brain

We are given a one-dimensional array a of length n. Each value of this array defines weights over all intervals in a very specific way: every pair of indices (x, y) with x ≤ y corresponds to a grid point on a triangular board, and that point implicitly carries a value…

We are given a directed graph of n locations and m one-way roads. Traveling along any road costs exactly one minute.

The task is intentionally trivial from a computational perspective. We are given a multiple-choice exam consisting of 10 independent questions. Each question has four options labeled A to D, and the correct output is simply a sequence of chosen options, one per line.

We are given two observed constraints about three consecutive segments on a line. Think of a point $x$ as the start of the first segment.

We are given a rooted tree where each node initially holds a binary value, either 0 or 1. The tree is dynamic in the sense that two types of operations are applied over time. The first operation selects two nodes and treats them as endpoints of a simple path.

We are given a rooted binary tree where each node has a color value. Every node has at most two children, and children are explicitly given as left and right pointers (or zero if absent). The root is node 1.

We are working in a geometric setting where each enemy is represented by a circle in the plane, and the player is fixed at the origin. From the origin, a hook is fired along a straight ray in some direction.

We are given a small battlefield with at most seven identical enemy minions. Each minion starts with a protective shield that blocks the first incoming damage entirely.

Two hidden integers are chosen at the start of each test case, and they never change during our interaction. Both numbers lie in a fixed range below $2^{60}$, so they are effectively 60-bit values.

We are given multiple independent strings, and for each one we need to decide whether it can be decomposed into a sequence of substrings where every piece is a palindrome.

We are given a metro system where stations are nodes and each metro line is a fixed path through some of these stations. Each line has a travel time for every adjacent pair of stations on the line.

Working

We are given several stacks of cards. Each stack contains some distinct integers, and globally all card values form a permutation, so every value appears exactly once across all stacks. A game consists of multiple rounds.

Working

We are given a list of integers and a modulus value. The task is to compute the product of all numbers in the list and then output the remainder when that product is divided by the given modulus.

We are given a tournament-style directed graph: every pair of distinct vertices has exactly one directed edge between them. For any two nodes $u$ and $v$, either $u to v$ or $v to u$, never both and never none.

We are given two rectangular plywood pieces. They must be placed so that one rectangle is horizontal and the other is vertical, intersecting at a right angle. The resulting figure must be a proper cross.

We are given a number $n$, which is the total perimeter of a triangle. We want to build integer-sided triangles whose side lengths add up exactly to $n$.

We are given a shop that sells wallpaper rolls of different types. Each type has a fixed price per roll and a limited remaining length available in the store.

We are given a total number of points scored in a basketball match, where every successful scoring action contributes either 1, 2, or 3 points. The actual sequence of shots is unknown, only the final sum matters.

I can’t reliably write a correct Codeforces editorial for this yet because the actual problem statement is missing from what you provided.

We are given a company hierarchy that forms a rooted tree. Employee 1 is the root, and every other employee has exactly one direct boss whose ID is smaller, which guarantees that all edges point from a node to a smaller-index parent and the structure is a tree rooted at 1.

We are interacting with a hidden geometric object: a circle placed somewhere inside a very large square grid. The square spans coordinates from 0 to 100000 on both axes, and the circle has integer center coordinates and an integer radius.

We are given a collection of tasks and two employees who will execute them. Each employee starts with the same initial skill value.

We are given a collection of source containers, each containing a mixture of two liquids A and B in fixed proportions. From each container, we are allowed to take any fraction of its contents, and that fraction always preserves the original ratio of A to B inside that container.

We are given a line of $n$ tarot cards indexed from left to right. A random process repeatedly reduces this line until only one card remains. Each round, a fair six-sided die is rolled. Suppose it shows $x in {1,dots,6}$.

We are given a set of labeled chayas placed along a straight line. The exact order is unknown, and we want to count how many full left-to-right permutations of these chayas are consistent with a list of historical observations.

We are given an $n times n$ grid that starts in a fixed checkerboard pattern. A cell $(i, j)$ is initially black if $i + j$ is odd and white otherwise. Then we repeatedly apply operations that flip entire rows or entire columns. A flip means every cell in that line changes color.

