brain

We are maintaining a growing social contact network where edges are created day by day. Each edge represents a meeting between two people, and these meetings only remain relevant for a fixed time window of length $k$ days.

Let $x=\sqrt{m}$ and $y=\sqrt{m+d}$.

I can't write a correct editorial for Codeforces 1423A from the problem statement alone. This is a 3500-rated problem, and the statement by itself is not enough to reliably reconstruct the intended solution.

The problem presents a one-dimensional garden of flowers, each with a type represented by an integer. Sarah can change the garden by replacing a contiguous section of flowers with a new type, and residents evaluate the garden's "beautiness" by looking at contiguous windows of…

We are tasked with managing land acquisition for 5G antenna towers. Each tower occupies a circular area defined by a center (x, y) and a radius r. The land database consists of properties defined as polygons with a unique integer ID.

I can't write a correct editorial for Codeforces 1423A from the problem statement alone. This is a 3500-rated problem, and the statement by itself is not enough to reliably reconstruct the intended solution.

We are asked to simulate navigation on a map of the sea with islands, ports, and food supply points, taking into account daily wind patterns and limited food.

We are given two groups of equal size, one representing factories and one representing airports. Some pairs between them are connected by potential roads, and each road has a construction time.

The traceback reveals that the program is not actually failing on the algorithm. It is failing before any meaningful computation starts. The key line is: This means the code is doing: and the first line of the input is: which is clearly not a single integer.

We are given a collection of pages from a fragmented dictionary. Each page has an identifier and contains a fixed number of words. The key hidden structure is that these words were originally sorted according to some unknown alphabet order, not the standard English order.

The error is not in the logic of computing the floor. The RuntimeError you are seeing is a NameError: solve is not defined. This is a scoping issue: your testing harness calls solve()before it is actually defined.

We are asked to reason about the final box that will contain a single super toy created by sequentially combining all other toys via multiplication. Each toy has a fun value that falls into one of four ranges, which correspond to four boxes.

I can't reliably write a complete editorial and accepted implementation for Codeforces 1425I from the statement alone. This is a 2800-rated data structure problem whose solution depends on a fairly specific exploitation of the height ≤ 10 ternary-tree structure.

We have an unknown array $A1, A2, dots, AN$, where $Ai$ is the number of flamingoes in cage $i$. The only operation available is asking for the sum of a contiguous segment. A query of the form $(L,R)$ returns $$AL + A{L+1} + cdots + AR$$ with the restriction that $L < R$.

We are given a sequence of $N$ atoms, each with a cost to excite $Di$ and a reward when excited $Ai$. Atoms have default one-way bonds: exciting atom $i$ automatically excites atom $i+1$ for free. Before doing any excitations, we are allowed to change exactly $K$ of these bonds.

I can't reliably write a correct editorial for Codeforces 1425C from the problem statement alone. This is a 3100-rated math problem, and the core of the solution is a nontrivial closed-form derivation for $$G(X,Y)=sum{i=X}^{N}sum{j=Y}^{M}F(i,j),$$ where $F(i,j)$ is the minimum…

The problem gives a set of points on a 2D grid, each point representing a snake with a weight called its danger level. We choose exactly M distinct snakes as attack targets.

The problem is a two-player coin game. There is a pile of $N$ gold coins. Players alternate turns, starting with Mr. Chanek. On a turn, a player may either take one coin or, if the pile contains an even number of coins, take exactly half of the pile.

The problem asks us to find the floor number of a given apartment in a building with a slightly unusual layout. The first floor always has exactly two apartments, and every subsequent floor has the same number of apartments, which is given by $x$.

We are given a string composed of the letters "a", "b", "c", and the special character "?". Each "?" can be replaced independently by any of the letters "a", "b", or "c".

We are asked to determine whether it is possible to tile an (m times m) square using (2 times 2) tiles so that the resulting square is symmetric with respect to its main diagonal. Each tile has fixed numbers in its four cells, and rotations are not allowed.

