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tamnd's digital brain — notes, problems, research

41641 notes

CF 104887I - Injurious Company

We are given a starting point in the plane and a fixed sequence of moves. Each move has two pieces of information: a maximum length $Ki$ and a constraint on direction type, either horizontal or vertical.

codeforcescompetitive-programming
CF 104887H - Harana

Each position in the input represents a note in a song. At position i, there is an intended note si and Bob actually sings bi. If nothing else changed, the mismatch at position i is simply the absolute difference between these two values.

codeforcescompetitive-programming
CF 104887F - Five-Needle Telegraph

The structure in this problem is a rotated grid that looks like a diamond. Each position in this diamond contains a letter, except the middle horizontal line of length $n$, which contains needles instead of letters.

codeforcescompetitive-programming
CF 104887D - Dragon These Nuts

We are given a multiset of strengths associated with positions 1 through n, and we are allowed to output a permutation of these positions.

codeforcescompetitive-programming
CF 104887G - Ghost Gym

Working

codeforcescompetitive-programming
CF 104887E - Experiment! AMOGUS Edition

Working

codeforcescompetitive-programming
CF 104887C - Canonizing Cannonade

We are working on an $r times c$ grid where some cells contain soldiers. The goal is to place exactly $m$ soldiers so that a specific “destruction game” has a very precise difficulty.

codeforcescompetitive-programming
CF 104887B - Balarila

We are given a single lowercase string. We are allowed to choose an ordered pair of distinct consonants, written as x followed by y. In a modified counting system, every occurrence of the adjacent substring xy is treated as one character instead of two.

codeforcescompetitive-programming
CF 104887A - ABCs of Men and Women, Part 2

We are given a timeline of cooking assignments for three people, encoded as a string where each character is one of A, B, or C. Each position represents one day, and exactly one person cooks on that day.

codeforcescompetitive-programming
TAOCP 7.2.2.1 Exercise 362

We restart from the definition of the object being counted and keep the modification from Exercise 360 precise.

taocpmathematicsalgorithmsvolume-4simple
CF 104895B - Two avenues

I can’t reliably write a correct editorial for “Codeforces 104895B - Two avenues” without the actual problem statement.

codeforcescompetitive-programming
CF 104895D - Serious Business

The problem statement is missing from your prompt (both the “Problem Statement” and input/output sections are empty), so there isn’t enough information to reconstruct what Codeforces 104895D - Serious Business is asking.

codeforcescompetitive-programming
CF 104895C - Strange sum

I can’t reliably write a correct editorial yet because the actual problem statement for Codeforces 104895C - Strange sum is missing from your prompt.

codeforcescompetitive-programming
CF 104895A - Good arrays

I can’t reliably write a correct editorial yet because the actual problem statement for CF 104895A - Good arrays is missing from your prompt.

codeforcescompetitive-programming
CF 104896A - Plane stretching

We are given a set of points in the plane, and we repeatedly apply a geometric transformation: every point keeps its y-coordinate unchanged while its x-coordinate is multiplied by a given factor α.

codeforcescompetitive-programming
CF 104896C - Third grader's task

We are given two integer arrays, which we should think of as multisets of symbols. From the first array, we can form any permutation, meaning any ordering of the same elements. From the second array, we get a fixed reference sequence.

codeforcescompetitive-programming
CF 104901M - Almost Convex

We are given a set of points in the plane, with no duplicates and no three collinear. From these points we want to form polygons whose vertices are chosen from the set. A valid polygon must be simple, meaning its edges do not intersect except at consecutive vertices.

codeforcescompetitive-programming
CF 104901B - Graph Partitioning 2

We are given a tree, and we want to “cut” some edges so that the remaining connected components all have very specific sizes: each component must contain exactly k or k + 1 vertices.

codeforcescompetitive-programming
CF 104901L - Ticket to Ride

We are given a line of cities from 0 to n, and between every adjacent pair we may or may not place a rail segment. Choosing a subset of these segments determines a collection of connected intervals on the line. A ticket is a triple (l, r, v).

codeforcescompetitive-programming
CF 104901J - Computational Intelligence

We are given two line segments in the plane. From each segment, a point is chosen uniformly along its length, independently of the other segment. For every test case, we need the expected Euclidean distance between these two random points.

codeforcescompetitive-programming
CF 104901K - Rainbow Subarray

We are given an integer array and we are allowed to modify it a limited number of times. Each modification increases or decreases a single element by exactly one.