We are given a single string made of lowercase letters, and we want to rewrite it in a compressed form that is defined by a small grammar.

We are given a stream of quiz results for a single player, where each result is either correct or incorrect. The player starts at rank zero, and ranks can only increase. The rule for increasing rank is based on looking backward at the most recent portion of the history.

We place $2n$ gondolas on a circle. Each gondola must be assigned one of $k$ colors. After coloring, we try to connect gondolas in pairs, with two constraints: every gondola is matched with exactly one other gondola of the same color, and the drawn segments representing these…

We are given a small rectangular grid, where each cell contains one of six letters: Y, O, K, O, H, A, M, A. From this grid we want to count how many ways we can trace a specific fixed word of length eight: Y followed by O, K, O, H, A, M, A.

We are given a very small universe of items, exactly eight types of souvenirs. Each type has a limited stock, described by an array of eight integers. Separately, there are $n$ people, and each person independently requests exactly one of these eight types.

We are asked to construct a binary string consisting only of 0 and 1 such that the number of subsequences equal to 01 is exactly m. A subsequence 01 means we pick a 0 somewhere in the string and a 1 later in the string. Every such pair contributes one to the total count.

We are simulating a turn-based survival process where a character starts with an initial health value and repeatedly loses health over a sequence of rounds. The twist is that the damage applied at the end of each round is not fixed.

We are given a triangular grid of depth $n$. The bottom row contains a single cell, and each row above it expands by one cell on both sides, so the top row has $2n-1$ cells.

We are given a triangular arrangement of cells with $n$ rows. The bottom row has a single cell, and each row above it expands symmetrically so that the top row contains $2n - 1$ cells.

We are given many independent checks of a very small “program”: an integer x is stored in a 32-bit signed int, then it is converted into some unknown integer type, and the resulting value is compared against a given integer y.

We are given two strings consisting of lowercase letters. The only allowed operation takes any consecutive block of four characters and deletes its middle two characters, effectively turning a pattern of length four into a pattern of length two while keeping the first and last…

We are given a function applied to every integer from 1 up to a limit $n$, and for each integer we decide whether it contributes a value of 1 or 0. The final answer for each test case is the total number of integers in the range that satisfy a certain structural property.

We are given a line of elements, each carrying a positive cost equal to its value. We start with a fixed energy budget and want to delete elements from the line as long as we never go negative in energy. Two types of deletions are allowed.

We are given a process that takes an array and builds a new array by scanning indices from left to right. At each position, the current element is either pushed to the front of a growing result array or appended to its back depending only on whether the position is odd or even.

We are given a function defined on natural numbers. For a number $x$, we look at whether there exists an integer exponent $k 1$ such that $x^k$ is a rational number. The function $f(x)$ outputs 1 if such an exponent exists, otherwise it outputs 0.

We are given a subtraction game played on a pile of balls. A state of the game is defined by the current number of balls, say $a$. On a player's turn, the allowed move size is determined by a function of the current state: compute the sum of digits of $a$, call it $x$.

We are given a calculator where every button is initially disabled. The buttons include digits from 0 to 9 and the four basic arithmetic operators plus an equals sign. Once we choose some subset of these buttons to activate, we are allowed to use them any number of times.

We are given two arrays, both of length $n$, and a fixed target number $k$. The task is to count how many pairs of indices $(i, j)$ produce the property that the least common multiple of $ai$ and $bj$ is exactly $k$.

We are given a sequence of integers representing flavors placed on a line of layers. A valid interval is any contiguous subarray, but only some of these intervals are counted.

We are given a grid where each cell behaves like a piece of floor with a limited tolerance to being stepped on. Every friend starts at the top-left corner and tries to reach the bottom-right corner by moving only in four directions.

We are given a circular structure with a fixed number of positions around it. Between these positions, there are intervals marked by non-overlapping “retainer wires”, which effectively partition the circle into consecutive cleaning segments.

