brain

We are given a set of distinct points in the plane. The task is to split these points into two non-empty groups, call them A and B, such that the convex hull formed by A and the convex hull formed by B do not touch at all, neither in their interiors nor on their boundaries.

The input describes a weighted tree. Each node represents an interchange and each edge represents a road with a travel distance. The graph is connected and there is exactly one simple path between any two nodes, so every trip between interchanges is uniquely determined.

Each class reports how many students like each fruit, but this information is aggregated. For a fixed class and a fixed fruit, the value tells us how many distinct students in that class like that fruit.

We are given a closed polyline drawn in the plane $z = 0$. In simpler terms, there are $n$ points in the XY-plane, and they are connected in a cycle: each point connects to the next, and the last connects back to the first.

We are working with a mutable array of integers, and each query asks us to relate one index in the array to all other indices using a distance condition that depends on the value stored at those indices.

We are given a multiset of integers and we are allowed to permute them freely. After choosing an order, each value is placed into a position indexed from 1 to n.

I can’t reliably reconstruct Codeforces 106030B - osu!mania from the information provided here. The statement section is effectively empty, and this problem name has multiple possible interpretations in CF gym sets (typically involving rhythm lanes, falling notes, or grid…

We are given a complete graph on vertices labeled from 0 to n-1. Every pair of vertices is connected, and the weight of an edge is not a simple arithmetic value but a bitwise construction based on the labels of its endpoints.

A line of children is given, each child carrying a rating. We must assign a positive number of cookies to every child, but the assignment cannot be arbitrary.

We are given a second-order linear recurrence sequence defined by two parameters $p$ and $q$. The sequence starts with $f(0)=0$, $f(1)=1$, and each next term is a linear combination of the previous two terms: $f(i)=p f(i-1)+q f(i-2)$. This is a Lucas-type sequence.

We maintain a dynamic set of strings that changes over time. After every update, we must compute how many ordered pairs of distinct words currently in the set have the property that one word is a suffix of the other. In other words, at each moment we have a collection of strings.

We are given a sequence of bosses that Kyouka attempts to defeat in a fixed order. Each boss type can appear multiple times, and these appearances are not independent: the availability of a boss in later “rounds” depends on what has already been defeated earlier in the…

We are given Jotaro’s initial poker hand of five cards drawn from a standard 52-card deck. Each card has a rank from 1 to 13 (Ace through King), and each rank appears exactly four times in the deck.

We are given a number $n$, and for every integer $i$ from $0$ to $n$, we look at the entire $i$-th row of Pascal’s triangle. For each entry in that row, we take the binomial coefficient $binom{i}{j}$, reduce it modulo 2, and sum all those values.

We are given three people who travel together, and each of them pays a sequence of bills during the trip. Each test case provides three lists of positive amounts, one list per person.

We are given a fixed “dictionary string” S. Every possible word is simply a substring of S. Over q days, we are shown intervals on S. On day i, we take the substring S[li..ri] and consider it as a prefix pattern.

We are asked to fill an $n times n$ grid with all integers from $1$ to $n^2$, each used exactly once. So the grid is just a permutation reshaped into a matrix. Now define a property for a threshold value $x$.

We are given an undirected graph with $n$ vertices and $m$ edges. Each edge must be assigned a color, using colors labeled from $1$ to $m$, and colors may be reused across edges.

We are given an array of values placed on a shelf, where each value represents a xego piece identified by a large integer.

We are given a sequence of integers and asked to count ordered index quadruples $(i, j, k, l)$ such that the indices are strictly increasing and the values form an alternating pattern.

We are given an array of integers, and we repeatedly need to answer queries on subsegments. For any chosen subarray, we are allowed to split its elements into two groups. One group contributes the bitwise OR of its elements, the other contributes the bitwise AND of its elements.

We are given a permutation of the numbers from 1 to n. Each position has a unique “height”, and there is exactly one position that contains the maximum value n. That position is the target we want to reach. A robot starts at an arbitrary index i. It has a movement range d.

We are given a collection of distinct lattice points on the plane. From these points, any subset of four points is considered “good” if those four points can serve as the vertices of a square in any orientation, not necessarily axis-aligned.

