brain

tamnd's digital brain — notes, problems, research

41230 notes

CF 103476C - Divisor Circle

I don’t have the actual statement for Codeforces 103476C - Divisor Circle in the prompt, and I can’t reliably reconstruct the problem from the title alone without risking hallucinating key rules.

codeforcescompetitive-programming
CF 103478H - 莫卡与阿拉德大陆

We are given several circles drawn on an infinite plane. These circles interact only in a very structured way: any two circles are either completely separate, one fully contains the other, or they just touch.

codeforcescompetitive-programming
CF 103478I - 皮卡丘与 PCPC 集训队

We are given a sequence of integers that is claimed to be generated by a linear recurrence with modular reduction. The sequence starts from a known value and evolves using fixed parameters $a$ and $b$, but the modulus $p$ is unknown.

codeforcescompetitive-programming
CF 103478G - Serval 的数学课堂

We are given an array $A$ of length $n$. For every subarray of length at least three, we first compute a modified average: we remove the minimum and maximum element of that subarray and then take the average of what remains.

codeforcescompetitive-programming
CF 103478F - 魔法少女莫卡的诞生

We are given a permutation of length $2n$, meaning it contains every integer from $1$ to $2n$ exactly once. We are allowed to perform swaps of adjacent positions, exchanging the values at positions $i$ and $i+1$. The target condition is not global sorting.

codeforcescompetitive-programming
CF 103478E - 最后的轻语

We are given a fixed word s and another string t. A student repeatedly tries to type s, but his typing process is not continuous in a clean way.

codeforcescompetitive-programming
CF 103478D - 不动数组

We are asked to construct a very special integer array of length $n$. The array $a$ uses indices from $0$ to $n-1$, and we also define another array $cnt$ of the same length where $cnt[i]$ is the number of times the value $i$ appears in $a$.

codeforcescompetitive-programming
CF 103478B - Serval 的元素周期表

We are given a single uppercase string representing a “word” built from letters A to Z. The task is to determine whether this word can be segmented completely into a sequence of chemical element symbols, but only using a restricted set: the first 20 elements of the…

codeforcescompetitive-programming
CF 103478C - Popcount Game

We are given a universe of integers from 0 up to $2^n - 1$. From this universe, a game is played starting at the number $x = 0$. Two players alternate moves, and each move consists of choosing a new value $y$ from the same universe and replacing $x$ with it.

codeforcescompetitive-programming
CF 103478A - 皮卡丘与 Codeforces

We are given multiple Codeforces accounts, each starting with its own rating value. Over time, a sequence of contests happens, and each contest contributes a fixed rating change. For every contest, we must choose exactly one account to participate.

codeforcescompetitive-programming
CF 103480L - Ayanoto 变形记

We are given a circular track with $n$ equally spaced positions labeled from $0$ to $n-1$. A frog starts at position $0$. Each move forces the frog to jump exactly $x$ steps forward along the circle, meaning from position $i$ it always lands at $(i + x) bmod n$.

codeforcescompetitive-programming
CF 103480M - P 龙学长的教诲

We are given several independent lines of text. Each line represents a sentence that has been distorted by a specific reordering rule applied to its words.

codeforcescompetitive-programming
CF 103480K - 欢迎来到杭师大

We are given a single integer n, and we are asked to print a fixed message exactly n times, each occurrence on its own line. The message itself is always identical and does not depend on any input besides n.

codeforcescompetitive-programming
CF 103480J - 毁灭凤凰人

We are given a very small hand of at most ten cards and a single boss monster with fixed combat statistics. Our goal is to determine whether we can remove this boss from the game in a way that prevents it from ever coming back. The boss interacts with our cards in two phases.

codeforcescompetitive-programming
TAOCP 7.2.1.2 Exercise 96

Let $n > c_t > \cdots > c_1 \ge 0$ with the constraints from exercise 57 and the additional condition $c_{j+1} > c_j + 1 \qquad (t > j \ge 1).$ Define the shifted variables $d_j = c_j - (j-1), \qquad...

taocpmathematicsalgorithmsvolume-4medium
CF 103480I - 好想听肆宝唱歌啊

We are given a collection of songs, where each song has a unique popularity value and a unique name. The popularity value acts like a strict ranking key: no two songs share the same score, and higher values mean a song is more desired.

