1 -> a2 -> ... l2: b1 -> b2 -> ... Return a list that contains all nodes from both inputs, ordered....

Wiki › Algorithms › 01. Searching and Sorting › 8. Integer and Distribution Sorting ›

Integer Sample Sort

Integer Sample Sort Integer sample sort is a specialization of sample sort for integer keys. It selects sample elements to estimate the distribution, chooses splitters, and partitions the array into buckets. Each bucket is then sorted recursively or with a suitable subroutine. Because keys are integers, classification can use arithmetic or bit operations, and buckets can be balanced more precisely than in general comparison sorting. Problem Given an array $A$...

Wiki › Algorithms › 01. Searching and Sorting › 8. Integer and Distribution Sorting ›

In Place Radix Sort

In Place Radix Sort In place radix sort sorts keys by digits while avoiding a full auxiliary output array. It keeps only small bucket metadata, such as counts, offsets, and next write positions. The common form is MSD based. At each digit position, the algorithm partitions the current subarray into digit buckets, then recursively sorts each bucket by the next digit. Problem Given an array $A$ of keys whose digits...

Wiki › Algorithms › 01. Searching and Sorting › 6. Elementary Sorting ›

Double Selection Sort

Double Selection Sort Double selection sort improves selection sort by selecting both the minimum and maximum elements in each pass. It places the minimum at the beginning and the maximum at the end, reducing the number of passes by roughly half. Problem Given a sequence $A$ of length $n$, reorder it such that $$ A[0] \le A[1] \le \cdots \le A[n-1] $$ Algorithm Maintain two boundaries, left and right. In...

Wiki › Algorithms › 01. Searching and Sorting › 6. Elementary Sorting ›

Patience Sort

Patience Sort Patience sort builds a set of piles using rules similar to the patience card game. Each element is placed on the leftmost pile whose top element is greater than or equal to it. After all elements are distributed into piles, the piles are merged to produce a sorted sequence. This algorithm is closely related to the longest increasing subsequence problem. Problem Given a sequence $A$ of length $n$,...

Wiki › Algorithms › 01. Searching and Sorting › 10. External Memory, Cache, and Database Sorting ›

Distribution Sweeping Sort

Distribution Sweeping Sort Distribution sweeping sort is an external-memory sorting method based on partitioning. Instead of repeatedly merging sorted runs, it divides the input into key ranges, places each element into the correct range, sorts each range separately, and then concatenates the sorted ranges. The method is useful when range partitioning can be done efficiently and each partition can later be sorted with bounded memory. Problem Given a dataset too...

Wiki › Algorithms › 01. Searching and Sorting › 9. Partial, Online, and Adaptive Sorting ›

Galloping Merge

Galloping Merge Galloping merge is an optimized merge procedure used in adaptive merge sorts such as Timsort. It starts like ordinary merging, but when one run wins many comparisons in a row, it switches to exponential search to copy a larger block at once. You use it when merging two sorted runs where one run often contains a long streak of smaller elements. Problem Given two sorted runs ( L...

Wiki › Algorithms › 01. Searching and Sorting › 11. Parallel, Distributed, and GPU Sorting ›

Bitonic Sorting Network

Bitonic Sorting Network A bitonic sorting network is a fixed sequence of compare and exchange operations that sorts a fixed number of elements. It is based on the idea of repeatedly building bitonic sequences and merging them. A bitonic sequence increases and then decreases, or can be rotated into that shape. The network first creates bitonic sequences of small size, then merges them into larger sorted sequences until the full...

Wiki › Algorithms › 01. Searching and Sorting › 6. Elementary Sorting ›

Optimized Bubble Sort

Optimized Bubble Sort Optimized bubble sort improves the basic version by stopping early when the array becomes sorted. During a pass, if no swaps occur, the algorithm concludes that the sequence is already ordered and terminates. This reduces unnecessary passes, especially for nearly sorted inputs. Problem Given a sequence $A$ of length $n$, reorder it such that $$ A[0] \le A[1] \le \cdots \le A[n-1] $$ Algorithm Track whether any...

Wiki › Algorithms › 01. Searching and Sorting › 9. Partial, Online, and Adaptive Sorting ›

Lazy Selection Sort

Lazy Selection Sort Lazy selection sort produces sorted output incrementally. Instead of sorting the entire array, it finds the next smallest element only when requested. You use it when you need a few smallest elements or when output is consumed step by step. Problem Given an array ( A ), support an operation: next() that returns the next smallest element without sorting the entire array in advance. Idea Keep track...

Wiki › Algorithms › 01. Searching and Sorting › 7. Divide and Conquer Sorting ›

Hoare Partition Quicksort

Hoare Partition Quicksort Hoare partition quicksort uses the original two pointer partition scheme introduced by Tony Hoare. It scans from both ends of the range, swaps misplaced elements, and returns a split point. Compared with Lomuto partition, Hoare partition usually performs fewer swaps and handles many inputs more efficiently. Its return value is a boundary, not necessarily the final position of the pivot. Problem Given an array $A$ of length...

Wiki › Algorithms › 01. Searching and Sorting › 8. Integer and Distribution Sorting ›

LSD Radix Sort

LSD Radix Sort LSD radix sort sorts keys by scanning digit positions from right to left, starting with the least significant digit. Each pass uses a stable sorting method on one digit position. The usual inner method is stable counting sort. Stability is essential because later passes must preserve the order already established by earlier, less significant digits. Problem Given $n$ keys of fixed width $m$, where each digit is...

Wiki › Algorithms › 01. Searching and Sorting › 7. Divide and Conquer Sorting ›

Weak Heapsort

Weak Heapsort Weak heapsort is a heapsort variant that uses a weak heap instead of an ordinary binary heap. A weak heap stores elements in an implicit array and uses one extra reverse bit per node to define a modified tree structure. The main advantage is comparison efficiency. Weak heapsort can use fewer comparisons than standard binary heapsort while still sorting in place. Problem Given an array $A$ of length...

Wiki › Algorithms › 01. Searching and Sorting › 11. Parallel, Distributed, and GPU Sorting ›

Parallel Bitonic Sort

Parallel Bitonic Sort Parallel bitonic sort is a sorting network based algorithm. It sorts by repeatedly forming bitonic sequences and then merging them into sorted order. A bitonic sequence first increases and then decreases, or can be rotated into that shape. The algorithm works especially well on parallel hardware because the compare and exchange pattern is regular and independent of the input values. Problem Given an array $A$ of size...

Wiki › Algorithms › 01. Searching and Sorting › 6. Elementary Sorting ›

Shell Sort with Hibbard Gaps

Shell Sort with Hibbard Gaps Shell sort with Hibbard gaps replaces the simple halving sequence with a more structured progression: $$ g_k = 2^k - 1 $$ This sequence produces gaps such as: $$ 1, 3, 7, 15, 31, \dots $$ In practice, you use the largest value less than $n$, then proceed in decreasing order down to 1. This improves performance over the basic Shell gap sequence by reducing...

Wiki › Algorithms › 01. Searching and Sorting › 11. Parallel, Distributed, and GPU Sorting ›

Parallel Counting Sort

Parallel Counting Sort Parallel counting sort extends counting sort by distributing counting and placement across multiple workers. It assumes keys are integers within a bounded range. Instead of comparing elements, it counts occurrences and reconstructs the sorted output. The algorithm consists of three main stages: local counting, prefix sum computation, and parallel scatter. Problem Given an array $A$ of size $n$ with integer keys in range $[0, k)$, produce a...

Wiki › Algorithms › 01. Searching and Sorting › 4. Tree and Indexed Search ›

SA-IS Suffix Array

SA-IS Suffix Array Construction SA-IS constructs a suffix array in linear time by classifying characters and recursively sorting a reduced problem of LMS substrings. It is one of the most efficient practical algorithms for suffix array construction. Problem Given a string $T$ of length $n$, construct its suffix array: $$ SA[0 \dots n-1] $$ such that suffixes of $T$ are in lexicographic order. Key Idea Each position in the string...

Wiki › Algorithms › 01. Searching and Sorting › 6. Elementary Sorting ›

Smoothsort

Smoothsort Smoothsort is an adaptive comparison-based sorting algorithm designed by Edsger Dijkstra. It is related to heapsort, but it uses a forest of Leonardo heaps instead of one binary heap. The main advantage is adaptivity. Smoothsort runs in linear time on already sorted or nearly sorted data, while preserving the same worst-case bound as heapsort. Problem Given a sequence $A$ of length $n$, reorder it such that $$ A[0] \le...

Wiki › Algorithms › 01. Searching and Sorting › 8. Integer and Distribution Sorting ›

Uniform Bucket Sort

Uniform Bucket Sort Uniform bucket sort is a specialization of bucket sort where elements are assumed to be uniformly distributed over a known interval. Buckets are defined with equal width, and a direct arithmetic mapping assigns each element to a bucket. The design goal is to keep bucket sizes balanced so that each bucket remains small and can be sorted quickly. Problem Given an array $A$ of $n$ values drawn...

Wiki › Algorithms › 01. Searching and Sorting › 11. Parallel, Distributed, and GPU Sorting ›

GPU Sample Sort

GPU Sample Sort GPU sample sort partitions the input into buckets using sampled splitters, then sorts each bucket independently on the GPU. It is a distribution based algorithm similar to parallel sample sort, adapted to GPU execution with attention to memory coalescing and load balancing. This method scales well for large inputs because most work after partitioning becomes independent across buckets. Problem Given an array $A$ of size $n$ on...

