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tamnd's digital brain — notes, problems, research

41641 notes

CF 103624C - One Piece

I don’t have the actual problem statement for Codeforces 103624C - One Piece in your prompt, so I can’t reliably reconstruct the task or produce a correct editorial without guessing.

codeforcescompetitive-programming
CF 103625E - Dead Man's Chest

Let $wk(x)$ denote the $k$th Walsh function on $[0,1)$ in the Paley ordering, as defined in Section 7.2.1.1, so that each $wk$ is a ${pm 1}$-valued step function whose discontinuities occur only at dyadic rationals and whose sign pattern is determined by the binary digits of $k$.

codeforcescompetitive-programming
CF 103625J - Pirate Races

The problem statement for “Codeforces 103625J - Pirate Races” is missing from your prompt, so I don’t have enough information to write a correct editorial or derive any solution.

codeforcescompetitive-programming
CF 103625I - Redbeard's Trials

I can write the full editorial in the exact style you want, but I don’t actually have the statement of Codeforces 103625I - Redbeard’s Trials in the prompt, and I can’t reliably reconstruct it from the title alone without risking inventing the wrong problem.

codeforcescompetitive-programming
CF 103625G - Current Objective: Survive

We are given a game-like process on a structure that behaves like a sequence of states, where each state represents a position in a world and transitions between states represent possible moves.

codeforcescompetitive-programming
CF 103625H - X Marks the Spot

I’m missing the actual problem statement for Codeforces 103625H - X Marks the Spot, so I can’t safely reconstruct the solution or write a correct editorial yet.

codeforcescompetitive-programming
CF 103625F - Sinking Ship

I can’t write a correct, detailed Codeforces editorial without the actual problem statement. “Codeforces 103625F - Sinking Ship” is not included in your message, and I don’t have reliable access to that specific problem content.

codeforcescompetitive-programming
CF 103625C - One Piece

I can’t reliably write a correct editorial for “Codeforces 103625C - One Piece” because the actual problem statement is missing from your prompt. Without the statement, any solution would be guesswork, and that would defeat the purpose of a serious editorial.

codeforcescompetitive-programming
CF 103625D - Gold Coins Game

The problem statement is missing from your prompt, so I can’t reliably reconstruct the rules, game mechanics, or required output for “Codeforces 103625D - Gold Coins Game”.

codeforcescompetitive-programming
CF 103627L - Curly Racetrack

We are given a rectangular grid that represents a partial configuration of a racetrack made of curved tiles. Some cells are already fixed as containing a curly tile, while others are empty and can later be filled by the admin.

codeforcescompetitive-programming
CF 103627J - Diameter Pair Sum

We are working with a tree that is being dynamically modified, and each query asks us to compute a quantity that depends on distances inside a connected component of that tree.

codeforcescompetitive-programming
TAOCP 7.2.1.2 Exercise 13

Let Algorithm R denote the revolving-door generation of $t$-combinations of ${0,1,\dots,n-1}$ in the order described in Section 7.

taocpmathematicsalgorithmsvolume-4math-medium
CF 103627I - Streetlights

We are given a line of streetlights, each with a height, and a sequence of updates and queries. The updates change the height of a specific streetlight over time, while the queries ask us to count how many “visible pairs” of streetlights currently exist.

codeforcescompetitive-programming
CF 103627H - Endless Road

We are given a collection of segments on a line, where each segment represents a member and the interval of road they cover. The road itself is conceptually continuous, but the only interesting structure comes from segment endpoints.

codeforcescompetitive-programming
CF 103627E - Yet Another Interval Graph Problem

We are given a collection of weighted intervals on a line. Each interval can be thought of as an edge that connects its endpoints, and if two intervals overlap or touch through a chain of overlaps, they belong to the same connected component in the induced interval graph.

codeforcescompetitive-programming
CF 103627D - Two Bullets

We are given a sequence of values indexed from left to right. Each index represents a building, and each building has a height.

codeforcescompetitive-programming
CF 103627C - AND PLUS OR

We are given a universe of elements indexed from 0 to N − 1. Every subset of this universe is associated with a value through a function a(S).

