brain

We are given a graph where every positive integer is a node, and for any two nodes $x$ and $y$, the cost of connecting them is determined by the number of distinct prime factors of their least common multiple.

We are given a grid where some cells are open and some are blocked. From a starting open cell, George can attempt to move in the four cardinal directions, but a move only succeeds if the adjacent cell exists and is open; otherwise he stays in place.

We are given two strings of equal length. One string, call it the reference string, defines a collection of patterns: every prefix of this string is a pattern, and each pattern has an associated weight.

We are given a sequence of values representing the happiness gained from a series of contests. After each contest, we want to compute a “memory-weighted mood” that depends on all past contests, but with exponentially decreasing influence for older events.

We are given an initial collection of “knowledge points”, each associated with a positive integer cost representing how many brain cells are required to maintain it. This collection is treated as a multiset, so only the frequencies of equal values matter, not their order.

We are given a large rectangular grid whose height is $2^N$ and width is $2^N - 1$. The grid is not arbitrary: it is built recursively by repeatedly splitting rectangular regions into smaller ones.

We are given a fixed integer $x$, which represents the length of one leg of a right triangle. The task is to count how many distinct right-angled triangles with integer side lengths exist such that one of the legs is exactly $x$.

We are given a line of positions from 1 to n, each position having a required minimum brightness. We also have several lamps, each lamp covering a contiguous segment of positions.

We are given a short string over lowercase English letters and a deterministic transformation that modifies it in two stages. First, the string is extended by inserting exactly one extra character.

We are given three positive lengths, which represent the sides of a triangle made from rigid wires. After that, an operation is repeated multiple times: every side is shortened by exactly one unit per operation.

We are asked to look at all possible labelled trees on $n$ vertices and compute a single numeric value for each tree: the sum of distances over all unordered pairs of vertices. This value is often called the Wiener index of the tree.

We are given a positive integer $a$. We want to construct a function $f$ on positive integers such that applying it twice behaves like multiplication by $a$, meaning that starting from any value $x$, if we apply $f$ once and then again, we land exactly on $a cdot x$.

We are given several independent games. Each game consists of a number of piles of stones. Two players alternate turns, starting with Mandy.

We are given a permutation of length $n$, and for any contiguous subarray we look at its maximum element. For a fixed permutation, we compute a global value $G(S)$, which is the sum of these maxima over all $n(n+1)/2$ subarrays.

We are given a sequence of integers, and this sequence is being modified through point updates. After each modification, we need to compute a value that comes from a rather unusual counting process involving polynomials.

We are given a collection of stick lengths and asked whether it is possible to pick exactly k of them so that they can serve as sides of a simple polygon.

We are given an undirected simple graph and asked to count how many subgraphs are exactly isomorphic to a fixed six-vertex pattern called “Four K3”. Although the diagram is not written in text, the structure is describable in words.

We are given a linear chain of islands from 1 to n. Consecutive islands are connected by directed edges from i to i+1, and each such edge has a fixed cost.

We are given a directed acyclic graph where each node represents a city and each city has a numeric charm value. The traveler must go from city 1 to city n along directed roads. The graph structure guarantees there are no cycles, so every valid route is a simple path in a DAG.

We are given a rooted tree with vertex 1 as the root. Each vertex has a depth, defined as how many vertices lie on the path from the root to that vertex.

We are given a collection of identical right triangles with side lengths 3, 4, and 5. Each triangle is a rigid tile, and we are allowed to place multiple copies on a plane without overlap.

We are given a single lowercase string and asked to count how many of its substrings contain the pattern "sysu" as a subsequence. A substring is defined by choosing a contiguous segment of the string, while a subsequence allows skipping characters without changing order.

We are working with a point on a number line from 1 to n. A frog starts at position 1 and wants to reach position n. At each move, it can jump forward by exactly 1 or exactly 2 steps.

We are asked to count how many binary $n times n$ grids exist under a local restriction: each cell is either 0 or 1, and we are forbidden from placing two 1s in adjacent cells that share a side. Diagonal adjacency does not matter, only up, down, left, and right.

We are given several music genres, each genre having a fixed number of songs. The task is to decide whether it is possible to arrange all songs in a single playlist so that no two adjacent songs belong to the same genre.

We are given a grid whose rows and columns are not uniform in size. Each row has a positive height given by array A, and each column has a positive width given by array B.

We are given a tree with $n$ vertices, meaning there is exactly one simple path between any two nodes. On this tree we consider adding exactly one extra edge, connecting any two vertices that are not already directly connected. This creates exactly one cycle in the graph.

