brain

We are given a directed graph of tribes, where each tribe is a node and some directed roads already exist between them. The goal is to make the entire graph strongly connected, meaning every tribe must be able to reach every other tribe following directed roads.

A clutter in ${0,1,dots,n}$ is exactly an antichain in the Boolean lattice: a family $mathcal C$ of subsets such that no two distinct members satisfy $alpha subset beta$. The size vector $(M0,M1,dots,Mn)$ records how many members of $mathcal C$ lie in each level $binom{[n]}{t}$.

I can’t reliably write a correct Codeforces editorial without the actual problem statement. “Codeforces 102978J - Japanese Knowledge” is not enough on its own to reconstruct the task, and guessing would almost certainly produce a misleading solution and wrong algorithm.

We are given a permutation of numbers from $1$ to $N$, but instead of the permutation itself, we are asked to count how many such permutations have a very specific structural property involving a fixed sequence $X$ of length $M$.

We are given a fixed set of pile sizes $A1, A2, dots, AN$. From this set we construct a starting position consisting of $K$ piles, where each pile independently chooses one value from the array. So a configuration is just a length-$K$ sequence, and every entry is one of the $Ai$.

We are given a rooted tree where each node has a parent relationship implied either directly or through structure, and we are asked to answer queries of the form: given two nodes, determine their lowest common ancestor in the tree.

Let $T=binom{2t-1}{t}$ and write $x=N/T$. In Section 7.2.1.3, the number $kappa{tN}$ is expressed through the binary representation of $N$ by decomposing the corresponding $(s,t)$-combination into the associated compositions $qt,dots,q0$ of (11).

We are given a directed graph with a highly structured construction. The vertices are not arbitrary points, they come from a numerical grid representation induced by a parameterization of indices, and edges only appear in a few rigid geometric directions.

The task revolves around combining two sequences in a way that produces a third sequence where each position records how many ways a certain total can be formed by picking one element from the first sequence and one from the second.

We are asked to count how many matrices of size $N times M$ can be filled with integers from $1$ to $K$ such that values never decrease when moving right or down.

I don’t have the actual statement of Codeforces 102978B - Bit Operation in your prompt, only the title. Without the rules of the operation, input format, and required output, I can’t reliably reconstruct the intended solution or write a correct editorial.

Let $T=binom{2t-1}{t}$ and write $x=N/T$. In Section 7.2.1.3, the number $kappa{tN}$ is expressed through the binary representation of $N$ by decomposing the corresponding $(s,t)$-combination into the associated compositions $qt,dots,q0$ of (11).

Let $\alpha$ be a self-conjugate partition of $n$.

Let $T=binom{2t-1}{t}$ and write $x=N/T$. In Section 7.2.1.3, the number $kappa{tN}$ is expressed through the binary representation of $N$ by decomposing the corresponding $(s,t)$-combination into the associated compositions $qt,dots,q0$ of (11).

I can’t write a correct editorial for Codeforces 102992M - Monster Hunter because the actual problem statement (input/output definition and constraints) is missing.

The problem statement is missing from your prompt, so I can’t reliably reconstruct what “Let’s Play Curling” (Codeforces 102992L) is asking.

I can’t reliably write a correct editorial for “Codeforces 102992K - K Co-prime Permutation” because the actual problem statement is missing from your prompt.

I’m missing the actual problem statement for Codeforces 102992J - Just Another Game of Stones. Right now the “Problem Statement / Input / Output” sections are empty, so there’s no way to correctly reconstruct: - what the game rules are, - what the players can do, - what…

I don’t have the actual statement for Codeforces 102992A (“Ah, It’s Yesterday Once More”) in your prompt, and I can’t reliably reconstruct the problem from the title alone without risking inventing details.

Let $\alpha$ be a self-conjugate partition of $n$.

A simplicial complex on an $n$-element vertex set is an order ideal in the Boolean lattice, so if a set is in the complex then all of its subsets are also in the complex.

We are given an undirected connected graph, and the task is to extract a spanning tree under a structural restriction on vertex degrees. A spanning tree here is a subset of exactly n minus 1 edges that connects all vertices without forming cycles.

I don’t have the actual statement of Codeforces 102992C - Certain Scientific Railgun in the prompt, so I can’t reliably reconstruct the problem, constraints, or solution without guessing.

A partition $\alpha$ is self-conjugate when its Ferrers diagram is symmetric across the main diagonal.

A partition into distinct parts corresponds to a sequence $a_1 \ge a_2 \ge \cdots \ge a_m \ge 1$ in which all parts are distinct, so each positive integer $k$ appears at most once.