Wiki › Algorithms › 01. Searching and Sorting › 6. Elementary Sorting ›

Bingo Sort

Bingo Sort Bingo sort is a selection-style sorting algorithm that handles duplicate values efficiently. Instead of selecting one minimum value per pass, it selects the current minimum value and moves all of its occurrences into the sorted prefix. This makes it useful for inputs with many repeated values. Problem Given a sequence $A$ of length $n$, reorder it such that $$ A[0] \le A[1] \le \cdots \le A[n-1] $$ Key...

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Timsort Run Detection

Timsort Run Detection Timsort run detection is the first phase of Timsort. It scans the array, detects natural runs, and normalizes them into a form suitable for efficient merging. You use it as part of adaptive sorting where exploiting existing order matters. Problem Given an array ( A ), partition it into runs such that: each run is monotonic (non-decreasing or strictly decreasing) runs satisfy a minimum length constraint Idea...

Wiki › Algorithms › 01. Searching and Sorting › 9. Partial, Online, and Adaptive Sorting ›

Min Heap K Sorted Sort

Min Heap K Sorted Sort Min heap k sorted sort is the canonical heap based method for sorting a k sorted array. It maintains a sliding window of size ( k + 1 ) in a min heap and repeatedly extracts the next smallest element. This is the standard optimal solution for k sorted input. Problem Given an array ( A ) where each element is at most ( k...

Wiki › Algorithms › 01. Searching and Sorting › 11. Parallel, Distributed, and GPU Sorting ›

GPU Bitonic Sort

GPU Bitonic Sort GPU bitonic sort is a GPU implementation of bitonic sort. It uses a fixed compare and exchange pattern that fits SIMD style execution well. The algorithm performs more comparisons than quicksort or merge sort, but its memory access and control flow are regular. This makes it useful for small to medium arrays, block local sorting, graphics workloads, and GPU kernels where predictable execution is more important than...

Wiki › Algorithms › 01. Searching and Sorting › 7. Divide and Conquer Sorting ›

Block Quicksort

Block Quicksort Block quicksort is a refinement of quicksort that improves partitioning performance by operating on blocks of elements instead of one element at a time. It reduces branch misprediction and improves cache locality, which are critical for modern CPUs. The algorithm keeps the same divide and conquer structure as quicksort but replaces the standard partition step with a block based approach. Problem Given an array $A$ of length $n$,...

Wiki › Algorithms › 01. Searching and Sorting › 8. Integer and Distribution Sorting ›

Word Radix Sort

Word Radix Sort Word radix sort is a radix sorting method specialized for fixed width machine words such as 32 bit or 64 bit integers. It processes keys a byte or group of bits at a time using fast bit operations. This approach matches hardware representation and is widely used in high performance systems. Problem Given an array $A$ of $n$ fixed width integers, sort the array efficiently. Each key...

Wiki › Algorithms › 01. Searching and Sorting › 9. Partial, Online, and Adaptive Sorting ›

Partial Sort

Partial Sort Partial sort places the smallest ( k ) elements of a sequence into sorted order at the front, while leaving the remaining elements unordered. It avoids the cost of a full sort when only a prefix of sorted data is needed. You use it when you care about top ( k ) elements rather than the entire ordering. Problem Given an array ( A ) of length (...

Wiki › Algorithms › 01. Searching and Sorting › 8. Integer and Distribution Sorting ›

Counting Sort

Counting Sort Counting sort is a non-comparison sorting algorithm for integer keys within a bounded range. It counts how many times each value appears, then reconstructs the sorted order using these counts. It runs in linear time when the key range is not significantly larger than the number of elements. Problem Given an array $A$ of $n$ integers where each value lies in a range $[0, k]$, produce a sorted...

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External Replacement Selection

External Replacement Selection External replacement selection is the disk-oriented version of replacement selection. It generates long sorted runs from data that does not fit in memory, forming the first phase of external merge sort. You use it when sorting large datasets stored on disk. Problem Given a dataset too large to fit into memory and a memory buffer of size ( M ), generate sorted runs on disk such that:...

Wiki › Algorithms › 01. Searching and Sorting › 9. Partial, Online, and Adaptive Sorting ›

Top K Sort

Top K Sort Top K sort finds the ( k ) smallest or largest elements and returns them in sorted order. Unlike full sorting, it avoids ordering the entire dataset. You use it when only the best ( k ) items matter, such as ranking, search results, or recommendation systems. Problem Given an array ( A ) of size ( n ) and integer ( k ), compute: the smallest...

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Suffix Array Radix Sort

Suffix Array Radix Sort Suffix array radix sort is the radix-optimized version of the suffix array doubling method. It still sorts suffixes by rank pairs, but uses counting sort or radix sort instead of comparison sorting. This reduces each doubling round from comparison sorting over pairs to linear sorting over integer ranks. Problem Given a string $S$ of length $n$, construct the suffix array: $$ SA = \text{sorted indices of...

Wiki › Algorithms › 01. Searching and Sorting › 4. Tree and Indexed Search ›

DC3 Suffix Array

Skew Suffix Array Sort (DC3) DC3, also called skew algorithm, builds a suffix array in linear time by splitting suffix positions into residue classes modulo 3 and recursively sorting a subset. It reduces the full suffix ordering problem into a smaller problem, then merges results using rank comparisons. Problem Given a string $T$ of length $n$, construct its suffix array: $$ SA[0 \dots n-1] $$ such that all suffixes are...

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Parallel Sample Sort

Parallel Sample Sort Parallel sample sort is a parallel sorting algorithm based on partitioning by sampled splitters. It first chooses representative keys from the input, uses them to divide the data into buckets, sorts each bucket independently, then concatenates the buckets in order. The method is useful when many processors are available because most work after partitioning is independent. Its quality depends on how well the samples represent the input...

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Parallel Merge Sort

Parallel Merge Sort Parallel merge sort extends merge sort by executing recursive subproblems concurrently. The structure remains divide and conquer, but the recursion tree becomes a parallel computation graph. You split the array into halves, sort each half in parallel, then merge the results. The merge step can also be parallelized using partitioning techniques. Problem Given an array $A$ of size $n$, produce a sorted array in nondecreasing order using...

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Bottom Up Heapsort

Bottom Up Heapsort Bottom up heapsort improves the heapify operation used in heapsort. Instead of repeatedly comparing and swapping down the heap, it first follows a path to a leaf, then moves upward to place the element in its correct position. This reduces the number of comparisons and improves performance while keeping the same asymptotic complexity. Problem Given an array $A$ of length $n$, reorder it such that: $$ A[0]...

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Suffix Array Doubling Sort

Suffix Array Doubling Sort Suffix array doubling sort builds a suffix array by repeatedly sorting suffixes based on prefixes of length (2^k). Each step uses previously computed ranks to compare longer prefixes efficiently. This method avoids direct string comparison and reduces the problem to sorting integer pairs. Problem Given a string (S) of length (n), construct the suffix array: $$ SA = \text{sorted indices of all suffixes of } S...

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DC7 Suffix Array Sort

DC7 Suffix Array Sort DC7 suffix array sort is a linear-time suffix array construction method based on a difference cover modulo 7. It generalizes the DC3 idea by sorting a larger sampled subset of suffixes, then using the resulting ranks to sort and merge the remaining suffixes. The method is mostly of theoretical and specialist interest. DC3 and SA-IS are more common in practice. Problem Given a string $S$ of...

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Dual Pivot Quicksort

Dual Pivot Quicksort Dual pivot quicksort extends quicksort by using two pivots instead of one. It partitions the array into three regions in a single pass: elements less than the first pivot elements between the two pivots elements greater than the second pivot This approach reduces comparisons in practice and improves performance on modern hardware. It is used in standard library implementations such as Java for primitive arrays. Problem Given...

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Bitonic Merge Network

Bitonic Merge Network The bitonic merge network is the core component of bitonic sorting. It takes a bitonic sequence and transforms it into a fully sorted sequence using a fixed pattern of compare and exchange operations. A sequence is bitonic when it consists of an increasing part followed by a decreasing part, or can be rotated into that form. Problem Given a bitonic sequence of length $n$, produce a sorted...

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Parallel Quicksort

Parallel Quicksort Parallel quicksort follows the same partition based divide and conquer structure as quicksort, but executes recursive calls concurrently. The key idea is that once the partition step finishes, the left and right subarrays become independent and can be processed in parallel. Compared to parallel merge sort, this method avoids the cost of merging but introduces challenges in load balancing and pivot quality. Problem Given an array $A$ of...

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Natural Merge Sort

Natural Merge Sort Natural merge sort improves merge sort by exploiting existing order in the input. Instead of splitting blindly, it scans the array to find already sorted runs, then merges those runs. This approach adapts to partially sorted data and can reduce the number of passes. Problem Given an array $A$ of length $n$, reorder it such that: $$ A[0] \le A[1] \le \dots \le A[n-1] $$ Idea A...

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Sample Sort

Sample Sort Sample sort is a generalization of quicksort and bucket sort. It selects a sample of elements, uses them to define partition boundaries, and distributes the data into multiple buckets that are sorted independently. It is widely used in parallel and distributed systems because it produces well balanced partitions. Problem Given an array $A$ of length $n$, reorder it such that: $$ A[0] \le A[1] \le \dots \le A[n-1]...

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Merge Sort

Merge Sort Merge sort is a divide and conquer sorting algorithm. It splits the input into smaller parts, sorts each part recursively, then merges the sorted parts into a single sorted sequence. It guarantees stable ordering and predictable time complexity. It performs well on large datasets and external memory systems. Problem Given an array $A$ of length $n$, reorder it such that: $$ A[0] \le A[1] \le \dots \le A[n-1]...