codeforcescompetitive-programming
CF 103627B - Bingo

We are working with an $n times n$ grid where each cell can either be filled or left empty. The goal is to construct a pattern of empty cells that avoids forming any complete “bingo line”, where a bingo line corresponds to a fully empty row, fully empty column, or a fully…

codeforcescompetitive-programming
CF 103630J - Рудольф и разноцветная таблица

The problem statement is missing from the prompt, so I can’t reconstruct the logic, constraints, or required output for “Codeforces 103630J - Рудольф и разноцветная таблица” reliably.

codeforcescompetitive-programming
CF 103630I - Рудольф и подарочные наборы

I’m missing the actual problem statement for Codeforces 103630I - “Рудольф и подарочные наборы”, so I can’t reliably reconstruct the logic or write a correct editorial yet.

codeforcescompetitive-programming
CF 103630B - Рудольф и игра

Let $X[0],X[1],dots,X[n-1]$ be the array to be permuted, and let the inner loop in (42) denote the operation that is executed once per produced permutation, typically a visit or output of the current array state.

codeforcescompetitive-programming
CF 103630H - Рудольф и вышивка крестиком

I can’t write a correct editorial for this yet because the actual problem statement is missing. Right now I only have the title (“Rudolf and cross-stitch embroidery”), but no description of the rules, input format, or what needs to be computed.

codeforcescompetitive-programming
CF 103630F - Рудольф и пчёлы

The problem statement for Codeforces 103630F - “Рудольф и пчёлы” is missing from your prompt, so there isn’t enough information to construct a correct editorial. Right now I don’t know: - what the input represents (grid, tree, queries, etc.

codeforcescompetitive-programming
CF 103630G - Рудольф и Бернард

I can’t write a correct editorial for this yet because the problem statement is missing. “Codeforces 103630G - Рудольф и Бернард” alone doesn’t include the actual task description, so there’s no way to reliably reconstruct what is being asked, the…

codeforcescompetitive-programming
CF 103630D - Рудольф и мастерское зачарование

I can’t reliably write a correct editorial for this yet because the actual problem statement is missing. Right now I only have the title (“Rudolf and master enchantment”), but no description of what the input represents, what operations are allowed, or what needs to be…

codeforcescompetitive-programming
CF 103630E - Рудольф и звезды

The statement for CF 103630E - “Рудольф и звезды” is missing from your prompt, so I don’t have enough information to reconstruct the problem or produce a correct editorial.

codeforcescompetitive-programming
CF 103630A - Рудольф и сборка компьютеров

I don’t have the actual statement for Codeforces 103630A (“Рудольф и сборка компьютеров”) in your prompt, so I can’t reliably reconstruct the problem or write a correct editorial without guessing.

codeforcescompetitive-programming
CF 103630C - Рудольф и IQ ПФО

I’m missing the actual problem statement for Codeforces 103630C - “Рудольф и IQ ПФО” in your prompt.

codeforcescompetitive-programming
TAOCP 7.2.1.2 Exercise 12

Let Algorithm R generate successive $t$-combinations $c_t \dots c_2 c_1$ in revolving-door order, and let $j_k$ denote the index computed in step R3 on the $k$th visit, so that step R3 identifies the...

taocpmathematicsalgorithmsvolume-4math-medium
CF 103631A - Урок физкультуры

Let $X[0],X[1],dots,X[n-1]$ be the array to be permuted, and let the inner loop in (42) denote the operation that is executed once per produced permutation, typically a visit or output of the current array state.

codeforcescompetitive-programming
CF 103631D - Прожекторы

We are given a set of points, each point representing a projector placed on a plane. Every projector must be assigned one of several fixed directions. Once a direction is chosen, the projector illuminates a region of the plane determined by its position and its direction.

codeforcescompetitive-programming
CF 103631B - Оптимизация закупок

We are given two arrays that define weighted intervals on the same index line. One array contributes “cost” values and the other contributes “profit” values.

codeforcescompetitive-programming
CF 103631C - Интересные выходные

We are effectively dealing with a process that builds a rooted tree dynamically from a sequence of instructions, and then answers queries about relationships between nodes in that tree.

