brain

We are given a weighted tree with $n$ cities. Every pair of cities is connected by exactly one simple path, and each road has a positive length. Two special cities $s$ and $t$ are fixed, and the main object of interest is the shortest path between them in this tree.

We are given two sequences of length n, representing numbers written on two bracelets. The goal is to make the two multisets of numbers identical, meaning that after reordering, both bracelets contain exactly the same values with the same multiplicities.

We are given an n by n chessboard, where n is at most 16, and we must place exactly k queens. A queen behaves normally, attacking along its row, column, and both diagonals. A cell is considered protected if at least one queen attacks it or if a queen stands on it.

We are given a set of distinct integers, each having at least two digits. For every ordered pair of different numbers, we want to check a simple digit condition: the last digit of the first number must match the first digit of the second number.

We are given a sequence of elements and a parameter that controls what makes a subarray “interesting”. The task is to consider all contiguous subsegments of the array and determine how many of them satisfy a constraint based on how diverse their contents are.

We are given a railway line of cities arranged in a straight sequence. Each city has a platform with a fixed height. There are train routes, and each route connects an interval of cities. A train route also has two important parameters: a class and a floor height.

We are given several test cases. In each test case, there is an array of positive integers, and the task is to determine whether we can pick a subsequence of length at least two whose average value is an integer.

We are simulating a population of rabbits that evolves over time with two independent behaviors. We start with two fully grown rabbits on day zero.

We are given an array of numbers and a binary string of the same length. We process indices from left to right. At position i, if the binary character is 1, we take the prefix of the array from 1 to i and reverse it in place; otherwise we do nothing.

We are given an integer array, and we are allowed to modify its elements. The goal is to make the array follow a very rigid structure: every pair of adjacent elements must have the same XOR value.

We are given a length $n$, and we consider all permutations of the numbers from $1$ to $n$. For each permutation $p$, we define its score as the sum of bitwise XORs between adjacent elements, meaning we look at $p1 oplus p2 + p2 oplus p3 + dots + p{n-1} oplus pn$.

We are given two arrays of the same length, and we want to count subarrays based on a relationship between values in the first array and values in the second array over the same segment.

We are asked to construct a permutation of numbers from 1 to n such that consecutive triples behave in a very specific alternating way when viewed through parity of adjacent sums.

We are working with permutations of the numbers from 1 to n. For any such permutation, we look at each position i and compare the value pi with its index i. Some positions satisfy pi < i, some satisfy pi i, and the remaining satisfy pi = i.

We are given a string over the alphabet {s, y, s, u} and we are interested in extracting as many disjoint subsequences equal to the pattern sysu as possible.

We are given a string $S$ and a pattern string $T$. The operation allowed is to choose any substring of $S$ whose length equals $ A key way to reinterpret this is that we are not directly editing characters one by one.

We are given a rectangular arrangement of cells with n rows and m columns. Each row i initially contains a block of ai stones packed on the left side, so in row i, columns 1 through ai are filled, and the remaining cells are empty.

We are working on a hidden grid of size $R times C$, where some unknown cells contain mines. The exact number of mines is not given, and their positions are completely hidden.

We are given a 3 × 3 Tic-Tac-Toe board. Each cell contains either X, O, or .. The board is not guaranteed to be a valid state from a normal game, so the counts of X and O do not matter. Nobita gets a special power: he may place two O marks consecutively on any two empty cells.

We are given a graph of locations. There is a special node labeled 0, which represents Doraemon’s workshop, and there are n other nodes representing houses. Each house is marked as either good or bad.

We are given a sequence of vertical poles placed at integer coordinates on a line, where pole i sits at position x = i and has height h[i].

We are working on an infinite triangular grid where each cell is a location you can stand on, and each move corresponds to “flipping” a rigid tetrahedron from one cell to an adjacent cell.

We are given an array of length $n$, where every entry must be an integer between $1$ and $m$. Among all such arrays, we are asked to count those that satisfy a very rigid structural constraint involving values of the array acting like a function on indices.

I can't write a correct editorial and solution for this problem from the statement alone. The problem you provided is from a recent ICPC contest (Gym 106118G), and the key part needed for an editorial is deriving the actual accepted solution.

