brain

We are given a group of people trying to cross a river using a very small boat. There are two types of people: cannibals and missionaries.

We are given a circular array of length $n$. Each position initially contains some number of items, and we are allowed to redistribute these items using a very specific local operation.

We are given a very large integer, but instead of treating it as a number, we should think of it as a multiset of decimal digits. Bomboslav removes all digits from the cheque and wants to reassemble them into a new integer using every digit exactly once.

We are given a line of $n$ boxes and several initial configurations of $m$ identical stones distributed across them. Each configuration is simply an array of $n$ nonnegative integers whose sum is fixed to $m$.

We are looking at integers written in decimal form, but the key constraint is not about their numeric value alone. Each number is interpreted as a string, and every contiguous block of digits inside that string is turned back into an integer by stripping leading zeros.

The game simulates a basketball match where two teams each start with five active players and five substitutes. Over time, two things happen: players are swapped between the court and the bench, and scoring events occur.

We are given two points on an integer grid. Both the starting point and the destination lie strictly away from the coordinate axes, meaning neither coordinate is zero at either endpoint. Such points are called free points.

We are given a sequence of bytes, each written as a two-digit hexadecimal number, so each value lies in the range from 0 to 255.

We maintain a very large array indexed up to $10^9$, but only the first $n$ positions are initially non-zero. All remaining positions are implicitly zero. Each position holds a 30-bit integer. There are two operations. First, we can update a single position to a new value.

We are given a network of restaurants where edges represent a “neighbor” relation. Some restaurants already cooperate with Timur at the start.

We are given four fixed integers in each test, and we form two products: the first is the product of the first two numbers, and the second is the product of the last two numbers.

We are given a fixed number of days, and each day Igor must choose exactly one of two actions. He can either study, which reduces his “energy” by a fixed amount, or go to sleep early, which increases it by another fixed amount.

We are given a sequence of integers shown one by one. After each new number appears, we need to determine whether it can be “constructed” by taking two earlier numbers and concatenating their decimal representations in order, without inserting anything in between.

We are given several chests, each containing a certain number of coins. Two friends want to split coins so that each chest ultimately contributes equally to both of them, but a chest can only be “cashed out” if its coin count is even.

We are given two types of books. There are A math books and B programming books. Each math book contributes X new facts, and each programming book contributes Y new facts.

A merchant travels along a river route carrying two kinds of goods: caviar and honey. Initially, he has a fixed amount of each commodity, and each unit can later be sold at a known price.

We are given a tree with vertices numbered from 1 to n. The edges are given in a very specific way: each new vertex i + 1 is connected to an earlier vertex pi.

We are given a sequence of integers that represent net traffic changes over time. Each value can be positive or negative, and we are allowed to discard any elements we want, preserving order among the remaining ones.

We are given a string that represents a correct bracket sequence, meaning it behaves like a well-formed parenthesis structure: as we scan from left to right, we never see more closing brackets than opening ones, and the total numbers of both types are equal.

We are given a function defined on the segment from 0 to n. Its values at integer points are fixed by an array a, where f(i) = a[i].

We are given up to one hundred thousand triangles drawn on a 2D plane. The canvas starts entirely red. Each triangle is applied one after another with a very specific paint rule: the boundary of the triangle is permanently painted black, while every point strictly inside the…

We are given a one-dimensional highway from position 0 to position L. Along this line there are special marked points, each placed at an integer coordinate, and each point is either an entrance or an exit.

We are given a directed system of locations, where each routing program behaves like a conditional edge: it only moves the drone from its starting location to its destination if the drone is currently at the correct start node. Otherwise it does nothing.

We are given a calendar UI that can be manipulated through three independent controls: year, month, and day selection.

We are given an array of length n that describes a sequence of maintenance bans. Each second i forbids exactly one frequency ai from being used. There are n + 1 possible frequencies, labeled from 0 up to n, where smaller labels are more desirable.

We are looking at a stochastic wealth process on $n$ people. Everyone starts with exactly one unit of money. After that, many additional unit transfers happen.