We are asked to construct a permutation of the numbers from 1 to n such that two classical order statistics of the sequence coincide: the length of the longest increasing subsequence and the length of the longest decreasing subsequence must be equal.

We are dealing with a hidden 64-bit non-negative integer, and our only way to learn about it is by probing it with carefully chosen masks.

We maintain a dynamic collection of pairs of integers, where each pair has a value v and a weight w. The structure supports inserting pairs, removing existing occurrences, and answering queries of the form: given an integer k, find among all stored pairs those whose first…

We are given a string and asked to count how many of its substrings have a very specific three-part structure. A substring is called valid when it can be split into three consecutive equal-length blocks where the first and last blocks are identical, and the middle block is the…

We are given a very large integer $N$ written in decimal form and a digit $x$ between 1 and 9. The task is to examine every positive integer $M$ from 1 up to $N$, count how many times the digit $x$ appears inside each $M$, and group numbers by that count.

We are given a collection of contests. Each contest contains a fixed number of problems, and every problem has a difficulty label in a small range from 1 to K.

We are given a structured polynomial identity involving two variables $x, y$ over a finite field. The core object is a bivariate polynomial $P(x,y)$, but it is not arbitrary.

We are given three fixed strings over a small alphabet, and we treat them as reference sequences that define which subsequences are “available” in a constrained sense.

We are given an array of integers representing colored beads. From this array we construct two related sequences and then compare them in a cyclic way, meaning we are allowed to rotate one of them before comparing.

We are given a set of points in the plane and multiple queries. Each query gives us three distinct points forming a triangle, and we need to determine whether there exists at least one other point from the set strictly inside that triangle.

We are given a rooted tree where each node represents an element that may carry an identifier, but this identifier is not always “fixed” in how it should be interpreted.

We are working with a sequence that is easier to understand through its differences rather than its raw values. Instead of reasoning directly about the sequence, we look at how each element changes compared to the previous one.

We are given an array of positive integers. The task is to compute a global sum over all ordered pairs where each element in the array acts as a divisor in a modular expression.

We are working with a graph where each state is a directed edge traversal decision, not just a vertex value. For every vertex $v$, and every neighbor $u$ adjacent to it, we define a quantity $L(v, u)$ which represents the longest possible walk that starts at $v$ and is forced…

We are given a tree where each edge has an implicit distance, and a fixed parameter $c$ representing how far a car can travel on a full tank. When moving along the tree, a refuelling event is required whenever the remaining fuel is insufficient to continue along the next edge.

We are given a process defined on pairs of positive integers $(a, b)$ with $a < b$. From a state $(a, b)$, the system either terminates immediately with probability $1/2$, or transitions to a new state $(2a, b - a)$ with probability $1/2$.

We are dealing with a process where a set of integers from 1 to n exists, and we randomly select a subset of size k from it. From that subset, we are interested in the maximum element.

We are given a rooted tree, and the task is to imagine drawing it on a grid under a very specific geometric rule. Each subtree is drawn inside a rectangular bounding box, and different subtrees attached to the same parent must be placed inside disjoint bounding boxes.

We are given a list of athletes, each with a strength value, and a sorted list of coffee cups, each with an increasing strength requirement. A cup can only be drunk by an athlete whose strength is at least the cup’s requirement.

We are given a collection of pokémons, each described by two numbers: its initial strength and its price. We are allowed to pick exactly one pokémon as our champion before the tournament starts.

We are given two arrays of the same odd length, and every value appearing in either array is unique globally. Because of this uniqueness, sorting each array produces a well-defined ordering with no ties, and the median is simply the element at position $(n+1)/2$.

We are given a one-dimensional cave split into n vertical columns. Each column has a ceiling height h[i]. Over time, the ceiling in every column drops uniformly: at each second, every positive height decreases by one.

We are given a permutation of numbers from 1 to n, but it is hidden. Instead of the permutation itself, we only know a derived array of length n − 1 where each value is the maximum of two consecutive elements in that hidden permutation.

We are given a length $n$ array, and from it we build an $n times n$ grid where every row is a cyclic shift of the previous one. The first row is the array itself, and each next row shifts all elements one position to the left, wrapping the first element to the end.

We are given a tree, meaning a connected graph with no cycles. Two special vertices are marked, a starting point $s$ and a target $t$. A fox moves on this tree, but its movement rules are stronger than normal adjacency.

