brain

Each city in the kingdom chooses exactly one destination city and a road is built between them. The result is a directed choice per city, but the road itself is undirected and has an integer length.

We are given a structure that is best understood as a tree of rooms connected by corridors. Every pair of rooms is connected by exactly one simple path, so there are no cycles and between any two rooms there is a unique route.

We are given a process that behaves like a random accumulation counter. Each time Lucy presses the roll button, the counter increases by an independent random value uniformly drawn from the interval $(0, d)$.

We are given a small-capacity multiset game where the state is just a collection of integers, each always either a power-of-two-like value starting from 2 or 4, and the only way to change values is by pairing equal numbers and merging them into a larger one.

We are given a chronological list of problem names, where each name consists of two words. We need to verify whether this sequence could have been produced by a specific selection rule. The rule describes how the sequence is constructed. The first problem can be any problem.

We are working with an infinite grid where every integer coordinate cell is independently colored either black or white with equal probability. The only operation allowed is to query a cell and receive its color.

We are given a digit string that originally came from writing two positive integers next to each other. Somewhere in between those two numbers, there was a division sign.

We are given several candidate shipping containers, each a rectangular box described by three side lengths. A souvenir box must also be a rectangular box, and it needs to be placed inside every one of the given containers.

We are given a non-negative integer that fits into 32 bits, and we need to convert it into a variable-length byte encoding. Instead of always using four bytes, we represent the number using chunks of 7 bits packed into bytes.

This problem removes all typical algorithmic structure and reduces the task to a fixed output decision. There is no input stream, no parameters, and no hidden state.

We are given a bipartite system between two cities. One side has $n$ entities and the other has $m$. Some pairs between the two sides are already connected by “links”.

We are given a sequence of integers representing friendliness values of towns arranged in a line. A traveler must choose a contiguous segment of this sequence, but the segment length is restricted: it must contain at least L towns and at most R towns.

Two players engage in a turn-based simulation where each maintains two resources and a queue of actions. Each action is either an attack, a defence, or a hide move, and every action carries a numeric strength.

Each light source is placed on an integer line at position $xi$, and each source has a strength $vi$. A source does not illuminate everything uniformly.

We are given a sequence of values that represents measurements stored in a system. These values have been corrupted by a series of operations. Each operation selects a continuous segment of the array and flips the sign of every value in that segment.

We are given two very large integers, each representing a number written on a separate record card. The task is not to compute the full sum in its entirety, but only to determine the last digit of their sum.

We are given a system of $n$ components, each of which must be assigned a non-negative integer value $di$. These values are not independent. There are directed constraints between pairs of components.

We are given an array of integers and asked to compare two expressions built from it. The first expression takes the greatest common divisor of all array elements and then applies factorial to that result.

We are given several groups of gnomes, each group having a fixed size, and several royal courts, each requiring a delegation of a specified size.

We are given several axis-aligned rectangles, and each rectangle has its bottom-left corner fixed at the origin while the top-right corner is given as $(wi, hi)$. So each input pair defines a rectangle that covers all points $(x, y)$ such that $0 le x le wi$ and $0 le y le hi$.

We are given a mountain represented as a vertical line from height 0 up to height n. Movement is linear: going up costs tu per meter and going down costs td per meter. On this line there are tasks. Each task consists of two heights ai and bi.

We are interacting with a hidden pair of integers $l$ and $r$, initially unknown but guaranteed to satisfy $1 le l le r le 10^6$. Our only way to learn about them is through an interactive process.

We have a linear dungeon made of n chambers ordered from exit to entrance. Each chamber can hold at most m bandits. Initially all chambers are empty. Time progresses in discrete minutes, and every minute consists of two actions applied in a fixed order.

We are given a fixed sequence of stages in a game, where stage $i$ corresponds to unlocking or obtaining the $i$-th ending.

We are given a geometric structure built from $n$ “layers”. For each integer $i$, there is a special point at $(i,i)$. From every such point, two straight segments extend: one goes vertically down to $(i,0)$, and the other goes horizontally left to $(0,i)$.

We are given an array of fixed multipliers of length n, where each position corresponds to a bit position in a binary number of up to n bits.

