brain

The problem involves two circular sequences of unique hieroglyphs. We are asked to "cut" these circles at some point to turn them into linear arrays, then find the longest contiguous segment from the first array that appears as a subsequence in the second array.

We are given an array nums, and we must consider all non-empty subsequences of that array. A subsequence preserves the original order of elements, but elements do not need to be contiguous.

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…

This problem asks us to determine whether a given message should be classified as spam. We are given two arrays of strings: - message, which contains the words appearing in the message. - bannedWords, which contains words that are considered banned.

The problem is asking whether it is possible to disconnect a path from the top-left corner (0, 0) to the bottom-right corner (m - 1, n - 1) in a binary matrix by flipping at most one cell from 1 to 0 or 0 to 1. A path only allows moves down or right into cells containing 1.

The problem asks us to determine the minimum number of swap operations required to sort the values of a binary tree level by level in strictly increasing order. Specifically, at each level of the tree, we can only swap values of nodes that exist on that level.

The problem asks us to count how many integers within the inclusive range [low, high] satisfy two independent conditions. The first condition is based on the digits of the number. A number is considered beautiful only if it contains an equal number of even digits and odd digits.

We are given an integer array nums and an integer x. We need to find two elements whose indices are separated by at least x, and among all such valid pairs, return the minimum possible absolute difference between their values.

This problem is asking us to determine whether there exists a path from the top-left corner (0, 0) to the bottom-right corner (m-1, n-1) of a 2D grid containing only '(' and ')' characters, such that the sequence of characters along the path forms a valid parentheses string.

We are given a collection of segments on a number line. Each segment spans from a left endpoint to a right endpoint, and we must assign each segment one of two colors.

This problem asks us to determine whether each passenger's ticket is confirmed or placed on the waitlist, based on the booking order and the capacity of the flight they booked.

This problem asks us to repeatedly modify an array according to a very specific rule. We are given: - An integer array nums - An integer k, representing how many operations to perform - An integer multiplier For each of the k operations, we must find the smallest value…

We are given an undirected tree with n nodes. A tree is a connected graph with exactly n - 1 edges and no cycles. Each node has a special propagation delay determined entirely by its parity: - Odd-numbered nodes become marked 1 time unit after one of their neighbors is marked.

We are given a multiset of cards, each card showing either the digit 0 or the digit 5. From these cards we may choose any subset and arrange the chosen digits into a number written in a single line. Our goal is to build the largest possible number that is divisible by 90.

The problem is asking for the maximum integer value that can be created by concatenating the binary representations of all elements in a list of three integers. Each number should be converted to its binary representation without leading zeros.

We are given an undirected graph where every vertex has a very strong local condition: each node is connected to at least $k$ other distinct nodes. From this structure we are asked to extract a simple cycle whose length is not just positive, but at least $k+1$.

This problem asks us to count the number of paths in a 2D integer matrix from the top-left corner (0, 0) to the bottom-right corner (m - 1, n - 1) such that the sum of the values along the path is divisible by a given integer k.

We are given an array of integers, and for every element we must find another array element whose bitwise AND with it is zero. Two numbers are compatible exactly when they do not share any bit set to 1.

The problem asks us to count how many pairs of indices (i, j) satisfy two conditions: 1. i < j 2. 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.

That is a long, multi-section technical guide with code, worked examples, test cases, and detailed explanations. I can provide the full reference document, but it will be quite large.

This problem asks us to transform a given string s into another string t such that the total transformation cost does not exceed k. Among all possible valid strings, we must return the lexicographically smallest one. The key detail is how the transformation cost is defined.

This guide is long enough that a complete, high quality response will exceed a practical single-message length if I include all requested sections in full detail, including detailed worked examples, Python and Go implementations, test coverage, and edge case analysis.

This problem asks us to identify how many numbers in an unsorted array are still guaranteed to be found by a randomized binary-search-like process. The array nums contains unique integers.

The problem asks us to count the number of operations required to reduce either of two non-negative integers num1 or num2 to zero. An operation is defined as subtracting the smaller number from the larger one (or subtracting either if they are equal).