Alice and Bob are planning to play a fixed number of rounds of Rock, Paper, Scissors. Alice has already decided how many times she will throw rock, scissors, and paper. Bob has made the same type of plan.

We are given a sequence of nonzero integers and are allowed to insert arbitrary integers anywhere between adjacent elements. The goal is to modify the sequence so that no contiguous segment of the final array has sum exactly zero, while using as few inserted elements as possible.

We start with a single-element array containing the number 1. We are allowed two operations: either increment any element by 1 or copy any element to the end of the array.

We are given an array of integers and the task is to reorder its elements so that no prefix sum of the resulting array is zero. The array can contain positive, negative, and zero values, and we must maintain the multiset of original values.

We are asked to compute the minimum speed $v$ at which two guards can prevent a prisoner from escaping a convex polygonal prison. The prisoner starts outside the main perimeter on a fixed point far to the left.

We are given an $n times n$ grid representing a wall made of tiles. Some tiles are already painted with a shade of grey (an integer from 1 to $10^9$), some are broken and cannot be painted (marked as $-1$), and the rest are unpainted (marked as 0).

There are 256 deputies and each answered 8 binary questions, with all answers distinct.

We are given a deck of 6n cards numbered consecutively from 1 to 6n. Two players, Federico and Giada, alternately take turns picking exactly three consecutive cards from the remaining deck. Federico starts, and after all 2n turns, each player has exactly 3n cards.

We start from a single odd integer placed on a board. From there, we are allowed to repeatedly create new numbers by either adding two already available numbers or taking their bitwise XOR.

We are given a deck of n cards, each labeled with a unique integer from 1 to n, in an arbitrary order. The goal is to sort the deck into ascending order using a special operation.

We are given the results of a series of chess games as a string consisting of 'W' for wins and 'L' for losses. Each win grants points depending on whether it continues a streak of previous wins: the first win or a win following a loss gives 1 point, while a win immediately…

The task is to maximize the number of celebrities a paparazzi can photograph in a city represented as an (r times r) grid of streets. Each celebrity will appear at a specific intersection ((xi, yi)) at a specific time (ti), and the paparazzi starts at ((1, 1)).

The key issue is that this is a constructive problem. The output shown in the statement is only one valid sequence of operations, not the unique correct output. Your program's output is different from the sample output, but that does not mean it is wrong.

The problem is about distributing n carrots of various lengths among k rabbits in such a way that the total effort for the rabbits to eat them is minimized. Each carrot can be split into multiple pieces, but each resulting piece must be a positive integer in length.

We are asked to unlock a circular lock with n wheels. Each wheel has a number from 0 to m-1. The lock has a hidden target combination, and we can query the lock with a proposed sequence of wheel positions.

We are asked to help a sheep maximize the "fortune" of a collection of numbers it writes. The sheep must write exactly $k$ non-negative integers that sum to a target $n$. Each digit of each number has an associated fortune, given in a table for digits $0$ through $5$.

The key issue is that this is a constructive problem. The output shown in the statement is only one valid sequence of operations, not the unique correct output. Your program's output is different from the sample output, but that does not mean it is wrong.

We are given a sequence of fruits represented as a binary string, where 1 stands for an apple and 0 for an orange. The goal is to compute, over all possible contiguous substrings, the length of the longest consecutive apples in that substring and sum these values.

A box sits on a grid point and needs to be moved to another grid point using a very specific interaction with a mover. The mover can walk freely in four directions, paying one second per unit step, but he is not allowed to occupy the box’s cell.

We are given a string consisting only of the characters A and B. We may repeatedly remove any adjacent substring equal to AB or BB. After removing such a pair, the remaining parts of the string join together, potentially creating new removable pairs.

The rooms form a cycle. Between every pair of consecutive rooms there is a conveyor belt, and each belt can be directed clockwise (), directed counterclockwise (<), or usable in both directions (-).