We are given a set of points on the plane representing insects. Exactly one of them must be chosen as the initial “source” that emits a signal at time zero.

We are given a collection of vertex pairs on an unknown tree with n vertices. Each pair represents a travel from one vertex to another, meaning it corresponds to the unique simple path between those two vertices once a tree is fixed.

We are given a character with $n$ attributes and a list of $m$ bosses, each also described by the same $n$ attributes. Over time, the character’s attributes change via updates, and a sequence of events describes battles against bosses.

We are given two very large integers a and b, each written in decimal form and potentially containing up to a very large number of digits.

A cube of edge length $a$ carries a steady current $I$ along a closed contour formed by its edges.

I can’t reliably write a correct editorial from that input because the actual problem content is missing. What you provided only shows the title “构造题” and no statement, constraints, or samples.

We are given a permutation, which can be viewed as a directed graph where every node has exactly one outgoing edge. Such a structure decomposes into disjoint directed cycles. Each cycle represents a group of positions that rotate among themselves.

We are given a rectangular seating layout that behaves like a grid with rows and columns. A person starts at one seat identified by its row and column, and wants to reach another seat in the same grid.

We are building sequences of length n using m distinct labels numbered from 0 to m-1, with the restriction that no label is repeated inside a sequence. So each valid sequence is essentially an ordered selection of n distinct elements from m, i.e.

We are given a simple undirected graph where each vertex carries a value. Along with the graph structure, the task involves applying a sequence of allowed operations on vertices and edges to eventually isolate and “extract” a special value, while also producing a concrete…

The task is essentially a direct comparison between two integers. Each test case provides two numbers, and the output depends only on their relative ordering. If both values are identical, the result is a draw.

We are given a weighted undirected graph. Each edge connects two vertices and carries a cost. The task is to select a set of edges that connects all vertices together, forming a single connected structure, while maximizing the total sum of chosen edge weights.

We are given two permutations of the numbers from 1 to N, written as two rows of a city layout. Each number represents a temperature zone, and every zone appears exactly once on each side.

We are given two piles of tiles, one pile contains white tiles and the other contains black tiles. The goal is to assemble the largest possible square chessboard using these tiles, with the additional constraint that the final board must follow a standard chess coloring rule…

We are given N points in the plane, each representing a cat at integer coordinates. A “circuit” is not a simple path but a very specific motion process: Catarina starts at some point with an initial direction, and repeatedly performs a move consisting of a forward walk, a…

We are given a sequence of colored balls that are inserted one by one into a growing structure. Each ball must end up in a stable pile where every ball is either placed on the ground or supported by exactly two balls directly below it.

We are given a row of stacks, each stack containing some number of books. The goal is not to move books individually but to apply a special operation on two chosen stacks.

We are given a system of runners where each standard runner, called an uma, has a starting parameter and a speed. There is also a special runner, Chippi Chappa, whose performance depends on a query value.

We are given a single integer $n$, and we want to determine the largest integer $x$ such that a certain geometric or combinatorial construction is possible.

We are given a multiset of integer labels representing oranges. After sorting these labels, we obtain an ordered sequence $b1 le b2 le dots le bn$.

We are working with numbers that are fundamentally treated through their digit structure rather than their arithmetic value. For any integer (x), we repeatedly apply a transformation that depends only on the multiset of its digits.

The problem describes a sequence of bosses in an infinite dungeon and a resource-driven decision process while traversing them.

A robot moves inside a one-dimensional corridor that can be thought of as a segment of integer points from 0 to L. The left wall is at position 0 and the right wall is at position L. The robot starts at position X and initially faces either left or right.

We are given a rooted tree with root at node 1. Each vertex can be painted either white or black, and we must paint exactly $k$ vertices black. All other vertices remain white.

We are given a sleeping interval from time a to time b. Inside this interval there are n fixed moments when nightmares occur, each one causing Vladimir to briefly wake up. These moments are strictly increasing. We are allowed to remove at most k of these nightmare moments.

We are given a hidden binary grid of size $n times n$. Some cells contain 1, others 0, and at least one cell is guaranteed to be 1. We cannot see the grid directly. Instead, we can ask whether a chosen subrectangle contains at least one 1, receiving a boolean answer.