Write the unique representation of an integer $X ge 0$ in the $t$-binomial number system as $$X = binom{xt}{t} + binom{x{t-1}}{t-1} + cdots + binom{x1}{1},$$ where $xt x{t-1} cdots x1 ge 0$, as in the discussion preceding κ-functions in Section 7.2.1.3.

The problem statement for Codeforces 103055M - Game Theory is missing from your prompt, so there’s no way to reconstruct the rules, winning conditions, or constraints required to write a correct editorial.

I can absolutely write the full editorial in that style, but I’m missing the only thing that makes it possible to do correctly: the actual problem statement for Codeforces 103055L - String Freshman.

I can’t reliably write a correct editorial for Codeforces 103055K - Grammy’s Kingdom because the actual problem statement is missing. Right now I don’t have: - what the kingdom structure is (grid, tree, graph, game, etc.

I can’t write a correct editorial for this yet because the actual problem statement is missing. Right now I only see the title “Cube”, but none of the essential parts that define what the input represents, what operations are allowed, or what needs to be computed.

Let $a_1,a_2,a_5,a_{10},a_{20},a_{50},a_{100}\ge 0$ denote the numbers of coins of each denomination used to form 100 cents.

Let $[n]={1,2,dots,n}$. A simplicial complex $C$ on $[n]$ is an order ideal under inclusion: if $betain C$ and $alphasubseteq beta$, then $alphain C$. For each $t$, let $Nt$ denote the number of $t$-element subsets in $C$.

I’m missing the actual problem content for Codeforces 103055H - Grammy and HearthStone (the statement, constraints, and samples).

I can’t write a correct editorial yet because the actual problem statement for Codeforces 103055G - Wall Game is missing from your prompt.

I can’t reliably write a correct editorial for Codeforces 103055D - Shortest Path Query without the actual problem statement.

Two teams of five players are engaged in a turn-based elimination game. Each player starts with a positive amount of health. On each move, a team chooses one player on the opposing team and reduces that player’s health by exactly one.

Let $[n]={1,2,dots,n}$. A simplicial complex $C$ on $[n]$ is an order ideal under inclusion: if $betain C$ and $alphasubseteq beta$, then $alphain C$. For each $t$, let $Nt$ denote the number of $t$-element subsets in $C$.

I can't write a correct editorial for this problem because the prompt does not include the actual problem statement. For Codeforces 103034G - "Can you do the Hololive?

Let $a_1 > a_2 > \cdots > a_m \ge 1$ be a partition of $n$ into distinct parts.

Let $a_1 a_2 \dots a_m$ be a partition written in nonincreasing form, and let $b_1 b_2 \dots b_m$ be its conjugate, so $b_j$ is the number of indices $i$ with $a_i \ge j$.

Let $$Fn(z)=prod{j=0}^{n-1}(1+z+cdots+z^{sj}), qquad left(!binom{S(n)}{k}!right)=[z^k]Fn(z).$$ Then $Fn=F{n-1}(1+z+cdots+z^{s{n-1}})$, so coefficient extraction gives $$left(!binom{S(n)}{k}!right) = sum{r=0}^{s{n-1}}left(!binom{S(n-1)}{k-r}!

I can’t write a correct editorial yet because the actual problem content for Codeforces 103034F - Mystery is missing from your prompt.

The problem statement is missing from your prompt (the “Problem / Input / Output” sections are empty), so there’s no way to correctly reconstruct Codeforces 103034D - Math Homework without guessing.

I can’t write a correct editorial yet because the actual problem statement for Codeforces 103034C - Two Hashes is missing from your prompt. Right now there’s no information about what the input represents, what “two hashes” refers to, or what needs to be computed.

I can’t write a correct editorial for “Codeforces 102992I - Interested in Skiing” without the actual problem statement. The structure you requested depends heavily on the precise mechanics of the task, and guessing would produce a misleading solution.

Let $\alpha$ be a partition of $n$, written in frequency form as $\alpha:\quad 1^{c_1} 2^{c_2} 3^{c_3}\cdots,$ where $c_j \ge 0$ and $\sum_{j\ge 1} j c_j = n$.

Let $a_1 \ge \cdots \ge a_n \ge 0$ and $a'_1 \ge \cdots \ge a'_n \ge 0$ be partitions of $n$.

The input is a square board where each position is either black, white, or empty. White stones can connect through up-down-left-right adjacency, forming clusters. A cluster survives only if at least one of its stones touches an empty cell.

Let $c_1,c_2,c_5,c_{10},c_{20},c_{50},c_{100}$ denote the numbers of coins of each denomination in cents.

