brain

We are given three piles of candies: red, green, and blue. Each pile has a certain number of candies, represented by integers $r$, $g$, and $b$. Every day, Tanya eats exactly two candies, but they must be of different colors.

We are given a small arithmetic sequence of positive integers: $a, a+d, a+2d, dots, a+(n-1)d$. The goal is to find another arithmetic sequence $b, b+e, b+2e, dots, b+(n-1)e$ such that the last 18 digits of the corresponding Fibonacci numbers contain the original numbers as…

There is not enough information to diagnose the bug or provide a corrected solution. The sample with expected output appears to belong to a string construction problem, but you have not provided: - the problem statement, - the original Python solution, - or even the name of…

There is not enough information to diagnose the bug or provide a corrected solution. The sample with expected output appears to belong to a string construction problem, but you have not provided: - the problem statement, - the original Python solution, - or even the name of…

We are given several independent strings, each consisting of the characters a, b, c, and ?. The task is to replace every ? with one of the letters a, b, or c so that the final string has no two equal adjacent characters.

The problem asks us to figure out whether it is possible to build a vertical tower of standard six-sided dice such that the sum of all visible pips equals a given integer. We have an unlimited number of dice, and for each die, we can choose its orientation.

Before I dive into writing the full editorial, I want to clarify one thing: Codeforces Problem 1267F, Foolprüf Security, involves a graph with weighted edges and some combinatorial security constraint.

There is not enough information to diagnose the bug or provide a corrected solution. The sample with expected output appears to belong to a string construction problem, but you have not provided: - the problem statement, - the original Python solution, - or even the name of…

We are given a row of colored balls represented as a string of uppercase letters. The task is to insert a single ball of any color at any position, including at the ends, so that after the insertion, a chain reaction of eliminations occurs until no segment of length three or…

The Young diagram can be viewed as a histogram whose column heights are given by a non-increasing array $a1,a2,dots,an$.

We have two arrays of equal length. We may choose a single non-negative value x, add it to every element of the first array, and take all results modulo m. After this transformation, the order of elements does not matter.

There is not enough information to diagnose the bug or provide a corrected solution. The sample with expected output appears to belong to a string construction problem, but you have not provided: - the problem statement, - the original Python solution, - or even the name of…

Each test case describes a single student group that must be split into two subgroups. Every subgroup has three independent “resource limits”: an auditorium limit for maths attendees, a computer lab limit for programming attendees, and a gym limit for PE attendees.

There is not enough information to diagnose the bug or provide a corrected solution. The sample with expected output appears to belong to a string construction problem, but you have not provided: - the problem statement, - the original Python solution, - or even the name of…

We are working on a grid where movement is restricted to four directions, so distance between two points is measured using Manhattan distance. A school is fixed at one coordinate, and each student lives at another coordinate on the same infinite grid.

We are given two sequences of brackets, s and t, which may individually be invalid as bracket sequences. The task is to produce the shortest string of brackets that is valid (balanced and properly nested) and contains both s and t as subsequences.

There is not enough information to diagnose the bug or provide a corrected solution. The sample with expected output appears to belong to a string construction problem, but you have not provided: - the problem statement, - the original Python solution, - or even the name of…

There is not enough information to diagnose the bug or provide a corrected solution. The sample with expected output appears to belong to a string construction problem, but you have not provided: - the problem statement, - the original Python solution, - or even the name of…

There is not enough information to diagnose the bug or provide a corrected solution. The sample with expected output appears to belong to a string construction problem, but you have not provided: - the problem statement, - the original Python solution, - or even the name of…

We are asked to simulate a massive array defined recursively using C-style macros. The macros expand in a very structured way: each macro level quadruples the number of elements generated by the previous level, with simple offsets added.

We are given a string s consisting of lowercase English letters, and we want to count all distinct substrings that appear in s or in any version of s where exactly one character has been replaced by an asterisk.

We are given a connected undirected graph of cities. Among all cities, two special nodes are distinguished, call them a and b, representing two fairs.

There is not enough information to diagnose the bug or provide a corrected solution. The sample with expected output appears to belong to a string construction problem, but you have not provided: - the problem statement, - the original Python solution, - or even the name of…

We are given a collection of binary strings, and we are allowed to optionally reverse some of them. After doing so, we want to arrange all strings in a single sequence such that every adjacent pair is compatible: the last character of a word must match the first character of…

There is not enough information to diagnose the bug or provide a corrected solution. The sample with expected output appears to belong to a string construction problem, but you have not provided: - the problem statement, - the original Python solution, - or even the name of…

We are given two integers, and we are allowed to repeatedly perform operations where the cost of the k-th operation is exactly k. Each operation lets us choose one of the two numbers and add the current operation index to it.