codeforcescompetitive-programming
CF 1036328 - Большие вызовы

I can’t write a correct editorial yet because the actual problem statement is missing. Right now I only see the title “Большие вызовы”, but no description of what the input represents, what needs to be computed, or even the constraints.

codeforcescompetitive-programming
CF 1036327 - Тяжелый груз

I can’t write a correct editorial for this yet because the actual problem statement is missing. Right now I only see the title (“Тяжелый груз”) but no description of the input, output, constraints, or what needs to be computed.

codeforcescompetitive-programming
CF 1036325 - Максимизация выигрыша

Let $X[0],X[1],dots,X[n-1]$ be the array to be permuted, and let the inner loop in (42) denote the operation that is executed once per produced permutation, typically a visit or output of the current array state.

codeforcescompetitive-programming
CF 1036326 - Экспедиция на Сириус

The problem statement section is empty, so there isn’t enough information to write a correct editorial yet. For a Codeforces editorial, I need at least: the full statement (or a link / text), plus input/output format and constraints.

codeforcescompetitive-programming
CF 103633B - Floor or xor ?

We are given an array of integers and three parameters: a target value and a modulus. The task is to count how many ordered quadruples of indices $(i, j, k, l)$ we can form such that the expression formed by two independent ratios matches the target.

codeforcescompetitive-programming
CF 103633A - Hatchet

We are given a sequence that represents a structured process, where the input describes an ordered list of values. The task is to choose two cut positions inside this sequence so that the array is split into three consecutive non-empty segments.

codeforcescompetitive-programming
CF 103634B - Xor or floor ?

We are given a collection of test cases, each test case contains two integers. For each pair, we are asked to compute two different values derived from these numbers: one is obtained by applying bitwise XOR, and the other is obtained by integer division in the floor sense.

codeforcescompetitive-programming
CF 103634A - Bamboo Coloring

I don’t have the actual statement of Codeforces 103634A (“Bamboo Coloring”) in your prompt, so I can’t reliably reconstruct the problem or write a correct editorial without risking inventing details.

codeforcescompetitive-programming
CF 103634C - Jump

I don’t have the statement for Codeforces 103634C - Jump in context, and I can’t reliably reconstruct the problem from the ID alone (it looks like a Gym or private archive problem).

codeforcescompetitive-programming
TAOCP 7.2.1.2 Exercise 113

Let Algorithm R generate successive $t$-combinations $c_t \dots c_2 c_1$ in revolving-door order, and let $j_k$ denote the index computed in step R3 on the $k$th visit, so that step R3 identifies the...

taocpmathematicsalgorithmsvolume-4hm-project
CF 103637L - Long integer

We are maintaining a very large integer that starts as an initial decimal string. The number is then modified step by step by a sequence of operations. Each operation either appends a single digit to the right end of the current number or removes the rightmost digit.

codeforcescompetitive-programming
CF 103637K - K-ones xor

We are given an array of $n$ integers, each represented with at most $m$ bits. We are allowed to choose a mask $x$, also an $m$-bit number, but with the restriction that it contains at most $k$ set bits.

codeforcescompetitive-programming
CF 103637J - Jenga

We are asked to count how many valid Jenga towers can be formed using exactly $n$ identical blocks, under a specific notion of stability. A tower is built in horizontal layers. Each layer contains one or more blocks, and adjacent layers are oriented perpendicular to each other.

codeforcescompetitive-programming
CF 103637I - Items in boxes

We are given two integers. One of them, $n$, determines how many boxes exist, specifically $2n$ boxes in total. The second value, $a$, describes how many distinct items are inside each box, and every box is independent of the others. From each box we must pick exactly one item.

codeforcescompetitive-programming
CF 103637G - Geometric shapes

We are given a rectangular grid of size $n times m$. One cell $(r, c)$ is forbidden and must remain empty. All other cells must be covered completely using tetrominoes, where each tetromino occupies exactly four cells and can be any of the standard Tetris shapes under rotation…

codeforcescompetitive-programming
CF 103637F - Function analysis

We are given a permutation-like sequence $p = (1, 2, dots, n)$. From this sequence we repeatedly sample $m$ elements, where each position is chosen independently and uniformly from the $n$ positions, so repetitions are allowed and the resulting multiset is not necessarily…

codeforcescompetitive-programming
CF 103637D - Dull game

We are given a sequence of heap sizes, and we are allowed to repeatedly modify individual heap values. After each modification, we must select a subsequence of indices that satisfies a very specific game-theoretic condition.

