brain

We are given two binary arrays of equal length. From each array we are allowed to pick one contiguous segment, and the only restriction on each segment is that its length must fall inside a given range.

We are given several test cases. In each test case we receive an array of integers, and we are asked to analyze a faulty piece of code that tries to compute the maximum value of the array.

Let variables $x_1,\dots,x_n$ be interpreted as characteristic bits of a subset $S \subseteq {1,\dots,n}$, where $x_i=1$ means $i \in S$.

We are given three piles of chips. On each turn, a player can either take chips from exactly one pile, choosing any positive number up to the size of that pile, or perform a global move where they take the same positive number of chips from all three piles simultaneously, but…

We are given a base string s of length N, where each position has an associated weight ai. From this string, we are allowed to “erase” characters by choosing a subset of letters from the alphabet.

We are given a line of monsters, each with a power value, positive or negative. Saitama can choose any consecutive segment of these monsters and defeat exactly that group.

We are given a fixed $N times N$ grid of elevations. Every query gives an interval $[a, b]$, and we must find the largest axis-aligned square subgrid such that every cell inside it has elevation within that interval. The answer is the area of that square, not its side length.

Let $M_2(x_1,x_2,x_3,x_4)$ denote the 4-way multiplexer.

We are given a multiset of cards, where each card has an integer label called a quirk number. From this initial collection, we want to end up with a very strict final collection: it must contain exactly one card of each quirk number from 1 up to some chosen value K, and…

We are given a rectangular grid of integers representing pixel intensities. The grid behaves like a torus, meaning moving off any edge wraps around to the opposite side.

We are maintaining a dynamic collection of “habitats”, where each habitat stores multiple named dragons, and every dragon has a unique size value. The system supports two operations over time. One operation inserts a new dragon into a chosen habitat.

Let $f(x_1,\ldots,x_n)$ have truth table $\tau$, and let $f^Z$ have truth table $\tau^Z$.

We are given three independent walls, each described as an array of section heights. Each array contains $n$ integers, where each integer represents the height of a segment in that wall.

We are given a collection of short text messages, each independent from the others. For every message, we need to decide whether it represents a “battle” or just casual conversation.

We are given a tree of houses. Each house initially has a certain number of friends living there. Over time, two kinds of events happen.

We are given a list of students, where each student comes with a name and four numerical attributes: kicking skill, magic skill, speed, and demon slaying skill. The task is to produce a ranking of all students based on a strict multi-level priority system.

The task is a pure transformation problem on text. We are given an ASCII picture of Bessie the cow, represented as multiple lines of characters. We must output what the picture looks like after being rotated 180 degrees.

We are given an undirected connected graph representing cities and bidirectional roads. Some roads have a special property: if removing such a road would disconnect the graph, then that road is considered expensive.

We are given a hidden position on a one-dimensional strip of cells numbered from 1 to n, where n can be as large as 10^9. Exactly one cell contains a buried treasure. We can interact with the judge by choosing a cell i and effectively placing a detector there.

Let $f(x_1,\ldots,x_n)$ have truth table $\tau$, and let $f^Z$ have truth table $\tau^Z$.

We are given a final sequence of cards that appeared on a table during a game. In the game, the players start with a hidden initial deck, and repeatedly remove either the top or the bottom card of the deck.

We are given a fixed 4×4 grid made of two types of cells: road cells represented by dots and fence cells represented by hashes. The grid encodes a small road junction.

We are given an array of integers, and we are allowed to modify it using a very specific operation. Each position in the array can be used at most once, and when we use position i, we multiply the value at that position by i.

We are given a permutation of size $n$, meaning it contains every integer from $0$ to $n-1$ exactly once. For every contiguous subarray, we compute two values. The first value is the mex of the subarray, which is the smallest non-negative integer missing from that subarray.

We are given a collection of straight lines on the plane, each defined by an equation of the form $y = kx + b$. We are not asked to analyze intersections between arbitrary pairs of lines or to find a geometric intersection point.

We are given an array of integers that is modified over time, and we must answer queries about its subarray GCD. Two operations happen online. The first operation adds a fixed value to every element in a prefix or a range.

We imagine a huge infinite tape formed by writing the integers from 1 up to 10¹⁰ in order, without any separators. So the string begins as 1234567891011121314... and continues by appending each next integer in decimal form.