codeforcescompetitive-programming
CF 103480G - 电子表校对

We are given two time displays written in a digital, seven segment style where each digit is rendered as a fixed 3 by 3 character block. Each time consists of six digits: two for hours, two for minutes, and two for seconds.

codeforcescompetitive-programming
CF 103480H - 简单的 LRU 问题

We are simulating how an operating system manages a small, fixed-size memory cache using the Least Recently Used policy. Memory is divided into a tiny number of slots, and we receive a sequence of memory access requests.

codeforcescompetitive-programming
CF 103480F - 月光奏鸣曲

We are given two square grids of the same size, each cell containing an integer color. The only operation allowed on the first grid is a rotation around its center by 90 degrees, either clockwise or counterclockwise, and we may apply this operation multiple times.

codeforcescompetitive-programming
CF 103480E - 计算最小值

We are given several arrays, and from each array we must choose exactly one value. After that selection, we conceptually have a multiset of size n.

codeforcescompetitive-programming
CF 103480D - 转动命运之轮

We are given an initial lineup of $n$ children, each child $i$ has a fixed happiness value $hi$. The toys are initially shuffled by a permutation: child $i$ receives a toy labeled $wi$, so the array $w$ is a permutation of $1 dots n$. The process then evolves in rounds.

codeforcescompetitive-programming
CF 103480C - 迷宫的十字路口

We are working on an infinite grid, but movement is heavily restricted: the player can only travel along the two coordinate axes. At the beginning, the player starts at the origin.

codeforcescompetitive-programming
CF 103480B - 7 的意志

We are given several independent test cases. In each test case we receive an array of positive integers, and the task is to count how many subarrays have sum exactly equal to 7777.

codeforcescompetitive-programming
CF 103480A - 解开束缚缠丝Ⅱ

We are given several test cases. In each case, we receive a multiset of single characters. Each character can be used at most once, and we are allowed to rearrange the chosen characters in any order.

codeforcescompetitive-programming
CF 103483L - Birthday

We are given a row of cards, each card having two possible values, one on the front side and one on the back side. For any contiguous segment of cards, we are allowed to choose which side of each card faces up.

codeforcescompetitive-programming
CF 103483K - Railroad sorting

The problem statement for “Codeforces 103483K - Railroad sorting” is not included, so there’s no way to reconstruct the task, constraints, or required algorithm.

codeforcescompetitive-programming
CF 103483J - Yurik and Woodwork Lesson

The problem statement for Codeforces 103483J - Yurik and Woodwork Lesson is not included in your prompt, so there is no information about what the input represents, what needs to be computed, or what constraints apply.

codeforcescompetitive-programming
CF 103483I - Wheel of Fortune

The problem statement is missing from your prompt, so there isn’t enough information to reconstruct what “Wheel of Fortune” is asking or to derive any meaningful solution.

codeforcescompetitive-programming
CF 103483H - Lots of Parabolas

The problem statement for Codeforces 103483H - Lots of Parabolas is missing from your prompt, so there isn’t enough information to reconstruct the task, constraints, or required computation.

codeforcescompetitive-programming
CF 103483G - The Math of Sailing

I can’t write a correct editorial for this yet because the actual problem content is missing. Right now I only see the title “The Math of Sailing”, but no statement, constraints, input/output definition, or samples.

codeforcescompetitive-programming
CF 103483F - Counting Antibodies

The problem statement section is empty, so there’s not enough information to reconstruct what “Counting Antibodies” is asking.

codeforcescompetitive-programming
CF 103483D - Exam registration

The problem statement for Codeforces 103483D - Exam registration is not included in your message, so I don’t have enough information to reconstruct the task or produce a correct editorial.

codeforcescompetitive-programming
CF 103483E - Fair Robbery

The editorial can’t be written yet because the actual problem content for Codeforces 103483E - Fair Robbery is missing from the prompt.

codeforcescompetitive-programming
CF 103483C - How Many Strings Are Less

I can absolutely write this editorial in the format you want, but I’m missing one critical piece: the actual problem statement for Codeforces 103483C.