We are given a line of mountains, each with an initial height. A journey is defined as walking from index $l$ to $r$, always moving one step to the right, and paying the cost of each move as the absolute difference between consecutive heights.

We are given a fixed set of n players, each with a strength value. We must choose a single ordering of these players, and that ordering will be reused unchanged against m different opponent teams.

We are simulating a performer who repeatedly jumps in cycles whose duration depends on his current energy. Each jump lasts exactly $E$ milliseconds at the moment it starts, and the jumps are chained back to back as long as energy remains positive.

We are given a directed graph where each vertex represents a person and each directed edge represents a “follows” relationship. If there is an edge from $u$ to $v$, then person $u$ follows person $v$.

We are given a social network of kids, represented as an undirected graph where vertices are kids and edges represent friendships. Each kid must be assigned exactly one game variant from a pool of k possible variants.

The input describes a triangular “pyramid-shaped” subset of a rectangular grid. Each row is centered inside a fixed-width grid of size $2N-1$, and row $i$ contains exactly $2i-1$ usable cells forming a symmetric triangle.

We are given a set of books, each book having a spine height and a thickness. We need to place every book into exactly one of two groups: one group is placed upright on the shelf, and the other group is stacked horizontally into a single pile.

We are given two timestamps that describe when a crochet competition started and when it ended. Each timestamp contains a weekday together with a clock time in hours and minutes. The goal is to compute how long the competition lasted, measured in days, hours, and minutes.

We are given a set of points in the plane, each representing a tower placed at distinct coordinates. The task is to select some of these towers and connect them in a cycle so that they form a simple polygon, and this polygon must satisfy a geometric constraint: every interior…

We are given a fixed sequence of authors, and each author comes with up to ten possible strings, each string being one part of their full name. We must choose exactly one string per author.

We are given a list of ingredients that appear on a product label. Some ingredients have a known percentage, and others are left unspecified.

We are given three strings consisting of the characters 1, 2, and 3. The hidden object is the real sequence of game winners. If player 1 wins a game, then players 2 and 3 write down 1, but player 1 forgets to record that game.

We are given a binary array of length $n le 1000$, initially all zeros. We do not directly set bits. Instead, we repeatedly choose a contiguous segment $[l, r]$, and the system “exposes” that segment to randomness, replacing every bit inside it with an independent fair coin…

We are given a group of $n$ players and a list of pairs of players who already know each other. The task is to divide all players into exactly two teams of equal size, and the constraint is that within each team every pair of players must already know each other.

We are given a multiset of characters that originally formed a valid arithmetic expression, but all characters have been shuffled. Our task is to decide whether we can rearrange these characters into a syntactically valid expression, and if yes, output one such expression.

We are given a bottle that initially contains two kinds of liquid: alcohol and everything else. Over time, both parts evaporate, but at different constant rates per day.

We are given a sequence of spell values, each a non-negative integer, and a shield with a very specific usage pattern.

We are given a system where a sender receives a binary string and must transmit it through a very unreliable channel. The channel does not preserve boundaries of the transmitted packet. Instead, what arrives is a cyclic shift of what was actually sent.

Once you provide it, I’ll write a complete, rigorous solution in the style typical of Kvant: clear structure, justified steps, and (when useful) a clean geometric or algebraic insight rather than just…

We are given a graph that is physically organized in a very rigid way. The junctions are split into villages, and these villages appear in a fixed circular order.

We are given an $h times w$ grid representing a pizza that was originally fully filled with square unit pieces. Some cells are still present, marked as , while others have been eaten, marked as .. We are not allowed to move any remaining pieces, only to partition what remains.

We are given a simple geometric structure: a convex polygon described by its vertices in counterclockwise order. The polygon is already well-behaved in a strong sense.

We are given a single bus line that starts at the university and goes through a sequence of stops in order until the city. There is a queue of passengers at the university, and each passenger has a fixed destination stop index.

We are simulating a very structured game involving two queues of players standing on opposite sides of a table. On the left side there are ℓ players arranged in a queue, and on the right side there are r players arranged in another queue.

We are given a tree, and we are allowed to repeatedly perform a very specific restructuring operation. Each operation first picks a node as the temporary root, which defines parent and child relationships for that step. Then we choose a non-root node $u$.