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Key Indexed Counting

Key Indexed Counting Key indexed counting is a stable linear time sorting method for items with small integer keys. It generalizes counting sort by separating keys from records and placing records directly into their correct index range. This form is widely used in string sorting and radix-based pipelines. Problem Given an array $A$ of records, where each record has a key in range $[0, k)$, reorder the array so that...

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Least Significant Byte Sort

Least Significant Byte Sort Least Significant Byte sort is the byte oriented version of LSD radix sort. It processes fixed width keys one byte at a time, starting from the least significant byte and moving toward the most significant byte. It relies on a stable inner sorting step, usually counting sort with 256 buckets. Problem Given an array $A$ of fixed width integer keys, sort the array in increasing order....

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American Flag Sort

American Flag Sort American flag sort is an in place variant of radix sort. It distributes elements into buckets based on a digit, then permutes them into correct positions using cycle leader permutation. Unlike standard radix sort, it avoids auxiliary arrays. This algorithm is commonly used for large datasets where memory allocation must be minimized. Problem Given an array $A$ of keys with digits in range $[0, b)$, reorder the...

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Cycle Sort

Cycle Sort Cycle sort is a comparison-based sorting algorithm designed to minimize the number of writes. Each element is moved directly to its correct position by following cycles in the permutation defined by the array. This makes it useful in situations where write operations are expensive, such as EEPROM or flash memory. Problem Given a sequence $A$ of length $n$, reorder it such that $$ A[0] \le A[1] \le \cdots...

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Pattern Defeating Quicksort

Pattern Defeating Quicksort Pattern Defeating Quicksort, often called pdqsort, is a modern quicksort variant designed to handle structured and adversarial inputs efficiently. It improves on classical quicksort by detecting patterns that lead to bad partitions and adapting its behavior. It combines fast partitioning, smart pivot selection, and fallback strategies. Problem Given an array $A$ of length $n$, reorder it such that: $$ A[0] \le A[1] \le \dots \le A[n-1] $$...

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Pairwise Sorting Network

Pairwise Sorting Network Pairwise sorting network is a comparison sorting algorithm defined as a fixed network of compare and swap operations. It performs sorting through a sequence of pairwise comparisons arranged in stages. Unlike adaptive algorithms, its structure does not depend on input values. This makes it suitable for parallel execution and hardware implementation. Problem Given an array $A$ of length $n$, reorder it such that: $$ A[0] \le A[1]...

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CUDA Block Sort

CUDA Block Sort CUDA block sort sorts a tile of data using all threads in a block. It extends warp level sorting to larger sizes by using shared memory and synchronization within a thread block. Each block loads a chunk of the array into shared memory, sorts it cooperatively, then writes it back. This is often used as a building block for full GPU sorting algorithms such as merge sort...

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Most Significant Byte Sort

Most Significant Byte Sort Most Significant Byte sort is an MSD radix sort that processes fixed-width keys one byte at a time, starting from the most significant byte. It partitions the array into byte buckets and recursively sorts each bucket using the next byte. It is effective for large datasets and for keys where higher-order bytes quickly distinguish values. Problem Given an array $A$ of $n$ fixed-width keys (such as...

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K Sorted Array Sort

K Sorted Array Sort K sorted array sort handles a nearly sorted array where every element is at most ( k ) positions away from its final sorted position. This stronger assumption allows a heap based method faster than general sorting. You use it when the disorder is locally bounded. Problem Given an array ( A ) of length ( n ), where each element is at most ( k...

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Replacement Selection Run Generation

Replacement Selection Run Generation Replacement selection run generation is the first phase of an external sort. It produces sorted runs from an input stream using a heap. Unlike simple chunk sorting, which creates runs of about memory size, replacement selection often creates runs about twice as large when input order is random. Longer runs reduce the number of later merge passes. Problem Given an input stream too large for memory,...

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Gnome Sort

Gnome Sort Gnome sort is a simple comparison-based sorting algorithm. It scans forward through the array, and when it finds two adjacent elements out of order, it swaps them and steps backward. When elements are in order, it moves forward. The behavior resembles insertion sort, but instead of shifting elements, it repeatedly swaps while moving backward. Problem Given a sequence $A$ of length $n$, reorder it such that $$ A[0]...

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Quicksort

Quicksort Quicksort is a divide and conquer sorting algorithm. It chooses a pivot value, partitions the array so that smaller elements go before the pivot and larger elements go after it, then recursively sorts both sides. It is one of the most important practical sorting algorithms because it is fast in memory, has good cache behavior, and usually needs only logarithmic stack space. Its main weakness is that bad pivot...

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Order Maintenance Sort

Order Maintenance Sort Order maintenance sort maintains a total order of elements under dynamic insertions. Instead of re-sorting, it assigns labels that preserve relative order and supports fast comparisons. You use it when elements are inserted over time and you need to maintain their sorted or logical order efficiently. Problem Maintain a sequence that supports: inserting an element after another element comparing the order of two elements preserving total order...

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Odd Even Merge Sort

Odd Even Merge Sort Odd even merge sort is a comparison sorting algorithm designed as a sorting network. It uses a fixed pattern of compare and swap operations, independent of the input values. It is closely related to bitonic sort but uses a different merging strategy. It is especially useful in parallel hardware and SIMD execution environments. Problem Given an array $A$ of length $n$, reorder it such that: $$...

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Tape Merge Sort

Tape Merge Sort Tape merge sort is an external sorting algorithm designed for sequential storage. It was historically used with magnetic tapes, where random access was expensive or unavailable. The algorithm writes sorted runs to multiple tapes, then repeatedly merges runs from input tapes onto output tapes. The same idea still matters for sequential external storage: make long sequential reads and writes, avoid random seeks, and reduce the number of...

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MSD Radix Sort

MSD Radix Sort MSD radix sort processes digits from most significant to least significant. It partitions the array by the leading digit, then recursively sorts each partition. This approach follows lexicographic order naturally and works well for strings and variable length keys. Problem Given an array $A$ of $n$ keys, each represented as a sequence of digits or characters, sort them lexicographically. A key can be written as: $$ x...

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Funnel Sort

Funnel Sort Funnel sort is a cache oblivious sorting algorithm that achieves optimal cache complexity without knowing cache size or block size. It relies on a recursive multiway merge structure called a funnel . The algorithm matches the lower bound for comparison sorting in the external memory model. Model Assume: $N$ elements block size $B$ cache size $M$ tall cache condition $M = \Omega(B^2)$ The algorithm does not know $M$...

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Multikey Quicksort

Multikey Quicksort Multikey quicksort is a string sorting algorithm that combines quicksort partitioning with radix-style character inspection. Instead of comparing whole strings each time, it partitions strings by the character at a current depth. It is especially effective for strings with shared prefixes because it avoids repeatedly comparing characters that are already known to be equal. Problem Given an array $A$ of strings, sort the strings in lexicographic order. For...

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Smoothsort Adaptive Heap Sort

Smoothsort Adaptive Heap Sort Smoothsort is an adaptive heap-based sorting algorithm. It preserves the in-place and worst-case guarantees of heapsort, but it performs much less work when the input is already close to sorted. You use it when constant extra space matters and the input may contain existing order. Problem Given an array ( A ) of length ( n ), sort it in place while taking advantage of nearly...

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Timsort

Timsort Timsort is a hybrid stable sorting algorithm designed for real world data. It combines ideas from merge sort and insertion sort, with strong emphasis on exploiting existing order. It is the default sorting algorithm in languages such as Python and Java (for objects). Its design focuses on practical performance rather than purely theoretical bounds. Problem Given an array $A$ of length $n$, reorder it such that: $$ A[0] \le...

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Heapsort

Heapsort Heapsort is a comparison based sorting algorithm that uses a binary heap. It first transforms the array into a heap, then repeatedly extracts the maximum element and places it at the end of the array. It provides a strict worst case guarantee of $O(n \log n)$ and uses constant extra space. Problem Given an array $A$ of length $n$, reorder it such that: $$ A[0] \le A[1] \le \dots...

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Merge Insertion Sort

Merge Insertion Sort Merge insertion sort is a comparison efficient sorting algorithm. It aims to minimize the number of comparisons, approaching the theoretical lower bound for comparison sorting. It combines ideas from merge sort and insertion sort, but with a carefully designed insertion schedule that reduces comparisons. It is mainly of theoretical interest and is rarely used in practice due to complexity and overhead. Problem Given an array $A$ of...

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Incremental Sort

Incremental Sort Incremental sort maintains a sorted structure as new elements arrive. Instead of sorting after all data is available, it updates order step by step. You use it when data arrives over time or when intermediate sorted states are required. Problem Given a stream or sequence ( A ), process elements one by one and maintain a structure such that: elements seen so far remain sorted insertion preserves order...

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Lazy Sort

Lazy Sort Lazy sort delays sorting until the program needs ordered output. Instead of immediately sorting every inserted element, it stores unsorted data and performs sorting only when a query requires order. You use it when many updates happen before few sorted reads. Problem Maintain a collection that supports: inserting elements requesting sorted output avoiding unnecessary sorting work when sorted output is never requested Idea Keep inserted elements in an...

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Sliding Window Sort

Sliding Window Sort Sliding window sort maintains the elements inside a fixed-size moving window in sorted order. As each new element arrives, the oldest element leaves and the new element enters. You use it when sorted queries are needed over recent data, not over the full stream. Problem Given a stream ( x_1, x_2, \dots ) and a window size ( w ), maintain a sorted view of the active...