We are comparing two ways to exhaustively test all binary strings of length $n$. There are $2^n$ possible secrets. A classical machine tests exactly one candidate per $a$ seconds, so its total time is proportional to $a cdot 2^n$. A quantum machine behaves differently.

We are working with a product space formed by two independent trees. A state is a pair of vertices, one chosen from the first tree and one from the second tree.

We are working with a triangle whose three side lengths are not given directly, but are instead constrained through three ratios between them.

We are given a weighted undirected graph representing a road network between intersections. Each road has a physical length, which determines how long it takes to traverse depending on chosen speed, and a cost coefficient that determines a penalty based on how fast we drive on…

We are given a city with several “dark stores”, each acting like a local service hub, and a sequence of delivery orders appearing over time. Every order is just a point in the plane.

We are given a system of states, where each state behaves like a custom dice roll. From a current state, the game “rolls a dice” whose faces are not just uniform outcomes, but a collection of weighted faces with known probabilities.

The problem statement in your prompt is incomplete and corrupted. The sample input and sample output are truncated, and crucial parts of the statement are missing or malformed.

We are given a set of points on a 2D plane, and we are asked to compute the sum of Euclidean distances over all unordered pairs of points. For every pair of distinct points, we take the straight-line distance between them and add it to a global total.

I don't have enough information to write a correct editorial and solution for this problem. The statement you provided contains the problem description, but it is missing the most important part needed to derive the algorithm: the official definition of what counts as a…

We are asked to construct a connected simple undirected graph on vertices numbered from 1 to n. The graph must not be a cactus, meaning it must contain at least two simple cycles that overlap in at least two vertices. Self-loops and multiple edges are forbidden.

We are given a positive integer $x$. From this number we conceptually generate a family of numbers by permuting its decimal digits in every possible way, then removing any leading zeros that might appear after permutation.

The requested editorial cannot be written correctly because the prompt is missing essential information. The problem statement describes the tournament format, but it does not describe how to reconstruct a team's finishing position from its win/loss string.

I don't have enough information to write a correct editorial and solution because the problem statement in your prompt is corrupted.

We are given a straight road segment from position 0 to position L. Gleb walks from 0 toward L at speed 1 meter per second, and at certain integer positions there are pedestrian crossings where he may cross to the other side of the avenue.

We are simulating a randomized “sock pairing” process after a wash. All socks are grouped by color, and within each color the socks are indistinguishable. The process repeatedly removes a random sock from the machine.

We are given an integer array. We must increase exactly one element by 1 and then check whether the resulting array is not a palindrome. The task is to decide whether such a choice of position exists. An array is palindromic when every element matches its mirrored counterpart.

I can’t write a correct Codeforces editorial for this problem yet because the actual problem statement is missing from your prompt. Right now I only see the title “New Year Festival”, but no description of: what the inputs are, what needs to be computed, or any constraints.

We are given a convex polygon representing the outline of a cake. Each vertex is connected by straight edges, forming a closed shape. The decoration process repeatedly “trims” the cake in a very structured way.

I can't write a correct editorial for this problem because the actual problem statement is missing. For Codeforces 104849J - Traveling Salesperson in an Island, the statement you've provided only contains: "Please read the problem statements here.

I can’t produce a correct Codeforces editorial from this prompt because the actual problem content is missing. The link placeholder “Please read the problem statements here” doesn’t include the statement, so there is no way to reconstruct what “Quiz Contest” is…

I can't write a correct editorial for this problem because the actual problem statement is missing. The prompt only contains: Problem: Codeforces 104849G - Remodeling the Dungeon followed by "Please read the problem statements here.

I can’t reliably reconstruct Codeforces 104849F - Make a Loop from the provided prompt alone because the actual statement link content is missing and Codeforces Gym problems are not uniquely identifiable from the ID without the original page text.

I can’t reliably write an editorial for this yet because the actual problem statement for “Codeforces 104849E - Incredibly Cute Penguin Chicks” isn’t included in your message, and I don’t have access to fetch it from Codeforces directly.

The problem statement in your prompt is incomplete. It only contains: Problem: Codeforces 104849D - Move One Coin Problem Statement: Please read the problem statements here. The actual statement, input format, output format, and constraints are missing.