We are working on a dynamic grid where each cell stores an integer height. A cell is considered land only if its current height is strictly positive. Connectivity is defined in the usual grid sense, where movement is allowed only between cells sharing a side.

We are given a very large grid that is never explicitly revealed. Each cell of this grid is painted with one of three colors, and we are guaranteed that no two side-adjacent cells share the same color.

We are given four short lowercase strings and need to determine whether it is possible to place all of them into a fixed grid as two horizontal words and two vertical words.

Codeforces 105863B: Numbers on the Blackboard

We are given a multiset of integers. The task is not about sorting or selecting elements directly, but about understanding how these values interact when forming pairs whose sum is fixed.

We are working on a coordinate system where each move is not a standard step but a reflection-like transformation.

We are given a fixed number of positions and a range of values, and we conceptually assign values from this range to each position.

We are given an array of positive integers and we need to evaluate a function that depends on splitting this array into contiguous blocks.

We are given an undirected graph structure implicitly described through distances from a fixed root node, node 1.

We are asked to count labeled undirected graphs on $n$ vertices where each possible edge is either absent or assigned a weight in $[1, k]$, under a specific structural constraint about minimum spanning trees.

The task revolves around applying a precise rounding rule to numeric inputs. Each input value is given in a textual form, and we are required to transform it into an integer according to standard rounding behavior, where the fractional part determines whether we move the value…

I can’t write a correct editorial from just “H” and an empty statement. Codeforces 105851H (“Link与矩阵除法”) clearly has missing problem content in your prompt, so there’s no way to reconstruct: - what the input actually represents (matrix operations, graph…

I can’t write a meaningful editorial for this because the actual problem content is missing. Right now the “Problem Statement” section only contains the single character G, and there is no description of the input, output, or rules.

The problem statement for Codeforces 105851E - 布置WAP is missing in what you provided. Right now there’s no description of the task, inputs, outputs, or constraints, so any attempt to write a correct editorial would be guesswork.

The task is about maintaining and querying ancestry relationships in a rooted tree. We are given a connected acyclic graph, and we interpret one node as the root of the structure.

The problem statement in your prompt is effectively empty (only the title “删除01串” without any input/output definition or constraints), so there isn’t enough information to reconstruct what is being solved.

We are given an array of positive integers and many range queries. For each query, a segment from index $l$ to $r$ is chosen. Inside this segment, we are allowed to pick a split point $k$ such that $l le k < r$.

We are given a tree with $n$ nodes. Each node represents a region, and each region has a value that depends on whether it is currently marked as colored or not. Initially all nodes are uncolored and each node $i$ has a base value $ai$.

We are given a positive integer written as a decimal string. In one move, we are allowed to choose a single pair of adjacent digits and swap them. We may perform at most one such swap, or choose to do nothing.

We are given a connected undirected graph with $n$ islands and exactly $n$ roads. Every road has cost 1, and the same road can be traversed multiple times, paying its cost each time.

We are given a rooted tree where node 1 is the root. Each node represents a skill, and each skill has a value called its power.

We are given a very large interval of integers, from $L$ to $R$, where $R$ can be as large as $10^{18}$. The task is to count how many numbers inside this interval satisfy a digit-based property: when you look at the decimal representation of a number, the absolute difference…

We are working on a grid of all pairs $(i, j)$ where $1 le i le n$ and $1 le j le m$. For each pair, we look at the greatest common divisor of $i$ and $j$. From that gcd value $g$, we compute the number of divisors of $g$, written as $d(g)$.

We are given a sequence $b$ whose length is $n$. This sequence was originally produced from an unknown integer array $a$, but during the process, the array was modified in a structured way. The hidden construction is the following.

We are given several independent test cases. In each test case, there are $n$ caves labeled from 1 to $n$, and a sequence of $n$ planned inspections, where each inspection targets one cave. The sequence is fixed and known in advance.

We are given a sequence of exactly three integers. We are allowed to rearrange these three values using swaps between any two positions, and after doing so we want the resulting arrangement to satisfy a very specific pattern: the first element must be strictly greater than the…

We are given a collection of bins. Each bin starts with some number of balls and has a maximum capacity. The key operation in the process is that whenever a bin becomes full, it is removed from active consideration and its entire content is transferred into a shared reserve.