We are given a lowercase string. Before the game starts, we may rearrange its characters in any order we like. A single elimination operation chooses a contiguous block consisting of the same character, and that block must have length at least 3.

We are given a binary string representing a row of coins. Each position is either 0 or 1, and the goal is to transform the entire string into all 1s. The only allowed operation is choosing two adjacent positions and flipping both coins simultaneously.

Thinking

We are given a grid with $n+2$ rows and $m$ columns. The top row and the bottom row are safe, while the $n$ middle rows each contain exactly one stone statue. Each statue sits at a specific column in its row and faces either left or right.

We are playing a turn-based placement game on a fixed 4 by 4 board, so there are only 16 cells in total. Two kinds of tetromino pieces are available: T-shaped pieces and L-shaped pieces. We are given a limited supply, at most three of each type.

We have an $n times n$ cake represented as a grid. A cell contains either no fruit (0) or a fruit (1). The piece that Xiao Z cuts must come from the top-left corner of the cake.

We are given two descendingly sorted arrays of horse speeds. One belongs to Tian Ji and the other to the King. A match is formed by pairing one unused horse from each side, and the outcome depends on a strict comparison: Tian Ji earns money only when his chosen horse is…

We are interacting with a hidden permutation of size $n$. The permutation is fixed before any queries, and each query allows us to submit any length-$n$ array. The system responds with how many positions match exactly between our submitted array and the hidden permutation.

A patient is given a weight in kilograms and a prescribed total drug dosage in milligrams. The drug has a safety guideline expressed per unit weight: every kilogram of body mass allows a safe dosage between 10 and 20 milligrams, inclusive.

We are working with a tree where each vertex can be chosen as a starting point for a preorder DFS traversal. In such a traversal, we visit a node, then recursively traverse its neighbors in some arbitrary order, producing a linear sequence of all vertices.

We are given a single arithmetic expression written as a compact string. The expression contains only decimal digits, plus signs, and multiplication signs. Each digit is a standalone number, so there are no multi-digit integers and no parentheses.

We are maintaining a very large array of integers, supporting two kinds of operations over it. The first operation applies an affine transformation to every element in a contiguous segment: each value a[i] is replaced by a[i] c + d.

We are given a static array of integers and many independent operations. Each operation describes a segment of the array, and we conceptually perform three actions for that segment: reverse the subarray inside the interval, compute how many inversions the whole array would…

We are working with a tree where each node carries an integer weight. For every pair of distinct nodes, we look at the unique path between them and collect all node weights along that path.

We are asked to construct a strictly increasing sequence of length $n$, where every element is a non-negative integer below $2^{30}$.

We are given an initial multiset of integers that already has a very rigid structure: it is an arithmetic progression of length $n$, starting at $a1$ with common difference $d$. So the starting set is completely determined and sorted automatically.

We are given a large grid where each cell is either land, water, or lava. Lava is forbidden, while land and water are traversable.

We are given a list of ingredient freshness values and two fixed recipe coefficients. Each day, Maddy must pick exactly two unused ingredients and assign them to the two recipes in any order.

We start with a decimal number written on a stone. Each time we press a mechanism, we transform the number by replacing every digit independently with the square of that digit, written in decimal, and then concatenating these squared values in the same order.

We are given two small integers for each test case, and we must decide whether we can interpret them as the two fields of a valid 24-hour clock time in the format HH:MM.

We are given a small integer range defined by a starting point l. The hidden number a is guaranteed to lie somewhere in the interval from l up to l + 5, so at most six consecutive integers are possible candidates.

We are given a string, and we place integer markers on positions from 0 to n, where position i represents the boundary between characters.

I can’t write a correct editorial from “J” alone because there’s no problem content to reconstruct the logic, constraints, or even the task being solved. Anything I produce right now would be guesswork, and that would break the whole point of a Codeforces-style editorial.

We have an initially empty n × m grid. An operation can be performed at any cell. A type 1 operation fills every cell in the chosen row and every cell in the chosen column. A type 2 operation fills every cell on the two diagonals passing through the chosen cell.

The problem statement is missing from what you provided. All that appears is a single “I”, which isn’t enough to reconstruct the task, constraints, or required output.