codeforcescompetitive-programming
CF 103483A - Natives

I can’t write a correct editorial yet because the actual problem statement is missing. Right now you’ve only provided the title “103483A - Natives”, but the input/output description and constraints are empty.

codeforcescompetitive-programming
CF 103483B - Balanced Illumination

We’re missing a key ingredient for a correct editorial: the actual statement we are supposed to solve. For Codeforces 103483B - Balanced Illumination, I cannot safely reconstruct the intended task from partial context without risking inventing details that are not in the…

codeforcescompetitive-programming
CF 103485M - Constellation collection

The problem statement section is empty, so there’s not enough information to write a correct editorial for “Codeforces 103485M - Constellation collection”.

codeforcescompetitive-programming
CF 103485O - The perfect base

I can’t write a correct editorial for Codeforces 103485O - The perfect base because the actual problem statement is missing from your prompt.

codeforcescompetitive-programming
CF 103485N - Game Show

I’m missing the actual statement for Codeforces 103485N - Game Show, and without it I can’t reliably reconstruct the intended model, constraints, or solution.

codeforcescompetitive-programming
CF 103485K - Tributes to the Pharaohs

We are given one year model with a circular calendar of length k, where days repeat every k steps. There are n pharaohs, and each pharaoh is assigned a region with two phases: planting takes p[i] time units, and harvesting takes c[i] time units.

codeforcescompetitive-programming
CF 103485L - A tale of two cities

I can write the full editorial in exactly that format, but I am missing the most important piece: the actual problem statement.

codeforcescompetitive-programming
CF 103485J - Feedback Meetings

The statement is missing, so there’s nothing concrete to restate or derive a solution from. “Codeforces 103485J - Feedback Meetings” is referenced, but the actual problem definition (input, output, constraints, and rules) is empty in your prompt.

codeforcescompetitive-programming
TAOCP 7.2.1.2 Exercise 95

Let $n = s + t$ as in (1), and consider a $t$-combination $c_t \cdots c_1$ with $n > c_t > \cdots > c_1 \ge 0$ together with the additional adjacency restriction $c_{j+1} > c_j + 1 \qquad (t > j \ge 1...

taocpmathematicsalgorithmsvolume-4medium
CF 103485H - On the Way to Shopping - Easy

We are given a shopping scenario on a line of locations, where each position represents a point on a path and some of these positions are special.

codeforcescompetitive-programming
CF 103485I - On The Way To Shopping

I don’t have the actual statement for Codeforces 103485I - On The Way To Shopping in your prompt, and I can’t reliably reconstruct it from the title alone without risking inventing details.

codeforcescompetitive-programming
CF 103485G - The Diversity of the Library of Alexandria

I can’t produce a correct editorial yet because the problem statement is missing. Right now, I only see the title “Codeforces 103485G - The Diversity of the Library of Alexandria” but no description of the task, inputs, outputs, or constraints.

codeforcescompetitive-programming
CF 103485E - Protecting Roads

We are given a tree of villages connected by weighted roads. Each road has a length, and the entire structure allows travel between any two villages along unique simple paths. On top of this tree, we receive two kinds of online operations.

codeforcescompetitive-programming
CF 103485F - Ramesses, Ra, and Roots

We are given a list of integers, and for each query value $r$, we must count how many of those integers are perfect $r$-th powers. In other words, for a fixed $r$, we want to know how many values $ai$ can be written as $x^r$ for some integer $x$.

codeforcescompetitive-programming
CF 103485D - Circular Pharaoh

We are given a string placed on a circle, so its last character is adjacent to its first. This string is formed by repeatedly concatenating copies of some unknown base word, the pharaoh’s original name.

codeforcescompetitive-programming
CF 103485B - Carlitos and the end of the world!