The problem asks us to maximize a running total reward by selecting elements from an integer array rewardValues. Each element in the array represents a reward at that index. Initially, the total reward x is 0, and no indices are marked.

The problem asks us to split a string into consecutive groups, where every group must contain exactly k characters. We process the string from left to right. The first k characters form the first group, the next k characters form the second group, and so on.

The problem asks us to count how many distinct subsequences of a binary string are considered “good.” A subsequence is any sequence formed by deleting zero or more characters without changing the relative order of remaining characters.

The problem gives us a string s and a character c. We must count how many substrings of s both start and end with the character c. A substring is any contiguous portion of the string. For every possible substring, we check two conditions: 1. The first character must equal c 2.

We are asked to count the number of distinct circular contours that can be formed on a plane where two black-painted rings are placed. Each ring is defined by two concentric circles, an inner radius and an outer radius.

The problem asks us to determine whether a given string qualifies as a "valid word" according to four specific rules. First, the word must contain at least 3 characters. Any string shorter than 3 is automatically invalid.

We have a line of soldiers, each with a height. The general only cares about two positions in the lineup. The tallest soldier must stand at the very front, and the shortest soldier must stand at the very end. The order of everyone else is irrelevant.

The problem asks us to count the number of ways we can split a given binary array nums into contiguous subarrays such that each subarray contains exactly one 1. The input is a binary array, meaning it only contains 0s and 1s.

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 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.

The problem is asking us to determine the optimal way for Bob to distribute his numArrows across 12 scoring sections (from 0 to 11) in an archery competition in order to maximize his total points against Alice. Alice's arrow distribution is given in aliceArrows.

The problem gives us an array of strings called words and a list of range queries called queries. For each query [li, ri], we must determine how many strings in words between indices li and ri, inclusive, both start and end with a vowel.

The problem gives us a string word containing uppercase and lowercase English letters. We must count how many letters are considered "special". A character c is special if two conditions are true: 1. The lowercase version of the letter appears somewhere in the string. 2.

The problem gives us an integer array nums, and we need to find the maximum distance between the indices of any two prime numbers in the array. More specifically, we are interested in indices i and j such that both nums[i] and nums[j] are prime numbers.

We are given a set of containers, each containing some fixed amount of mercury. Over time, two kinds of operations happen. The first operation changes the mercury amount in a single container.

The problem asks us to find the minimum number of operations needed to ensure that every element in an array is at least k. Each operation consists of removing the smallest element from the array.

This problem gives us a boolean expression containing only: - '0' and '1' - binary operators '&' and '|' - parentheses The expression is guaranteed to be valid, which means every operator has valid operands and every parenthesis is properly matched.

The problem asks us to find the smallest positive integer that cannot be represented as a bitwise OR of any subsequence of a given array nums. The input array contains positive integers, and the subsequences can have any length, including length 1.

We are given a line of cups, each cup carrying a unique label from 1 to n. The initial left-to-right order of these labels is unknown. What we do know is the exact sequence of m operations performed on this line.

Vasya receives food every morning. The food from day i can only be eaten on day i or day i + 1. Every day Vasya himself must consume exactly v kilograms.

The problem asks us to transform the integer 1 into the integer target using the minimum number of moves. At every move, we are allowed to perform one of two operations: 1. Increment the current number by 1 2.

We need to count how many integer-sided right triangles exist such that all three sides are at most n. A right triangle with sides (a, b, c) satisfies the Pythagorean equation: $a^2+b^2=c^2$$a$$b$$c = sqrt{a^2 + b^2} approx 21.21$$a^2 + b^2 = c^2 approx 225.00 + 225.00 = 450.

This problem asks us to design a class named Calculator that supports basic arithmetic operations while enabling method chaining. Method chaining means that after calling one method, we can immediately call another method on the same object.

This problem asks us to determine the minimum number of coins required to acquire all fruits in a market where buying a fruit grants a special reward. You are given a 0-indexed array prices, where prices[i] represents the cost of purchasing the (i + 1)th fruit.