We are given a sequence of durations, where each value represents how long Vasya needs to recite one part of a verse. He must recite the parts in order, from left to right, and he earns a reward equal to how many parts he manages to fully complete before time runs out.

We are asked to rearrange a scrambled 2-row grid of alien organs into a prescribed order. The grid has dimensions 2 × (2k + 1) with 4k + 1 organs numbered 1 through 4k + 1 and exactly one empty cell.

The process starts with a short string made only of digits 1, 2, and 3. Alongside this string, we maintain a cursor that moves from left to right over positions between characters, and a clipboard that can store a copied suffix of the string.

We are given a person moving along a straight line segment from position a to position b at constant speed 1 unit per minute. Independently, there is a network base station at position c that covers everything within distance r.

We are given a directed assignment problem on $n$ people where each person must end up choosing exactly one other person to give a gift to, and at the same time must receive exactly one gift from someone else.

We need the total number of framed segments across all permutations of length n. For a fixed permutation, a segment [l, r] is framed when the values inside it form a set of consecutive integers.

There is not enough information to diagnose the bug or provide a corrected solution. The sample with expected output appears to belong to a string construction problem, but you have not provided: - the problem statement, - the original Python solution, - or even the name of…

We have an array representing the tastiness of cupcakes, and two players. Yasser always takes all the cupcakes, summing up the full array. Adel can pick any contiguous subarray that does not cover the entire array.

We are asked to maintain a string S and an integer array W dynamically as queries arrive. Each query adds a new character to S and a weight to W.

We are given a row of n bulbs, each numbered from 1 to n. Some bulbs are missing, indicated by zeros in the input array.

There is not enough information to diagnose the bug or provide a corrected solution. The sample with expected output appears to belong to a string construction problem, but you have not provided: - the problem statement, - the original Python solution, - or even the name of…

We need to count pairs of arrays $(a,b)$, both of length $m$, whose values lie between $1$ and $n$. Array $a$ must be non-decreasing, array $b$ must be non-increasing, and at every position we require $ai le bi$. The answer can be very large, so we output it modulo $10^9+7$.

For each test case, we have a deadline of n days and a program that normally needs d days to finish. Before running the program, we may spend x days optimizing it.

We have a line of n lamps, each either on or off. The goal is to compute, for every prefix of the lamps, the minimum number of subset toggle operations required to turn all lamps in that prefix on.

We are given a collection of n distinct toy boxes, each labeled with a positive integer ai. ROBO can perform a very specific action multiple times: pick three distinct boxes where one box's label divides the other two, and then remove the third box to place it on his pile.

We are given a 2-row by $n$-column grid representing a maze. The player starts at the top-left cell $(1,1)$ and wants to reach the bottom-right cell $(2,n)$. Movement is allowed only between orthogonally adjacent cells. Initially, all cells are passable ground.

There is not enough information to diagnose the bug or provide a corrected solution. The sample with expected output appears to belong to a string construction problem, but you have not provided: - the problem statement, - the original Python solution, - or even the name of…

We are given an $n times m$ matrix. The target matrix is completely fixed: row-major order from $1$ to $n cdot m$. The value that should end up in position $(r,c)$ is $$(r-1)cdot m + c.$$ We may perform two kinds of operations.

For each test case, we are given a single integer n. We must determine whether n can be written as the product of three distinct integers a, b, and c, where each of them is at least 2. If such a decomposition exists, we print "YES" and one valid triple.

We are asked to decide whether a given number of coins can be distributed among three sisters so that they all end up with the same total number of coins. Each sister already has some coins: Alice has a, Barbara has b, and Cerene has c.

We are given a contest with n problems, where each problem i has a range [li, ri] representing the possible number of accepted solutions. Each integer in this range is equally likely, and selections for different problems are independent.

There is not enough information to diagnose the bug or provide a corrected solution. The sample with expected output appears to belong to a string construction problem, but you have not provided: - the problem statement, - the original Python solution, - or even the name of…

We are given two strings, s and t. Initially, we have an empty string z, and we want to transform z into t. The allowed operation is to append any subsequence of s to z. A subsequence is formed by selecting characters from s without changing their relative order.

We have a string of lowercase letters. Every position must be assigned one of two colors, 0 or 1. After choosing the colors, we are allowed to swap neighboring characters only when their colors are different. We may perform such swaps as many times as we want.