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Bitonic Sort on Hypercube

Bitonic Sort on Hypercube Bitonic sort on a hypercube maps the bitonic sorting network onto processors connected as a hypercube. Each processor communicates with neighbors that differ in one binary address bit. The fixed communication pattern matches the regular compare and exchange stages of bitonic sort. This model is useful for parallel sorting theory and for systems whose communication topology resembles a hypercube. Problem Given $n$ keys distributed across $p...

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Burstsort String Sorting

Burstsort String Sorting Burstsort string sorting is a trie based method for lexicographic string sorting. It stores strings in buckets attached to trie leaves. When a bucket grows too large, the bucket is split by the next character position. The method is designed for large string collections where comparison sorting repeatedly examines the same prefixes and causes poor cache behavior. Problem Given an array $A$ of strings, sort the strings...

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Radix Sort

Radix Sort Radix sort sorts keys by decomposing them into smaller parts such as digits, bytes, or characters. Instead of comparing whole keys directly, it groups keys by one position at a time. It is most useful when keys have fixed width or bounded length, such as integers, fixed length strings, byte arrays, or identifiers. Problem Given an array $A$ of $n$ keys, sort the keys by their full value...

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Spreadsort

Spreadsort Spreadsort is a hybrid sorting algorithm that combines ideas from radix sort and comparison-based sorting. It partitions data based on key ranges and recursively sorts partitions, switching to comparison sorting when partitions become small or distribution becomes irregular. It is designed to achieve near linear performance on structured data while retaining robustness on arbitrary inputs. Problem Given an array $A$ of sortable keys, possibly integers, floating point values, or...

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Suffix Array Doubling Sort

Suffix Array Doubling Sort Suffix array doubling sort constructs a suffix array by iteratively sorting prefixes of length $1, 2, 4, 8, \dots$ until all suffixes are uniquely ranked. It replaces full suffix comparisons with rank comparisons that double in length each round. Problem Given a string $T$ of length $n$, construct a suffix array: $$ SA[0 \dots n-1] $$ such that suffixes of $T$ are sorted lexicographically. Idea Each...

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Shell Sort with Shell Gaps

Shell Sort with Shell Gaps Shell sort with Shell gaps uses the original gap sequence proposed for Shell sort. The sequence starts with roughly half the array length and repeatedly halves the gap until it reaches 1. This version is simple and easy to implement, but its worst-case behavior remains quadratic. Problem Given a sequence $A$ of length $n$, reorder it such that $$ A[0] \le A[1] \le \cdots \le...

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Insertion Sort

Insertion Sort Insertion sort builds the sorted array one element at a time. At each step, it takes the next element and inserts it into the correct position within the already sorted prefix. It mirrors the process of sorting cards in hand. Compared to swap-based methods, it reduces writes by shifting elements. Problem Given a sequence $A$ of length $n$, reorder it such that $$ A[0] \le A[1] \le \cdots...

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Bytewise Radix Sort

Bytewise Radix Sort Bytewise radix sort sorts fixed-width keys by processing one 8-bit byte at a time. Since each byte has 256 possible values, every pass uses a counting array of size 256. It is a practical form of radix sort for machine integers, binary records, and fixed-size keys because byte extraction is cheap and bucket arrays fit easily in cache. Problem Given an array $A$ of $n$ fixed-width unsigned...

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Winner Tree Merge

K Way Winner Tree Merge K way winner tree merge is a tournament-tree method for merging multiple sorted streams. Each leaf represents one input stream, and each internal node stores the winner of a comparison between its children. The winner is usually the smallest current element among the competing streams. After the winner is emitted, only the path from that stream's leaf to the root must be recomputed. Problem Given...

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Memory Mapped External Sort

Memory Mapped External Sort Memory mapped external sort uses memory-mapped files to sort data larger than ordinary working memory. Instead of manually reading and writing file blocks with explicit I/O calls, the program maps file regions into virtual memory and lets the operating system page data in and out. This can simplify implementation, but it does not remove the external-memory problem. The algorithm still needs chunking, sorted runs, and merging...

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PSRS

Parallel Sorting by Regular Sampling (PSRS) PSRS is a structured parallel sorting algorithm designed for shared memory or distributed systems. It combines local sorting, deterministic sampling, and balanced redistribution. Unlike naive sample sort, PSRS uses regular sampling to guarantee better load balance without heavy randomness. Problem Given $n$ elements distributed across $p$ processors, sort them in nondecreasing order. Each processor initially holds about $n/p$ elements. Algorithm PSRS proceeds in five...

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DC3 Suffix Array Sort

DC3 Suffix Array Sort DC3 suffix array sort is the concrete formulation of the skew algorithm based on a difference cover modulo 3. It builds the suffix array in linear time by sorting a subset of suffixes, assigning them ranks, and merging with the remaining suffixes. It is widely used in high-performance string processing systems. Problem Given a string $S$ of length $n$, construct the suffix array: $$ SA =...

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Tournament Tree Partial Sort

Tournament Tree Partial Sort Tournament tree partial sort uses a tournament tree to repeatedly extract the next smallest or largest element. It is useful when only a sorted prefix of length ( k ) is needed. You use it when you want partial sorted output with predictable comparison structure. Problem Given an array ( A ) of length ( n ) and an integer ( k ), output the smallest...

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In Place Merge Sort

In Place Merge Sort In place merge sort is a merge sort variant that tries to keep the extra memory small. Standard merge sort uses an auxiliary array of size $n$ during merging. In place merge sort instead merges two adjacent sorted ranges inside the original array. The main difficulty is the merge step. Splitting is easy, but merging two sorted adjacent ranges without a large buffer is more complex...

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Natural Runs Sort

Natural Runs Sort Natural runs sort is an adaptive sorting method that first finds sorted subsequences already present in the input. These subsequences are called natural runs. The algorithm then merges the runs until the whole sequence is sorted. You use it when input data often contains long ordered stretches. Problem Given an array ( A ) of size ( n ), sort it by exploiting existing non-decreasing regions. A...

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Bottom Up Merge Sort

Bottom Up Merge Sort Bottom up merge sort removes recursion and builds the sorted array iteratively. It starts by treating each element as a sorted run of size one, then repeatedly merges adjacent runs of increasing size. This form improves control over memory access and avoids recursion overhead. It is commonly used in systems where stack usage must remain bounded. Problem Given an array $A$ of length $n$, reorder it...

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Comb Sort

Comb Sort Comb sort improves bubble sort by comparing elements that are far apart before comparing adjacent elements. It starts with a large gap and repeatedly shrinks that gap until it reaches 1. The main idea is to remove small elements near the end and large elements near the beginning earlier than bubble sort would. Problem Given a sequence $A$ of length $n$, reorder it such that $$ A[0] \le...

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Patience Sort with Piles

Patience Sort with Piles Patience sort with piles is the full sorting version of patience sorting. It builds piles using the same rule as the LIS method, then merges the piles to produce a sorted sequence. You use it when you want a conceptually simple sorting method based on binary search and merging. Problem Given an array ( A ), sort it by: building piles using patience sorting rules merging...

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Coordinate Compression Sort

Coordinate Compression Sort Coordinate compression sort maps arbitrary values to a dense integer range based on their sorted order, then sorts using these compact indices. It is useful when values are large, sparse, or not directly suitable for counting or radix methods. Problem Given an array $A$ of values, possibly large integers or non-integer comparable items, sort the array efficiently by reducing the value domain. Idea Replace each value with...

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Cartesian Tree Adaptive Sort

Cartesian Tree Adaptive Sort Cartesian tree adaptive sort builds a Cartesian tree from the input sequence and uses its structure to produce sorted output. The tree encodes both the order of elements and their relative values. You use it when input has structure that can be exploited through tree shape. Problem Given an array ( A ), sort it by: constructing a Cartesian tree extracting elements in sorted order A...

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Shell Sort with Sedgewick Gaps

Shell Sort with Sedgewick Gaps Shell sort with Sedgewick gaps uses a carefully designed sequence that improves both theoretical and practical performance over earlier sequences such as Shell and Hibbard. Two common Sedgewick sequences are used in practice. A widely cited version is: $$ g_k = \begin{cases} 9 \cdot 2^k - 9 \cdot 2^{k/2} + 1 & \text{if } k \text{ even} 8 \cdot 2^k - 6 \cdot 2^{(k+1)/2} +...

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Induced Sorting

Induced Sorting Induced sorting is a technique used to construct suffix arrays in linear time. Instead of sorting all suffixes directly, it sorts a subset of suffixes and then induces the order of the remaining ones. This idea forms the foundation of modern linear-time suffix array algorithms such as SA-IS. Problem Given a string $S$ of length $n$, construct the suffix array: $$ SA = \text{sorted indices of all suffixes...

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Stooge Sort

Stooge Sort Stooge sort is a recursive sorting algorithm with very poor efficiency. It repeatedly sorts overlapping parts of the array. The algorithm has theoretical interest but no practical use. Problem Given a sequence $A$ of length $n$, reorder it such that $$ A[0] \le A[1] \le \cdots \le A[n-1] $$ Algorithm For a subarray $A[l..r]$: If the first element is greater than the last, swap them If the size...

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Replacement Selection

Replacement Selection Replacement selection is a run generation technique used in external sorting. It produces sorted runs that are often longer than the available memory size by using a priority queue. You use it when sorting data that does not fit in memory. Problem Given a stream of elements and limited memory of size ( M ), produce sorted runs on disk such that: each run is sorted runs are...