We are given a grid of size $n times m$, where each cell has a height value. Syrup is poured onto some starting cells, and from each starting point it spreads across the grid following a rule that depends on height and movement constraints.

We are working with nine-digit integers that represent possible configurations of Janise’s baklava layers. Each valid configuration is just an integer $N$ in the range from $100{,}000{,}000$ to $999{,}999{,}999$.

We start with a square pastry of side length $l$. Mila performs a repeated geometric construction: each round she draws a smaller square inside the current one using midpoints of its sides, producing a new, rotated, and strictly smaller square.

We are given two arrays of equal length. One array represents target quantities for different orders, and the other represents current quantities in prepared batches.

We are given a grid where each cell represents a piece of baklava that can tolerate a limited number of times being stepped on. Every friend starts at the top-left corner and tries to reach the bottom-right corner by moving one cell at a time in the four cardinal directions.

We are given a circular arrangement of teeth, where some intervals are covered by retainers. These retainers partition the circle into several free arcs. Each free arc is a contiguous segment of teeth that must be cleaned.

We are given a rectangular grid of size $n times m$, where each cell contains a height value. Think of this grid as a landscape of baklava pieces with different elevations. Zeynep repeatedly pours syrup onto some starting cells.

We are given two arrays of the same length. One array represents customer orders, where each value is the number of baklavas a customer wants. The other array represents how many baklavas are currently prepared in each batch.

We start with a square pastry of side length l. Mila repeatedly performs a geometric operation that replaces the current square with a smaller square formed by joining midpoints in a symmetric way.

We are looking at 9-digit numbers that represent possible baklava layer counts. Each such number is a valid configuration, so the search space is simply all integers from 100,000,000 to 999,999,999 inclusive. There are two conditions attached to a valid configuration.

We are given several independent bakery orders. Each order describes a stack of layers, where the first layer has some initial thickness and every next layer becomes exactly one unit thicker than the previous one.

We are given a fixed set of bases $pi$ and associated weights $ci$. Each query gives a short digit string $s$, and we are allowed to split it into several consecutive parts. Each part must be a valid decimal number without leading zeros.

We are given a set of directions on a circle, each direction representing a straight line passing through the origin. Each line is encoded as an angle in scaled form: instead of storing the angle directly, we are given an integer $ai$, and the actual angle is $ai / Q$ degrees.

We are given a graph of rooms connected by corridors. The structure is special: every room is reachable from every other room, there is at most one corridor between any pair of rooms, and there are no cycles except those that are forced by traversing the same path forward and…

I can’t responsibly write a correct Codeforces editorial yet because the actual problem statement for 104836D - “Идеальная турнирная система” is not available in the provided context, and it is not something I can reliably reconstruct from memory…

We are given two movie franchises, each with multiple screening start times. Each screening has a fixed duration, so every start time implicitly defines a full interval on the time axis.

We start with a pile of candies and want to understand how many friends should be invited so that after a very specific distribution process, a fixed number of candies remains. The distribution rule is cyclic.

We are given a standard $n times n$ chessboard where the top-left square is colored black and colors alternate perfectly both horizontally and vertically. This creates the usual checkerboard pattern. The task is to determine how many squares of size $1 times 1$ are white.

We are given a rectangular grid that represents a partially observed battlefield for a simplified Battleship-like game. Each cell of the grid can be in one of three states: it is either known to be empty water, known to contain a ship segment, or unknown.

We are given a set of words, all distinct, and a directed system of allowed replacements between them. Each replacement rule says that one word can be substituted by another, and this process can be repeated any number of times, following chains of replacements.

We are given several strings, and we are allowed to reorder them and glue them together into a single long string. When we glue two strings, we are not simply concatenating them blindly.

We are given a set of cars that all enter a tunnel at known times. Each car is uniquely identified, and we also know the exact order in which cars leave the tunnel.

We are given a set of points on a plane, each point representing a possible location where an event can occur. Each point also carries a weight that reflects how important or likely that event is.

We are given a collection of segments on the number line. Each segment represents a range of “realities” that must be searched as a single item.

We are given a process that builds an infinite sequence by repeatedly selecting a natural number that has not yet appeared anywhere in the sequence and then appending three values derived from it.

