brain

We are given an undirected graph representing cities connected by roads, where each road has the same travel cost. A traveler starts at a source city S and wants to reach a destination city T.

We are given a weighted undirected graph of cities connected by normal roads, where every road can be used in both directions and has a fixed travel cost. In addition to roads, cities may contain special teleportation devices of different types.

We are given up to 35 power-ups, each of which contributes a fixed change to two attributes: attack and defense. Starting from zero in both dimensions, we choose any subset of these power-ups, apply all chosen ones (order does not matter because addition is commutative), and…

We are given a sequence of values that are inserted one by one into an initially empty binary heap array. Each insertion uses the standard “sift-up” procedure: the new element is appended at the end, and then it is repeatedly swapped with its parent while the heap property…

We are given an $n times n$ grid where every cell is white except for exactly one black cell that must remain uncovered.

We are given several test cases, and each test case consists of a collection of segments on the real number line. Every segment covers a closed interval from $li$ to $ri$, and each segment is labeled with one of two colors, either red or blue.

We are given a set of points on a 2D grid, each point representing the position of a tree that must be protected. The government wants to build a fence that is an axis-aligned simple closed boundary, meaning its sides are parallel to the coordinate axes.

We are given a repeated decision process over multiple rounds. In each round there is a group of $N+1$ players: Inés and $N$ others. Each round presents two possible mechanisms for distributing gold. In the first mechanism, a subset of players chooses to “share”.

We are given a convex polygon that represents a fenced garden. One vertex is special: the goat is tied to this vertex with a rope of length $L$. The goat can move freely outside the polygon, but it cannot pass through the fence, and the rope itself cannot cross the fence either.

We are given a single string of fixed length ten, consisting only of uppercase Latin letters. From this string, we are allowed to delete characters, but we are not allowed to rearrange what remains.

The task is intentionally minimal: there is no input to process and no computation to perform. The only requirement is to produce a single fixed sentence exactly as specified in the output format.

We are given a tree where every node carries an integer value. For multiple queries, each query provides two nodes u and v, and we must decide whether the product of all values along the unique simple path between u and v forms a perfect square.

We are given a stack of concentric convex polygons, one inside another, where each polygon fully contains the previous one. Each layer has an associated score.

The grid can be seen as a board of ice tiles and walls. From any starting ice cell, a move consists of choosing an initial direction and then continuously sliding in that direction until an obstacle stops the motion.

We are building strings of length $n$ using a fixed alphabet of exactly seven symbols, from $a$ to $g$. Every position in the string is chosen independently from this alphabet, but not every resulting string is allowed. The restriction comes from a set of forbidden rules.

We are given a fixed list of points on a plane, stored in order, and we are asked to answer many independent queries. Each query selects a contiguous segment of these points and also gives a viewpoint located strictly above all points.

Ten judges each pick a number between 1 and 10, representing which problem they want added to the contest. After all votes are collected, the selected problem is the one with the highest number of votes.

The task is intentionally minimal. We are given a single string, and the input is always the same fixed token. The output must reproduce that token exactly, without modification, interpretation, or transformation.

We are given a pile of stones. Two players alternate turns, and on each turn a player removes some positive number of stones. The restriction is that the number of stones removed must be strictly smaller than the most significant bit value of the current pile size.

We are given a tree with nodes labeled from 1 to N, but the tree itself is lost. What remains is a list of pairs of nodes that were remembered as being at maximum possible distance in that tree, meaning each listed pair has distance equal to the tree’s diameter.

We are given two permutations of the same length, and each position represents a paired choice between two values, one coming from the first permutation and one from the second. At every index we are allowed to “activate” some transformation on the values at that index.

We are given a 3D wooden block composed of unit cubes arranged in a grid of size $L times W times H$. Each cube $(i,j,k)$ can be reinforced at some cost, and if we choose to reinforce it, we pay $V(i,j,k)$.

We are asked to design a tournament population so that a very specific elimination system can run without ever getting stuck. Each player starts with zero wins and zero losses. A match always produces a winner and a loser.

We are given a sequence of commands processed by a robot that moves between restaurant tables and records orders. The robot starts at table 1.

We start with a deck of N positions. Each position initially holds a card with some value, and we are given a target arrangement describing what value we want at each position after repeated shuffles.