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Bubble Sort

Bubble Sort Bubble sort is a simple comparison-based sorting algorithm. It repeatedly scans the sequence and swaps adjacent elements when they are in the wrong order. After each pass, the largest unsorted element moves to its correct position at the end. The name comes from the way larger elements gradually “bubble up” toward the right side. Problem Given a sequence $A$ of length $n$, reorder it such that: $$ A[0]...

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Randomized Quicksort

Randomized Quicksort Randomized quicksort modifies quicksort by choosing the pivot at random. This removes dependence on input order and prevents consistently bad partitions. The algorithm retains the same structure as quicksort but replaces deterministic pivot selection with a random choice. Problem Given an array $A$ of length $n$, reorder it such that: $$ A[0] \le A[1] \le \dots \le A[n-1] $$ Idea Instead of always choosing a fixed pivot position,...

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IPS4o

IPS4o IPS4o stands for in-place parallel super scalar samplesort. It is a high performance comparison sorting algorithm designed for modern multicore CPUs. It combines samplesort partitioning, cache efficient block movement, and parallel execution while keeping extra memory usage small. The algorithm is useful when comparison sorting is required but ordinary quicksort or mergesort does not make full use of hardware parallelism. Problem Given an array $A$ of $n$ comparable elements,...

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Shear Sort

Shear Sort Shear sort is a parallel sorting algorithm for data arranged on a two dimensional mesh. It alternates between sorting rows and sorting columns. Rows are sorted in a snake like order: even rows left to right, odd rows right to left. Columns are sorted top to bottom. This alternating pattern gradually moves small values toward the beginning of the snake order and large values toward the end. Problem...

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Tournament Sort

Tournament Sort Tournament sort selects elements by organizing comparisons as a tournament. Each leaf represents an input value. Internal nodes store the winner of comparing their children. For ascending order, the winner is the smaller value. After the minimum is emitted, its leaf is replaced by infinity, and the path from that leaf to the root is recomputed. The next root gives the next smallest value. Problem Given a sequence...

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Stream Sort by Buffer

Stream Sort by Buffer Stream sort by buffer sorts incoming data in memory-sized batches. It reads a fixed number of elements, sorts that buffer, emits the sorted block, and repeats. You use it when the full input is too large or too delayed to sort all at once. Problem Given a stream of values and a buffer capacity ( B ), produce sorted chunks or sorted runs from the stream....

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Quicksort Median of Three

Quicksort Median of Three Quicksort median of three improves pivot selection by choosing the median value among the first, middle, and last elements of the current range. This avoids some common bad cases, such as already sorted or reverse sorted arrays, where choosing the first or last element as pivot can produce highly unbalanced partitions. The algorithm keeps the same recursive structure as quicksort. Only the pivot selection step changes....

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Cache Aware Sorting

Cache Aware Sorting Cache aware sorting refers to algorithms that are designed with explicit knowledge of the memory hierarchy, especially cache size and cache line (block) size. The goal is to minimize cache misses by structuring memory access patterns carefully. This model is more detailed than the standard RAM model and closer to real hardware behavior. Model Assume a two-level memory model: Fast memory (cache) of size $M$ Slow memory...

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Cache Efficient Merge Sort

Cache Efficient Merge Sort Cache efficient merge sort improves merge sort by reducing cache misses. It reorganizes recursion and merging so that working data fits into cache levels. The goal is to minimize memory transfers rather than just comparisons. Problem Given an array $A$ of length $n$, reorder it such that: $$ A[0] \le A[1] \le \dots \le A[n-1] $$ while improving cache locality. Idea Standard merge sort performs well...

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Strand Sort

Strand Sort Strand sort builds the sorted result by repeatedly extracting increasing subsequences, called strands, from the input and merging them into an output list. It is particularly natural for linked lists, where removing elements is efficient. Problem Given a sequence $A$ of length $n$, reorder it such that $$ A[0] \le A[1] \le \cdots \le A[n-1] $$ Key Idea Take the first element as the start of a strand...

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Binary Insertion Sort

Binary Insertion Sort Binary insertion sort improves insertion sort by using binary search to locate the correct insertion position in the sorted prefix. This reduces the number of comparisons, though element shifting still dominates the runtime. The algorithm keeps the same structure as insertion sort but replaces the linear scan with a logarithmic search. Problem Given a sequence $A$ of length $n$, reorder it such that $$ A[0] \le A[1]...

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Adaptive Heap Sort

Adaptive Heap Sort Adaptive heap sort modifies standard heapsort to take advantage of existing order in the input. While classical heapsort treats all inputs the same, adaptive variants reduce work when the input is already partially sorted. You use it when you want heap-based guarantees with some sensitivity to input structure. Problem Given an array ( A ), sort it while: preserving ( O(n \log n) ) worst-case bounds reducing...

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Cache Oblivious Sorting

Cache Oblivious Sorting Cache oblivious sorting uses recursive structure to obtain efficient memory hierarchy behavior without knowing the cache size $M$ or block size $B$. The algorithm is written as if memory were flat, but its recursive subproblems eventually fit into every cache level. This approach is useful when the same implementation should perform well across different machines and storage hierarchies. Model The cache oblivious model assumes: memory is transferred...

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Buffer Tree Sort

Buffer Tree Sort Buffer tree sort uses a buffer tree to sort data in the external-memory model. Instead of sorting all records directly, it inserts records into a high fanout search tree whose internal nodes hold buffers. When a buffer fills, records are pushed downward in batches. The purpose is to reduce random I/O. Records move through the tree in large blocks, which makes the algorithm efficient when data is...

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Radix Exchange Sort

Radix Exchange Sort Radix exchange sort is an in place radix sorting algorithm for binary keys, usually integers. It processes bits from most significant to least significant and partitions the array into two regions at each bit. At each step, all keys with bit 0 move before all keys with bit 1. The algorithm then recursively sorts both regions using the next bit. Problem Given an array $A$ of nonnegative...

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Tournament Merge Sort

Tournament Merge Sort Tournament merge sort uses a tournament tree to merge sorted sequences. Each element competes in a structured tree, and the winner at the root is the smallest element. After removing the winner, the tree is updated to find the next smallest. It is conceptually similar to multiway merge, but uses a tournament structure instead of a heap. Problem Given an array $A$ of length $n$, reorder it...

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Parallel Radix Sort

Parallel Radix Sort Parallel radix sort sorts fixed width keys by processing one digit group at a time. A digit group may be a byte, a few bits, or another small radix unit. Each pass groups elements by the current digit while preserving the order needed by the radix variant. For integer keys, parallel radix sort is often faster than comparison sorting because it uses key digits directly. Its main...

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Sparse Key Counting Sort

Sparse Key Counting Sort Sparse key counting sort handles large key ranges by storing counts only for keys that appear in the input. It replaces the dense count array of counting sort with a map from key to frequency. This is useful when the key universe is huge but the number of distinct keys is small. Problem Given an array $A$ of $n$ keys drawn from a large domain, sort...

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Cache Oblivious Merge Sort

Cache Oblivious Merge Sort Cache oblivious merge sort is a merge sort variant designed for memory hierarchies. It improves locality without knowing the cache size, block size, or number of cache levels. The algorithm uses recursive structure to make subproblems eventually fit into cache automatically. Problem Given an array $A$ of length $n$, reorder it such that: $$ A[0] \le A[1] \le \dots \le A[n-1] $$ while reducing cache misses...

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External Bucket Sort

External Bucket Sort External bucket sort extends bucket sort to data that does not fit in memory. It partitions records into ordered buckets stored on external storage, sorts each bucket independently, and concatenates the buckets in key order. The method works well when the key distribution is known well enough to create buckets of manageable size. Problem Given a large dataset and a key function, sort all records using bounded...

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Parallel Odd Even Sort

Parallel Odd Even Sort Parallel odd even sort is the parallel form of odd even transposition sort. It works like bubble sort, but splits adjacent comparisons into two independent phases. One phase compares pairs starting at even indices, and the other compares pairs starting at odd indices. Because pairs in the same phase do not overlap, all comparisons in one phase can run at the same time. Problem Given an...

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External Sample Sort

External Sample Sort External sample sort is a distribution-based external sorting algorithm. It selects a sample of the input to determine splitters, partitions the data into balanced buckets using those splitters, and then sorts each bucket independently. The method reduces the number of merge passes by ensuring that buckets are roughly equal in size. Problem Given a large dataset that does not fit in memory, sort it efficiently while minimizing...

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Lomuto Partition Quicksort

Lomuto Partition Quicksort Lomuto partition quicksort uses a simple partition scheme based on a single boundary index. It scans the array once, moving elements smaller than the pivot to the left. It is easier to implement and reason about than Hoare partition, though it performs more swaps and comparisons in practice. Problem Given an array $A$ of length $n$, reorder it such that: $$ A[0] \le A[1] \le \dots \le...

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Odd Even Sorting Network

Odd Even Sorting Network The odd even sorting network is a fixed comparator network derived from odd even transposition sort. It repeatedly applies two phases: compare adjacent pairs starting at even indices, then compare adjacent pairs starting at odd indices. The schedule is fixed and independent of input values. All comparisons within one phase are independent and can run in parallel. Problem Given $n$ elements, sort them in nondecreasing order...

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Burstsort

Burstsort Burstsort is a high performance string sorting algorithm designed for large datasets. It combines trie based partitioning with deferred sorting of small buckets to improve cache locality and reduce memory traffic. Instead of sorting the entire dataset directly, it incrementally builds a trie where leaves store buckets of strings. When a bucket grows beyond a threshold, it "bursts" into child nodes. Problem Given a large array of strings, sort...

