brain

I can write the full editorial in exactly the format you requested, but I’m missing the actual problem statement.

I don’t actually have the problem statement for “Codeforces 1049506 - Бактерии” in your prompt, and I can’t reconstruct the task reliably from just the title and metadata.

We are given a long sequence of years, each year carrying two integer values: one describing the number of “good” events and another describing the number of “bad” events. Two years can be related in two different direct ways.

We are given a collection of grimoirs, each one carrying two attributes: a difficulty value and a potential value. The order in which they were purchased is fixed and matters as a final tie-breaker. At each of $n$ moments, we must select exactly one unused grimoir.

The continent is a tree of cities. Traveling along any road takes exactly one year, and because the graph is a tree there is a unique simple path between any two cities.

Codeforces 104959B: Фрирен и барьер

We are given several independent test cases. In each one, we receive a list of integers, all written using exactly k binary bits. The value of each number is therefore in the range from 0 to 2^k - 1.

We are given a tree of rooms. Each room initially contains a fixed number of pancakes, and every corridor between two rooms also contains pancakes.

We are given a straight line of metro stations connected by consecutive segments, where segment $i$ connects station $i$ and $i+1$ and has a travel cost $ci$.

We are given a number of identical sticks, and the task is to form rectangular grid structures using exactly all of them. A grid of size $n times m$ is a rectangle subdivided into unit squares, where every unit edge in the grid is represented by a stick.

We are given a cycle of n houses. Each house is placed on a circle, so every house has a natural notion of moving left or right along the cycle. We are allowed to choose a parameter k.

We are maintaining a multiset of large non-negative integers under three kinds of operations, and after each operation we must report the bitwise XOR of all current elements. The operations are dynamic in two different ways.

We are asked to count how many different ways a fixed amount of money $N$ can be paid exactly using banknotes of denominations 50, 100, and 200, where each denomination can be used any number of times.

Each pizza comes with a structure that can be interpreted as a small graph. There is a central point and a ring of $si$ slice vertices. Every slice vertex is connected to the center with cost $qi$, and each slice is also connected to its two neighbors on the ring with cost $ci$.

We are given a sequence of students arriving in a fixed order, and each student consumes a specific number of pizza slices. There are K pizzas prepared, and every pizza must have the same number of slices, call this value X.

We are given two finite point sets in the plane. One set represents topping points, and the other represents crust points. Every valid pizza slice is formed by choosing the origin together with any two crust points, forming a triangle whose third vertex is fixed at the origin.

We are given a large set of distinct points on a grid. Each point represents a pepperoni slice, and we are asked to construct a straight line such that the line passes very close to many of these points.

We are arranging a permutation of pizzas labeled from 1 to $n$, where each label is the radius of that pizza. Once we choose an order, we look at all pairs of positions in the stack: if a larger pizza appears below a smaller one, we call that pair “proper”.

We are given a line of people before Shelly arrives. Each of those people can take food from a shared pool consisting of pizza slices, tacos, and sauces. Every person can take up to two items freely, where an item is either a pizza slice or a taco.

We are given a pile of pizzas, each pizza cut into 8 identical slices. With $n$ pizzas, the total number of slices is fixed at $8n$. These slices must be distributed among $m$ friends. The distribution has two constraints at the same time.

The pizza is represented as a square grid of size $N times N$, where each cell contains a single alphabet character. Among these characters, only two symbols matter for us: uppercase ‘P’ and lowercase ‘p’.

Each pizza consists of a circular arrangement of slices plus a center point. Every slice has a cost parameter and the crust around the pizza also has a cost parameter.

Let $s = a+b+c+d+e$.

Codeforces 104973A: Median

We are given a collection of databases arranged in a line. Each database behaves like a queue with a fixed capacity. We also have a sequence of operations, and each operation takes a value and pushes it into every database whose index lies inside a given interval.

