brain

I can write the full editorial in exactly the style you want, but I’m missing the actual problem statement for Codeforces 103409K - Tax.

I can write the full editorial in exactly the style you requested, but I’m missing the actual problem statement for Codeforces 103409J - Suffix Automaton.

Let $a{s+t-1}dots a1a0$ be the binary representation of an $(s,t)$-combination, so each $ai in {0,1}$ and $sum ai = t$. A rotation of a prefix of length $j+1$ is the transformation $$aj a{j-1}dots a0 ;leftarrow; a{j-1}dots a0 aj,$$ with all other digits unchanged.

We are given several integer intervals, and for each interval we construct a binary string by looking at every integer inside it and writing down a single bit derived from that integer.

Let the degree-$t$ combinatorial representation (57) of $N$ be written in the form N = \binom{c_t}{t} + \binom{c_{t-1}}{t-1} + \cdots + \binom{c_1}{1}, where

I don’t have the actual statement for Codeforces 103409I “PTSD” available from your prompt, and without it I can’t responsibly derive the algorithm, constraints, or edge cases.

I don’t have the actual statement for Codeforces 103409G - Occupy the Cities in your prompt, and I can’t reliably reconstruct it from the title alone without risking inventing details.

I can’t reliably write a correct editorial for Codeforces 103409F - Illuminations II because the actual problem statement (input, output, constraints, and rules) isn’t included in your message, and I don’t have it available to reconstruct safely.

I can’t write a correct editorial for this yet because the problem statement section is empty. “Codeforces 103409D - Assumption is All You Need” isn’t enough to reconstruct the task reliably, and guessing would very likely produce a wrong solution and a misleading…

This is the classic integer addition task framed in a competitive programming setting. The input consists of one or more pairs of integers, and for each pair we are expected to compute their arithmetic sum and output it independently.

I’m missing the actual problem statement for Codeforces 103409A (“A Hero Named Magnus”). Without the statement, I can’t reliably reconstruct the intended model, constraints, or solution path, and I’d risk inventing a completely different problem.

The exercise cannot be completed as stated because the statement of “the alternating combination law (30)” is not included in the provided material.

Let $G$ be a graph with $m = 10^6$ edges, and let $K_t(G)$ denote the number of $t$-cliques in $G$.

The binomial tree $T_n$ used in this section has $2^n$ nodes, each node corresponding to a binary string of length $n$, and $T_\infty$ is the limiting structure in which nodes correspond to all finite...

Write $N$ in binary form N = (a_m a_{m-1}\dots a_0)_2 = \sum_{i=0}^m a_i 2^i.

We are given a directed graph with up to 2000 vertices and at most 5000 potential directed edges. Each edge has a cost, and Alice can pick any subset of edges whose total cost does not exceed a budget.

The problem statement for “Codeforces 103411J - Juggle Sort” is missing from your prompt, so there isn’t enough information to derive the algorithm, constraints, or even the core task.

Write $N$ in binary form N = (a_m a_{m-1}\dots a_0)_2 = \sum_{i=0}^m a_i 2^i.

I can’t reliably write a correct editorial for Codeforces 103411L - AGTC Matrix because the actual problem statement is missing from your prompt.

Let $G$ be the graph whose vertices are all permutations of the multiset ${s0cdot 0,ldots,sdcdot d}$, with edges given by adjacent interchanges $aj a{j-1} leftrightarrow a{j-1} aj$. Let $N$ be the number of vertices of $G$, so $$N = frac{(s0+s1+cdots+sd)!}{s0!,s1!cdots sd!}.

We are given a line with several squids placed at integer positions. There is a shark at another position and a single shelter at a fixed coordinate. Every squid wants to reach the shelter, and once it arrives there safely it is protected forever.

Algorithm L lists the $t$-combinations $c_t \dots c_2 c_1$ of ${0,1,\dots,n-1}$ in lexicographic order, starting from $c_j = j-1$ for $1 \le j \le t$.

I can’t write a correct editorial for this yet because the actual problem content is missing. Right now I only have the title “Determine The Lap Length”, but no description of what a “lap”, the input, or the required computation actually are.

The problem gives two square matrices of size $n times n$, where $n$ is even. Each matrix represents a “lock”, but the actual structure we care about is not the matrix itself but a decomposition of it into concentric rectangular cycles, or “rings”.

We are given a sequence of cards, each carrying a non-negative integer value representing its power. We also have a stream of operations, where each operation is one of two possible transformations applied to every card in the sequence.

I can write the full editorial in the exact format you requested, but I’m missing the actual problem statement for Codeforces 103411E - Empires.