I can’t reliably write a correct, detailed editorial for this problem yet because the actual problem statement content is not fully available from what I retrieved.

codeforcescompetitive-programming
CF 103485A - Trying to Impress Cleopatra

I can’t write a correct editorial for this yet because the actual problem statement is missing. Right now I only see the title and empty Input/Output sections, but no description of what “Trying to Impress Cleopatra” is asking us to compute.

codeforcescompetitive-programming
CF 103485C - Construction of precious stones

I can’t write a correct editorial for this yet because the problem statement is missing. “Codeforces 103485C - Construction of precious stones” isn’t enough to reconstruct the task reliably, and guessing would risk producing a completely incorrect solution.

codeforcescompetitive-programming
CF 103486L - Suzuran Loves String

We are given a string $S$. From this string we consider all of its suffixes, meaning substrings that start at some position $i$ and run to the end. So suffix $si$ is $S[i dots n-1]$, and there are $n$ such suffixes.

codeforcescompetitive-programming
CF 103486M - Sequence

We are given a sequence of integers and asked to compute a single derived value based on its spread. The “interesting value” is defined as the product of two quantities: the length of the sequence and the range of the sequence, where the range is the difference between the…

codeforcescompetitive-programming
CF 103486K - Bracket Sequence

We are asked to count how many valid bracket structures of total length $2N$ exist when there are $K$ different kinds of brackets. Each kind behaves like a matched pair, for example type 1 could be “()”, type 2 could be “[]”, and so on.

codeforcescompetitive-programming
CF 103486I - Nim Game

We are given an array of piles, where each position stores a number of stones. The system supports two operations over time. One operation increases all pile values in a given interval by some constant.

codeforcescompetitive-programming
CF 103486J - Shuffle

We are given a deck containing $n cdot m$ distinct cards labeled from 1 to $nm$. Initially the cards are arranged in increasing order from bottom to top, so card 1 is at the bottom and card $nm$ is at the top. A shuffle operation is then repeatedly applied.

codeforcescompetitive-programming
CF 103486H - Visit the Park

We are given an undirected graph where each edge carries a digit from 1 to 9. Alongside this graph, we are given a fixed walk described by a sequence of vertices $A1, A2, dots, AK$. The traveler starts at $A1$ and attempts to move step by step from $Ai$ to $A{i+1}$.

codeforcescompetitive-programming
CF 103486G - Matrix Repair

We are given an $N times N$ binary matrix, except some entries are missing and written as $-1$. Every unknown entry must be replaced with either $0$ or $1$. Along with the matrix, we are given the XOR of each row and each column after reconstruction.

codeforcescompetitive-programming
CF 103486D - Rush Morning

We are given a weighted tree with N markets connected by N − 1 roads. Each road has a cost, and Chiang’s daily routine is equivalent to choosing any simple path in this tree and summing the weights along that path.

codeforcescompetitive-programming
CF 103486F - Cooking

We are given a collection of strings, each representing an ingredient name. For every ordered pair of ingredients $(i, j)$, we define a value that measures how well the end of the $i$-th string aligns with the beginning of the $j$-th string.

codeforcescompetitive-programming
CF 103486E - Great Detective TJC

We are given several independent test cases. In each one, there is an array of positive integers, and the task is to determine whether we can pick two different positions such that the values at those positions differ by exactly one bit in binary, specifically their XOR equals 1.

codeforcescompetitive-programming
TAOCP 7.2.1.2 Exercise 94

Let $n = s + t$ as in (1), and consider a $t$-combination $c_t \cdots c_1$ with $n > c_t > \cdots > c_1 \ge 0$ together with the additional adjacency restriction $c_{j+1} > c_j + 1 \qquad (t > j \ge 1...

taocpmathematicsalgorithmsvolume-4medium
CF 103486C - Random Number Generator

We are given a linear congruential generator that starts from an initial value and repeatedly applies an affine transformation modulo a prime number.

codeforcescompetitive-programming
CF 103486B - Arithmetic Exercise

We are given three integers $A$, $B$, and $K$. The task is to compute the value of the fraction $A / B$ as a decimal number and output it with exactly $K$ digits after the decimal point.

codeforcescompetitive-programming
CF 103486A - Random Number Checker

We are given a sequence of integers and need to judge whether it looks “balanced” in terms of parity. Each number is either odd or even, and we simply count how many fall into each category.

codeforcescompetitive-programming
CF 103488L - Lexicographic Order

We are given a reference string s of length n, and an upper bound m on the length of another string t that we are allowed to construct.