We are given several independent test cases. In each test case there is an array of integers, and then a sequence of operations.

We are given a group of $n$ students who must be split into exactly two teams. Both teams must be non-empty. There is also a lower bound $k$, meaning each team must contain at least $k$ students.

We are given two disjoint integer intervals: one interval for x and one interval for y. Specifically, x must be chosen strictly greater than a and at most c, and y must be strictly greater than b and at most d.

We are given a group of n children who each collected some number of chestnuts and then placed them into a single pile. The first child in order, Sasha, puts his chestnuts into the pile first. Every next child contributes twice as many chestnuts as the previous child.

We are given a single month where the weekday of one specific day is known. That known anchor consists of a day number between 1 and 31 and a weekday name such as Monday or Sunday. Using this anchor, we must determine the weekday of another day in the same month.

The Z-transform is defined recursively on binary strings with special behavior depending on whether the second argument is a block of zeros, identical to the first half, or a general concatenation cas...

The problem statement is not included in your message, so there isn’t enough information to reconstruct what needs to be solved.

We are given two non-negative integers, a and n. A program starts with a value b = 0 and then applies the same update step exactly n times: b := (b - a) & a Here subtraction and bitwise AND are done on 64-bit integers using two’s complement arithmetic.

We are given a chain of $N$ numbered rings arranged in a line. The traveler wants to be able to pay exactly one ring per day for $N$ consecutive days, but he is allowed to cut the chain beforehand into separate usable pieces.

We are given a small set of cards, each card showing a pair of integers. One of these cards is secretly the “prize” card. The first player sees only the left number of that card, the second player sees only the right number.

We are repeatedly building a growing sum of very specific numbers. The k-th summand is a number made of a single digit 2 at both ends, with zeros filling the middle as the number grows, starting from 2, then 22, then 202, then 2002, and so on.

We are given a state consisting of two integers, and we are allowed to transform this pair using exactly three reversible operations. One operation subtracts the second value from the first, another adds the second value to the first, and the third swaps the two coordinates.

We are looking at a continuous analog clock where the hour and minute hands move smoothly rather than jumping once per minute. The minute hand completes a full circle in 60 minutes, while the hour hand completes a full circle in 12 hours.

We are given a grid that represents an archipelago. Each cell is either land, marked as 1, or water, marked as 0. Any two land cells that touch up, down, left, or right belong to the same island, so the grid naturally splits into multiple connected components of 1s.

I can write the full editorial, but I need the actual problem statement in a clean, uncorrupted form first.

We are given a row that alternates between empty positions and fixed comparison symbols. There are $N+1$ positions that must be filled with distinct numbers from 1 to $N+1$, and between every two neighboring positions there is exactly one constraint, either “<” or “”…

We are told that Natasha has cats, and each cat behaves in a very rigid way during the night. Every time a cat “acts”, it produces exactly the same effect: a fixed number of items fall, from level A down to level B, and Natasha hears a total of N falling events in total.

We are asked to construct a single regular expression over decimal digits that accepts exactly those integers whose digits can be rearranged to form a number divisible by 6. A number is divisible by 6 if and only if it is divisible by 2 and by 3.

We are given a string built from only two characters, a caret and an underscore. We are allowed to insert additional characters anywhere in the string, but we are not allowed to delete or reorder existing ones.

We are given a multiset of axis-aligned rectangles with fixed orientation. Each rectangle has a height and a width, and no rotation is allowed, meaning a rectangle (a, b) is distinct from (b, a) unless both coordinates are equal.

We are given several independent scenarios. In each scenario there are n shops visited in order, and there are m possible apple types. Each shop may contain some subset of apple types.

We are given an array of integers and we want to compute the maximum possible subarray sum, but with one extra freedom: before choosing the subarray, we are allowed to reverse at most one contiguous segment of the array.

We are given an undirected multigraph with up to 2000 vertices and 2000 edges. Each edge has an identity from 1 to m. A hidden subset of these edges is “good” (repaired roads), and this subset is fixed for the entire interaction.

We are given an array of nonnegative integers. We are allowed to perform exactly one operation: choose a contiguous segment of the array and overwrite every element in that segment with a single chosen nonnegative value.