I can’t write a correct Codeforces editorial for this yet because the actual problem content is missing. What you provided (“Desert Travel”, “Hard fence”, empty input/output section) doesn’t contain the rules of the problem: there’s no description of the…

I can’t reliably write a correct editorial for this yet because the actual problem content is missing. What you provided only includes the title (“Which Number”) and a tag (“maxsat”), but none of the real statement, constraints, or input/output definition.

I can’t reliably write a correct Codeforces editorial for “106082D - Pseudo Pseudo Random Numbers” from the information provided, because the actual problem statement (inputs, operations, and required output) is missing.

I can’t write a correct editorial without the actual problem statement. Right now, the input/output section is empty, and “Number Maximization” alone isn’t enough to reliably reconstruct the task.

We are managing a line of reactors, each one behaving like a small system with two internal values: a current pressure and a maximum pressure threshold. Initially every reactor has zero pressure, while each position starts with its own threshold value.

We are given a 4 by 4 Latin square over four symbols representing fruits, except that some cells are already empty. The valid full configuration is always a Latin square: every row and every column contains each of the four fruits exactly once.

We are given several independent queries. Each query contains two integers, and we need to decide whether these two numbers form a pair of twin primes.

We are given a polynomial described by its coefficients in increasing order of degree. In other words, the input defines a function F(x) = f0 + f1 x + f2 x^2 + ...

We are working with a graph where the process starts from a single distinguished vertex, initially vertex 1, and we maintain a dynamically growing set of vertices, called $c$. Conceptually, $c$ is always treated as a single “compressed” component.

We are given a long sequence of levels, each level carrying a difficulty value. The player can remove exactly one contiguous block of fixed length $k$, and everything outside that block remains and contributes to the total difficulty.

We are given a rooted tree with vertices labeled from 1 to 2n, rooted at 1. Each vertex represents a “teaching area” that must appear as a connected region inside a grid of size (n+1) by (2n). Each cell of the grid either contains 0 or one of the labels 1 through 2n.

I can write the full Codeforces-style editorial, but I’m missing the actual problem content. Right now, “Codeforces 106467D - Left & Right” in your prompt does not include the statement, constraints, or samples, so I cannot reconstruct the intended solution or guarantee…

We are given a tree, but we do not directly work with edges. Instead, we are given access to its distance matrix, where entry $D{i,j}$ stores the length of the unique path between vertices $i$ and $j$.

We are given an array of non-negative integers. Each query asks about a subarray defined by a range, but the actual range is not given directly.

The task revolves around counting contributions of certain structured binary strings that are implicitly generated by a process that walks along a fixed “main string” and records how far it can match prefixes while extending.

The problem defines a notion of a “level” where movement between tiles follows chess bishop-like behavior, and each pair of tiles has an associated minimum time required to move between them.

A group of N participants wants to visit tourist spots numbered from 1 to K. Each participant comes with a list of places they refuse to visit.

We are asked to count how many different ways we can build a sequence of participants whose individual contributions to a “fun score” add up exactly to a given target value $D$. Each participant contributes either 1 unit of fun in a normal state or 2 units if enhanced by AI.

We are simulating a commuter who travels over a sequence of days, where each day requires access to a bike from one or both of two providers.

We are given a weighted grid. Each cell has a positive value, and we want to select a simple closed shape drawn along grid edges. The shape must not self-intersect and must form a single closed loop. The region enclosed by this loop is a connected set of unit cells.

We are given a construction that starts with a square and then repeatedly places additional squares inside it. Each new square is rotated by 45 degrees relative to the previous one, so the whole picture becomes a nested system of overlapping diagonals and edges rather than a…

We are given a list of positive integers. From this list, we conceptually form every unordered pair of distinct elements. For each pair, we compute the least common multiple of the two numbers, producing a very large multiset of values.

We are given a circular structure with n positions, each carrying a value. A process is defined where we choose a “step size” d, and then repeatedly jump around the circle by adding d modulo n.

We are given an array that is partitioned into consecutive groups of fixed size, and the task is to determine whether the structure can be rearranged into a globally sorted order under constraints that preserve group structure.