I’m missing the actual problem statement for Codeforces 106139H - Prime Segments. Right now the prompt only contains the title and an “H”, but no definition of the input, output, or task, so there’s no way to reconstruct the algorithm correctly or write a meaningful…

I can’t write a correct Codeforces editorial from just “G” without the actual problem statement. Right now the input/output and constraints are missing, so any solution would be guesswork and would likely describe the wrong problem entirely.

The statement for Codeforces 106139F - Mod is missing from your prompt (only the title and empty I/O sections are provided).

I don’t have the actual statement for “Codeforces 106139E - Matrix Construction” in your prompt (it’s effectively empty), so I can’t reliably reconstruct the intended problem or write a correct editorial without risking inventing details.

I can’t reliably write a correct, problem-specific Codeforces editorial here because the actual statement of “106139B - Cut ellipse” is missing from your prompt (it only shows placeholders for input/output and no geometry description).

I can’t reliably write a correct editorial for “Codeforces 106139A - Customized Shortest Path” from what you provided, because the actual problem statement (graph definition, what “customized” means, constraints, and query format) is missing.

We are tracking a very unusual climb. Instead of a single position moving up a staircase, we have four distinguishable paws of a cat, each sitting on integer steps. The cat starts with all four paws at position 0, and wants to end with all four paws at position n.

We are given two sequences of the same length. One sequence represents Morty’s grades over n days, the other represents Rick’s grades over the same days. Each grade is an integer from 0 to 5, where 0 is a special value meaning absence.

Each input object is a convex polygon described not by vertices but by its directed edges in counterclockwise order.

We are given an array of distinct strengths representing gorillas positioned in a line. A segment $[l, r]$ is considered valid if the two strongest gorillas inside that segment sit exactly at the ends of the segment, meaning no interior element is larger than either endpoint.

We are given a row of independent rotors. Each rotor stores a value that wraps around, so rotor i behaves like a number on a circle from 0 to mi - 1. The system starts with every rotor at zero, and we want to reach a target configuration b.

Label the birdhouses by their positions $P_1,\dots,P_n$ in the plane, with all pairwise distances distinct.

The allowed tool is a straightedge together with the ability to construct a line parallel to a given line at a fixed distance equal to the ruler width.

We are given an $n times n$ grid where each cell is already colored either red, blue, or white. White cells are flexible, we are allowed to repaint each of them independently into either red or blue. Blue and red cells that are already fixed must stay unchanged.

We are given a grid of free and blocked cells, and we need to count how many distinct closed robot routes exist. The robot always starts on a free cell, moves to any of the 8 neighboring cells (including diagonals), and forms a cycle that returns to the starting cell.

We are given two fixed side lengths of a triangle, $a$ and $b$, and we want to understand what integer values a third side $c$ can take so that the three segments form a valid triangle with positive area.

We are working with a line of $n$ cells. Starting from an empty state, we perform $n-1$ painting operations. In operation $i$, we choose any contiguous segment of the line and repaint all cells in that segment with color $i$, overwriting anything previously painted.

We are observing a traffic light that cycles through four phases in a fixed order. The light starts at red, then switches to yellow, then green, then yellow again, and finally returns to red, repeating this cycle forever.

We are given an array of integers and a threshold value $d$. After we optionally delete exactly one contiguous segment from the array, the remaining elements must form a sequence whose maximum value minus minimum value is at most $d$.

We are given a hidden permutation of length $n$. Only two special elements matter: the position where the smallest value $1$ sits, and the position where the largest value $n$ sits.

We are given all integers from 1 to n, each written on exactly one card, and these cards are arranged into a single sequence using a fixed construction rule.

Please go ahead and provide the Kvant problem statement you want solved.

We are given a binary string representing a line of battlefield cells. Each cell is either empty or contains an enemy. The goal is to eliminate every enemy using two kinds of actions. A lightning strike removes exactly one chosen enemy.

We are maintaining a graph that starts empty and evolves through a sequence of edge insertions. Each inserted edge has one of two colors, red or blue, but the underlying connectivity of the graph ignores colors.

We are given a positive integer n whose decimal representation contains no zeros. From this number, we define a family of transformations: a “cyclic shift” where each operation moves the last digit of the number to the front.

We are given a tree where every vertex carries a color label. The task is to repeatedly delete parts of the tree until nothing remains, but deletions are constrained in a specific way. In one move, we may choose any set of colors and remove all vertices of those colors at once.