codeforcescompetitive-programming
CF 103637E - Elegance in moves

We are working on a very large chessboard where most cells are usable, but some disjoint rectangular regions are forbidden. The rectangles do not overlap, and each cell belongs to at most one of them.

codeforcescompetitive-programming
CF 103637B - BSUIR Open X

We are given a collection of strings, each representing the code name of a task set. From this collection we must choose exactly two distinct strings, and we are allowed to place them in either order, concatenating one after the other.

codeforcescompetitive-programming
CF 103637C - Crossed out letter

We are given two strings, both of the same length. Each of them is known to come from some unknown original string by deleting exactly one character, but not necessarily the same position in both cases.

codeforcescompetitive-programming
CF 103640J - Joining Pairs

Let $x in [0,1)$ and write its dyadic expansion $$x = 0.x1 x2 x3 ldots,qquad xj in {0,1}.$$ Let $rj(x)$ denote the $j$-th Rademacher function, $$rj(x) = (-1)^{xj}.

codeforcescompetitive-programming
CF 103640M - Most Ordered Way

The problem statement for “Codeforces 103640M - Most Ordered Way” is not included in your message, so I can’t accurately reconstruct the solution or write a meaningful editorial yet.

codeforcescompetitive-programming
CF 103640K - KIARA is a Recursive Acronym

I don’t have the actual statement for Codeforces 103640K (“KIARA is a Recursive Acronym”), so I can’t safely reconstruct the intended model, constraints, or solution path without risking inventing details that may be wrong.

codeforcescompetitive-programming
CF 103640L - Leaving Yharnam

I can’t write a correct Codeforces editorial without the actual problem statement. “103640L - Leaving Yharnam” isn’t something I can reliably reconstruct from metadata alone, and guessing would very likely produce a completely wrong solution and explanation.

codeforcescompetitive-programming
CF 103640I - Invested Money

The problem statement is missing, so I don’t have the actual rules, inputs, or required computation for “Codeforces 103640I - Invested Money”. Without that, I’d be guessing the entire solution, which would defeat the purpose of a correct editorial.

codeforcescompetitive-programming
CF 103640H - Hamilton - The Musical

I can’t write a correct, detailed editorial for “Codeforces 103640H - Hamilton - The Musical” without the actual problem statement. Right now the prompt contains only the title and format placeholders, but no description of the input/output or the task.

codeforcescompetitive-programming
CF 103640B - Because, Art!

Let $x in [0,1)$ and write its dyadic expansion $$x = 0.x1 x2 x3 ldots,qquad xj in {0,1}.$$ Let $rj(x)$ denote the $j$-th Rademacher function, $$rj(x) = (-1)^{xj}.

codeforcescompetitive-programming
CF 103640F - Fields Division

The problem statement is not included in your message, so I don’t have enough information to reconstruct what “Fields Division (103640F)” is asking or what the input/output represent.

codeforcescompetitive-programming
CF 103640G - Generator Tree

I don’t have the actual statement of Codeforces 103640G - Generator Tree in your prompt, so I can’t safely reconstruct the problem or produce a correct editorial without risking inventing details.

codeforcescompetitive-programming
CF 103640D - Daily Turnovers

We are given a sequence of daily financial results, where each element represents the company’s profit or loss on that day. A negative value means loss, positive means profit.

codeforcescompetitive-programming
CF 103640E - Expedition Plans

The prompt is missing the actual content of Codeforces 103640E - Expedition Plans (problem statement, input/output description, constraints, and samples).

codeforcescompetitive-programming
CF 103640A - Ancient Towers

The editorial request can’t be completed yet because the actual problem statement is missing. Right now we only have the title “103640A - Ancient Towers”, but no description of what the towers are, what operations are allowed, or what needs to be computed.

codeforcescompetitive-programming
CF 103640C - Cyclists versus Clouds

I can’t reliably reconstruct Codeforces 103640C (“Cyclists versus Clouds”) from the title alone, and I don’t have the actual statement in your prompt.