We start with an array a whose elements contribute to a total sum we want to maximize. We are allowed to delete elements from a, but deletions are not arbitrary: each deletion is triggered by choosing a position from a second array b, and removing the corresponding indexed…

We are given an undirected graph with $n$ cities and $m$ proposed tunnels. Each tunnel connects two cities and carries a numeric tag. We are allowed to assign each city a label, also a number.

We are given a stack of hats, where each hat has a unique label and only the top of the stack is accessible at any time. People arrive one by one in fixed order from 1 to n.

We are working with a tree of rooms where room 1 is the entrance, but the root is not actually important for the computation.

We are given a permutation of the numbers from $0$ to $N-1$, but the permutation itself is unknown. What is known is that every value belongs to a natural pair: $0$ is paired with $1$, $2$ with $3$, and so on.

We are given a multiset of integers, and two players take turns selecting numbers from it under a strict constraint.

We are given a tree of $N$ dinosaurs representing Danny’s friend network. Each node has a value $ai$. There are $K$ possible invitations, and each invitation is identified by an integer $i$. If Danny accepts invitation $i$, we remove every node $j$ such that $i$ divides $aj$.

We are counting sequences of gift-giving events within a finite timeline of $L$ days. Bob starts on day 1 and may choose any day as his first gift. After that, each next gift must occur within at most $K$ days from the previous one.

We are given a rooted tree where each node stores a value representing a chocolate type. The tree structure is fixed, but two kinds of operations are performed over time.

We are given several test cases. In each test case, there are several flower types, each type having a fixed “beauty coefficient” and exactly 100 identical flowers available. Every individual flower costs 1 dinar, and we can buy at most c flowers in total.

We are given a set of distinct points on a 2D plane. The task is to count how many ways we can choose four different points such that all four lie on the same straight line.

We are given a collection of strings, each attached to a distinct index from 1 to N. The task is to determine whether we can choose four different indices such that if we concatenate the first two strings in order, we get exactly the same string as concatenating the other two…

We are given a rectangular grid where each cell is either empty or contains a shop that sells exactly one paint color. Bob starts at the top-left cell and wants to reach the bottom-right cell, moving only in four directions with unit cost per move.

Each test case gives a small phonebook of people, where every person has a unique name and an 8-digit phone number. After that, we receive many queries. Each query does not reveal a full phone number; instead, it reveals only a handful of digits, and their order is irrelevant.

We are moving along a straight road from position 0 to position X, walking at exactly one meter per second. Along the way there are traffic lights placed at fixed coordinates.

We are simulating a very small file system that supports three operations applied sequentially. Each operation either creates a named file, deletes a named file, or asks how many files currently exist.

We are working with an array of length $n$, initially filled with zeros. Then we receive $q$ operations that either ask for a range sum or apply a structured update. A query of the first type asks for the sum of values in a subarray $[l, r]$.

We are given a short sequence of integer adjustments applied one after another to a running total. Each value can either increase or decrease the sum depending on whether it is positive or non-positive, but in practice they are simply added as-is.

We are given a large undirected weighted graph and then many independent queries. Each query asks for the cheapest way to travel between two given vertices, but with a strict restriction: the route is allowed to use at most three edges.

We are given a sequence of programming contest submissions ordered by time. Each submission records a team name, a problem identifier, a timestamp, and whether the attempt was accepted or rejected.

We are asked to count how many sequences of length $n$ can be formed using numbers from $1$ to $k$, but only those sequences that survive three simultaneous structural rules. The sequence has a fixed odd length, so it has a unique middle position.

We are given a source string s and a target string t. Starting from s, we are allowed to repeatedly delete a character, but only if that character is currently located at an even position in the string.

We are given a sequence of integers representing the “strength” of gods arranged in a line. Between every pair of adjacent gods, we look at how different their strengths are. The instability of the whole arrangement is defined as the largest such adjacent difference.