We are given several independent scenarios. In each scenario there are multiple watchtowers. Each tower has two attributes: a strength parameter and a height.

We are given two groups of vertices. The first group contains $a$ black nodes and the second contains $b$ white nodes. We must construct an undirected simple graph using these $a+b$ vertices. The graph must satisfy two conditions at the same time.

We are given a circular arrangement of N vertices, labeled from 0 to N − 1, and a fixed jump size S. Starting from vertex 0, we repeatedly move forward by exactly S positions modulo N, forming an infinite deterministic walk on this cycle.

We are given a stick of integer length $n$. We choose two distinct integer cut positions from the internal points $1$ to $n-1$, and cut the stick at those positions. This produces three positive integer segments whose lengths depend only on the two chosen cut positions.

We are given two polynomials, one acting as an outer function and one acting as an inner function. The first polynomial $P(x)$ defines how we transform a value once we already have it, and the second polynomial $Q(x)$ defines the value that gets fed into $P$.

The task describes a hierarchical route planning problem over three layers of locations. At the lowest level there are individual locations inside a city, inside cities grouped into a country, and finally countries grouped into a global structure.

We are given a rooted structure that behaves like a tree, where each node carries a value that is constrained by how paths behave from the root down to the leaves.

We are given a string consisting only of two symbols, which we can think of as G and E. We reinterpret this string as a walk on a number line: reading a G increases a running value by one, and reading an E decreases it by one.

We are given a rooted tree where every node carries a numeric value. The tree is fixed, but the values change over time under constraints that preserve a global monotonic property: every parent must always have a value at least as large as each of its children.

We are given a rooted binary tree whose nodes are labeled from 1 to n. Each node corresponds to one pair of matching parentheses in some unknown valid bracket sequence of length 2n.

Sure. Please provide the full Codeforces problem statement (or the problem link/code), and I'll write a comprehensive competitive-programming editorial including: - Problem observation and intuition - Key insights - Proof of correctness - Algorithm design - Complexity analysis…

We are given a line of seats, each seat either usable or broken. Two players alternate placing passengers onto usable seats, starting with Alice.

We are given a weighted undirected graph whose nodes store integer values. Every edge contributes a cost equal to the XOR of the values stored at its endpoints, and the total “energy” of the system is the sum of these edge costs. The system evolves through random operations.

We are given several independent intervals, and from each interval we must pick a single value. After choosing one value per interval, we treat those values as magnitudes of vectors.

We are given a collection of blocks, each block having a positive integer size. We want to stack all of them into a single vertical tower. The only rule is that a block can be placed on top of another block only if its size is strictly smaller than the block below it.

We start from a positive integer $x$. At each step, we apply the classic Collatz transformation. If the current value is odd, it becomes $3x+1$. If the current value is even, it becomes $x/2$. The task is not to simulate forever.

We are simulating a sequential card game where players repeatedly draw cards from a fixed deck and place them into a growing line of cards called the pond. The players act in a fixed cycle: player 1, then 2, up to n, and then repeating.

We are given a target integer $x$, and we must construct a sequence of stack operations that builds exactly one final set $T$ such that a recursively defined “size” function $f(T)$ equals $x$. The system manipulates sets of sets starting from the empty set.

A rigid square table of side $2a$ is supported by four identical legs located at its corners, modeled as point supports.

A thin diverging lens with focal length $F = -10~\text{cm}$ is fixed in space, and a luminous point source is initially located on the principal optical axis at distance $d = 40~\text{cm}$ from the le…

We are given a rooted tree on vertices labeled from 1 to $x$, where vertex 1 is the root and every other vertex $i$ has exactly one parent with a smaller label. So the labels already impose a valid parent structure, but the actual structure of the tree is otherwise free.

We have a layered defense grid. The drone starts somewhere on the bottom row and moves upward one row at a time. From (r, c) it may go to (r - 1, c - 1), (r - 1, c), or (r - 1, c + 1) as long as the destination is inside the board and not blocked.

We are given an array of positions from 1 to n. Each position behaves like a lock that can be either free or already locked by some query. Initially every position is free.