We start with the integers from 1 through n written on a whiteboard. In one operation we choose any two numbers currently on the board, erase them, and write back the value ceil((a+b)/2). After exactly n-1 operations only one number remains.

The key issue is that this is a constructive problem. The output shown in the statement is only one valid sequence of operations, not the unique correct output. Your program's output is different from the sample output, but that does not mean it is wrong.

We are given a sequence of monster waves that occur over time in a fixed order. Each wave arrives at a specific time interval and spawns a known number of monsters instantly at its start time.

The key issue is that this is a constructive problem. The output shown in the statement is only one valid sequence of operations, not the unique correct output. Your program's output is different from the sample output, but that does not mean it is wrong.

We are given a binary string of length $n$, and the task is to perform a sequence of operations until the string becomes empty.

The key issue is that this is a constructive problem. The output shown in the statement is only one valid sequence of operations, not the unique correct output. Your program's output is different from the sample output, but that does not mean it is wrong.

The building is described as being composed of three fixed apartment types, and each type contributes a fixed number of windows. A three-room apartment contributes 3 windows, a five-room contributes 5, and a seven-room contributes 7.

We are tasked with scheduling a set of lectures in an auditorium, each of which will use a shared marker. Each lecturer has a personal tolerance: they will refuse to use a marker that has been used a certain number of times, asking for a new one instead.

Codeforces 1431I: Cyclic Shifts

We are given a sorted array a of length n. Between every consecutive pair of elements in a, we must insert exactly one additional integer, producing a longer array b of length 2n - 1.

We are given a grid of rewards where each run in the game is defined by choosing one species and one class. Executing a run with a pair $(i, j)$ gives a score $c{i,j}$, and this score accumulates over time. At the beginning, only some species and classes are already available.

The key issue is that this is a constructive problem. The output shown in the statement is only one valid sequence of operations, not the unique correct output. Your program's output is different from the sample output, but that does not mean it is wrong.

Let the two circles be $\Gamma_1$ and $\Gamma_2$, with centers $O_1$ and $O_2$.

We are given a collection of distinct integers. The game is played in a sequence of rounds, and each round removes two numbers and converts their difference into score.

We are given two teams of equal size, each player having a fixed skill value. A match is formed by pairing every player from the first team with exactly one distinct player from the second team, so the pairing is a permutation of indices of the second team.

The key issue is that this is a constructive problem. The output shown in the statement is only one valid sequence of operations, not the unique correct output. Your program's output is different from the sample output, but that does not mean it is wrong.

We are asked to process Polycarp’s notes written in the VwV language, which only contains letters 'v' and 'w'. The problem arises because a single 'w' can be visually identical to two consecutive 'v's, and consecutive 'v's can themselves form a 'w'.

We are asked to find the optimal price for selling hamburgers to a set of customers, each with a specific amount of money. Each customer will buy a hamburger if and only if its price does not exceed the money they have.

We are asked to identify a dominant piranha in a linear aquarium. Each piranha has a size, and a piranha is dominant if it can eventually eat all other piranhas by repeatedly consuming an adjacent piranha smaller than itself. Every time it eats, its size increases by one.

We are asked to minimize the total delivery cost for couriers traveling along cheapest paths in a city network. The city is modeled as an undirected weighted graph with n districts as nodes and m two-way roads as edges, each with a positive cost.

The key issue is that this is a constructive problem. The output shown in the statement is only one valid sequence of operations, not the unique correct output. Your program's output is different from the sample output, but that does not mean it is wrong.

We are given a grid of numbers with $n$ rows and $m$ columns. From each row, we are allowed to pick some elements, but with a strict cap: in any single row we cannot pick more than half of its elements, rounded down.

We are given several independent scenarios. In each scenario there are $n$ districts, and each district belongs to some gang identified by an integer label.

The key issue is that this is a constructive problem. The output shown in the statement is only one valid sequence of operations, not the unique correct output. Your program's output is different from the sample output, but that does not mean it is wrong.