codeforcescompetitive-programming
CF 103643T - Revert to Zero

I can’t write a correct Codeforces editorial without the actual problem statement. “Codeforces 103643T - Revert to Zero” is not enough to reconstruct the task reliably, and guessing would lead to a completely wrong solution and analysis.

codeforcescompetitive-programming
CF 103643S - Gin-chan's Odd Jobs

I cannot reliably reconstruct a correct editorial for Codeforces 103643S - Gin-chan’s Odd Jobs from the available context, because the actual problem statement is not present in the accessible sources, and this specific Gym problem is not part of the standard indexed…

codeforcescompetitive-programming
CF 103643K - Cards

Let $x in [0,1)$ and write its dyadic expansion $$x = 0.x1 x2 x3 ldots,qquad xj in {0,1}.$$ Let $rj(x)$ denote the $j$-th Rademacher function, $$rj(x) = (-1)^{xj}.

codeforcescompetitive-programming
CF 103643R - Quantum Fluctuations

I can’t write a correct editorial for this yet because the actual problem statement for Codeforces 103643R - Quantum Fluctuations is missing from your prompt.

codeforcescompetitive-programming
CF 103643Q - Kirito's Password

I don’t have the actual statement of Codeforces 103643Q - Kirito’s Password in your prompt, so I can’t reliably reconstruct the problem or produce a correct editorial without risking inventing details.

codeforcescompetitive-programming
CF 103643P - Reincarnation

I’m missing the actual problem statement for “Codeforces 103643P - Reincarnation”, so I can’t safely write a correct editorial yet. Right now the input/output sections are empty, which usually means either the statement wasn’t pasted or it got truncated.

codeforcescompetitive-programming
CF 103643O - Painting Fences (Hard Version)

I don’t have the actual statement of Codeforces 103643O - Painting Fences (Hard Version) in your prompt, so I can’t safely reconstruct the problem or write a correct editorial without risking inventing details.

codeforcescompetitive-programming
CF 103643N - Chiisana Boukensha

I’m missing the actual problem content for Codeforces 103643N - Chiisana Boukensha in your prompt (statement, input/output, constraints).

codeforcescompetitive-programming
CF 103643M - Thomas Game Revisited

I don’t have the actual problem statement for Codeforces 103643M - Thomas Game Revisited, so I can’t reliably reconstruct the rules, constraints, or intended solution.

codeforcescompetitive-programming
CF 103643L - Circle Game

I’m missing the actual problem statement for Codeforces 103643L - Circle Game, and without it I can’t reliably reconstruct the rules, constraints, or intended solution path.

codeforcescompetitive-programming
CF 103643J - P=NP Revisited

The problem statement is missing from your prompt, so I can’t reliably reconstruct what “Codeforces 103643J - P=NP Revisited” is asking. For a proper editorial, I need at least the following: The exact input description, output requirement, and constraints.

codeforcescompetitive-programming
CF 103643I - Late Midnight Assignment

I can’t write a correct editorial yet because the actual problem statement for Codeforces 103643I - Late Midnight Assignment is missing from your prompt.

codeforcescompetitive-programming
CF 103643A - Meeting Minutes

Let $x in [0,1)$ and write its dyadic expansion $$x = 0.x1 x2 x3 ldots,qquad xj in {0,1}.$$ Let $rj(x)$ denote the $j$-th Rademacher function, $$rj(x) = (-1)^{xj}.

codeforcescompetitive-programming
CF 103643H - Ziplines

I don’t have the actual statement of Codeforces 103643H - Ziplines in your prompt, so I can’t accurately reconstruct the problem, constraints, or solution.

codeforcescompetitive-programming
CF 103643G - Shokugeki no Waifu

I can’t write a correct editorial for this because the actual problem statement is missing. Right now I only see the template and metadata, but there is no description of the task (what the input is, what operations or constraints exist, what needs to be computed).

codeforcescompetitive-programming
CF 103643F - Changing Numbers

I can’t write a correct editorial for this yet because the problem statement for Codeforces 103643F - Changing Numbers is missing from your prompt.

codeforcescompetitive-programming
TAOCP 7.2.1.2 Exercise 112

Let $G = S_n$ and let \rho = (1\ 2\ \dots\ n-1), \qquad \sigma = (1\ 2\ \dots\ n).

taocpmathematicsalgorithmsvolume-4math-hard
CF 103643E - Oops, It's Yesterday Thrice More!