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Pancake Sort

Pancake Sort Pancake sort orders a sequence using only prefix reversals. A flip operation reverses the first $k$ elements of the array. By applying a sequence of flips, the algorithm moves the largest remaining element to its correct position at the end. The model comes from sorting pancakes with a spatula, where only prefix flips are allowed. Problem Given a sequence $A$ of length $n$, reorder it such that $$...

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Balanced K Way Merge Sort

Balanced K Way Merge Sort Balanced k way merge sort is an external sorting algorithm that repeatedly merges sorted runs in groups of at most $k$. Unlike polyphase merge sort, it tries to keep the merge work evenly distributed across passes. It is a simple and common model for large file sorting. The input is first divided into memory-sized chunks, each chunk is sorted internally, and then the resulting sorted...

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Cascade Merge Sort

Cascade Merge Sort Cascade merge sort is an external sorting method that organizes merging into a pipeline of stages. Each stage merges a group of sorted runs and passes the resulting larger runs to the next stage. The purpose is to reduce repeated redistribution and make external merging easier to schedule. It is most useful when runs arrive gradually or when storage bandwidth can be used by several merge stages...

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Slow Sort

Slow Sort Slow sort is a deliberately inefficient recursive sorting algorithm. It is based on the multiply and surrender paradigm, a parody of divide and conquer. The algorithm recursively sorts both halves, compares their maximum elements, places the larger one at the end, and then recursively sorts the remaining prefix. It is mostly useful as a teaching example for bad recursion design. Problem Given a sequence $A$ of length $n$,...

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Bead Sort

Bead Sort Bead sort, also called gravity sort, sorts non-negative integers by simulating beads falling under gravity. Each number is represented as a column of beads, and beads “fall” downward to form a sorted arrangement. The model relies on a physical analogy rather than comparisons. Problem Given a sequence $A$ of non-negative integers, reorder it such that $$ A[0] \le A[1] \le \cdots \le A[n-1] $$ Representation Each value $A[i]...

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Pigeonhole Sort

Pigeonhole Sort Pigeonhole sort is a direct address sorting algorithm for integers in a small contiguous range. It creates one slot, or pigeonhole, for each possible key value, places elements into their matching slot, then scans the slots in order to rebuild the sorted array. It is close to counting sort, but the usual presentation stores the actual elements in holes rather than only their counts. Problem Given an array...

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Floating Point Radix Sort

Floating Point Radix Sort Floating point radix sort sorts floating point numbers by transforming their binary representation into an order-preserving integer form, then applying standard radix sort. The main challenge is that IEEE floating point bit ordering does not match numeric ordering for negative values. Problem Given an array $A$ of floating point numbers (typically IEEE 754), sort the array in increasing order. Idea Each floating point number is represented...

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Adaptive Shivers Sort

Adaptive Shivers Sort Adaptive Shivers sort is a run-based merge sort that improves how runs are merged. It detects natural runs and applies a stack discipline with carefully chosen merge rules to keep merges balanced. You use it when input contains natural runs and you want tighter control over merge cost than simple strategies. Problem Given an array ( A ), sort it by: detecting natural runs merging them in...

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Odd Even Sort

Odd Even Sort Odd-even sort, also called brick sort, is a variation of bubble sort that separates comparisons into two alternating phases. One phase compares elements at odd-even index pairs, and the other compares even-odd pairs. This structure makes the algorithm suitable for parallel execution, since comparisons within each phase do not overlap. Problem Given a sequence $A$ of length $n$, reorder it such that $$ A[0] \le A[1] \le...

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Batcher Merge Sort

Batcher Merge Sort Batcher merge sort is a sorting network algorithm. It sorts two halves recursively, then merges them using Batcher's odd even merge network. Its comparison pattern is fixed before execution. The same compare and swap operations run regardless of the input values. This makes it useful for parallel machines, SIMD code, GPUs, and hardware circuits. Problem Given an array $A$ of length $n$, reorder it such that: $$...

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Three Way Quicksort

Three Way Quicksort Three way quicksort extends quicksort by handling duplicate keys efficiently. Instead of partitioning into two parts, it splits the array into three regions: elements less than the pivot elements equal to the pivot elements greater than the pivot This reduces unnecessary comparisons when many elements are equal. Problem Given an array $A$ of length $n$, reorder it such that: $$ A[0] \le A[1] \le \dots \le A[n-1]...

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American Flag String Sort

American Flag String Sort American flag string sort is an in-place MSD radix sort for strings. It partitions strings by the character at the current position, then recursively sorts each bucket by the next character. It uses the same bucket permutation idea as American flag sort, but the digit source is a string character rather than an integer digit. Problem Given an array $A$ of strings, sort the strings in...

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Patience Sorting (LIS)

Patience Sorting for LIS Patience sorting is a technique that simulates a card game to compute the longest increasing subsequence (LIS) . It builds piles with specific ordering rules and uses binary search to maintain efficiency. You use it when you need the LIS in ( O(n \log n) ) time. Problem Given a sequence ( A ) of length ( n ), find the longest strictly increasing subsequence: [...

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Binary Tree Online Sort

Binary Tree Online Sort Binary tree online sort inserts elements into a binary search tree (BST) as they arrive, then produces sorted output via in-order traversal. You use it when data arrives incrementally and you want ordered queries or final sorted output without a separate sorting phase. Problem Given a stream ( x_1, x_2, \dots, x_n ), maintain a structure such that: insertion is performed online elements can be retrieved...

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Spill Sort

Spill Sort Spill sort is a practical external sorting pattern used when an operator begins as an in-memory sort but exceeds its memory budget. When memory fills, the current data is sorted and spilled to temporary storage as a run. After all input has been read, the spilled runs are merged. This is common in databases, query engines, log processors, and stream processors. Problem Given an input stream and a...

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Histogram Sort

Histogram Sort Histogram sort constructs a frequency histogram over the key domain and uses it to reconstruct the sorted sequence. It generalizes counting sort to cases where the domain may be sparse or where counts are derived from a histogram structure. It appears in data processing pipelines where histograms are already computed or where frequency aggregation is natural. Problem Given an array $A$ of $n$ elements with keys drawn from...

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Ska Sort

Ska Sort Ska sort is a high performance radix sorting algorithm designed for modern CPUs. It focuses on minimizing cache misses, branch mispredictions, and memory movement by using block based partitioning and branchless classification. It is particularly effective for sorting large arrays of integers, pointers, or fixed width keys. Problem Given an array $A$ of fixed width keys, sort it efficiently using a radix based method optimized for hardware performance....

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SIMD Sorting Network

SIMD Sorting Network A SIMD sorting network sorts a fixed number of elements using a predetermined sequence of compare and exchange operations. Each stage can be mapped to vector instructions such as lane permutation, vector minimum, vector maximum, and blend. Unlike comparison sorts with branches, the schedule does not depend on input values. This makes the method useful for short arrays, database kernels, vectorized partitioning, and base cases inside larger...

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SA IS

SA IS SA IS is a linear-time suffix array construction algorithm. It sorts a carefully chosen subset of suffixes, called LMS suffixes, then induces the order of all remaining suffixes from them. It is one of the standard practical algorithms for building suffix arrays in linear time. Problem Given a string $S$ of length $n$, construct its suffix array: $$ SA = \text{sorted indices of all suffixes of } S...

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Block Merge Sort

Block Merge Sort Block merge sort is a stable merge sort variant designed to reduce auxiliary memory while keeping good practical performance. Instead of copying the whole array into a second array, it divides sorted ranges into blocks and rearranges those blocks before finishing with local merges. The algorithm is more complex than ordinary merge sort, but it gives an important tradeoff: stable sorting with less extra memory. Problem Given...

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CUDA Warp Sort

CUDA Warp Sort CUDA warp sort sorts a small group of values within one warp. A warp is a fixed group of GPU threads that execute together. On NVIDIA GPUs, a warp commonly contains 32 lanes. The algorithm is usually implemented with compare and exchange steps using warp shuffle instructions. Since all lanes execute the same instruction stream, warp sort works best with regular sorting networks such as bitonic sort...

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Loser Tree Merge

K Way Loser Tree Merge K way loser tree merge is an optimized method for merging multiple sorted runs. It replaces the standard heap with a tournament tree that stores the loser of each comparison. This reduces the number of comparisons and improves performance in external sorting. It is widely used in high-performance external merge sort implementations. Problem Given $k$ sorted input streams, merge them into one sorted output efficiently....

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MapReduce Sort

MapReduce Sort MapReduce sort sorts a large dataset across many machines using the MapReduce execution model. The input is split into blocks, mapper tasks emit key value records, the shuffle phase partitions records by key range, and reducer tasks sort their assigned partitions. The result is a set of sorted output shards. If partition boundaries are chosen correctly, concatenating reducer outputs in partition order gives one globally sorted sequence. Problem...

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Online Insertion Sort

Online Insertion Sort Online insertion sort is insertion sort used in an online setting. It accepts elements one at a time and keeps all seen elements sorted after each insertion. You use it when the input is not available all at once, but the sorted prefix must remain queryable during processing. Problem Given a stream of values ( x_1, x_2, \dots, x_n ), maintain a sorted sequence ( S )...

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Skew Suffix Array Sort

Skew Suffix Array Sort Skew suffix array sort, also known as the DC3 algorithm, constructs a suffix array in linear time by recursively sorting a subset of suffixes whose positions are not divisible by 3. The remaining suffixes are then merged using the already computed order. Problem Given a string $S$ of length $n$, construct its suffix array: $$ SA = \text{sorted indices of all suffixes of } S $$...