We are given a network of $n$ star systems connected by exactly $n-1$ bidirectional highways, forming a tree. Between any two systems there is exactly one simple path.

Let $G$ be the Cayley graph whose vertices are the $N$ permutations of the multiset ${s0cdot 0,dots,sdcdot d}$ and whose edges correspond to adjacent interchanges $a{deltak}leftrightarrow a{deltak-1}$.

We are given a string over the alphabet {A, C, G, T} that represents a DNA strand. Each character has a fixed complement: A pairs with T, and C pairs with G.

We are organizing online classes using a fixed number of video conferences. Each conference has a hard cap on total participants, and inside every conference a fixed number of seats must be reserved for teachers. The remaining seats, if any, can be filled by students.

Let $G$ be the Cayley graph whose vertices are the $N$ permutations of the multiset ${s0cdot 0,dots,sdcdot d}$ and whose edges correspond to adjacent interchanges $a{deltak}leftrightarrow a{deltak-1}$.

Let the multiset be ${s0 cdot 0,; s1 cdot 1,; ldots,; sd cdot d}, qquad s0 + s1 + cdots + sd = n.$ Let $V$ be the set of all distinct permutations of this multiset.

I can write the full editorial in the exact format you requested, but I’m missing the actual problem statement for Codeforces 103414L - Permutation Transformation.

I can’t reliably write a correct editorial for “CF 103414J - Computational ethnography” because the actual problem statement (input/output definition and constraints) is missing from your prompt.

Let the multiset be ${s0 cdot 0,; s1 cdot 1,; ldots,; sd cdot d}, qquad s0 + s1 + cdots + sd = n.$ Let $V$ be the set of all distinct permutations of this multiset.

I’m missing the actual core of the task statement in your prompt, and without it I can’t produce a correct Codeforces editorial. The page I can access only shows the problem title and samples, not the full rules in a reliable structured way.

The problem statement for Codeforces 103414G - Maximaze XOR sum is missing from your message, so I can’t reconstruct the actual task, constraints, or required algorithm yet.

I’m missing the actual statement of Codeforces 103414F - Race in your prompt. Right now, the problem section is empty, so I don’t have enough information to correctly derive: - what the input represents, - what the output should compute, - or what algorithmic structure is…

I’m missing the actual statement of Codeforces 103414E - Haiku, so I can’t safely derive the solution or write a correct editorial. Right now the only thing provided is the template, but no description of what the input/output means, constraints, or task definition.

I can’t reliably write a correct editorial for this yet because the actual problem statement for Codeforces 103414B - “Guess the Array” isn’t included.

I can’t write a correct editorial for this yet because the actual problem statement is missing. Right now I only see the title “Army of Clones”, but none of the key details: what the clones are, what operations are allowed, what the input describes, or what needs to be…

I’m missing the actual problem statement for Codeforces 103414C - Moving Cells, so I can’t reliably reconstruct the task, constraints, or intended solution path.

Let the multiset be ${s0 cdot 0,; s1 cdot 1,; ldots,; sd cdot d}, qquad s0 + s1 + cdots + sd = n.$ Let $V$ be the set of all distinct permutations of this multiset.

Let $A$ be a family of $t$-combinations, and let $\partial A$ denote its shadow, the family of all $(t-1)$-combinations contained in members of $A$.

Let $n = s + t$ and consider a binary string $a_{n-1}\dots a_0$ representing an $(s,t)$-combination, where exactly $t$ entries are $1$.

Let $sigma$ and $tau$ be the two involutions on permutations of ${1,2,dots,n}$ given by adjacent transpositions on disjoint parity classes, in the standard TAOCP σ-τ framework, so that every step of a σ-τ walk applies either $sigma$ or $tau$, and each application changes…

We are maintaining a growing set of points in the plane. The structure starts empty and receives operations over time. Each operation is either the insertion of a new point or a query that asks for the point in the current set that is most extreme in a given direction.

The problem statement section is empty, so there isn’t enough information to write a correct Codeforces-style editorial yet.

Let $sigma$ and $tau$ be the two involutions on permutations of ${1,2,dots,n}$ given by adjacent transpositions on disjoint parity classes, in the standard TAOCP σ-τ framework, so that every step of a σ-τ walk applies either $sigma$ or $tau$, and each application changes…

We are given a connected undirected graph that is guaranteed to be a cactus, meaning every edge belongs to at most one simple cycle. Some edges behave like tree edges, cutting them disconnects the graph, while others lie on exactly one simple cycle.