The problem statement for Codeforces 103643E - “Oops, It’s Yesterday Thrice More!” is not included in your prompt, so there’s no way to correctly reconstruct the solution or write a meaningful editorial yet.

codeforcescompetitive-programming
CF 103643D - Sticky Spelling Situation

The problem statement is missing from your prompt, so there’s no way to reconstruct what “Sticky Spelling Situation” is asking without guessing.

codeforcescompetitive-programming
CF 103643C - Painting Fences (Easy Version)

I’m missing the actual problem statement for Codeforces 103643C - Painting Fences (Easy Version), so I can’t reliably reconstruct the task or derive a correct solution.

codeforcescompetitive-programming
CF 103643B - Operations

I can’t reliably reconstruct Codeforces 103643B (“Operations”) from the ID alone, and the statement is required to write a correct editorial. Please paste the full problem statement (input/output format and constraints).

codeforcescompetitive-programming
CF 103647I - Adeleke's Bird Flocks

The problem statement for Codeforces 103647I - Adeleke's Bird Flocks is missing from your message, so I don’t have enough information to write a correct editorial.

codeforcescompetitive-programming
CF 103647B - Friendly Flamingos

Let $x in [0,1)$ and write its dyadic expansion $$x = 0.x1 x2 x3 ldots,qquad xj in {0,1}.$$ Let $rj(x)$ denote the $j$-th Rademacher function, $$rj(x) = (-1)^{xj}.

codeforcescompetitive-programming
CF 103647G - Dove Dance

The problem statement for Codeforces 103647G - Dove Dance is missing from your prompt, so I don’t have enough information to write a correct editorial.

codeforcescompetitive-programming
CF 103647H - Fledgling Fight

I can’t write a correct editorial for this yet because the problem statement is missing. Right now I only see the title “103647H - Fledgling Fight”, but no description, input/output format, or constraints.

codeforcescompetitive-programming
CF 103647F - Firebird

I can’t write a correct editorial for “Codeforces 103647F - Firebird” because the actual problem statement is missing from your prompt.

codeforcescompetitive-programming
CF 103647E - Bird Watching

I can’t reliably write an editorial for this yet because the actual problem statement is missing. Right now the prompt only contains placeholders: - Input: empty - Output: empty - No description of what “Bird Watching” asks Without the problem definition, any solution or…

codeforcescompetitive-programming
CF 103647D - Parrot Riddles

I can’t write a correct Codeforces editorial for “103647D - Parrot Riddles” without the actual problem statement.

codeforcescompetitive-programming
CF 103647C - Peacock Party

I can absolutely write this editorial in the requested style, but I’m missing the most critical ingredient: the actual statement of Codeforces 103647C - Peacock Party.

codeforcescompetitive-programming
CF 103647A - Night Nesting

I can’t write a correct editorial yet because the actual problem statement for Codeforces 103647A - Night Nesting is missing from your prompt.

codeforcescompetitive-programming
TAOCP 7.2.1.2 Exercise 111

The previous solution fails because it never defines a correct Eulerian object.

taocpmathematicsalgorithmsvolume-4math-medium
CF 103648I - Adeleke's Bird Flocks

Let $x in [0,1)$ and write its dyadic expansion $$x = 0.x1 x2 x3 ldots,qquad xj in {0,1}.$$ Let $rj(x)$ denote the $j$-th Rademacher function, $$rj(x) = (-1)^{xj}.

codeforcescompetitive-programming
CF 103648L - Communist Crows

I can’t write a correct editorial yet because the actual problem statement is missing. Right now I only see the title, input/output placeholders, and formatting instructions, but no description of what “Communist Crows” is asking us to compute.

codeforcescompetitive-programming
CF 103648K - Food Search

I’m missing the actual problem statement, input/output format, and constraints for Codeforces 103648K - Food Search. Without those, any “editorial” would be guesswork, and I’d risk inventing a solution that doesn’t match the problem.

codeforcescompetitive-programming