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GPU Merge Sort

GPU Merge Sort GPU merge sort adapts merge sort to GPU execution by replacing recursive merging with parallel merge kernels. The algorithm operates in passes, merging sorted runs of increasing size. Unlike GPU radix sort, this method works for arbitrary comparable keys. Its performance depends on efficient parallel merge and memory throughput. Problem Given an array $A$ of size $n$ stored on a GPU, sort it in nondecreasing order. Algorithm...

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Binary Radix Sort

Binary Radix Sort Binary radix sort sorts integers by examining their binary representation bit by bit. Instead of using counting arrays, it partitions elements into two groups based on whether a bit is 0 or 1. This yields a simple and memory efficient radix sort specialized for base 2. Problem Given an array $A$ of integers, sort them in increasing order using their binary representation. Each number can be written...

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Introsort

Introsort Introsort, short for introspective sort, is a hybrid sorting algorithm. It starts with quicksort because quicksort is fast in practice. It monitors recursion depth, and when the recursion becomes too deep, it switches to heapsort to avoid quadratic worst case behavior. This gives the practical speed of quicksort with the worst case guarantee of heapsort. Problem Given an array $A$ of length $n$, reorder it such that: $$ A[0]...

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Insertion Sort with Sentinel

Insertion Sort with Sentinel Insertion sort with sentinel is a small optimization of insertion sort. It first places the minimum element at the beginning of the array. That element acts as a sentinel, so the inner loop can stop without checking whether it has reached the start of the array. You use it when implementing insertion sort as a low-level routine, especially inside hybrid sorts. Problem Given an array (...

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Adaptive Samplesort

Adaptive Samplesort Adaptive samplesort is a samplesort variant that chooses splitters from the input and adjusts partitioning to the observed distribution. It is useful when the input has skew, duplicates, or uneven key ranges. You use it when ordinary quicksort or fixed bucket sorting may create badly imbalanced partitions. Problem Given an array ( A ) of length ( n ), sort it by dividing values into buckets whose boundaries...

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Ternary Heapsort

Ternary Heapsort Ternary heapsort replaces the binary heap with a ternary heap, where each node has up to three children instead of two. This reduces the height of the heap, which can reduce the number of levels traversed during heap operations. The tradeoff is that each step may require more comparisons to select the largest child. Problem Given an array $A$ of length $n$, reorder it such that: $$ A[0]...

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Quicksort Ninther

Quicksort Ninther Quicksort ninther improves pivot selection by using a stronger sampling strategy called Tukey's ninther. Instead of taking the median of three elements, it takes the median of three medians, each computed from three elements. This increases the likelihood of selecting a pivot close to the true median, which leads to more balanced partitions. Problem Given an array $A$ of length $n$, reorder it such that: $$ A[0] \le...

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TPMMS

Two Phase Multiway Merge Sort Two Phase Multiway Merge Sort (TPMMS) is a practical external sorting algorithm used in database systems. It assumes that all sorted runs can be merged in a single pass using available memory buffers. The method minimizes the number of disk passes, which dominates cost in external memory settings. Model Let: $N$ = total number of elements $M$ = memory capacity $B$ = block size Memory...

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Stable Quicksort

Stable Quicksort Stable quicksort modifies the standard quicksort to preserve the relative order of equal elements. Standard quicksort is not stable because partitioning swaps elements arbitrarily. To achieve stability, the algorithm avoids in-place swaps and instead builds ordered partitions. Problem Given an array $A$ of length $n$, reorder it such that: $$ A[0] \le A[1] \le \dots \le A[n-1] $$ and for any equal elements $A[i] = A[j]$ with $i...

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Three Way String Quicksort

Three Way String Quicksort Three way string quicksort is a refinement of multikey quicksort that uses three-way partitioning to efficiently handle repeated characters. It splits the array into less than, equal to, and greater than partitions based on the character at a given position. It is one of the most practical general-purpose string sorting algorithms. Problem Given an array $A$ of strings, sort them in lexicographic order. For string $s$,...

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External Radix Sort

External Radix Sort External radix sort extends radix sort to datasets larger than memory. It processes keys digit by digit and uses external storage to hold intermediate buckets. Unlike comparison-based external sorts, it exploits the structure of keys to achieve linear-time sorting. This method is effective when keys have fixed length or can be decomposed into digits. Problem Given a large dataset with keys that can be decomposed into digits...

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Database External Sort

Database External Sort Database external sort is the disk-based sorting procedure used inside relational database query engines. It appears in query plans for operations such as ORDER BY , GROUP BY , DISTINCT , window functions, and sort-merge joins. The method is usually a variant of external merge sort with database-specific concerns: rows, tuple comparison, memory quotas, spill files, collation rules, NULL ordering, and stable execution under limited working memory....

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External Merge Sort

External Merge Sort External merge sort is a disk-based sorting algorithm designed for datasets that exceed main memory. It minimizes random I/O and relies on sequential reads and writes, which are efficient on disks and object storage. You use it when the input size is much larger than RAM, for example multi-gigabyte or terabyte scale data. Model Assume: Input size: $N$ elements Memory capacity: $M$ elements Block size: $B$ elements...

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LSM Compaction Sort

LSM Tree Compaction Sort LSM tree compaction sort organizes sorting as a sequence of merges across levels in a Log Structured Merge (LSM) tree. Data is inserted in batches, stored as sorted runs, and periodically merged into larger sorted structures. Sorting emerges as a byproduct of compaction. Each level maintains sorted order, and merges ensure global ordering across levels. Model Assume: data arrives in batches memory buffer of size $M$...

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SIMD Bitonic Sort

SIMD Bitonic Sort SIMD bitonic sort sorts a small fixed number of elements using vector registers. It maps a bitonic sorting network onto SIMD lanes, replacing scalar compare and exchange with vector min and max operations plus lane shuffles. The schedule is fixed. No branches depend on data. This property fits SIMD execution where all lanes execute the same instruction. Problem Given a vector of $W$ elements held in SIMD...

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Library Sort

Library Sort Library sort is an insertion-based sorting algorithm that leaves empty spaces between stored elements. These gaps make later insertions cheaper because elements often move only a short distance instead of shifting an entire suffix. The idea is similar to leaving empty spaces on a bookshelf so new books can be inserted without moving many existing books. Problem Given a sequence $A$ of length $n$, reorder it such that...

Wiki › Algorithms › 01. Searching and Sorting › 6. Elementary Sorting ›

Tree Sort

Tree Sort Tree sort sorts a sequence by inserting its elements into a binary search tree, then reading the tree with an inorder traversal. The binary search tree property places smaller values in the left subtree and larger values in the right subtree, so inorder traversal visits values in sorted order. The algorithm is simple when a binary search tree is already available. Its performance depends heavily on tree balance....

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Multiway Merge Sort

Multiway Merge Sort Multiway merge sort generalizes merge sort by splitting the input into $k$ parts instead of two, and merging $k$ sorted sequences at each step. It is especially useful when merging cost dominates, such as in external memory or database systems. Problem Given an array $A$ of length $n$, reorder it such that: $$ A[0] \le A[1] \le \dots \le A[n-1] $$ Idea Instead of binary splitting: $$...

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Polyphase Merge Sort

Polyphase Merge Sort Polyphase merge sort is an external sorting algorithm for merging many sorted runs using a limited number of files or tapes. It avoids the rigid redistribution step used by balanced merge sort. Instead, it places different numbers of runs on different input files so each merge phase naturally prepares the next phase. This method was especially important for tape drives, where rewinding and redistribution were expensive. The...

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Online Topological Sort

Online Topological Sort Online topological sort maintains an ordering of a directed acyclic graph while updates arrive over time. Unlike ordinary topological sort, the graph is not fixed before the algorithm starts. You use it when dependencies are discovered incrementally, such as build systems, schedulers, package managers, and dynamic workflow engines. Problem Given a directed graph ( G = (V, E) ), maintain an ordering ( \pi ) such that...

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Bitonic Sort

Bitonic Sort Bitonic sort is a comparison sorting algorithm based on bitonic sequences. It is important because its compare and swap pattern is fixed, which makes it suitable for parallel hardware and sorting networks. A bitonic sequence first increases and then decreases, or can be rotated into that form. Problem Given an array $A$ of length $n$, reorder it such that: $$ A[0] \le A[1] \le \dots \le A[n-1] $$...

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Selection Sort

Selection Sort Selection sort divides the array into a sorted prefix and an unsorted suffix. At each step, it selects the smallest element from the unsorted portion and swaps it into the next position of the sorted prefix. Unlike bubble-based methods, it performs a fixed number of swaps, which can be useful when swaps are expensive. Problem Given a sequence $A$ of length $n$, reorder it such that $$ A[0]...

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Chunked Sort

Chunked Sort Chunked sort divides a large input into smaller chunks, sorts each chunk, and then combines the sorted chunks. It is a practical pattern for sorting data that is too large or too inconvenient to process as one array. The method appears in external sorting, streaming systems, parallel sorting, and batch data pipelines. Problem Given a sequence of $N$ records and a memory limit that can hold only $M$...

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Distributed Sample Sort

Distributed Sample Sort Distributed sample sort sorts a dataset spread across multiple machines. It uses sampled keys to choose global splitters. These splitters divide the key space into ordered buckets. Each machine sends records to the bucket owner, each bucket is sorted locally, and the sorted buckets form the final output. The main purpose of sampling is load balance. Good splitters make every worker receive roughly the same amount of...