codeforcescompetitive-programming
CF 104901I - Strange Sorting

We are given a permutation, meaning an array of length $n$ containing every integer from $1$ to $n$ exactly once in some order. Our task is to transform this array into increasing order using a specific operation that modifies a contiguous segment.

codeforcescompetitive-programming
CF 104901G - Gifts from Knowledge

We are given a binary matrix, but the only operation we are allowed is to optionally reverse each row. Reversing a row flips it horizontally, so the first column becomes the last, the second becomes the second last, and so on.

codeforcescompetitive-programming
CF 104901H - Basic Substring Structure

Working

codeforcescompetitive-programming
CF 104901F - Say Hello to the Future

We are given an array of problem difficulties, and we want to count how many valid ways exist to split the index range from 1 to n into contiguous segments.

codeforcescompetitive-programming
CF 104901D - Largest Digit

We are given two closed integer intervals. One interval describes the possible values of an integer $a$, and the other describes the possible values of an integer $b$.

codeforcescompetitive-programming
CF 104901E - I Just Want... One More...

Working

codeforcescompetitive-programming
CF 104901C - Turn on the Light 2

We are asked to design, for each test case, a connected simple graph that uses exactly $m$ edges and as few or as many vertices as we choose (but at most $m+1$), under a degree constraint $d$.

codeforcescompetitive-programming
CF 104901A - Many Many Heads

We are given a string that looks like a bracket sequence containing round and square brackets. This string is not necessarily a valid bracket sequence.

codeforcescompetitive-programming
CF 104915D - Шторы

We are given a line of hooks indexed from 1 to n. The two boundary hooks, 1 and n, are considered already used before the process begins. After that, the system repeatedly performs a deterministic operation on the remaining unused hooks.

codeforcescompetitive-programming
CF 104916B - Прогнозы

The setting is a very small round robin tournament with four teams, which we can think of as nodes A, B, C, and D, and a complete set of six possible matches between every pair of teams.

codeforcescompetitive-programming
CF 104916E - Фонари

The system models a park with multiple lanterns, each lantern holding a lamp that eventually burns out. Every lamp has a known lifetime, so each lantern can be thought of as producing an “expiration event” at a specific time.

codeforcescompetitive-programming
CF 104916D - Камышовый кот

We are given a sequence of events ordered by time. At each time moment, the cat catches some number of mice. Multiple catches may happen at the same time moment, so the raw input can contain repeated timestamps with associated counts.

codeforcescompetitive-programming
CF 104916A - Зарядка для кота

We are simulating a simple interaction between a cat and a moving glowing point on a 2D grid. The point changes position step by step, and after each move we evaluate what the cat does in response.

codeforcescompetitive-programming
CF 104916C - CAT

We are given a string consisting of uppercase Latin letters, and we are interested in counting how many ordered subsequences of the form “C-A-T” exist inside it.

codeforcescompetitive-programming
CF 104921C - Word on the Paper

We are given several independent 8 by 8 character grids. Each grid is mostly filled with dots, but somewhere inside it a single word is hidden. The word is written straight down in exactly one column, occupying consecutive rows without interruption.

codeforcescompetitive-programming
CF 104921A - Rook

The input describes positions of a rook on a standard 8 by 8 chessboard. Each position is given in algebraic notation, where a letter from a to h identifies the column and a digit from 1 to 8 identifies the row.

codeforcescompetitive-programming
CF 104922I - Paired roads

I don’t have the actual statement of Codeforces 104922I - Paired roads, so I can’t reliably reconstruct the problem or derive a correct editorial.

codeforcescompetitive-programming
CF 104922H - Lunch

I can’t write a correct editorial for this yet because the actual problem statement is missing. Right now I only see the title “104922H - Lunch”, but no description of the input, output, or rules.

codeforcescompetitive-programming
CF 104922G - Space accident

I can’t reliably write a correct Codeforces editorial for “104922G - Space accident” because the actual problem statement (what is being asked, what the input/output represent, and the constraints) is missing here.

codeforcescompetitive-programming
CF 104922D - Hard problem

The problem statement section is empty, so there isn’t enough information to reconstruct what Codeforces 104922D is asking.

codeforcescompetitive-programming
CF 104922F - Tournament

I can’t reliably write an editorial for Codeforces 104922F - Tournament because the actual problem statement is missing from your prompt. Right now I don’t know: - what structure the “tournament” refers to (bracket, graph, game outcomes, DP on tree, etc.

codeforcescompetitive-programming
CF 104922E - Colorful graph

I can’t write a correct editorial for this yet because the actual problem statement (what “Colorful graph” asks for, input format, and output definition) is missing from your prompt.