This problem asks us to recursively filter a JSON-like structure that may contain nested objects and arrays. The input consists of two parts: - obj, which can be either: - a primitive value, - an array, - or an object containing nested arrays and objects - fn, a predicate…

The problem asks us to compute the total digit difference across every pair of numbers in the array. All numbers have the same number of digits. For any two numbers, their digit difference is defined as the number of positions where the digits are different.

The problem gives us two integers, red and blue, representing the number of red and blue balls available. We want to build a triangle where: - Row 1 contains exactly 1 ball - Row 2 contains exactly 2 balls - Row 3 contains exactly 3 balls - And so on There are two additional…

We are given a list of strings called words and another string called target. The task is to construct target by concatenating several smaller strings, where each smaller string must be a prefix of at least one word in words. A prefix means the beginning portion of a word.

We need to compute the n-th pentagonal number. Pentagonal numbers form a sequence generated by a direct mathematical formula: $$Pn = frac{3n^2 - n}{2}$$ The input contains a single integer n, and the output is the value of this formula for that position in the sequence.

We are given a rooted tree with n nodes, each node labeled with a 0 or 1. We are also given a target configuration of 0s and 1s for each node. The only operation allowed is to "pick" a node, which flips its value and every second-level descendant down the tree.

The problem asks us to compute the distinct difference array for a given integer array nums. For each index i in the array, we calculate the difference between the number of distinct elements in the prefix nums[0, ...

We have a rectangular grid with n rows and m columns. Vasya starts at position (xc, yc). Then he processes k movement vectors one by one. For a vector (dx, dy), he repeatedly moves: He keeps moving in that direction until the next move would leave the grid.

We are given an undirected social network where each user is identified by a string name and friendships are given as pairs of names.

This problem asks us to calculate how much money each user has spent across all of their purchases. We are given two database tables: The Sales table stores purchase records.

The problem asks us to find the maximum possible sum of a contiguous subarray where the absolute difference between the first and last element of that subarray is exactly k. More formally, for a subarray nums[i..

We are given a sequence of hills placed along a line. Each hill has a fixed horizontal position and a height, and we imagine it as a vertical segment rising from the ground.

This problem asks us to take a binary array nums, which contains only 0s and 1s, and transform it so that all elements become 1 using the minimum number of allowed operations.

We are asked to simulate movement across a 2D plane from a starting point $A$ to a destination $B$ while avoiding a periodic laser. The laser alternates between charging and firing, with durations $a$ and $b$ seconds, respectively.

The problem asks us to transform one integer n into another integer m by repeatedly modifying individual digits of n. At each step, we can increase a digit that is not 9 or decrease a digit that is not 0.

The problem gives us a 0-indexed integer array nums of length n and asks us to compute the maximum sum score among all indices of the array.

We are asked to take a positive integer and express it as a product of prime numbers, showing each prime the number of times it appears in the factorization. For example, the number 245 can be expressed as 5 multiplied by 7 twice, so the output would be 577.

The problem gives us two integers, n and t. We must find the smallest integer greater than or equal to n whose digit product is divisible by t. The digit product of a number is obtained by multiplying all of its digits together.

This problem asks us to implement a utility function called promisify. The purpose of this function is to convert a callback-based asynchronous API into a Promise-based API. The input is a function fn.

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.

This problem asks us to determine whether a given string is a pangram. A pangram is a sentence that contains every lowercase English letter, from 'a' through 'z', at least once. The input is a single string named sentence.

The problem gives us two separate undirected trees. The first tree contains n nodes and the second tree contains m nodes. A tree is an acyclic connected graph, so every pair of nodes has exactly one simple path between them.

We are given an integer array nums, and we must find three indices (i, j, k) such that: - i < j < k - nums[i] < nums[j] < nums[k] Among all valid increasing triplets, we want to maximize the expression: The task is not to maximize the sum of the triplet.

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 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 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.

The problem gives us a three digit integer n. We must determine whether n is a fascinating number. A number is considered fascinating when we concatenate three values together: 1. n 2. 2 n 3.