Let $Q(f)$ denote the number of nodes in a reduced ordered decision diagram when sharing identical subgraphs, where the model allows both kinds of decomposition used in the section: Shannon decomposit...

We are given a tree, meaning a connected graph with no cycles. A fox starts at some vertex and can move in a single jump using an unusual rule: from a vertex v, it may jump to a vertex u either if there is an edge directly connecting them, or if there exists some intermediate…

We have two rows of points aligned above and below a single horizontal street. At each integer position $i$ from 1 to $n$, there is a café on the upper side with weight $ai$ and a café on the lower side with weight $bi$.

We are working with strings of fixed length n, but the real object of interest is not a single string. Instead, we maintain a dynamic set of strings over the alphabet {a, b, c, d}. Each update either inserts a string into the set or removes it.

The reviewer correctly identifies that the previous argument failed because it treated $m_k$ as if it ranged over arbitrary subset sums without justifying how this arises from Algorithm B.

We are given a binary string and we build a square matrix whose rows are all cyclic shifts of that string. Row zero is the string itself, row one is shifted right by one position, row two is shifted right by two positions, and so on until row n minus one.

We are given a system of $n$ positions, each initially holding a student. The initial arrangement is unknown and is represented by a permutation $b$.

We are given a rooted tree with root fixed at vertex 1. Each vertex stores two attributes: a label t[v], which groups vertices into types, and a jump parameter d[v], which defines how far a token should move upward along the path to the root.

Four players sit in a fixed order and repeatedly play cards against a shared discard pile whose current top card determines what is legal to play.

We are given a recursively defined family of strings built from a single kind of primitive bracket structure. The base object is the simplest valid pair “()”.

The problem statement is missing from your prompt, so I don’t have enough information to write a correct editorial.

We are given two sets of points in a plane, each point also having a time coordinate. The first set represents people, where each person has a recorded position at a specific time. The second set represents crime events, each occurring at a position and time.

We are given two strings, $A$ and $B$. We start with an empty string $C$, and we are allowed to build $C$ by repeatedly copying a substring from $A$ and appending it to the end of $C$.

I can’t write a correct Codeforces editorial without the actual problem statement. Right now the prompt only includes the template, so there’s no information about what the “golden jade matrix checker” is supposed to verify, what the input looks like, or what conditions…

The problem statement is missing from the prompt, so there’s no way to correctly reconstruct the task, constraints, or intended solution.

Let $B(f)$ and $Z(f)$ denote the reduced ordered BDD and reduced ordered ZDD of a Boolean function f(x_1,\ldots,x_n), constructed with the same variable ordering.

We are asked to count how many ways we can completely tile a board that has exactly two rows and $n$ columns. Each tile comes from a fixed set: a domino of size $1 times 2$, which can be placed horizontally or vertically, and a square block of size $2 times 2$.

We are given a procedure that behaves exactly like a standard binary search, except instead of returning the position of a target value, it returns how many loop iterations are executed until the search finds the target element.

I don’t have the actual statement of Codeforces 104317C (“Converse the string”) available in your prompt, so I can’t safely reconstruct the correct editorial without risking inventing rules, which would defeat the purpose of a proper solution write-up.

We are asked to output five integers $a, b, c, d, e$ within the range $[-10, 10]$, with $a neq 0$, such that the quartic polynomial $$a x^4 + b x^3 + c x^2 + d x + e$$ has no real roots. In other words, no real number $x$ should make the expression equal to zero.

I don’t have the actual problem content for “Codeforces 104322L - 投票” in your prompt (the statement section is empty), so there’s nothing concrete to base an editorial on.

I don’t have enough information about Codeforces 104322K - 卡片游戏 to write a correct editorial. Right now the statement section is empty, so there is no way to reliably reconstruct: - what the cards represent, - what operations are allowed, - what the players or rules…

I don’t have the actual statement of Codeforces 104322J - Bit Operation beyond the title, so I can’t reliably reconstruct the problem or derive a correct solution/editorial without guessing.

I can’t write a correct editorial for this problem yet because the statement you provided is effectively empty. Right now we only know the title “海选”, but there is no description of the input, output, constraints, or even what is being computed.