There is not enough information to diagnose the bug or provide a corrected solution. The sample with expected output appears to belong to a string construction problem, but you have not provided: - the problem statement, - the original Python solution, - or even the name of…

We have an array of integers. An operation allows us to pick two different positions and copy the value from one position into the other. Since we may repeat this operation any number of times, values can be duplicated throughout the array.

There is not enough information to diagnose the bug or provide a corrected solution. The sample with expected output appears to belong to a string construction problem, but you have not provided: - the problem statement, - the original Python solution, - or even the name of…

The task is to convert a raw number of likes into a compact, human-readable format for display. Numbers less than a thousand remain as-is, numbers in the thousands are rounded to the nearest thousand with a 'K' suffix, and numbers in the millions are rounded to the nearest…

We are given a strictly convex polygon $P$ in the plane as a list of its vertices in counterclockwise order. Each vertex has integer coordinates, and no three vertices are collinear.

We are given an array of integers and want to make two properties simultaneously true: the sum of the elements must not be zero, and the product of the elements must not be zero. The only operation allowed is incrementing a single element by one.

We are given a rectangular grid where every cell represents a city, and each city has one of a small number of colors.

There is not enough information to diagnose the bug or provide a corrected solution. The sample with expected output appears to belong to a string construction problem, but you have not provided: - the problem statement, - the original Python solution, - or even the name of…

We are given a sequence of length n. Although the statement talks about a string, the characters are represented by integers, and the alphabet is extremely large. The large alphabet size means we cannot rely on tricks that depend on a small number of distinct symbols.

There is not enough information to diagnose the bug or provide a corrected solution. The sample with expected output appears to belong to a string construction problem, but you have not provided: - the problem statement, - the original Python solution, - or even the name of…

We are asked to maintain an array of integers that starts with all zeros and answer a series of queries. Each query is either an assignment, setting a specific element to a value, or a range sum query, asking for the sum of a contiguous subarray.

We are given a binary string, a sequence of 0's and 1's, and the goal is to manipulate it so that all the 1's appear in one contiguous block. The only allowed operation is to remove some 0's.

We are given a tree with $n$ vertices, where each vertex is connected such that there is exactly one path between any two vertices. Then we are asked multiple queries.

Yes, the inequality $nu(n) le 2^{l(n) - lambda(n)}$ holds for all positive integers $n$. Consider an addition chain of minimal length $l(n)$ and let $lambda(n)$ be the length of a shortest chain consisting only of doubling steps.

The algorithm itself is correct. The bug is in the editorial's test harness code, not in the algorithm. In the posted solution, the pairs initialization was accidentally split across lines: That formatting artifact can cause issues when copied, and more importantly, the helper…

Yes, the inequality $nu(n) le 2^{l(n) - lambda(n)}$ holds for all positive integers $n$. Consider an addition chain of minimal length $l(n)$ and let $lambda(n)$ be the length of a shortest chain consisting only of doubling steps.

We are given a string of lowercase English letters. A message is any subsequence whose chosen indices form an arithmetic progression. The progression can have any positive difference, including the special case of length one. The task is not to find the message itself.

Yes, the inequality $nu(n) le 2^{l(n) - lambda(n)}$ holds for all positive integers $n$. Consider an addition chain of minimal length $l(n)$ and let $lambda(n)$ be the length of a shortest chain consisting only of doubling steps.

Codeforces 1310A: Recommendations

Yes, the inequality $nu(n) le 2^{l(n) - lambda(n)}$ holds for all positive integers $n$. Consider an addition chain of minimal length $l(n)$ and let $lambda(n)$ be the length of a shortest chain consisting only of doubling steps.

Yes, the inequality $nu(n) le 2^{l(n) - lambda(n)}$ holds for all positive integers $n$. Consider an addition chain of minimal length $l(n)$ and let $lambda(n)$ be the length of a shortest chain consisting only of doubling steps.

We are given a fixed string s that represents a sequence of button presses in a fighting game combo. The player repeatedly attempts to type this entire string from left to right. However, the process is interrupted.

Yes, the inequality $nu(n) le 2^{l(n) - lambda(n)}$ holds for all positive integers $n$. Consider an addition chain of minimal length $l(n)$ and let $lambda(n)$ be the length of a shortest chain consisting only of doubling steps.

Yes, the inequality $nu(n) le 2^{l(n) - lambda(n)}$ holds for all positive integers $n$. Consider an addition chain of minimal length $l(n)$ and let $lambda(n)$ be the length of a shortest chain consisting only of doubling steps.

We are given a rooted construction of many strings where every node represents a string and every edge corresponds to appending one character. The root is the empty string, and each node i is created by taking its parent string pi and appending a lowercase letter ci.