The problem gives us an undirected weighted graph with n nodes and m edges. Each edge connects two nodes and has a positive weight. We need to determine which edges belong to at least one shortest path from node 0 to node n - 1.

This problem asks us to maximize the total value of coins collected from multiple piles while following a strict removal rule. Each pile is ordered from top to bottom, meaning we cannot arbitrarily pick any coin in a pile. We may only remove coins from the top, one at a time.

The problem gives us a binary string s, containing only '0' and '1' characters. We are allowed to rearrange the bits in any order we want, but we must use exactly the same bits that appear in the original string.

This problem asks us to maximize the total number of fruits collected by three children traversing a square grid of rooms, each with a certain number of fruits. The grid has dimensions n x n, and the fruits are given in a 2D array fruits[i][j].

This problem asks us to find the maximum sum of a balanced subsequence from a given integer array nums. A subsequence is a selection of elements from the array in their original order, possibly skipping elements.

This problem asks us to determine the best candidate for every project based on required skills and a scoring system. We are given two database tables. The Candidates table stores information about each candidate's skills and proficiency levels.

The problem gives us a numeric string word and an integer m. For every prefix of the string, we must determine whether that prefix represents a number divisible by m. A prefix word[0...i] means the substring starting at index 0 and ending at index i, inclusive.

This problem asks us to find the longest contiguous subarray that follows a very specific alternating pattern. Given an integer array nums, we need to identify subarrays where: 1. The subarray length is at least 2. 2.

This problem asks us to compute how much rainwater can be trapped between vertical bars after rainfall. The bars are represented in a database table named Heights, where each row contains an id and a height.

The problem asks us to implement a function that filters an array based on a custom condition defined by another function fn.

The graph in this problem is almost a simple path. Every vertex has degree at most 2, except possibly one special vertex that may have larger degree. A tree with this shape looks like several chains glued together at one center. Initially every edge is black.

The problem asks us to compute, for every index i in the array nums, the total distance between i and every other index j where nums[j] == nums[i]. More formally, for each position i, we need to calculate: for all indices j such that: - nums[j] == nums[i] - j !

The problem gives us a string s containing only lowercase English letters. We are allowed to perform operations where we change any single character into any other lowercase character.

=== 1996-N5 === Origin: ROM Let denote the set of nonnegative integers. Find a bijective function from into such that for all , We first observe that the given functional equation is equivalent to This gives us the idea of introducing a function defined as By the above…

We are asked to construct three permutations $a$, $b$, and $c$ of length $n$ such that for every index $i$ the sum of $a[i]$ and $b[i]$ modulo $n$ equals $c[i]$ modulo $n$.

The problem defines a special type of array called a "good" array. A good array must be a permutation of: 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 to n + 1 The input is…

We are given a company where employees participate in several independent chat groups. Each chat has a fixed membership defined in advance. Over time, a log records messages: each event says that a particular employee posts in a particular chat.

The city is represented by a grid. Every cell is either a building, a street tile with a traversal cost from 1 to 9, or a junction labeled by a lowercase letter. Movement rules are unusual.

Paw the Spider's web consists of n main threads radiating from the center, dividing the plane into n equal sectors. Each sector may have bridges connecting its bounding main threads. Every bridge has attachment points at the same distance from the center.

Codeforces 251B: Playing with Permutations

This problem asks us to equalize the water levels in a series of buckets while accounting for a spill loss. Each bucket initially contains some quantity of water given in an array buckets, and every time we pour water from one bucket to another, a percentage of that water…

We are given a chronological log of a single night in a club. Every character in the input string represents one event: a “+” means someone entered the club, and a “-” means someone left.

We are given two integer arrays, nums1 and nums2, along with a positive integer k. A pair of indices (i, j) is considered good if: In other words, nums1[i] must be divisible by nums2[j] k. The task is to count how many such index pairs exist.

In this problem, we are given a list of stock prices over different days. Each element in stockPrices is a pair: 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…

The problem asks us to determine whether two JSON values, o1 and o2, are deeply equal. Deep equality goes beyond simple reference or shallow equality. For primitive values such as numbers, strings, booleans, or null, equality is straightforward using strict comparison (===).