brain

We are given a line of houses indexed from 1 to n. Each house starts with an initial bank balance. Then a sequence of events happens over time. Some events modify balances over a whole interval of houses by adding a value that can be positive or negative.

We are given an array of integers and a fixed modulus value $m$. One player, Berta, gets to choose two elements that end up in the same group, and she wins if the sum of those two elements is divisible by $m$.

We are interacting with a judge that has fixed but hidden integers $x$ and $y$, each up to $10^{18}$. Our only way to learn about them is by asking queries of the form $(a,b)$, and receiving back the value of $gcd( The goal is to determine both coordinates exactly, using at…

We are given a process that evolves on an undirected connected graph with $n$ vertices. The process depends on a sequence of integers $a1, a2, dots, am$, which we can think of as “distance jumps over time”. A starting vertex is chosen and marked as painted at day 0.

We are given several independent scenarios, each describing a group of friends attending a theater. Each friend has already been assigned a seat, specified by a pair of integers representing a row and a column. The seating layout is unusual in how columns are numbered.

We are given a rewriting system over strings. Each rule describes how a single character can expand into a two-character string. If a rule says c → ab, then every time we choose a position in the string containing c, we are allowed to replace that character by the pair ab.

Let $f(x1,dots,xn)$ be represented by an ordered reduced BDD with root node $r$. For each node $k$ in the BDD, write $V(k)$ for its variable index, and write $mathrm{LO}(k)$ and $mathrm{HI}(k)$ for its two successors. The sinks are $bot$ and $top$.

We are given a row of $n$ connected cups. Each adjacent pair of cups is linked by a straw placed at a certain height $Ai$. Water is poured only into the first cup, and then it can propagate through these connections depending on how much water has accumulated.

We are given several independent test cases. In each test case, there are n types of cookies, and the i-th type has a pile size ai. The task is to completely consume all cookies, but the consumption is constrained by a very specific daily rule.

We are building a sequence that depends on a starting value and a rule that keeps “rounding up” to multiples of increasing indices. We choose a positive integer $m$, which becomes the first element $a1$.

We are given a set of points in the plane. Each point behaves like a source that emits a ray. Initially every ray points straight down. Over time, all rays rotate counterclockwise at the same constant speed.

Let $f(x1,dots,xn)$ be represented by an ordered reduced BDD with root node $r$. For each node $k$ in the BDD, write $V(k)$ for its variable index, and write $mathrm{LO}(k)$ and $mathrm{HI}(k)$ for its two successors. The sinks are $bot$ and $top$.

We are given a grid where each cell either contains one diagonal segment or is blocked. A diagonal connects two opposite corners of a cell, so every non-blocked cell contributes a single edge between two grid vertices.

We are given a collection of sets, each set containing some elements from a universe whose size is also bounded by the number of sets. Each set also has an associated cost, which can be negative or positive. We are allowed to pick any subset of these sets, possibly empty.

We are given an integer array and we are allowed to modify it using a very specific operation: in one move we pick a non-negative integer m and a positive increment k, and then we add k either to a prefix of length m+1 or to a suffix of length m+1.

Each test case describes a football squad split into four fixed groups: goalkeepers, defenders, midfielders, and forwards. Every player has a fixed skill value.

Let $S_n$ be the set of permutations of ${1,2,\dots,n}$.

Let $f(x1,dots,xn)$ be represented by an ordered reduced BDD with root node $r$. For each node $k$ in the BDD, write $V(k)$ for its variable index, and write $mathrm{LO}(k)$ and $mathrm{HI}(k)$ for its two successors. The sinks are $bot$ and $top$.

The problem statement for “Codeforces 103810E - Экспедиция” is missing from your prompt, so there’s no way to reliably reconstruct the intended task, constraints, or solution strategy.

I don’t have the actual statement for Codeforces 103810D - Высадка in your prompt, and without it I’d be guessing the entire solution structure.

I’m missing the actual problem statement for Codeforces 103810A - right now only the title “Упаковка (Packing)” is provided, with no input/output description or constraints.

We are missing the actual statement of Codeforces 103810C, and this is not publicly inferable from contest metadata alone. Without the problem text, any “editorial” would be fabrication rather than explanation, which would defeat the purpose of a Codeforces-style writeup.

Let the contribution of a minterm corresponding to an assignment $x1 ldots xn$ be $$C(x1,ldots,xn)=prod{i=1}^n (1-pi)^{1-xi}pi^{xi}.

We are given a probabilistic system that simulates what happens when Justin clicks on a video. Each time he enters or refreshes the page, exactly one of several outcomes occurs according to fixed probabilities.