We are given $n$ colors of balls. For each color $i$, there are $ai$ indistinguishable balls of that color in a box. There is also a requirement array $b$, where $bi$ tells us how many balls of color $i$ we want to guarantee. We draw $x$ balls from the box without looking.

We are given an array of integers and asked to count how many pairs of positions produce a XOR value that lies inside a fixed numeric interval $[A, B]$.

We are given the first $N$ terms of the sequence $an = frac{1}{n}$, which produces the values $1, frac{1}{2}, frac{1}{3}, dots, frac{1}{N}$.

We are distributing three different types of candies to three friends, where each friend only accepts one specific type. The first friend only takes Snickers, the second only Mars, and the third only Bounty.

The sequence starts from a single digit string and grows by repeatedly taking the previous string, appending the decimal representation of the current index, and then appending the previous string again.

We are asked to construct a number with exactly n digits, where each digit must be from 1 to 9. There is no digit 0 allowed anywhere, so we are working entirely in the range of positive digit strings.

We are given a string over lowercase Latin letters. We are allowed to repeatedly pick any position and replace its character with any other letter. Each replacement has cost 1, and we want to minimize the total cost.

We are given a rectangular grid representing a mountain surface. Each cell contains an integer value, which can be positive or negative.

Two players start on a number line: Alice is at position $a$, Bob is at position $b$, with $a < b$. Each second Alice moves to the right by a fixed integer speed $c$, and Bob moves to the right by a fixed integer speed $d$.

We are given two grading systems: one uses scores from 1 to n, the other uses scores from 1 to m. Some scores in the first system are considered equivalent to some scores in the second system, but the problem does not give us arbitrary pairs.

We are given a height array that represents a skyline of vertical bars. After each operation, one bar is increased, and we must compute how much water would be trapped between these bars if rain filled the valleys.

We are given a collection of parcel types. Each type describes how many identical parcels exist, where each parcel has a weight either 1 or 2 and must be delivered to a specific floor.

We are simulating a very constrained card game where a player has two ordered structures: an initial hand and a draw pile. The hand contains a special winning card, and the draw pile contains utility cards that may increase hand size temporarily by drawing more cards.

We are given a counter that starts at zero and evolves through a long sequence of operations, but we never see the sequence itself. Each operation is either an increment by one or a reset that forces the counter back to zero.

We are given a rooted tree where each edge carries a label from a very large alphabet. If we walk from the root to any node, the sequence of edge labels along that path forms a string. Let us call this string the node’s path-string.

We are given an $n times n$ grid that must be covered as much as possible using identical puzzle pieces, where each piece occupies exactly four unit cells.

We are given a weighted grid graph. Each cell is a node, and edges exist only between horizontally or vertically adjacent cells.

We start with an array of length $m$, initially filled with zeros. Each operation $i$ takes a list of positions and overwrites all of those positions with the value $i$.

We are given a collection of gemstones, each with a price and a beauty value. We start with a fixed amount of money and want to maximize the total beauty of gemstones we end up with.

We are given a rooted tree where each node is colored either black or red. For any node, we look at its subtree and consider all root-to-leaf paths inside that subtree. A node is considered valid if every such path contains the same number of black nodes.

We are given a convex quadrilateral defined by four points in order, which forms a rotated rectangle in the plane. This shape is fixed for each test case.

We are given a prime number $P$ and a non-negative integer $m$. For each integer $g$ in the range $0 le g le m$, we are asked to check a condition involving bitwise XOR and modular arithmetic: whether $$(g oplus (P-1)) bmod P = 1.

I can write the full Codeforces-style editorial in the exact format you want, but I’m missing the actual problem content.

We are asked to count how many full permutations of the numbers from 1 to n can be completed from a partially known array, under a strong structural constraint. The constraint defines a valid permutation by a prefix rule.

We are given a grid of integers, and we must answer many queries that each describe a rectangular subregion. For every query, we need to decide whether all values inside that rectangle are pairwise different, meaning no number appears more than once inside the chosen submatrix.

We are given several independent test cases. Each test case provides a permutation of length n, and we are allowed to repeatedly apply a very specific local operation: choose any position i such that a block of three consecutive elements exists starting there, and reverse that…

We are given a sequence of integers, and we are allowed to flip the sign of any individual element any number of times before doing anything else.

We are given a large grid with $n$ rows and $m$ columns, and each cell must contain either 0 or 1. The grid is considered valid if neither any row nor any column contains three identical values in a consecutive block.

We are given an integer $a$. For each test case, we must choose the smallest positive integer $b$ such that the number $a + b$ divides the product $a cdot b$ exactly.