We are simulating a process where a snake moves through a fixed sequence of cells over time. At each time step $t$, the head of the snake occupies a known cell $c(t)$. Some cells may repeat over time, meaning the snake can revisit the same position later.

We are given a very small multiset of characters, and we are asked to consider every distinct string that can be formed by rearranging some or all of those characters.

We are given a system that repeatedly manipulates a stack of plates. There are P distinct plates, initially arranged in a stack. Over D days, each day specifies a number Ki.

We are given a sequence of purchase requests, each associated with a cost. Every request must be satisfied exactly once, and satisfying a request corresponds to making one purchase of that item at its full listed price.

We are given a line of spirits standing in a queue, each with an initial height. Two observers look at this queue from opposite ends, but each of them has a very specific visibility rule.

We are given a long uppercase string that represents a recording of a choir performance. Each hamster in the choir has a unique “song”, and each song is exactly two characters long.

We are given two binary grids of the same size, each cell containing a value that can be interpreted as either 0 or 1. The task is to transform the first grid into the second grid using a specific type of operation: choosing a cell (or position) and flipping its value.

We are given a collection of items, each with an integer weight. There is also an initial offset value, which behaves like a starting balance in the system. The process begins from this offset, and each item can be chosen at most once.

We are asked to select exactly k characters from a pool of n, maximizing total strength, but the choice is restricted by two independent classification rules derived from each character’s attributes. Each character has a value ci which we want to maximize in sum.

We are given a system of multiple buildings, each associated with a production rate. Time progresses in discrete days, and as time increases, each building accumulates demand for “food boxes” according to its own rate.

The statement you provided is effectively empty. It only contains the problem title “秘源机兵统御械 - 疾攻” and no description of the input, output, constraints, or rules of the task. A Codeforces editorial depends entirely on those details.

We are given a rectangular grid of size $h times w$. Every cell must be filled with one of three letters: ‘K’, ‘I’, or ‘T’. The counts of these letters are fixed in advance, so the grid is essentially a multiset of characters that must be arranged into a matrix.

We are given a set of points on a triangular lattice defined by two basis vectors, typically denoted $e1$ and $e2$. Every point in the input is expressed as an integer combination $u cdot e1 + v cdot e2$.

We are given two parameters, a value limit m and a window size k. We must construct a sequence a, where each element is between 1 and m, such that a certain process produces different results when the window size is k versus when it is k+1.

We are given 8 teams, and we must arrange them into a fixed single-elimination bracket with 8 seed positions. The bracket structure is completely predetermined: seeds 1 vs 2, 3 vs 4, 5 vs 6, 7 vs 8 in the first round, then winners of (1-2) play winners of (3-4), and winners of…

We are given an array of length $N$, where each position $i$ is associated with a forbidden value $Ai$. The task is to construct a permutation $P$ of numbers $1$ to $N$ such that no position matches its forbidden value, meaning $Pi ne Ai$ for every index $i$.

We are given a set of points on a plane, and the task is to cover all of them using at most two circles. Each circle can be placed anywhere and can have any radius, including zero.

We are given multiple independent queries. Each query provides two prime numbers, both strictly less than 10000, and we treat them as four-digit numbers by padding with leading zeros when necessary.

We are given a long string representing a sequence of enemy types in a game level. Each query selects a contiguous segment of this string, and for that segment we must measure how repetitive its internal substrings can be.

We start with a sequence of non-negative integers. Each move picks two adjacent elements, adds their sum to a running score, and inserts that same sum back into the array between those two elements.

Each item in this problem is a key that has a rigid base length and a single protruding segment somewhere along that base. When a key is placed, its base contributes to a growing horizontal line, because all chosen keys are concatenated in some order without gaps.

We are dealing with three arrays of equal length, representing daily expenses split into food, equipment, and tavern spending. For the original data, every day has the same total spending across all three categories.

We are given a geometric progression defined by its first term and ratio. Concretely, the sequence is A: q, q·r, q·r², q·r³, and so on, continuing infinitely.

We are given a rooted tree of employees. Employee 1 is the root, and every other employee has exactly one direct manager with a smaller index, so the structure is a rooted tree. Each node carries a label, a single lowercase letter representing that employee’s specialty.

We are working on an integer grid where each entity moves in discrete time under two competing forces: player-controlled movement and a deterministic attraction toward the origin.