I can’t write a correct editorial for this yet because the actual problem content is missing. Right now the statement only shows the title “距离” (“Distance”), but there are no definitions of the input, output, or constraints.

I can’t write a correct editorial here because the actual problem content is missing. Right now the “Problem Statement” section contains no description of the task, inputs, or outputs.

We are given a line of cells, each cell containing a binary state that can be interpreted as a tile being either on or off. A move consists of selecting a position and flipping it in a way that affects the configuration of the line according to a fixed rule from the problem.

I can’t reliably write a correct editorial yet because the actual problem statement content is missing. Right now we only have the title “The Threshold of Masterpieces”, but no description of what the input/output means, constraints, or operations.

I can’t reliably write a correct editorial yet because the actual problem statement for Codeforces 104322E - Mabinogion isn’t included (only the title and empty input/output sections are present).

In the ZDD representation used in this section, a Boolean function is identified with the family of subsets on which it is true.

I can’t write a correct editorial here because the actual problem content is missing. What you provided only contains the title and empty input/output sections, so there is no information about what is being computed, what the operations are, or what the constraints look like.

I can’t produce a correct editorial for this yet because the actual problem content is missing. Right now I only see the title (“Keep Marching on Instead of Running off”), but there is no statement, input/output format, or constraints.

I can’t write a correct editorial yet because the actual problem statement is missing. Right now you’ve only provided the title and empty Input/Output sections, so there is no way to know what the task is (data structures, graph, strings, etc.

We are given a set of $n$ distinct postal codes, each written as a 5-digit string (leading zeros are allowed, so every code can be treated as a fixed-length string of length five over digits $0$ to $9$). Think of each postal code as a node in a graph.

Fix variable order $x_1 < x_2$.

We are trying to assemble a “team” from two pools of students. From the undergraduate pool we must choose exactly three distinct students, and the quality of this team is the sum of their strength values. From the graduate pool we choose exactly one student to act as a coach.

We are given a line of monsters, each with a strength value. Daniyar fights them using a sword that can remove a contiguous block of monsters in a single swing, but only up to a fixed length k in the current remaining lineup.

A user is walking through a city along a route made of straight street segments aligned with axes. Each segment is either purely horizontal or purely vertical, so at any moment the user’s position moves linearly in one coordinate while the other stays fixed.

We are given a line of participants, each with two thresholds: a lower requirement $ai$, and a higher requirement $bi$, where $ai < bi$. Each participant becomes “satisfied” once they receive at least $ai$ steaks, and becomes “full” once they receive at least $bi$ steaks.

In a ZDD, each level corresponds to a variable, and a node labeled $k$ represents a decision on $x_k$, where the low edge excludes the variable and the high edge includes it in the represented family...

We are given a multiset of integers, originally arranged in some unknown order. The only structural clue about the original ordering is not about adjacency or sorting, but about a global arithmetic property tied to indices: if we take each element and add its position in the…

We are given a tree with n vertices, so there is exactly one simple path between any two nodes. Each vertex has a degree, and a traveler standing at a vertex chooses uniformly among its adjacent vertices and moves there in one step. This defines a simple random walk on the tree.

Two players independently choose an ordering of the same set of fighters numbered from 1 to n, where a larger number always represents a stronger fighter. They then play n rounds.

We are given a collection of $n$ toppings, each contributing a signed value to taste. A “dish” is defined by choosing any subset of these toppings, and its taste is simply the sum of values of the chosen elements.

We are asked to assign three types of medals to a fixed number of participants in a contest. Every participant can receive a medal, and medals come in a strict hierarchy: gold is best, then silver, then bronze. The rules do not directly give exact counts.

We are given a binary string and a transformation that compresses it into maximal runs of equal characters. Each maximal run is called a “series”, so the string is decomposed into alternating blocks of consecutive zeros and ones.

We are given a permutation of size $n$ that initially appears in strictly decreasing order. The goal is to transform it into increasing order using a very specific operation: we may pick a starting position $s$ and a block length $k$, then swap two adjacent segments of equal…

Let $f(x_1,\dots,x_n)$ be symmetric, so its value depends only on the Hamming weight w = x_1 + \cdots + x_n.

We are working with an array that changes over time, and we are asked to support two kinds of operations on it. One operation permanently sorts a contiguous segment of the array, physically rearranging the elements in that range.