codeforcescompetitive-programming
CF 104922C - Legs warm-up exercise

You are right to pause here: the problem identifier is misleading on its own, and without the actual statement it is impossible to write a correct editorial.

codeforcescompetitive-programming
CF 104922A - You need to train more

I’m missing the actual problem statement for Codeforces 104922A - “You need to train more” in your prompt, and I can’t reconstruct it reliably from the title alone.

codeforcescompetitive-programming
CF 104922B - Yet another queries

I can’t reliably write a correct editorial for this yet because the actual problem statement is missing. “Codeforces 104922B - Yet another queries” is not enough on its own, and there are multiple possible problems with similar names and formats.

codeforcescompetitive-programming
TAOCP 7.2.2.1 Exercise 359

The problem requires placing nine given pieces into a $65 \times 65$ square.

taocpmathematicsalgorithmsvolume-4hard
CF 104925A - Alternating Paths

We are given an undirected connected graph where each edge must be assigned one of two colors, red or blue. After coloring, we want a strong reachability property: between every pair of vertices, there must exist a walk that alternates colors on consecutive edges.

codeforcescompetitive-programming
CF 104925J - 'Ello, and What Are You After, Then?

We are repeatedly interacting with a collection of “task providers”, called slayer masters. Each master has a fixed list of tasks. A task has a frequency weight, a duration, and an XP rate per minute.

codeforcescompetitive-programming
CF 104925I - Rebellious Edge

We are given a directed graph on vertices labeled from 1 to n, with a distinguished root at vertex 1. The task is to choose a set of directed edges that forms a spanning arborescence rooted at 1, meaning every vertex is reachable from 1, and every vertex except the root has…

codeforcescompetitive-programming
CF 104925G - LCA Counting

We are given a rooted tree with root fixed at node 1, and we are told which vertices are leaves of this tree. From this set of leaves, we will choose exactly k of them, for every k from 1 up to the total number of leaves.

codeforcescompetitive-programming
CF 104925H - Minimum Cost Flow²

We are given a directed graph with a designated source node and sink node. Instead of choosing a discrete set of paths or integer flows, we assign a real-valued flow to every edge, possibly negative, as long as flow conservation holds at every vertex and the net flow from…

codeforcescompetitive-programming
CF 104925F - When Anton Saw This Task He Reacted With 😩

We are given a rooted binary tree where each internal node combines the results of its two children using a fixed operation: the vector cross product in three dimensions.

codeforcescompetitive-programming
CF 104925E - Freshman's Dream

We are given a number $n$, and for each test we must either construct two positive integers $a$ and $b$ (both below $2^{60}$) or report that no such pair exists. The required condition mixes addition and bitwise XOR in a way that forces carries and bit cancellations to interact.

codeforcescompetitive-programming
CF 104925D - Filesystem

We are given a set of files, each file having two independent total orders defined on it. One order is by file name, the other is by creation date. The file names order is fixed and already represented by indices from 1 to n.

codeforcescompetitive-programming
CF 104925B - Binary Sequence

The sequence starts from a single binary digit string and evolves by repeatedly describing the previous string in terms of runs of identical digits. Each run is converted into two parts: the length of the run and the digit being repeated.

codeforcescompetitive-programming
CF 104925C - Yet Another Balanced Coloring Problem

We are given two rooted trees that share the same set of leaf vertices labeled from 1 to k. Every other vertex is an internal node.

codeforcescompetitive-programming
CF 104930A - Up Up Down Down

We are given a fixed sequence of 11 words, each representing a button press in a game cheat code. Separately, there is a known reference sequence, the Konami Code, which is also 11 inputs long.

codeforcescompetitive-programming
CF 104930G - Dinnerbone and Array

We are given a small array of integers, each test case independent. From that array, we consider every possible subset of elements except that we are not allowed to take the entire array.

codeforcescompetitive-programming
CF 104930H - Australian Solitaire

We are asked to count sequences of length $N$ where each position contains a “rank” chosen from a fixed ordered set of 13 denominations: Ace is the smallest, followed by 2 up to King.

codeforcescompetitive-programming
CF 104930F - Down Up Disco

We are given an $N times M$ grid where each cell contains a binary value. A value of 1 means the tile is currently flipped, and 0 means it is already correct.

codeforcescompetitive-programming
CF 104930C - Gambler's Chocolate Cove

Each slot machine behaves like a stochastic reward generator. When you pull a machine once, it returns one value from a fixed finite set, each value having a known probability. Those probabilities do not change over time and every pull is independent of previous pulls.