I can’t reliably reconstruct Codeforces 104849C “Secure the Top Secret” from the sources available, and I don’t want to hallucinate an editorial for a problem whose constraints and exact rules are unclear.

I can’t reliably write a correct Codeforces editorial from what you’ve provided, because the actual problem statement is missing (“Please read the problem statements here” with no content).

I can't write a correct editorial for this problem because the actual problem statement is missing. The prompt only contains: "Please read the problem statements here." without the linked statement, input format, output format, or samples.

We are distributing a total number of cakes among a fixed number of children. Every child must receive exactly the same amount, but the cook is allowed to cut cakes into halves, meaning each cake can contribute either a whole unit or two half-units.

We are given a sequence of scheduled trips, each describing an interval of days during which Vasily must be present in a specific city. Every trip is active on all days from its start day to its end day, inclusive.

We are given an 8 by 8 grid with obstacles and one special cell, the finish located at the bottom-right corner. A robot can start from any empty cell in the grid. We must output a program consisting of movement commands.

We are asked to count how many valid strings can be formed using only three characters: a, o, and c, with two constraints. Each string must have fixed length N, and no character is allowed to appear more than K times inside a single string.

We are working with an infinite grid where every cell contains a natural number, arranged in expanding rhombus-shaped layers around a central cell. The central cell contains the value 1.

We are given a grid with a special numbering rule: the integer 1 sits at the origin, and numbers expand outward in layers shaped like diamonds.

We are given a list of scheduled business trips for an employee. Each trip occupies a continuous interval of days and specifies a city.

We are given a sequence of pillars, each with a height. A frog starts on some pillar and wants to reach another pillar to the right, but it can only jump forward and each jump can skip at most k positions.

We are given several piles of stones. Each pile has a fixed allowable range of how many stones we are allowed to take from it. From pile $i$, we must choose an integer $xi$ such that $li le xi le ri$.

We are given a collection of strings, each consisting only of digits from 0 to 9. For any ordered pair of indices $(i, j)$ with $i < j$, we concatenate the two strings $si$ and $sj$.

We start with two very large integers, call them $a$ and $b$. We are allowed to perform at most $k$ operations, where each operation independently increases either $a$ by one or $b$ by one.

We are given a game world consisting of several dungeons, each containing a monster with a fixed strength value. The player starts with an initial strength and is allowed to enter any dungeon in any order.

We are given a 2D continuous world split into two movement regimes by the horizontal line $y = 0$. Points with $y ge 0$ are land where Ken moves at speed $v{run}$, and points with $y < 0$ are sea where he moves at speed $v{swim}$, with $v{run} ge v{swim}$.

We can think of the situation as a directed graph where each gift type is a node and each possible exchange is a directed edge with a positive cost representing effort.

We are given a fixed embedding space of size $k$. Every sentence we construct is a sequence of words, and each word acts like a set of deterministic “write operations” on this embedding vector. We start from a zero vector of length $k$.

We are given a multiset of colored particles, where each particle is represented by a lowercase letter. The input string is already sorted, so equal letters appear in contiguous blocks.

We are given a single integer $d$, and we are told that two people independently computed triangular sums of the form $1 + 2 + dots + n$ and $1 + 2 + dots + m$, where $m n$. The only information we still have is the difference between these two sums, which equals $d$.

We are given a single integer $x$. Our task is to find the largest number $y$ that does not exceed $x$, with two properties at the same time. First, $y$ must be a prime number.

We are given a string made of three possible characters: opening brackets, closing brackets, and wildcard symbols. Each wildcard can later be replaced independently by either an opening or a closing bracket.

We are given a single integer $n$, and we conceptually write down all positive integers from 1 up to $n$ one after another with no separators, forming one long digit string. For example, if $n = 15$, the string is 123456789101112131415.

We are given a very large rectangular grid, but only a small number of special cells called lily pads are initially active. Two of these pads are always at the start cell and the target cell.

We are given a large integer $p$. Each test case asks us to look at all factorizations $p = a cdot b$, where both $a$ and $b$ are positive integers.