The problem statement is missing in your prompt (the Input/Output sections are empty), so there isn’t enough information to reconstruct what “Kario Mart” is asking.

I can’t write a correct, meaningful editorial for this problem yet because the actual statement of Codeforces 103811I - Inno Per Gli Sconfitti is not reliably available from the information provided, and the version that appears in search results is inconsistent and clearly…

I can’t reliably reconstruct Codeforces 103811G - Gold Medal Bout from the ID alone, and I don’t want to invent a problem statement and accidentally write a convincing but wrong editorial. Please paste the full problem statement (or even a screenshot / text dump).

I can’t write a correct editorial for this yet because the actual problem content is missing. Right now the prompt only includes the title and empty “Problem Statement / Input / Output” sections, but nothing describing the rules, constraints, or what “getting rice”…

I can’t reliably write a correct editorial for Codeforces 103811F - Furthest Travel because the actual problem statement (graph/array rules, constraints, and what “travel” means here) is missing from your prompt.

I’m missing the actual problem statement for Codeforces 103811E - Escape the Cube, and without it I can’t reliably reconstruct the intended solution or write a correct editorial.

I can’t reliably write an editorial for Codeforces 103811D - Double Queue without the actual problem statement.

I don’t have the actual problem statement for Codeforces 103811A - Allowance Exhaustion in your message, so I can’t safely reconstruct the solution or write a correct editorial without risking inventing details.

I can’t write a correct, detailed editorial for this problem yet because the actual problem statement is missing from your prompt.

The problem statement for Codeforces 103811B - Boat Assignment is not included in your prompt, so I don’t have the actual rules, input format, or required output to base an editorial on.

Let $w(x1,ldots,xn)$ denote the contribution of a minterm $$(1-p1)^{1-x1}p1^{x1}cdots (1-pn)^{1-xn}pn^{xn}.$$ Maximizing this quantity over all assignments satisfying $f(x1,ldots,xn)=1$ is equivalent to maximizing a product of independent local factors along a path in the BDD…

Let $f_n(k)$ be the binary de Bruijn cycle of order $n$ constructed in Exercise 97, so that the infinite periodic sequence f_n(0), f_n(1), \ldots, f_n(2^n-1) contains every $n$-bit string exactly once...

We are given a permutation of the numbers from 1 to N, and we define a score by scanning the permutation from left to right. Every time we place a value P[i], we look at all earlier values P[j] and add 1 if P[j] divides P[i].

We are given a timeline from moment 1 to moment M and a collection of movies, each represented by a closed interval [L, R], meaning the movie starts at time L and finishes at time R.

We are given a collection of balls where each ball has a color, so the input is essentially a multiset over colors. Alongside this, we are asked to distribute all balls into exactly K boxes.

Let $f$ be represented by a reduced ordered binary decision diagram, and let $F(p)$ denote the reliability polynomial under the specialization $p1=cdots=pn=p$.

We are given a set of points on a plane. Each point represents a tree placed at a fixed coordinate, and each tree independently “survives” with a given probability. If a tree survives, it becomes part of the final active set.

We are given a grid of digits where equal digits that touch by edges form connected components, exactly like standard 4-direction flood-fill regions.

Each test case describes one week of planning. For every week, we are given seven small integers, each representing how many jokes are told on a specific day from Saturday through Friday.

Let $f$ be represented by a reduced ordered binary decision diagram, and let $F(p)$ denote the reliability polynomial under the specialization $p1=cdots=pn=p$.

We are given two teams of size $N$. Team A starts with strengths $1, 2, 3, dots, N$, while team B starts with strengths $2, 3, 4, dots, N+1$. So the two teams are identical sequences shifted by one.

We are given a one-dimensional corridor of $N$ cells arranged in a line. A robot starts in the middle cell, specifically at index $lceil N/2 rceil$, and initially faces to the right.

We are given two horizontal rows of points on a grid. One team stands on the bottom edge at positions $(1,0)$ through $(n,0)$, and the other team stands directly above at $(1,n)$ through $(n,n)$.

We are given a rectangular grid of integers. Before the game starts, we are allowed to flip signs of entire rows and entire columns any number of times, where flipping a row or column multiplies every value in it by -1. After all flips are chosen, the board is revealed.

Let $v$ be a node of the reduced ordered BDD for $f$, and let $Fv(p)$ denote the reliability polynomial of the subfunction represented at $v$ under the specialization $p1=cdots=pn=p$. Let $F'v(p)$ denote its derivative with respect to $p$.