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Signed Integer Radix Sort

Signed Integer Radix Sort Signed integer radix sort extends radix sorting to handle both negative and positive integers correctly. Since radix sort operates on digit or bit patterns, special handling is required to maintain numeric ordering. Problem Given an array $A$ of signed integers, sort the array in increasing order. Integers are represented in two's complement form, where direct unsigned interpretation does not preserve ordering. Idea Transform each integer into...

Wiki › Algorithms › 01. Searching and Sorting › 6. Elementary Sorting ›

Stable Selection Sort

Stable Selection Sort Stable selection sort modifies selection sort to preserve the relative order of equal elements. Instead of swapping the minimum element into position, it removes the minimum and shifts the intervening elements right by one position. This ensures stability at the cost of additional data movement. Problem Given a sequence $A$ of length $n$, reorder it such that $$ A[0] \le A[1] \le \cdots \le A[n-1] $$ and...

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Shell Sort

Shell Sort Shell sort extends insertion sort by allowing exchanges of elements that are far apart. It sorts elements at a certain gap, then progressively reduces the gap until it becomes 1. The final pass with gap 1 is a standard insertion sort, but on a partially ordered array. This reduces the number of shifts required compared to plain insertion sort. Problem Given a sequence $A$ of length $n$, reorder...

Wiki › Algorithms › 01. Searching and Sorting › 6. Elementary Sorting ›

Cartesian Tree Sort

Cartesian Tree Sort Cartesian tree sort builds a Cartesian tree from the input array, then uses traversal to produce a sorted sequence. A Cartesian tree is a binary tree that satisfies both: heap property on values inorder traversal reproduces the original sequence For sorting, the tree is typically built as a min-heap, so the root holds the smallest element. Problem Given a sequence $A$ of length $n$, reorder it such...

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B Tree Bulk Load Sort

B Tree Bulk Load Sort B tree bulk load sort constructs a B-tree from a dataset by first sorting the data and then building the tree in a single pass. The sorting phase produces ordered records, and the bulk loading phase organizes them into tree nodes efficiently. This method avoids inserting records one by one into a B-tree, which would cause many random I/O operations. Problem Given a large dataset,...

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DC7 Suffix Array

DC7 Suffix Array Sort DC7 is a generalization of DC3 suffix array construction. It splits suffix positions into residue classes modulo 7 and recursively sorts a subset of suffixes, then induces the remaining order. The goal is to reduce comparison depth by encoding suffixes into fixed length tuples and merging sorted partitions. Problem Given a string $T$ of length $n$, construct its suffix array: $$ SA[0 \dots n-1] $$ such...

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Distributed Range Partition Sort

Distributed Range Partition Sort Distributed range partition sort divides the key space into fixed ranges and assigns each range to a worker. Each worker sends records to the correct range owner, then sorts its received records locally. This method is simpler than sample sort because it uses predefined ranges. It works well when the key distribution is known or bounded. Problem Given $n$ records distributed across $p$ workers, sort all...

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Adaptive Merge Sort

Adaptive Merge Sort Adaptive merge sort improves standard merge sort by detecting existing order in the input. Instead of blindly splitting into fixed halves, it identifies already sorted subsequences called runs and merges them. You use it when the input often contains partial order. Problem Given an array ( A ) of size ( n ), sort it while taking advantage of any existing sorted segments. Idea If the array...

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Counting Sort with Negative Keys

Counting Sort with Negative Keys Counting sort normally assumes keys lie in a nonnegative range. This variant handles negative integers by shifting all values so that the minimum becomes zero, then applying standard counting sort. Problem Given an array $A$ of $n$ integers that may include negative values, sort the array. Let: $$ \min = \min(A),\quad \max = \max(A) $$ Idea Shift every value by $-\min$ so all keys become...

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Sort Merge Join Sort Phase

Sort Merge Join Sort Phase The sort phase of sort-merge join orders each input relation by the join key before the merge phase begins. If an input is already ordered by a suitable index or previous query operator, the database can skip sorting that input. This phase is important because the merge join itself requires ordered streams. Without sorted inputs, the join cannot advance both sides efficiently. Problem Given two...

Wiki › Algorithms › 01. Searching and Sorting › 10. External Memory, Cache, and Database Sorting ›

Parallel External Merge Sort

Parallel External Merge Sort Parallel external merge sort extends external merge sort by using multiple processors, threads, and storage devices to increase throughput. It parallelizes both run generation and merging while keeping I/O mostly sequential. The algorithm is used in large-scale systems where sorting terabytes of data requires distributing work across CPUs and disks. Problem Given a dataset much larger than memory, sort it efficiently using multiple processors and parallel...

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Cocktail Shaker Sort

Cocktail Shaker Sort Cocktail shaker sort extends bubble sort by performing passes in both directions. One pass moves the largest element to the end, and the next pass moves the smallest element to the beginning. This reduces the number of passes needed compared to standard bubble sort. It is also called bidirectional bubble sort. Problem Given a sequence $A$ of length $n$, reorder it such that $$ A[0] \le A[1]...

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Top Down Merge Sort

Top Down Merge Sort Top down merge sort is the canonical recursive form of merge sort. It starts from the full array, splits it into halves recursively until single elements remain, then merges upward. This form directly follows the divide and conquer recurrence and is the most common presentation in textbooks. Problem Given an array $A$ of length $n$, reorder it such that: $$ A[0] \le A[1] \le \dots \le...

Wiki › Algorithms › 01. Searching and Sorting › 7. Divide and Conquer Sorting ›

Ford Johnson Sort

Ford Johnson Sort Ford Johnson sort is a comparison efficient sorting algorithm that minimizes the number of comparisons. It is one of the best known algorithms in terms of comparison count and closely approaches the theoretical lower bound. It refines merge insertion sort by carefully controlling the order of insertions using a specific sequence. Problem Given an array $A$ of length $n$, reorder it such that: $$ A[0] \le A[1]...

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Weak Heap Sort

Weak Heap Sort Weak heap sort is a comparison-based sorting algorithm that improves upon heapsort by reducing the number of comparisons. It uses a structure called a weak heap, where the tree shape is similar to a binary heap but ordering constraints are relaxed and encoded using a bit array. The algorithm maintains a single root heap and repeatedly extracts the maximum element. Problem Given a sequence $A$ of length...

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GPU Radix Sort

GPU Radix Sort GPU radix sort sorts fixed width integer keys by processing a small number of bits at a time. Each pass groups keys by the current digit. On GPUs, the main work is building histograms, computing prefix sums, and scattering keys into their next positions. For integer keys, GPU radix sort is often one of the fastest general sorting methods because it avoids comparisons and exposes large amounts...

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TeraSort

TeraSort TeraSort is a benchmark style distributed sorting procedure for very large datasets. It is commonly associated with sorting one terabyte or more of records using a cluster. The core idea is simple: sample keys, choose range partitions, shuffle records to the correct partitions, sort each partition locally, and write ordered output shards. TeraSort is close to MapReduce sort in structure, but it is usually discussed as a performance benchmark....

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Stable Counting Sort

Stable Counting Sort Stable counting sort extends counting sort by preserving the relative order of equal elements. This property is required in multi-pass algorithms such as radix sort. The algorithm uses prefix sums to compute exact output positions for each element. Problem Given an array $A$ of $n$ elements with integer keys in range $[0, k]$, produce a sorted array while preserving the relative order of elements with equal keys....

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Rolling Median Sort

Rolling Median Sort Rolling median sort maintains the median value over a sliding window. Instead of fully sorting the window, it keeps just enough structure to extract the median efficiently. You use it when median or percentile queries are needed over recent data. Problem Given a stream ( x_1, x_2, \dots ) and window size ( w ), compute the median of: [ [x_{t-w+1}, \dots, x_t] ] after each step....

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Exchange Sort

Exchange Sort Exchange sort is a basic comparison-based sorting algorithm. It compares every pair of elements and swaps them when they are in the wrong order. It is one of the simplest sorting methods and serves as a conceptual baseline for understanding comparison sorting. Problem Given a sequence $A$ of length $n$, reorder it such that $$ A[0] \le A[1] \le \cdots \le A[n-1] $$ Algorithm Compare each pair $(i,...

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Powersort

Powersort Powersort is a stable adaptive merge sort that improves how runs are merged. It builds on the same idea as Timsort, detecting natural runs in the input, but uses a principled method to decide merge order based on a notion of power derived from positions in the array. The goal is to achieve near optimal merge trees with low overhead. Problem Given an array $A$ of length $n$, reorder...

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Nearly Sorted Insertion Sort

Nearly Sorted Insertion Sort Nearly sorted insertion sort is ordinary insertion sort applied to input that is already close to sorted order. Insertion sort adapts well to this case because each element moves only a short distance. You use it when the input has small disorder, such as data produced by appending a few new records, merging mostly ordered logs, or correcting a sequence after minor edits. Problem Given an...

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Bucket Sort

Bucket Sort Bucket sort partitions elements into a set of buckets based on their value, then sorts each bucket separately and concatenates the results. It is effective when input values are uniformly distributed over a known range. Problem Given an array $A$ of $n$ elements drawn from a range $[a, b)$, sort the elements. Idea Divide the range into $k$ equal sized intervals Place each element into its corresponding bucket...

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Flashsort

Flashsort Flashsort is a hybrid distribution sorting algorithm that first classifies elements into buckets using an approximate linear mapping, then refines the partially ordered array using insertion sort. It is designed for datasets that are approximately uniformly distributed, where it can achieve near linear performance. Problem Given an array $A$ of $n$ elements, sort the array efficiently by exploiting approximate distribution information. Idea Flashsort has two main phases: Classification phase...

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