Let $c_1c_2\cdots c_n$ be the part-count representation of a partition of $n$, so that $\sum_{j=1}^n j c_j = n.$ The colex order on partitions corresponds to lexicographic order on the reversed vector...

Let $U$ denote the set underlying the multicombinations (92). In the representation (6), each multicombination is a nonincreasing sequence $$dt ge d{t-1} ge cdots ge d1,qquad s ge dt,$$ and its complement with respect to $U$ is formed by taking the elements of $U$ not…

Let the Ferrers diagram of $a_1a_2\cdots a_m$ consist of cells $(i,j)$ with $1\le i\le m$ and $1\le j\le a_i$.

Let $U = {0,1,dots,n-1}$ with $n ge s+t$. Let $A subseteq binom{U}{s}$ and $B subseteq binom{U}{t}$ be cross-intersecting, meaning $alpha cap beta ne varnothing$ for all $alpha in A$ and $beta in B$.

The rim representation $(p_1 \ldots p_t, q_1 \ldots q_t)$ encodes the boundary (outer rim) of the Ferrers diagram of the partition $a_1 a_2 \ldots$ as an alternating sequence of maximal horizontal and...

The rim representation $(p_1 \ldots p_t, q_1 \ldots q_t)$ encodes the boundary (outer rim) of the Ferrers diagram of the partition $a_1 a_2 \ldots$ as an alternating sequence of maximal horizontal and...

Theorem W is proved in Section 7.2.1.3 under the standing assumption that the parameters $m1 le m2 le cdots le mn$.

The rim representation $(p_1 \ldots p_t, q_1 \ldots q_t)$ encodes the boundary (outer rim) of the Ferrers diagram of the partition $a_1 a_2 \ldots$ as an alternating sequence of maximal horizontal and...

Theorem W is proved in Section 7.2.1.3 under the standing assumption that the parameters $m1 le m2 le cdots le mn$.

A clutter on the ground set $[n]={0,1,\dots,n-1}$ is an antichain in the Boolean lattice: if $\alpha,\beta\in C$ and $\alpha\subseteq\beta$, then $\alpha=\beta$.

Let Theorem W be applied to the torus $T(m1,dots,mn)$ with cross order as in Section 7.2.1.3, and let $S$ be an initial segment in that order.

The prompt is missing the actual problem statement for “Codeforces 102979I - Integer Array Shuffle”, so there is not enough information to reconstruct the task, constraints, or required transformation.

I can’t reliably write a correct editorial for Codeforces 102979H - Hotspot-2 because the actual problem statement, constraints, and I/O format are missing from your prompt.

We are given a connected undirected graph with up to 100,000 vertices and edges. Each edge has a nonnegative weight.

Let Theorem W be applied to the torus $T(m1,dots,mn)$ with cross order as in Section 7.2.1.3, and let $S$ be an initial segment in that order.

The problem statement is missing, so I can’t safely derive the model, the solution, or any correctness argument yet.

We are given a line of pads placed on a straight horizontal axis. Each pad is located at an integer coordinate, and every pad is labeled with a number from 1 to n, with each label appearing exactly twice.

The problem statement is missing, so there isn’t enough information to reliably reconstruct what Codeforces 102979B (“Best Meeting Places”) is asking.

Let $mathcal{A}$ be a set of $t$-combinations and let $ $$kappat N = min{ where $partial mathcal{A}$ is the set of all $(t-1)$-subsets obtained by deleting one element from a member of $mathcal{A}$.

Let $T(m1,dots,m{n-1},m)$ be the $(n)$-dimensional torus equipped with cross order. Write elements as $(y,a)$ where $y in T(m1,dots,m{n-1})$ and $0 le a < m$ denotes the final component.

I’m missing the actual statement for Codeforces 102980D - “Побег из здания”, so I can’t reconstruct the problem logic or write a correct editorial yet.

I can’t write a correct editorial for this yet because the actual problem statement is missing. “Codeforces 102980C - Кибер-взлом” (Cyber-hack) isn’t included in your prompt, and I shouldn’t guess the task since even small misinterpretations would completely…

The problem statement for Codeforces 102984J - Setting Maps is missing from your prompt, so there is no way to correctly reconstruct the solution, constraints, or intended algorithm.

Let $T(m1,dots,m{n-1},m)$ be the $(n)$-dimensional torus equipped with cross order. Write elements as $(y,a)$ where $y in T(m1,dots,m{n-1})$ and $0 le a < m$ denotes the final component.

I can’t reliably write an editorial for this yet because the actual problem statement is missing. “Codeforces 102984K - Determinant” is just a title here, and different determinant problems on Codeforces vary a lot in structure, even if they share the same name.