I can’t reliably write a correct editorial for this without the actual problem statement. Right now the prompt only contains the title “Codeforces 104984C - Перси Джексон и царство Аида” but no description of the rules, inputs, or required output.

We are given a tree of servers where every edge has unit length. Each query specifies a vertex $ui$ and a distance limit $d$.

We are given a set of players, and each player must independently choose one of three available options. Each option is described by two values: a resource cost and a score gain. For player i, option j contributes a cost ai,j and a score ci,j.

Codeforces 104985D: Bill Restoration

We are given several episodes to download, and each episode comes with two parameters: a nominal download speed and a target download time if that speed stayed constant.

We are given a grid where each cell has a terrain value that can be interpreted as a required altitude to safely operate in that location. A helicopter starts at some cell and must move across the grid, changing cells in four directions.

We are working with a directed graph whose nodes represent themes and whose edges represent one-way relationships between them.

We are arranging all integers from 1 to n into a permutation, where each integer represents a play and its value represents how good it is. Small numbers are better plays and large numbers are worse plays.

We are given a long string that represents a text written as a sequence of uppercase letters. Alongside this text, we are given a collection of dictionary words.

We are given two collections of points on a number line. The first collection consists of bakeries with positions $x1, x2, dots, xN$.

We are given a fixed set of distinct “unknown words” that William encounters while rewriting a collection of sentences.

We are given a string of length $n$. The only allowed operation is to pick an index $i$ and swap the characters at positions $i$ and $i+k$. This operation can be repeated arbitrarily many times.

We are maintaining a grid of stacks. Each cell of an $N times N$ board contains a vertical stack of letters. The system supports three kinds of operations applied over time: pushing a letter onto a stack, popping the top letter from a stack, and querying whether a given letter…

Working

We are given two independent sequences that interact multiplicatively and additively across many decisions. Each bakery has a position value $xi$. Each mailbox has a position $yj$ and an associated cost $kj$. For every bakery, Cyrano chooses exactly one mailbox to visit.

We are given a long string representing a “text” of length $N$. Alongside it, we are also given a set of $M$ distinct words. The total length of all words combined is bounded, so although there may be many words, their combined structure is still compact.

We are given a string of length $n$. We are allowed to repeatedly apply a swap operation that exchanges characters at positions $i$ and $i+k$, as long as both indices are valid. These swaps can be performed any number of times in any order.

We are given a fixed list of distinct words that William does not know. During his work, he reads a sequence of sentences in order, and every word in those sentences belongs to this “unknown vocabulary” set.

We are maintaining a grid of stacks. Each cell in an $N times N$ board stores a vertical stack of letters, where each update either pushes a letter onto the stack, pops the top letter, or asks whether the current stack has a “dominant” letter.

Working

We are given a single line of text that may contain uppercase and lowercase English letters mixed with spaces. The task is to determine whether the contiguous sequence of characters “be” appears anywhere in this text when we ignore capitalization.

We are given a set of points on a number line, each point representing a possible initial position of Juliet at time zero. Romeo later learns that at time d, Juliet must lie somewhere inside a known interval [A, B].

Codeforces 105013J: 小Q的机器

We are given a binary string consisting only of opening and closing brackets. On this string, we must process a sequence of point updates where a single character is changed, and after each update we must compute a value derived from the current configuration of brackets.

I can’t produce a correct or meaningful editorial from what you’ve provided, because the actual problem statement is missing.

The input describes a binary string that is processed in fixed-size chunks of length k. You can think of splitting the string into consecutive blocks, each block being treated independently first, and then interacting with its neighbors later.

We are given a tree with n nodes, where each node carries a lowercase letter. Every node also has an implicit depth from the root. After building the tree, we receive q queries.

We are given a directed graph where each vertex represents a currency and each edge represents an exchange operation. If we go from currency u to currency v, the amount does not simply get multiplied by a rate, it also loses a fixed fee before conversion.