We maintain a dynamic multiset of problems. Each problem has a difficulty value and a beauty value, and operations either insert or delete a specific problem instance. After every update, we are asked to compute the maximum possible total beauty of a valid “contest”.

We are given a set of points on the plane and a regular polygon with a fixed number of sides $m$. The polygon is always centered at the origin, but we are free to rotate it.

We are given three arrays of equal length, and our task is to build a permutation of indices from 1 to n. For each position i, the value assigned to that position in the permutation determines which of three rewards we collect at i.

We are given a directed graph where each edge carries a label called a color. Starting from node 1, we can walk along directed edges as many times as we want, and we are allowed to revisit nodes and reuse edges.

We are given a very large rectangular grid. One cell is initially blue, and we are allowed to choose exactly $k$ additional cells and paint them pink. After this setup, two spreading processes take place alternately.

We are interacting with a hidden integer $x$ between $1$ and $10^9$. Our only tool is to ask queries of the form “give me some integer $a$” and receive back a value computed from how $a$ relates to $x$.

We are given a circular arrangement of boxes, each containing some number of identical items. A person starts at the first box and repeatedly performs a fixed routine: if the current box still has items, she removes exactly one item and increases a running counter, then she…

I don’t have the actual statement of Codeforces 1048565 (“Вечер кёрлинга”) available from your prompt, and without it I can’t reliably reconstruct the rules, constraints, or required algorithm.

I can’t reliably write a correct Codeforces-style editorial for “1048564 - Задачи на печать!” because the actual problem statement (input/output definition and constraints) is missing from your prompt.

We are working with a simple phone directory that stores associations between a person’s name and their phone number. The system receives a sequence of operations that either update the stored number for a name or ask for the current number associated with a given name.

I can’t reliably reconstruct Codeforces problem 1048562 “Рамка для рисунка” from the identifier alone, and the available references point to multiple unrelated gym tasks rather than a single clear statement.

I can’t reliably write a correct editorial for “Codeforces 1048561 - Ферзь” from just the title, because multiple different problems use that name (it simply means “Queen” in chess), and the solution depends entirely on the exact task.

We are given a directed graph where each vertex represents a student and each directed edge represents a possible way information can be passed from one student to another.

We are given a tree representing a campus, where each node is a building and each building has a positive importance value. We must split the tree into several groups by removing some edges.

We are given a connected undirected graph where each edge has a positive weight representing congestion. A path from node 1 to node n is not evaluated in the usual way. Instead of summing all edge weights, only the two largest edge weights along the path matter.

We are given a strange “language system” where there are $n$ symbols and they behave like digits in a base-$n$ number system, but the mapping from digits to symbols is unknown.

We are given two mutually recursive functions that grow with the input size, but instead of depending on slightly smaller integers in a linear way, each function depends on the other function evaluated at a significantly smaller argument, specifically a halved version of the…

We are given a binary string that represents attendance across a sequence of classes. A streak is a maximal contiguous segment of ones, meaning a block of consecutive attended classes that is bounded by zeros or by the ends of the string.

We are given an array that grows one element at a time, and after each new element we must decide whether the current prefix has a certain structural property.

We are given a sequence of balloon colors, where each balloon has a color represented by a short lowercase string. The task is to determine whether there exists a color that appears strictly more than half of the total number of balloons. If such a color exists, we output it.

We are given an $n times m$ grid where each cell contains an integer color. For every color, we look at all cells having that color and consider every ordered pair of such cells.

We are given a multiset of integers where values range from 1 to n, and each value i appears ai times. The task is to count how many distinct sequences b, which are permutations of this multiset, have a special property involving two queues.

We are given a circular string of digits. From this circle, every pair of indices defines a substring that can wrap around the end back to the beginning.

We are given three integers: a modulus $n$, and two residues $a$ and $b$, all positive, with $n$ odd and $gcd(a,n)=1$. The task is to recover a unique integer $x$ in the range $1 le x le n-1$ that satisfies two constraints at the same time.

We are placed in an implicit graph whose vertices are all non-negative integers. Two vertices are connected if their binary representations differ in exactly one bit, and the edge is labeled by the position of that bit (counting from the least significant bit as position 1).