We are given a permutation of numbers from 1 to n, which we can think of as a sequence placed along a line. For any query segment [l, r], we look only at the values inside that segment and ask for the length of the longest subsequence whose values strictly increase.

The task is not a typical interactive or input-driven problem. Instead, the statement describes a solved Japanese crossword puzzle (a nonogram) that encodes a single hidden picture.

We are given a row of positions, each position holding a stamp labeled with either an opening or closing parenthesis. We do not take substrings in the usual sense. Instead, we build a sequence by walking along these positions.

We are given a prime number $p$ and a string that represents the output of a hidden numeric process applied to an unknown sequence of coefficients $a0, a1, dots, a{n-1}$, where each coefficient is an integer in the range $[0, p-1]$.

I can’t write a correct Codeforces editorial from this yet because the actual problem content is missing. What you provided only includes the title “笨蛋题” and no description, input format, output format, or constraints.

The problem content you provided only contains the title and no actual statement, input format, output format, or constraints.

The problem statement is effectively missing here. What you provided only contains the title, with no input/output description, constraints, or sample behavior to anchor a solution.

I can’t produce a correct editorial for this yet because the actual problem content is missing. Right now, “Codeforces 106384D - 繁星坠海” is provided without any statement, constraints, input/output description, or samples.

We are given a string of length $n$, where each position represents a light bulb colored red, green, or blue. The only operation available is to pick a bulb and “touch” it, which immediately resets its color to one of the three colors uniformly at random, independently of…

Codeforces 106289D: Cube

Codeforces 106270B: Boulevard of Broken Cars

We are asked to build a fixed logic circuit over $n$ input nodes. Each input node carries one of four symbols: three colored signals $R, G, B$, and a special transparent signal $$ that behaves like an “empty” value.

We are given a nearly complete undirected graph on $n$ cities. Originally, every pair of cities had a road, so the graph was a clique. Then a small number of edges, at most 200, were removed.

We are given a sorted list of distinct points on a number line. The task is to cover all these points using at most $k$ segments, where a segment can be any interval $[a,b]$ and its cost is its geometric length $ A useful way to reframe the problem is to think of grouping points.

We are working with a tree where every node is either normal or special. A walk is allowed to move along edges freely, but there is one asymmetry in how nodes behave during the walk: normal nodes can be revisited any number of times, while each special node can appear at most…

We are given a graph whose vertices are points on a plane, but the geometry only matters through the x-coordinates. Each edge connects two vertices, and an edge can be thought of as a straight segment, although crossings between segments do not allow traversal.

We are given points placed on a circle, each point having an angle θ and an independent probability p of being “activated”. After activation, every triple of activated points forms a triangle, and all such triangles together act as a defensive region.

The grid describes a city map where each cell is either free ground, an obstacle building, a street tile, or one of two special positions: the starting point and the target.

We are asked to construct three non-empty strings over lowercase English letters such that the pairwise distances between them match three given integers.

We are given an array of integers. We are allowed to repeatedly apply a specific local operation on any adjacent pair. The operation takes two neighboring values, computes the bitwise AND of the pair, and then XORs that value into both elements.

We are given a rectangular grid made of two colors, represented by . and . This grid is not arbitrary; it is assumed to be a fragment of a much larger infinite tiling. The hypothesized structure is a chessboard-like arrangement of identical square blocks.

We are given a rectangular floor plan made of small square rooms arranged in an r by c grid. Between adjacent rooms there are walls, and each wall has a digit cost indicating how expensive it is to drill a pipe through that boundary.

We are given a tree with $n$ vertices. Each edge must be assigned a color from a palette $0$ to $K-1$, where $K$ is not fixed in advance and is part of what we are trying to maximize. Once edges are colored, we look at simple paths in the tree.

We are given a hall with $d$ doors. Exactly one door hides a prize, and all others are empty. The player is allowed to initially choose a group of $s$ doors instead of just one.

Each card type comes with a collection of buy and sell offers, each tied to a specific price level. A buy offer at price p means someone is willing to purchase at any market price up to p.

We are simulating a very specific construction process that builds a permutation indirectly. Instead of being given the final arrangement of cards, we are told how the deck is built step by step, and we are asked to reverse engineer the decisions that would produce a desired…