codeforcescompetitive-programming
CF 104930E - Up Down Matching

We are given several independent test cases. In each test case, a line of people stands in a fixed order, where each person is either from Uptown or Downside.

codeforcescompetitive-programming
CF 104930D - The World Turned Upside Down

We are given a starting point that is always the number 1, and we are allowed to build a sequence by repeatedly multiplying the current value by any positive integer.

codeforcescompetitive-programming
CF 104930B - Upside Downtown

We are given a house number written as a string of digits. The city has a symmetry rule: when you rotate the number by 180 degrees, it must still form a valid readable number using the same digit system. Only a restricted set of digits survives rotation: 0, 1, 6, 8, and 9.

codeforcescompetitive-programming
CF 104931J - Careful Cookout

We are placing shrimps on an $n times m$ grid, where each cell can either contain a shrimp or be empty. Each configuration is just a binary matrix. The grill has a rule that only activates locally on every $2 times 2$ subgrid.

codeforcescompetitive-programming
CF 104931E - Up Down Matching

We are given multiple test cases. Each test case consists of a line of people standing in a row, where each person belongs to one of two groups, encoded as U or D.

codeforcescompetitive-programming
CF 104931I - Pineapple Upside Down Cake

We are interacting with a hidden circular array of length $N$, where $1 le N le 2 cdot 10^5$. Each position on the circle contains an integer value, and these values are strictly increasing as we move around the circle in order: $s1 < s2 < dots < sN$.

codeforcescompetitive-programming
CF 104931H - Australian Solitaire

We are counting sequences of length $N$ formed from a fixed set of card ranks. The ranks behave like a total order: Ace is the smallest, then 2 up to King. The key restriction is on how consecutive cards are allowed to change. The first card in the sequence can be any rank.

codeforcescompetitive-programming
CF 104931F - Down Up Disco

The dance floor is a rectangular grid where each cell contains a person who is either in a normal orientation or flipped. We want to transform the entire grid into all zeros by applying a specific operation any number of times.

codeforcescompetitive-programming
CF 104931G - Dinnerbone and Array

We are given a small array of integers for each test case. From this array we may choose any subset of elements, but we are explicitly forbidden from choosing the full array. The subset can even be empty.

codeforcescompetitive-programming
CF 104931C - Gambler's Chocolate Cove

We are given several slot machines, each producing a random reward when pulled. Each machine has its own fixed probability distribution over a small set of possible reward values.

codeforcescompetitive-programming
CF 104931D - The World Turned Upside Down

We are given a set of distinct target numbers. We start from the value 1 and are allowed to build a sequence by repeatedly multiplying the current value by any positive integer.

codeforcescompetitive-programming
CF 104935A - Monotonically Increasing Tardiness Informatics Tournament

There are several organizers, each one getting progressively more late as meetings go on. The delay of each organizer does not stay fixed: for a given person, their lateness in the first meeting is known, and then every subsequent meeting they become even later by a fixed…

codeforcescompetitive-programming
CF 104935F - Array Gerrymandering

We are given a binary string for each test case, where each position represents a city that either supports Busy Beaver (1) or Lazy Lemur (0). We are allowed to partition this array into exactly $K$ contiguous nonempty segments, and each segment is considered a district.

codeforcescompetitive-programming
CF 104935E - Connecting Buildings

We are given several buildings placed around a circle. Each building has a fixed position on the circle and a height. There is also a special building at the center whose height is not fixed in advance; instead, it is given separately for each query.

codeforcescompetitive-programming
CF 104935D - Tree 2-Coloring

We are building a tree one vertex at a time. Initially there is only vertex 1. Each query adds a new vertex and connects it to some existing vertex, so the structure always remains a rooted-growing tree.

codeforcescompetitive-programming
CF 104935C - Tromino Packing

The grid can be thought of as a board where some cells are blocked, some are irrelevant empty space, and some cells are special anchors marked with o. Every o cell must become the center of an L-shaped tromino.

codeforcescompetitive-programming
CF 104935B - Min-Max Game

We are given a list of integers arranged in a line. Two players repeatedly compress this line until only one number remains. A move always picks two adjacent elements, removes them, and replaces them with a single value derived from the pair.

codeforcescompetitive-programming
CF 104937F - Solving Equations

Each test case describes a small system of polynomial equations over positive integers. Every variable is one of the first letters of the alphabet, and each equation is a sum of terms where a term is a coefficient multiplied by a product of variables.