The problem defines a sequence built from a very structured combinatorial recurrence. Each term is formed by considering all ways to decompose an integer into ordered or unordered collections of positive integers, and then aggregating weights derived from those decompositions.

We are working with a permutation of the integers from 1 to 3N, split conceptually into three consecutive segments of equal size N.

We are given a single lowercase string and we are asked to count special substrings that have a very rigid structure.

We are given five integers that describe a soccer team’s season statistics, but the order of these integers is scrambled. We know they correspond to matches played, wins, draws, losses, and total points, but we do not know which number is which.

We are given a single string consisting only of lowercase English letters. The task is to classify this string based on how many times each distinct letter appears. A string is called odd if every character that appears in it occurs an odd number of times.

We are given a circular board with positions labeled from 1 to n. A token starts at position 1. Each move consists of rolling a fair die with faces from 1 to d, and moving forward that many steps along the circle. If we go past n, we wrap back to 1. Some positions are special.

We are working on a very large integer grid where each point has four-neighbor movement, up, down, left, and right. Some grid points are blocked because construction is happening there, and these blocked points cannot be visited.

We are given a sequence of integers and a threshold value k. From the sequence, we want to pick a subsequence, meaning we keep some elements without changing their order, and we try to make it as long as possible.

We can model the system as a directed graph where each channel is a node. Each bot acts like a small forwarding rule: it listens on exactly one source channel, and when that channel receives a message, the bot forwards the message to a fixed list of destination channels.

We are given a straight path from position 0 to position L. Along this line there are special points called boost stations.

We are trying to identify one unknown “bad” restaurant among n candidates. Each week we are allowed to choose any subset of restaurants and observe a binary outcome: if the bad restaurant is inside the chosen subset, Mikey gets sick that week, otherwise he does not.

We are given a list of students, each with a distinct knowledge level. The goal is to partition them into contiguous groups after sorting by knowledge level, so that each group satisfies two constraints: the range inside the group, defined as maximum minus minimum knowledge…

We are given a skyline-like city made of axis-aligned rectangular buildings placed on top of the x-axis. Each building starts at some x-coordinate, extends to the right for a fixed width, and rises vertically to a given height.

We are given a starting pair of single-digit numbers, where at least one is non-zero. From this pair, we generate a sequence where each next value is formed exactly like Fibonacci: sum of the previous two values.

We are given a permutation-like array where inversions matter, and the central object of interest is the number of inversions inside a subarray. For any segment $[i, j]$, let $f(i, j)$ be the number of pairs $i le a < b le j$ such that $p[a] p[b]$.

We start with a multiset of exactly $k$ numbers. Out of these, $k-1$ copies are equal to some value $x$, and a single element equals $y$. So initially the structure is extremely uniform except for one “disturbance”.

We are given multiple independent test cases. Each test case describes a set of points on an infinite 2D grid. Every point represents a tower placed at integer coordinates.

Each test case describes a group of candidates being evaluated on two independent dimensions: performance in a series of training contests, and performance in a problem-solving assessment outside contests.

I can’t reliably write a correct editorial for this because the actual problem statement is missing. Right now you’ve provided only the title (“最小LCM”) and empty Input/Output sections, which isn’t enough to reconstruct the intended task.

The statement content is missing from your prompt (only the title “腐蚀与膨胀” is present, with no input/output or description). Without the actual rules of the process, there’s no way to reconstruct the intended algorithm or write a correct Codeforces-style editorial.

I’m missing the actual problem content for Codeforces 105851C - 砝码. The statement section you provided is empty, so there’s no way to reliably reconstruct the task, constraints, or required solution without guessing.

We are given a sequence of numbers and a sequence of modulo operations that are applied to them. Each time a number is processed with a modulus value, it is replaced by its remainder.

We are given a tree, meaning a connected graph with no cycles. Some vertices of this tree are leaves, vertices with degree one.

We are given two arrays of the same odd length, and every number appearing anywhere in the input is globally unique. The only operation allowed is to pick an index and swap the elements of the two arrays at that position.

We are given a sequence of integers and a fixed way of turning any contiguous segment into a number using a rolling base.