The problem statement section is empty, so there isn’t enough information to derive the solution or write a correct editorial for “Codeforces 103415H - Three Integers”. Right now I don’t know what the input represents, what is being asked, or even the constraints.

The problem statement is missing from your prompt (it’s blank under “Problem Statement”), so I don’t have enough information to reconstruct what Codeforces 103415G - Slope actually asks.

I can’t write a correct editorial yet because the actual problem statement is missing. Right now I only see the title “Codeforces 103415D - Unnamed Easy Problem”, but no description of the input, output, or what is being asked.

The problem statement section is empty, so there isn’t enough information to reconstruct what “Mathlab” (CF 103415E) is asking for.

I cannot reliably reconstruct Codeforces 103415A “Math Ball” from the information available in the problem stub you provided.

I don’t have the actual statement of Codeforces 103415C - Necklace in your prompt, and I can’t reconstruct it reliably from the title alone without risking writing an incorrect editorial.

Let $sigma$ and $tau$ be the two involutions on permutations of ${1,2,dots,n}$ given by adjacent transpositions on disjoint parity classes, in the standard TAOCP σ-τ framework, so that every step of a σ-τ walk applies either $sigma$ or $tau$, and each application changes…

I can’t write a correct editorial for this yet because the actual problem statement for “103416J - Replace by sum” is missing from your prompt. Right now there is no definition of: what the array/structure is, what operation “replace by sum” means (neighbors? prefix?

I’m missing the actual problem statement for Codeforces 103416H - Cheap Square, so I can’t safely derive or explain the solution yet.

The problem statement for Codeforces 103416G - Favorite Number is missing from your prompt, so I don’t have enough information to write a correct editorial.

Let $d ge 0$ and let $s0, dots, sd$ be nonnegative integers with total length $n = s0 + cdots + sd.$ Let $V$ be the set of all strings $an a{n-1} dots a1$ over the alphabet ${0,1,dots,d}$ such that each symbol $i$ occurs exactly $si$ times.

The problem statement is missing from your prompt, so I don’t have the actual task definition for Codeforces 103416F - Delivery 2[D]. Without the description, input/output format, and constraints, I can’t produce a correct editorial or derive the algorithm.

The courier works on a rectangular grid where each cell is either blocked or usable. Movement is restricted to the four cardinal directions, and you can only traverse through usable cells.

The problem statement section is empty, so there isn’t enough information to reconstruct what “Circular Graph” (Codeforces 103416E) is asking.

I can’t write a correct editorial without the actual problem statement. Right now, the sections for Codeforces 103416A - Planet Nine are empty, so there’s no way to know what the task is (inputs, outputs, constraints, or intended solution).

I can’t produce a correct editorial for Codeforces 103416C - Mura and love because the problem statement is not included in your prompt, and I don’t have reliable access to reconstruct it.

Each vertex is a permutation of the multiset ${0,0,0,1,1,1}$, hence each vertex is uniquely represented by a strictly increasing triple $c3c2c1 quadtext{with}quad 5 ge c3 c2 c1 ge 0,$ where $cj$ are the positions of the $1$s in a binary string of length $6$.

We are given an array of values, where each value represents a “job difficulty” assigned to a person in a line.

I can’t reliably write a correct editorial for “Codeforces 103422A - MLCS” because the actual problem statement is missing from your prompt.

Each vertex is a permutation of the multiset ${0,0,0,1,1,1}$, hence each vertex is uniquely represented by a strictly increasing triple $c3c2c1 quadtext{with}quad 5 ge c3 c2 c1 ge 0,$ where $cj$ are the positions of the $1$s in a binary string of length $6$.

We are given several stacks of coins, each stack representing a pile with a fixed initial height. Two players play a turn-based game starting from these piles. On each turn, a player chooses some stacks and removes coins from them.

I don’t have the actual statement of Codeforces 103423A - Bordered Subarrays in your prompt, and I shouldn’t guess it because that would lead to a completely incorrect editorial.

Let $\alpha$ be the $t$-combination $c_t \cdots c_1$ with $n > c_t > \cdots > c_1 \ge 0$, viewed as the $t$-element set ${c_1,\dots,c_t} \subseteq {0,1,\dots,n-1}$.

Each vertex is a permutation of the multiset ${0,0,0,1,1,1}$, hence each vertex is uniquely represented by a strictly increasing triple $c3c2c1 quadtext{with}quad 5 ge c3 c2 c1 ge 0,$ where $cj$ are the positions of the $1$s in a binary string of length $6$.

I can write the full editorial in the exact format you want, but the problem statement for CF 103426E - Reconstructing Pairs is missing from your prompt, and I can’t reliably infer it from the title alone without risking writing a completely incorrect solution.