codeforcescompetitive-programming
CF 103488K - Klee and Bomb

We are given a graph where each node represents a bomb and each bomb has a color. Edges represent connections between bombs.

codeforcescompetitive-programming
CF 103488J - Jiubei and Codeforces

We are simulating how a Codeforces rating evolves over time and how that rating translates into a visible title. Each user starts with an initial rating, then goes through a sequence of rating changes caused by contests.

codeforcescompetitive-programming
CF 103488I - If I Catch You

We are dealing with a game played on the perimeter of an $n times n$ grid, which forms a cycle of $4n - 4$ cells. Two players, Liola and Eastred, move only clockwise along this cycle. Liola starts at the top-right corner, and Eastred starts at the bottom-left corner.

codeforcescompetitive-programming
CF 103488H - Hile and Subsequences' MEX

We are given a very large increasing sequence that always looks like a permutation prefix, specifically the array contains all integers from 0 to n-1 in order.

codeforcescompetitive-programming
CF 103488G - Generate 7 Colors

We are given seven target quantities, one for each color from 0 to 6. The goal is to produce exactly those many pieces of each color using a limited operation.

codeforcescompetitive-programming
CF 103488C - Constructive Problem

We are asked to construct an array of length n with a very specific self-referential property. The value at position i is not arbitrary; instead, it must equal the number of occurrences of the value i inside the array itself.

codeforcescompetitive-programming
CF 103488B - Boboge and Tall Building

The building is modeled as a vertical structure split into a fixed number of equal-height floors. The total height of the building is given as a single value, and that height is distributed uniformly across all floors.

codeforcescompetitive-programming
CF 103488A - All in!

The task is intentionally minimal once you strip away the storytelling. There is no input at all, not even hidden parameters or multiple test cases. The program is required to print a single fixed string exactly as specified.

codeforcescompetitive-programming
CF 103491A - Very engaging

I can’t write a correct editorial for Codeforces 103491A without the actual problem statement. Right now there’s no description of the task, input/output format, or constraints, so any solution I produce would be guesswork and very likely wrong.

codeforcescompetitive-programming
CF 103491E - \texttt{inprast'rukt'uris saminist'ro}

I can’t write a correct editorial yet because the actual problem content for Codeforces 103491E - “inprast'rukt'uris saminist'ro” is missing from your prompt (the statement, input, and output sections are empty).

codeforcescompetitive-programming
CF 103491D - Cipher 5-1-15-10 and 3-1-15-10

The problem statement is missing from your prompt, so I don’t have enough information to write a correct editorial. Right now I only see the title “Cipher 5-1-15-10 and 3-1-15-10”, but no description of the input, output, or task.

codeforcescompetitive-programming
CF 103491C - Flynn's cars

I can’t reliably reconstruct CF Gym 103491C - Flynn’s cars from the available metadata alone. The contest page does not expose the statement in a readable form, and without the actual problem definition (input format, rules of the “cars”, and what is being asked), any…

codeforcescompetitive-programming
CF 103491B - Turing quarters

I don’t have the statement for Codeforces 103491B - “Turing quarters” available in context, and I can’t reconstruct a correct editorial without knowing what the input/output rules actually are.

codeforcescompetitive-programming
CF 103492K - Jumping Monkey

We are given a tree where each node has a distinct weight. From any starting node, a monkey is allowed to jump to another node if that destination node is the maximum-weight node along the unique simple path between the two nodes.

codeforcescompetitive-programming
CF 103492L - Contest Remake

We are asked to construct as many distinct “cards” as possible, where each card is actually a non-empty set of positive integers. Every set has a cost constraint: the sum of all numbers inside the set must not exceed a given limit $C$.

codeforcescompetitive-programming
CF 103492J - Bigraph Extension

We are given a bipartite graph with two fixed sets of vertices, each containing exactly n vertices. The vertices are already split into set A and set B, and every existing edge connects one vertex from A to one vertex from B.

codeforcescompetitive-programming
CF 103492H - Subpermutation

We are given a construction called a full permutation sequence of length n, which is formed by listing every permutation of the numbers from 1 to n exactly once, in lexicographical order, and concatenating them into a single long array.