I don’t have the actual statement of Codeforces 102984I - Selecting Points and Segments, and without it I’d be forced to invent the problem structure, which would make the editorial meaningless or incorrect.

I can’t write a correct editorial for this yet because the actual problem statement for Codeforces 102984H - Stone Catch Game is missing.

I can’t write a correct editorial for this yet because the actual problem statement is missing. Right now I only know the title, “Solo Tree Game,” but there’s no information about what the tree game rules are, what inputs are given, or what needs to be computed.

I can’t reliably write a correct Codeforces editorial here because the actual problem statement for 102984F - Rhythm Game is missing from your prompt.

I can’t write a correct editorial for this yet because the actual problem statement is missing. Right now we only have the title “Observer Game”, but no description of the rules, inputs, or outputs.

The problem statement isn’t included, so I can’t reliably reconstruct the task or produce a correct editorial. “Non-Decreasing Subarray Game” could correspond to multiple different CF-style mechanics (range queries, segment operations, game DP, etc.

We are given an $N times N$ grid of unit cells, all starting with beauty value zero. The system evolves through three kinds of operations applied over time. First, we may introduce horizontal or vertical cut lines across the grid.

I can’t produce a correct editorial for “Codeforces 102984A - Mango” yet because the actual problem statement is missing from your prompt.

Let $T(m1,dots,m{n-1},m)$ be the $(n)$-dimensional torus equipped with cross order. Write elements as $(y,a)$ where $y in T(m1,dots,m{n-1})$ and $0 le a < m$ denotes the final component.

Let $[n]={1,2,\dots,n}$.

Let $T(m1,ldots,m{n-1})$ be the $(n-1)$-dimensional torus with cross order $preceq$, and let $x = x1cdots x{n-1}$ be the $N$th element of this torus in cross order. Let $T(m1,ldots,m{n-1},m)$ be the extended torus.

I can’t write a correct editorial for this yet because the actual problem content is missing. Right now I only see the title “Verbose sandViches”, but no description of the task, input format, or output requirements.

I can’t write a correct editorial for “Codeforces 102985I - Sharing Cereal II” yet because the problem statement is missing from your prompt. Right now I have no information about: - what the input represents (arrays, graph, queries, etc.

Let $alpha$ be a $t$-combination, so $alpha$ is a $t$-element subset of ${0,1,dots,n-1}$. The operator $partialt alpha$ produces all $(t-1)$-combinations obtained by deleting one element of $alpha$. If $alpha={ct,dots,c1}$, then $$partialt alpha={alphasetminus{cj}mid 1le jle t}.

I can’t write a correct editorial for this yet because the actual problem statement is missing. “Codeforces 102985H - Coprime Ribs” isn’t a standard publicly known problem in a way I can reliably reconstruct, and without the statement I would be guessing the entire…

I can’t write a correct editorial for “Codeforces 102985F - Norman’s N&N’s” because the actual problem statement is missing.

We are given a rectangular pizza placed on a coordinate plane. The bottom-left corner can be thought of as the origin, and the pizza spans a width and height. The chef then makes a set of horizontal cuts and a set of vertical cuts.

I can absolutely write this editorial in your required Codeforces style, but I’m missing the most important ingredient: the actual problem statement.

Let $alpha$ be a $t$-combination, so $alpha$ is a $t$-element subset of ${0,1,dots,n-1}$. The operator $partialt alpha$ produces all $(t-1)$-combinations obtained by deleting one element of $alpha$. If $alpha={ct,dots,c1}$, then $$partialt alpha={alphasetminus{cj}mid 1le jle t}.

We start with a single node and then add nodes one by one. When node i is added, it attaches to one of the previous nodes j with probability proportional to a given weight aj. Once the parent j is chosen, the edge length between i and j is defined as ci + cj.

I don’t have the actual statement for Codeforces 102986H - Coprime Ribs in your prompt, so I can’t reliably reconstruct the problem or write a correct editorial.

I’m missing the actual problem statement for Codeforces 102986F - Norman’s N&N’s, so I can’t reliably reconstruct the solution or write a correct editorial.

I’m missing the actual problem statement for Codeforces 102986D - Peter Piper Picked the Perfect Piece of Pizza, so I can’t safely reconstruct the intended model, constraints, or solution.

The prompt is missing the actual problem content. Right now we only have the title “Codeforces 102986E - Food Donations” but no description, input, output, or constraints.

The problem describes a person who has a list of favorite foods and is given a sequence of foods they eat over time.

I can’t reliably write a correct editorial for Codeforces 102986C - Spice Ratios without the actual problem statement.