Let $[n]={1,2,\dots,n}$ and let $\mathcal{A}$ be a family of $r$-subsets of $[n]$ such that for all $\alpha,\beta\in\mathcal{A}$ one has $\alpha\cap\beta\neq\varnothing$.

Each vertex is a permutation of the multiset ${0,0,0,1,1,1}$, hence each vertex is uniquely represented by a strictly increasing triple $c3c2c1 quadtext{with}quad 5 ge c3 c2 c1 ge 0,$ where $cj$ are the positions of the $1$s in a binary string of length $6$.

Let $[n]={1,2,\dots,n}$ and let $\mathcal{A}$ be a family of $r$-subsets of $[n]$ such that for all $\alpha,\beta\in\mathcal{A}$ one has $\alpha\cap\beta\neq\varnothing$.

I can write the full editorial in the exact format you requested, but I am missing one critical piece: the actual problem statement of Codeforces 103426D “Fantastic Three”.

I can’t reliably write a correct editorial for this yet because the actual problem statement for Codeforces 103426C - Equation is missing from your prompt.

We are given a single lowercase string and asked to count how many times a specific pattern, namely the string "edgnb", appears as a contiguous substring.

We are given a single lowercase string. For every prefix of this string, we need to look at all possible contiguous substrings inside that prefix and pick the lexicographically largest one.

We start with a complete graph on $2n$ vertices, so every pair of vertices is initially connected. Then we are given a set of $2n-1$ edges that form a tree, and those edges are removed.

We are working with an initially empty square grid of size $n times n$, where every cell starts at zero. Then we process exactly $n$ operations.

We are given a 4-digit lock. Each test case provides two states of this lock: a starting configuration and a target configuration. Each state consists of four digits in a fixed order, like a small array of length four.

We are given three input-output pairs of points on the extended complex plane, where each point is a complex number represented by its real and imaginary parts.

We start with a connected undirected graph where each edge has a weight. From this graph, we construct another graph called the line graph. In this transformed graph, every original edge becomes a vertex.

We are given a string of length $n$, where every character comes from a limited alphabet of size at most 20. From this string, we consider every nonempty subsequence.

We are given a string of length $n$, and we look at every non-empty prefix of this string. For each prefix, we apply a deterministic transformation that depends on the positions of characters inside that prefix. The transformation works as follows.

We are given a small grid maze with dimensions up to 100 by 100, and inside this grid there are exactly n adventurers and n escape ropes. Each adventurer starts at a unique cell, and each rope is also placed at a unique cell.

We are simulating a turn-based fight where a monster starts with a given amount of health, and each turn you receive exactly one random card. The card is uniformly chosen among three types.

We are given a sequence of circles placed one by one on a horizontal line. Each circle is fully determined by its center position on the x-axis and its radius, so every circle lies in the plane with center at $(xi, 0)$ and radius $ri$.

Let $q$ be a primitive $m$th root of unity and let $$N = n1 + cdots + nt.$$ Write each index in base $m$ form $$ni = m ai + ri,qquad 0 le ri < m,$$ and define $$A = a1 + cdots + at,qquad R = r1 + cdots + rt,$$ so that $N = mA + R$.

We are given a grid maze where some cells are walls and others are empty. A character starts from a fixed cell marked H at time zero and can move each minute to any of the four adjacent cells or stay in place. Movement is blocked by walls.

We are given an array and a fixed window size. In one move, we choose a contiguous segment of exactly length k and overwrite every element in that segment with the minimum value currently inside that segment.

Let $q$ be a primitive $m$th root of unity and let $$N = n1 + cdots + nt.$$ Write each index in base $m$ form $$ni = m ai + ri,qquad 0 le ri < m,$$ and define $$A = a1 + cdots + at,qquad R = r1 + cdots + rt,$$ so that $N = mA + R$.

We are given two independent groups of athletes, one group for sport A and one group for sport B. Each athlete has a numerical skill value, and every athlete must stay in their own sport unless we explicitly decide to “swap” them, meaning they compete in the other sport…

The problem statement is missing, so there’s no way to reconstruct the actual task, constraints, or required algorithm.

Let $q$ be a primitive $m$th root of unity and let $$N = n1 + cdots + nt.$$ Write each index in base $m$ form $$ni = m ai + ri,qquad 0 le ri < m,$$ and define $$A = a1 + cdots + at,qquad R = r1 + cdots + rt,$$ so that $N = mA + R$.

The problem statement for Codeforces 103428L - shake hands is missing in your prompt (it’s empty after “Problem Statement / Input / Output”).