Each query describes a modular grid universe of size $n times m$, where positions wrap in a structured way. At any fixed time, there are $nm$ individuals, each indexed by a number $k$, and each individual follows a deterministic trajectory across grid cells over time.

Each input describes a disk made of concentric circular sectors. The $i$-th sector is a ring split into $Ai$ equal positions, and each position is painted with one of $K$ colors. So every sector is essentially a colored cyclic array whose length depends on the sector index.

We are given several memory blocks, each block has a size that is a power of two. If an element has value $Si$, its actual size is $2^{Si}$, and it also comes with a strict alignment rule: it can only be placed at a memory address divisible by $2^{Si}$.

We are given, for every node in an unknown tree, the identity of one special node: the node that is farthest from it in terms of shortest-path distance.

We are working on an $N times M$ grid where every cell represents a possible hiding location for a money bag. Yessine will place exactly $K$ bags, with at most one per cell.

We are given a very small grid, at most 5 by 5, filled with two possible colors, black and white. The game repeatedly removes connected regions of the same color, and each removal causes a physical reconfiguration of the grid: cells above fall down to fill gaps, and then empty…

We are given a sequence $P$ that is supposed to behave like a prefix-function array of some hidden integer array $A$.

We are given an array of positive integers and a fixed odd integer $k$. Two players take turns transforming the array. A move consists of choosing two elements, removing them, and appending their sum.

We are given a binary string and allowed to repeatedly perform a local transformation on adjacent equal characters. Whenever we see two consecutive 0s, we may delete them and insert a single 1.

We are given several independent scenarios. In each scenario, there are $N$ champions, each with an initial strength value.

We are given several independent test cases. Each test case contains a sequence of prices over time. The task is to look at every contiguous segment of time where the prices strictly increase step by step, and measure how much the price rises from the beginning of that segment…

We are given a text message that consists of several “animal names” embedded inside a normal sentence. Each animal name is written as a concatenation of words, where each word starts with a capital letter and continues with lowercase letters.

We are given a collection of videos, each video is a string made of uppercase letters. Each character represents a 10-second segment of a certain animal type. Watching a video means consuming the entire string, so the cost of a video is proportional to its length.

We are given a collection of $n$ containers, where each container holds two independent quantities: some number of cat food packs and some number of dog food packs. The total number of containers is odd.

We are given a collection of food items, each described by how soon it disappears from a warehouse and how many calories it provides. Time moves in discrete hours starting from the moment the bear arrives.

We are given a rectangular grid representing a yard divided into unit cells. Each cell is either marked as 0 or 1. The 1 cells form the drawn border of a single pool structure, and the 0 cells inside represent the interior area enclosed by that border.

A frog starts at the first stone in a row of n stones and wants to reach the last one. Normally it moves one step forward, visiting every stone in order.

The training process produces a sequence of exercises. Each exercise has a “correct answer” provided by the owl and a response written by Grisha. The same exercise may appear multiple times, because if Grisha’s answer is not accepted, the owl repeats that exercise later.

We are given a world populated by two kinds of creatures. Each creature of the first type has exactly 1 head and 19 legs, while each creature of the second type has exactly 7 heads and 4 legs.

We are looking at a system of identical animals, where each animal consumes a fixed integer number of carrots per meal. That per-meal amount is the same across all meals for a given animal, and also the same across all animals.

We are given a sequence of distinct ratings assigned to birds, where each position corresponds to a new bird encountered in order.

We are given a single string made of lowercase English letters, and we need to find a substring that appears as many times as possible inside it. Among all substrings with the highest frequency, we prefer the longest one.

We are given a collection of strings, each representing a fixed “spell”. We are allowed to rearrange these strings in any order and concatenate them into one long string.

We are given a rectangular grid where some cells contain artifacts. Each artifact sits at a specific coordinate, and we are only allowed to move from the top-left corner to the bottom-right corner using steps that go either right or down.