codeforcescompetitive-programming
CF 104941A - Ancient Math

We are given the radius of a circle, and we are asked to construct a square that has exactly the same area as that circle. The task is not geometric construction in the classical sense, but a direct numerical computation: we must output the side length of such a square.

codeforcescompetitive-programming
CF 104945M - In-order

We are given a binary tree over the numbers from 1 to N, but the tree structure is not explicitly provided. Instead, we are told three traversal descriptions.

codeforcescompetitive-programming
CF 104945L - Broken trophy

We are given a collection of rectangular tiles, each tile having an integer side lengths $Ak times Bk$ where both sides are at most 3, and the tile may be rotated. All tiles together have total area exactly $3N$.

codeforcescompetitive-programming
CF 104945K - Team selection

We are simulating a selection process over a dynamic set of players labeled from 1 to N. Initially all players are available. Two leaders alternate turns.

codeforcescompetitive-programming
CF 104945H - Break a leg!

We are given the vertices of a simple non-self-intersecting polygon in order. Think of it as a rigid flat tabletop whose mass is uniformly distributed across its area.

codeforcescompetitive-programming
CF 104945J - Olympic goodies

Codeforces 104945J: Olympic goodies

codeforcescompetitive-programming
CF 104945I - Throwing dice

Each player rolls multiple independent dice, and the final score is the sum of all face values shown by their dice. Every die is fair, but different dice may have different numbers of sides, so each die contributes a uniform integer in a different range.

codeforcescompetitive-programming
CF 104945G - Favourite dish

Each dish comes with two attributes: a taste score and a plating score. Each person also comes with two preferences, which act as weights for those same two attributes.

codeforcescompetitive-programming
CF 104945E - Nicest view

We are given a sequence of heights along a straight hiking trail. Each index represents a milestone placed at equal horizontal spacing, and each milestone has a distinct altitude.

codeforcescompetitive-programming
CF 104945D - Flag performance

We start with a permutation of size $N$, where person $i$ initially holds a flag of some color $pi$. A move consists of choosing any two positions and swapping the flags they hold.

codeforcescompetitive-programming
CF 104945F - Programming-trampoline-athlon!

Each team in this competition is described by a name, a count of solved programming problems, and six scores coming from trampoline exercises. The final result of a team is a single total score formed by combining two independent parts.

codeforcescompetitive-programming
CF 104945C - Metro quiz

We are given a collection of metro lines, where each line can be seen as a subset of stations from a fixed universe of size up to 18. A line is fully described by which stations it stops at.

codeforcescompetitive-programming
CF 104945A - Card game

We are given a sequence of cards held in a hand. Each card has a suit among five types, ordered by priority as silver, white, emerald, red, and cyan, and each card also has a numeric label within its suit.

codeforcescompetitive-programming
CF 104945B - Supporting everyone

Each country can be represented in one of two ways. Either Alice prepares a full flag drawing, which requires buying all the colors that appear in that country's flag, or she avoids drawing that flag entirely and instead uses a single pin for that country.

codeforcescompetitive-programming
CF 1049493 - Table Game

We are given a small grid of numbers. From this grid, we are allowed to repeatedly delete entire rows or entire columns. Each deletion permanently removes all values in that row or column, and the remaining parts of the table stay intact.

codeforcescompetitive-programming
CF 1049494 - Выбор столицы

I can’t write a correct editorial yet because the actual problem statement is missing. Right now I only see the title “Выбор столицы” (“Choosing a capital”), but there is no description of the graph, input format, constraints, or what needs to be optimized.

codeforcescompetitive-programming
CF 1049491 - Посадка в самолет

We are given a simplified model of an airplane cabin where seats are arranged in rows, and each row contains six seats indexed from left to right. The middle of each row is a fixed aisle between the third and fourth seat.

codeforcescompetitive-programming
CF 1049492 - Битоническая последовательность

I can’t reliably reconstruct the actual task from just the title “Битоническая последовательность” and the ID, because Codeforces has multiple problems around bitonic sequences with very different requirements (LIS-based, rearrangement…

codeforcescompetitive-programming
CF 1049508 - Binary Tree Traversal

The tree structure is fixed: each node has up to two children and node 1 is the root. What changes over time is a label attached to every node, chosen from three values that decide whether that node is visited before its subtrees, between them, or after them.

codeforcescompetitive-programming
CF 1049507 - Split into Triplets

We are given a multiset of numbers, represented as an array. The task is to partition all elements into groups of exactly three elements, with no element left unused.

codeforcescompetitive-programming