We are given pairs of trees. For each pair, we want to determine whether the first tree can be transformed into something isomorphic to the second tree after a very specific operation: we are allowed to take the second tree, add new vertices and edges, and then relabel…

We are given a permutation and we repeatedly rotate it left by one position, so the first element moves to the end.

We are given several independent scenarios. In each scenario, there are $n$ cloned individuals arranged in some order, but we only observe the multiset of labels written on them. Each label is an integer between 1 and $n$.

We are given a permutation placed in a stack-like structure a, where only the last element of a is directly accessible. There is a second empty stack b.

We are given a string made of lowercase English letters. Two players take turns playing a game on this string. On each move, a player chooses two distinct letters that both currently appear in the string.

We are given $n$ distinct points placed on a circle of circumference $l$. Each point lies on the boundary, and its position is given as a coordinate along the circle. After that, each point is independently colored red or blue with probability $1/2$.

We start at a fixed 2×2 identity matrix and want to reach a target 2×2 integer matrix. Each move corresponds to multiplying the current matrix on the right by one of four fixed 2×2 matrices.

We are given a tree with n cities connected by n − 1 undirected roads. Every road normally costs 1 credit to traverse in either direction.

We are given a collection of intervals on the line from 1 to n. Each interval contributes to a symmetric n by n matrix in a very specific way: for any pair of indices x and y, we count how many of the given intervals simultaneously cover both x and y, and that count becomes…

We are asked to design a custom integer encoding system for a fixed bit-based format. Each number is encoded using a leading 4-bit selector, followed by zero to four additional 4-bit groups.

Each card in this problem belongs to a lane and has two independent attributes: a rank from 1 to n, and a color which is either white or black. A lane is just a multiset of such cards.

We are given a group of people trying to cross a river using a very small boat. There are two types of people: cannibals and missionaries.

We are given a circular array of length $n$. Each position initially contains some number of items, and we are allowed to redistribute these items using a very specific local operation.

We are given a very large integer, but instead of treating it as a number, we should think of it as a multiset of decimal digits. Bomboslav removes all digits from the cheque and wants to reassemble them into a new integer using every digit exactly once.

We are given a line of $n$ boxes and several initial configurations of $m$ identical stones distributed across them. Each configuration is simply an array of $n$ nonnegative integers whose sum is fixed to $m$.

We are looking at integers written in decimal form, but the key constraint is not about their numeric value alone. Each number is interpreted as a string, and every contiguous block of digits inside that string is turned back into an integer by stripping leading zeros.

The game simulates a basketball match where two teams each start with five active players and five substitutes. Over time, two things happen: players are swapped between the court and the bench, and scoring events occur.

We are given two points on an integer grid. Both the starting point and the destination lie strictly away from the coordinate axes, meaning neither coordinate is zero at either endpoint. Such points are called free points.

We are given a sequence of bytes, each written as a two-digit hexadecimal number, so each value lies in the range from 0 to 255.

We maintain a very large array indexed up to $10^9$, but only the first $n$ positions are initially non-zero. All remaining positions are implicitly zero. Each position holds a 30-bit integer. There are two operations. First, we can update a single position to a new value.

We are given a network of restaurants where edges represent a “neighbor” relation. Some restaurants already cooperate with Timur at the start.

We are given four fixed integers in each test, and we form two products: the first is the product of the first two numbers, and the second is the product of the last two numbers.

We are given a fixed number of days, and each day Igor must choose exactly one of two actions. He can either study, which reduces his “energy” by a fixed amount, or go to sleep early, which increases it by another fixed amount.

We are given a sequence of integers shown one by one. After each new number appears, we need to determine whether it can be “constructed” by taking two earlier numbers and concatenating their decimal representations in order, without inserting anything in between.

We are given several chests, each containing a certain number of coins. Two friends want to split coins so that each chest ultimately contributes equally to both of them, but a chest can only be “cashed out” if its coin count is even.

We are given two types of books. There are A math books and B programming books. Each math book contributes X new facts, and each programming book contributes Y new facts.