We are given a sequence of distinct integers representing rating changes from upcoming contests. We are allowed to reorder these values arbitrarily and feed them to a process that simulates how many contests a player ends up actually playing.

We are given a string of lowercase letters and a target number of occurrences of the pattern “awa”. We are allowed to modify characters freely, but each modification changes exactly one position to any lowercase letter.

We are given a grid with dimensions $n times m$. Each operation allows Rabbit to shrink the grid by removing some positive number of rows or some positive number of columns.

We start with a permutation of size $n$, and we are allowed to perform swaps of any two positions freely. Each swap exchanges the values at two indices, so in effect we are working in the full symmetric group where any transposition is allowed.

Let $f(x1,ldots,xn)$ be a Boolean function and let $$G(z)=sum{x1=0}^1 cdots sum{xn=0}^1 z^{x1+cdots+xn} f(x1,ldots,xn)$$ be its generating function as defined in the preceding exercise.

The Chinese ring puzzle (Baguenaudier) has a standard representation as a binary state vector $(a_1,\dots,a_n)$ in which each $a_j \in {0,1}$ encodes whether ring $j$ is disengaged or engaged, and leg...

Let $f(x1,ldots,xn)$ be a Boolean function and let $$G(z)=sum{x1=0}^1 cdots sum{xn=0}^1 z^{x1+cdots+xn} f(x1,ldots,xn)$$ be its generating function as defined in the preceding exercise.

I don’t have the actual statement of Codeforces 103828N - Moving grid in the prompt, so I can’t safely reconstruct the solution or write a correct editorial without risking inventing the wrong problem.

The problem statement for “Codeforces 103828K - No Server? !Problem” is not included in your prompt, so there is no way to reconstruct the task, constraints, or required output.

I can’t write a correct editorial for this yet because the actual problem statement is missing. Right now I only have the title “Codeforces 103828M - Mobile Game”, but no description of the rules, input/output, or constraints.

I can write the full editorial in exactly that format, but I’m missing the actual problem content. The statement section is empty in your prompt (“ Problem Statement / Input / Output” have no details), so I don’t know what “Even Adjacent Product” is asking us to…

Let $G(z)=sum{x1=0}^{1}cdotssum{xn=0}^{1} z^{x1+cdots+xn} f(x1,ldots,xn)$ be the generating function defined in Exercise 25, and let $F(p)$ denote the reliability polynomial when $p1=cdots=pn=p$, so that $$F(p)=sum{x1=0}^{1}cdotssum{xn=0}^{1} (1-p)^{1-x1}p^{x1}cdots…

I can’t write a correct Codeforces editorial for “103828I - Bombing buildings” because the actual problem statement is missing from your prompt. Right now there is no description of: - what the buildings are (array, graph, coordinates, etc.

I cannot responsibly write a correct Codeforces editorial for “103828H - Kite” yet because the actual problem statement is not available in the prompt, and it is not retrievable from standard Codeforces archives.

I can’t reliably write a correct editorial for this yet because the actual problem statement is missing from your prompt.

I can’t write a correct editorial for Codeforces 103828F - Subgrid without the actual problem statement. Right now the prompt only includes formatting instructions, but the core information is missing: what the grid contains, what defines a valid subgrid, what needs to be…

We are simulating a very small “text editor” that starts empty and receives a sequence of key presses. Each key press is one of a few control actions that manipulate three conceptual pieces of state: the current text, the clipboard, and whether the entire text is currently…

I can’t reliably write a correct editorial yet because the actual problem statement for “Codeforces 103828A - 2 Arrays Problem” is missing from your prompt. Without the statement, anything I write would be guesswork, and that would break correctness for an editorial.

Let $H$ be an $mtimes n$ parity-check matrix over $mathbb{F}2$, and let $$f(x)= [Hx=0], qquad x=(x1,dots,xn)^T.$$ Fix a variable order $x1,dots,xn$.

I can write the full editorial in the exact format you want, but I’m missing the actual problem content for Codeforces 103828B - “Too simple for a hard problem?”.

The problem describes a fictional currency system with two types of money: wooden coins with several fixed denominations, and a single gold coin whose value in wooden coins is unknown.

There are up to 17 shops, and each pair of shops has a travel cost, possibly zero meaning no direct connection. You are allowed to move between shops in any order, paying those costs, and you start at shop 1 for free.

The Chinese ring puzzle (Baguenaudier) has a standard representation as a binary state vector $(a_1,\dots,a_n)$ in which each $a_j \in {0,1}$ encodes whether ring $j$ is disengaged or engaged, and leg...