We are given a fixed set of seven emoji entries from a chat system used by bugcat creatures. Each entry has a unique identifier from 1 to 7, and each entry can be referred to in exactly two ways.

A heated bathhouse contains air saturated with water vapor at temperature $T_{\text{in}}$ and pressure $p_{\text{in}}$, while the outdoor air is at temperature $T_{\text{out}}$ with $T_{\text{out}} <…

We are given a sequence of battles and a fixed-capacity hero. His strength is a number bounded above by a constant $H$, and it decreases whenever he fights. Between fights, he can freely use any number of magical artifacts.

We are given an array of integers, where each value is represented using a fixed number of bits. There is a special operation: we can choose any contiguous segment of the array and flip all bits of every number inside that segment.

We are given a system that can be thought of as a line or structure of “states” that evolve under a filtration process.

The problem statement you provided is essentially empty, so there isn’t enough information to reconstruct what Codeforces 106467I - Stardew Valley is asking. Right now, all we have is the title and no definition of the input, output, or rules.

We are given a sequence-like structure where each element behaves like a signal that can “echo” into adjacent positions under a deterministic rule.

I can’t reliably reconstruct Codeforces 106467F - Melody from the title alone, and the “problem statement” you provided is effectively empty. Without the actual rules, input format, or output definition, any editorial would be guesswork and very likely wrong.

We are given a rooted tree that represents a set of stalls connected in a hierarchy. The way we “visit” these stalls is fixed by a DFS-like traversal, and the order in which we first enter each subtree determines how we assign each stall to one of two teams.

We are given a directed structure of “portals” between stalls in a market. Each portal is itself a directed edge from one stall to another, and every portal also has a designated “next portal” that is forced after using it.

We are given a simple polygon described by its vertices in order along its boundary, so consecutive vertices form edges of the polygon. On this polygon, there are special “speech locations” placed on some of the grid points that lie on the boundary.

We are modeling a sequence of independent trials where each trial is either a success or a failure with known probabilities.

We maintain a dynamic subset of integers from the fixed universe $[1, n]$. The set supports insertion and deletion with idempotent behavior, meaning repeated inserts or deletes on the same element do not change anything after the first effect.

We are given a collection of fan strings over a tiny alphabet and a sequence of events that either mutate all strings simultaneously or evaluate a “draw” against a given winning string.

Each shop has a linear demand model depending on the selling price. If we set a price $p$, shop $i$ contributes demand $ai - bi p$, and every sold unit yields profit $p - ci$. The total profit from that shop is the product of these two expressions.

We are counting permutations of the numbers from 1 up to n, but not just any permutations. For each permutation, we scan it and care about two structural features: how many increasing patterns of length four appear in a specific sliding sense, and how long the final increasing…

Each shop in the system has three parameters: a baseline demand, a sensitivity of demand to price, and a production cost per unit. If we set a selling price $p$, the demand at a single shop becomes a linear function that decreases as price increases.

The task is about constructing a permutation of the integers from 1 to n that maximizes a certain “beauty” measure defined over the arrangement.

We are given an array of length n. For every position i, we temporarily take the first i elements, reverse that prefix, and then compute a single score over the entire array: the sum of index multiplied by value at that index.

We are given two identical spherical planets whose centers move in 3D but are always constrained to lie on a fixed circular orbit.

We are given a set of values placed on nodes of a directed graph. Between every ordered pair of distinct nodes $u$ and $v$, we may or may not have a directed edge from $u$ to $v$, and the rule is completely determined by their values $au$ and $av$.

We are given several ranked Christmas top-10 music charts. Each chart contains 10 artist names ordered from position 1 (best) to position 10. The same artist may appear multiple times in the same chart, and across different charts.

We are given a group of people sharing a flat, and a limited number of physical keys. Over time, each person repeatedly leaves the flat and returns. Every such outing is independent and is described by a single interval: a departure time and a return time.

A ship moves in still water with speed $v$ in the laboratory frame.

We are given a circular structure with $n$ evenly spaced points labeled from 1 to $n$. Starting from point 1, we repeatedly connect each point to the point $k$ steps ahead, wrapping around modulo $n$, until we return to the starting point.