codeforcescompetitive-programming
CF 103492I - Public Transport System

We are given a directed graph where each edge represents a transport route between two cities. Every route has a base cost and a discount parameter. A traveler starts from city 1 and may follow any directed path to reach other cities.

codeforcescompetitive-programming
TAOCP 7.2.1.2 Exercise 93

Let $n = s + t$ as in (1), and consider a $t$-combination $c_t \cdots c_1$ with $n > c_t > \cdots > c_1 \ge 0$ together with the additional adjacency restriction $c_{j+1} > c_j + 1 \qquad (t > j \ge 1...

taocpmathematicsalgorithmsvolume-4hard
CF 103492F - Nun Heh Heh Aaaaaaaaaaa

We are given multiple strings, and for each string we must count how many subsequences form a very specific structure. A valid subsequence is constructed in two phases. First, it must contain the fixed string nunhehheh as a subsequence in order.

codeforcescompetitive-programming
CF 103492E - Monopoly

We are given a circular board with n tiles, each tile contributing a fixed integer value when we step on it. Starting before the first tile, we begin at tile 1 and move deterministically to tile 2, then 3, and so on, wrapping back to 1 after n.

codeforcescompetitive-programming
CF 103492D - Primality Test

We are given a positive integer x, and we construct a value using primes around it. First, we define f(x) as the smallest prime strictly greater than x, so it is the next prime after x.

codeforcescompetitive-programming
CF 103492A - Median Problem

We are given a rooted tree with nodes numbered from 1 to n. Each node u must be assigned a distinct value au forming a permutation of 1 to n. In addition to these a-values, each node also has a derived value bu.

codeforcescompetitive-programming
CF 103492B - Kanade Doesn't Want to Learn CG

We are given a fixed projectile path described by a downward-opening parabola $y = ax^2 + bx + c$. A ball starts far to the left and moves strictly to the right along this curve. In the plane, there are two geometric objects.

codeforcescompetitive-programming
CF 103492C - GCD on Tree

We are given a tree where each node stores an integer value. The tree structure never changes, but the value at a node can be updated during the process. Alongside updates, we must answer queries that ask about all pairs of nodes in the tree.

codeforcescompetitive-programming
CF 103495K - Longest Continuous 1

We are building a very large binary string by repeatedly appending binary representations of integers. The construction starts from a single character string “0”.

codeforcescompetitive-programming
CF 103495L - Tree Game

We are given a rooted tree with nodes labeled from 1 to n, where node 1 is the root. Each node initially holds a value, and these values form a partial permutation: some nodes already contain distinct numbers, while others are empty and marked as zero.

codeforcescompetitive-programming
CF 103495J - Anti-merge

We are given an $n times m$ grid where each cell contains an integer value. There is a merging system that operates in two passes. First, within every column, vertically adjacent cells that share the same visible value get merged into a single taller block.

codeforcescompetitive-programming
CF 103495H - Reverse the String

We are given a string consisting only of lowercase English letters. In one move, we are allowed to pick a contiguous segment of the string and reverse it, or we may choose to leave the string unchanged.

codeforcescompetitive-programming
CF 103495G - Five Phases

We are given a system with five quantities corresponding to the five classical phases: Wood, Fire, Earth, Metal, and Water. Initially all five quantities are zero.

codeforcescompetitive-programming
CF 103495I - Fake Walsh Transform

We are given a full set of integers from 0 up to $2^m - 1$, meaning all binary masks of length $m$. From this universe we want to pick a subset of distinct numbers. The only requirement on the chosen subset is that the XOR of all chosen values must equal a fixed target value $n$.

codeforcescompetitive-programming
CF 103495F - Jumping Monkey II

We are given a tree where each node carries a numeric value. From any starting node, a monkey is allowed to walk along edges without revisiting nodes, so every valid walk corresponds to a simple path in the tree.

codeforcescompetitive-programming
CF 103495E - Stone Ocean

We are given several strings, and from each string we independently pick one character uniformly at random. If we call the chosen characters $T1, T2, dots, Tn$, then each $Ti$ is drawn from $Si$ with equal probability over its positions, and the resulting string $T$ has length…

codeforcescompetitive-programming