Let $H$ be an $mtimes n$ parity-check matrix over $mathbb{F}2$, and let $$f(x)= [Hx=0], qquad x=(x1,dots,xn)^T.$$ Fix a variable order $x1,dots,xn$.

We are given a circular arrangement of beads, where each bead is painted with one of M colors. The structure is a necklace, so positions wrap around: after position N comes position 1 again.

I can’t responsibly write a full editorial yet because the problem statement I initially saw is incomplete and likely mismatched.

The problem can be viewed as navigating a maze laid out on a grid. Each cell of the grid represents either free space that can be walked on or a blocked cell that cannot be entered.

The problem statement section is empty, so there isn’t enough information to reconstruct what “Rhomboid tiles” is asking.

I can’t write a correct editorial yet because the actual problem statement for Codeforces 103831B - Skis sorting is not available in the provided prompt, and it is not accessible from standard problem archives.

I can’t write a correct editorial yet because the actual problem statement for Codeforces 103833H - Parallel computing is missing from your message.

I can write the full editorial in exactly that structure, but I’m missing the actual problem content. “Codeforces 103833G - Clustering evaluation” isn’t included in your message, and I don’t have the statement, input/output format, or constraints needed to reconstruct…

Let $H$ be an $mtimes n$ parity-check matrix over $mathbb{F}2$, and let $$f(x)= [Hx=0], qquad x=(x1,dots,xn)^T.$$ Fix a variable order $x1,dots,xn$.

We are given a rooted tree. Each vertex carries a value that is either +1 or −1. You start at a fixed vertex at time zero with an initial life value of 1. Time advances in discrete steps.

I can’t reliably proceed yet because the actual problem statement for Codeforces 103833F - Yet another unusual equation is not included in your prompt, and this specific gym/problem ID does not have a stable canonical statement in the standard archive I can reconstruct with…

We are modeling a penalty shot as a discretized grid over the goal. Each cell in the grid corresponds to a possible shot placement. For the goalkeeper, each cell contains a value describing how likely it is that the goalkeeper saves a shot directed there.

The problem statement for Codeforces 103833A - Liberdance is not included in your prompt, so there is no way to reconstruct the required logic or produce a correct editorial.

The problem statement section is empty, so there isn’t enough information to reconstruct the task or produce a correct editorial. Please paste the full statement of Codeforces 103833B (input, output, constraints, and description).

The problem starts with a sequence of numbers and asks us to compute a global expression over all pairs of elements. For each array that appears in the input, we are effectively aggregating a function that depends on pairwise differences between elements.

Let $H$ be an $mtimes n$ parity-check matrix over $mathbb{F}2$, and let $$f(x)= [Hx=0], qquad x=(x1,dots,xn)^T.$$ Fix a variable order $x1,dots,xn$.

We are working on a circular arrangement of $N$ positions, each position carrying a label, most naturally interpreted as a binary type such as 0 or 1, or more generally two kinds of “buttons”.

We are given a game played on a grid-like structure where each state can be thought of as a rectangular region with two dimensions. Two players alternate moves, and each move modifies the current active region by effectively trimming it along its boundary.

Let $f = \text{COLOR}(x_1,\dots,x_n)$ be the Boolean function encoding proper 4-colorings of the US map, where each vertex variable $x_i$ takes values in ${0,1,2,3}$, represented in binary as in (73).

We are working on a grid where every cell contains a value, and we care about paths that move from the top-left corner to the bottom-right corner.

We are given a system that builds and manipulates collections of marbles, where each marble can be thought of as an atomic unit that may later be grouped into larger sets.

We are working with a sequence of stones, each stone having a color and a value. The operation that generates contribution is not local to a single stone, but depends on a triple of indices $i < j < k$.

We are given a sequence of stones arranged in a line, each stone having a color and a weight. The first structural observation is that consecutive stones of the same color can be compressed: within any maximal block of identical colors, only the maximum weight in that block…

We are given a set of weighted points on a grid. Each point represents a monster located at some coordinate $(x, y)$ and contributing some value (or implicitly one unit of value if weights are not explicitly stated in the statement variant).

We are given a string formed from characters that can be compared in a fixed “Rock Paper Scissors” style cycle, but the important restriction is that the dynamics we simulate only meaningfully depend on how characters compare pairwise.

We are working with a system that has a fixed target configuration of colors over several regions, and a set of tools that can modify those colors. Each region can take one of several possible colors, and each tool changes colors in a structured way.

We are repeatedly taking two groups of points in the plane and transforming them into a new pair of groups using a deterministic geometric rule.

We are given a configuration of chords drawn inside a convex polygon. Each chord connects two boundary vertices, and different chords may intersect each other inside the polygon.