We are given a binary string, and we are allowed to delete characters anywhere we like. After deletions, we look at the remaining sequence, and we want it to avoid a very specific kind of local disorder: no three consecutive positions (not necessarily adjacent in original…

We are given a list of employees, each with a numeric skill value. For every employee, we want to know the largest possible team that includes them, under a restriction: within any chosen team, the difference between the maximum and minimum skill must not exceed a fixed…

We are given a fixed permutation $p$ of size $n$, and we want to compare it against all other permutations of the same size that come lexicographically earlier than $p$.

We are given a pile of coins and two players who alternate turns. On a turn, a player starts with some number of coins, say $x$. They have two types of moves. They may always remove exactly one coin, leaving $x-1$.

We are working with a tree where every node is assigned a color from the range $1$ to $k$. For each color $i$, we need to count how many simple paths in the tree contain at least one node whose color is $i$.

We are given a connected undirected graph that has exactly one more edge than a tree with the same number of vertices. In other words, it is a tree plus one extra edge, so the structure contains exactly one cycle.

We are given several binary matrices of identical size. Each matrix can be seen as a function from grid positions to bits, and no two matrices in the input are identical.

We are interacting with a system that has a hidden integer threshold $l$, uniformly chosen from the integers in $[x, y]$. When we click a save button after typing some number of characters, the system checks how long we have been typing since the previous successful save.

We are simulating a simplified version of a Slay the Spire style system centered around “dark orbs”. The system evolves through a long sequence of operations, where we maintain a row of orbs, a global “focus” value, and a timeline of end-of-turn effects.

We are given a string of length $n$ where each position holds a visible ASCII character. Then we are given $m$ operations, each operation picks two distinct characters $(x, y)$.

We are given a fixed-size array of 32 integers representing a “warp”. Each operation describes a restricted in-place transformation on this array.

We are given a bicycle moving inside a very narrow corridor modeled as two infinite parallel lines with fixed distance between them. The bicycle itself is treated as a rigid segment of length l.

Codeforces 104823A: 赛前须知

I can’t produce a correct editorial for this yet because the actual problem statement is missing from your prompt (only the header is present).

I can’t write a correct editorial for that problem as-is because the actual problem statement is missing. “Codeforces 104824E - Medusa’s Snake (Subtask)” alone isn’t enough to reconstruct the rules, constraints, or required output.

I can’t write a correct editorial yet because the actual problem content is missing. Right now the prompt only shows: - “Codeforces 104824D - Garden (full)” - but the Problem Statement, Input, and Output sections are empty Without the statement, any solution would be…

I can’t write a correct Codeforces editorial here because the actual problem statement is missing. Right now we only have the title “Honey Heist (Subtask)”, but no definition of the input, output, or rules of the task.

I can write the editorial in exactly that format, but I’m missing the actual problem statement. Right now, “Codeforces 104824B - Honey Heist (Full)” isn’t included in your message, and I don’t have enough information to safely reconstruct it.

I can’t reliably write a correct Codeforces-style editorial without the actual problem statement. Right now the “Problem Statement / Input / Output” sections are empty, and for a Codeforces problem (especially something like a subtask), the solution structure depends…

We are given a row of candy, each candy labeled with a lowercase letter. From this row we will pick a starting position, and then eat that candy and everything to its right, producing a suffix string.

We are asked to find all integers $x$ in the range $0 le x < M$ such that a self-referential modular equation holds: the value $x^x$ and the value $x$ are congruent modulo $M$.

We are given a string that acts like a description of a positional numeral system, except it is not a fixed base like decimal or binary. Instead, each position has its own “carry rule”.

We are given a very simplified model of a road that consists of a flat horizontal segment, followed immediately by a vertical wall, and then a horizontal top surface of that wall. A car tries to pass through this structure.

We are given a set of axis-aligned rectangles on a plane. Each rectangle has a weight. Then we are given several query points. For each query point, we look at all rectangles that contain that point and extract their weights.

We are given a rooted tree with vertices numbered from 1 to n, with vertex 1 acting as the root. Each vertex u carries a value a[u].

We are given a grid where each cell is either empty or contains a single enemy unit. Empty cells and the area outside the grid are already controlled by us. The grid starts with all enemy cells still alive, and the goal is to eliminate every enemy cell.

We are given a tree with $n$ nodes, and each edge has an unknown integer weight. The tree structure is known in advance, but the weights are hidden.

We are given a sequence of integers and we want to cut it into contiguous non-empty segments. Every segment must satisfy a constraint on its bitwise XOR: the XOR of all elements inside the segment must be strictly greater than a given threshold $k$.

We are given a positive integer $n le 10^{12}$. For every integer $i$ from 1 to $n$, we define a value $f(i)$ based on the divisors of $i$. A divisor $d mid i$ is called valid if the complementary divisor $i/d$ shares no common prime factor with $d$.

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.