We are given an array of non-negative integers, and a base $k ge 2$. Starting from an array of zeroes of the same length, we can repeatedly pick a step $i$ and add $k^i$ to any single element of the array, or skip the step.

We are given a large line of positions from 1 to $m$, and a collection of $n$ intervals. Each interval represents a “spell” that, when used, adds one candy to every position inside its range. Each spell can be used at most once.

Yes, the inequality $nu(n) le 2^{l(n) - lambda(n)}$ holds for all positive integers $n$. Consider an addition chain of minimal length $l(n)$ and let $lambda(n)$ be the length of a shortest chain consisting only of doubling steps.

Each participant in the contest has two independent rankings: one from the first round and one from the second round. No ties exist in either round, so each round is a permutation of ranks from 1 to n. A participant’s final value is the sum of their two ranks.

We are given a string of length $n$, and Vasya wants to perform a sequence of substring reversals to produce the lexicographically smallest string possible. The operation is controlled by an integer $k$, which specifies the length of each consecutive substring to reverse.

We are given two polynomials, each represented by an array of positive integers, which are their coefficients. The first polynomial has $n$ terms and coefficients $a0, a1, dots, a{n-1}$, the second has $m$ terms with coefficients $b0, b1, dots, b{m-1}$.

Yes, the inequality $nu(n) le 2^{l(n) - lambda(n)}$ holds for all positive integers $n$. Consider an addition chain of minimal length $l(n)$ and let $lambda(n)$ be the length of a shortest chain consisting only of doubling steps.

Yes, the inequality $nu(n) le 2^{l(n) - lambda(n)}$ holds for all positive integers $n$. Consider an addition chain of minimal length $l(n)$ and let $lambda(n)$ be the length of a shortest chain consisting only of doubling steps.

We are given a tree with $n$ nodes, represented by $n-1$ edges connecting pairs of nodes. Each edge must be assigned a distinct integer label between $0$ and $n-2$.

We are asked to analyze permutations of a group of $n$ wise men, where some pairs of them know each other. For each permutation of these wise men, we can create a binary string of length $n-1$ indicating adjacency of acquaintances: a '1' if two consecutive wise men in the…

We need to construct a positive decimal number with exactly n digits. Every digit must be nonzero, and the whole number must fail divisibility by each digit that appears in it. For each test case, the input gives only the required length n.

We are given a string consisting of lowercase English letters, and the task is to construct the longest palindrome by combining a prefix and a suffix of this string.

The problem asks whether a given integer n can be expressed as the sum of exactly k distinct positive odd integers. Each test case provides n and k, and the answer is either "YES" or "NO". Odd integers are numbers not divisible by 2, so valid candidates are 1, 3, 5, 7,....

Each test case contains two positive integers. We may only perform one kind of operation: increase the first number by one.

The solution does not successfully establish what Exercise 4.6.3.13 asks. The positive part is that the displayed constructions are now genuine star chains.

The solution does not successfully establish what Exercise 4.6.3.13 asks. The positive part is that the displayed constructions are now genuine star chains.

The problem presents a single integer input that encodes two pieces of information. The integer can be decomposed as input = 1000 n + mod, where n is the number for which we want the double factorial and mod is the modulus to compute it under.

The problem asks us to compute a specific numeric property related to an integer input, denoted as a. While the problem statement is written in a poetic form, the underlying task is to find the number of integers less than a that are coprime to a.

The solution does not successfully establish what Exercise 4.6.3.13 asks. The positive part is that the displayed constructions are now genuine star chains.

We are given a tree with $n$ vertices. For every nonempty subset of edges $E'$, we build the edge-induced subgraph consisting of those edges and every endpoint that appears in at least one selected edge. For that subgraph we count its independent sets.

We are given a string s of length n and an integer k such that n is divisible by k. A string is considered k-complete if it is both a palindrome and periodic with period k. Being a palindrome means the string reads the same forwards and backwards.

The reviewer is correct. The displayed sequences are not addition chains, because the quantities $2^g,2^h,2^k,2^m$ were used as summands without first appearing as chain elements. The argument must be rebuilt from the definition of a star chain.

The reviewer is correct. The displayed sequences are not addition chains, because the quantities $2^g,2^h,2^k,2^m$ were used as summands without first appearing as chain elements. The argument must be rebuilt from the definition of a star chain.

We are asked to find all substrings of a string t that "match" another string s according to a flexible definition of equality.

We are given a number $D$ and need to reason about all of its divisors. The problem defines a graph whose vertices are all divisors of $D$. An edge exists from a divisor $y$ to a larger divisor $x$ if $x$ is divisible by $y$ and the quotient $x / y$ is prime.