We are given a bookshelf represented as a binary array. A value of 1 means a book is present at that position, while 0 means the position is empty.

We are given several independent games. Each game consists of a strictly increasing array of integers. Two players alternate moves, and on each move a player selects one element from the array.

The key issue is that this is a constructive problem. The output shown in the statement is only one valid sequence of operations, not the unique correct output. Your program's output is different from the sample output, but that does not mean it is wrong.

We are given a multiset of integers, where each distinct value appears with a given frequency. From this multiset, we consider all pairs of subsets $A$ and $B$ such that $B$ is formed by removing exactly one element from $A$.

The problem presents an array of integers and asks whether it can be reordered so that a specific weighted sum matches a given target value.

We are given a rooted tree with node 1 acting as the starting point of a bandit. Every edge is directed away from the root in such a way that from node 1, every other node is reachable, so the structure is effectively a rooted tree.

The key issue is that this is a constructive problem. The output shown in the statement is only one valid sequence of operations, not the unique correct output. Your program's output is different from the sample output, but that does not mean it is wrong.

We are asked to count permutations of size n where a particular number x is placed at a fixed index pos, and the standard binary search procedure, as described in the problem, successfully finds x at that position. A permutation here is any ordering of the numbers 1 through n.

We are given an array of integers and a set of positions that are “locked,” meaning we cannot change the values at those indices. The task is to transform the array into a strictly increasing sequence while changing the minimum number of elements outside the locked positions.

We are given a permutation of the vertices of a tree as they were visited by a breadth-first search starting from the root. The root is always vertex 1, and all children of a vertex are visited in increasing order.

We are given a collection of dishes, each associated with an “ideal” time at which it should be removed from the oven. Time in this problem is discrete and increases one minute at a time.

Ah, now I see exactly what is happening. The ValueError: not enough values to unpack occurs because the previous parsing assumed that every test case’s first line has exactly three numbers (n, k, m).

The key issue is that this is a constructive problem. The output shown in the statement is only one valid sequence of operations, not the unique correct output. Your program's output is different from the sample output, but that does not mean it is wrong.

We are given a perfect binary tree of height $h$, which contains $n = 2^h - 1$ nodes. Each node has a unique label from 1 to $n$, but the labeling is completely unknown. Our task is to determine the label of the root.

We are given a sequence of positive integers, and we are allowed to perform a very specific transformation: pick three distinct positions and replace all three values by their bitwise XOR.

The key issue is that this is a constructive problem. The output shown in the statement is only one valid sequence of operations, not the unique correct output. Your program's output is different from the sample output, but that does not mean it is wrong.

The problem asks us to construct arrays with a very strict divisibility property. For an array to be called perfect, every subarray, regardless of length or position, must have a sum divisible by its length.

We are given a grid of zeros and ones with dimensions n by m. Each cell can either be off (0) or on (1). Our goal is to turn all the ones into zeros using a specific operation.

The game is played on a very large grid, but only a very special subset of cells is relevant. A cell $(x, y)$ is considered valid only when the bitwise condition $x & y = 0$ holds.

Ah, now the issue is clear. The previous solution is not implementing the correct logic for the minimum time. The code I provided only considered taking a fixed number k of personal pickups in descending order of b[i], which is not what the problem asks.

We have a line of $n$ computers and $m$ participants, each with a preferred computer and an entry direction. Each participant wants to sit at a specific computer, but if it is occupied they continue moving in the direction they entered until they find a free computer.

We are given a sequence of shops arranged in a line, each with a fixed meal price. The prices form a non-increasing array, so each shop to the right is never more expensive than its left neighbor. There are two types of operations we need to support.

Consider triangle $ABC$ in the plane.

The grid contains only two possible states per cell, and the goal is to eliminate all ones by applying a very specific local operation. Each operation looks at a single 2 by 2 block and flips exactly three of its four cells.

We are given a sorted list of $nk$ numbers and asked to split it into $k$ groups, each containing exactly $n$ elements.

We are given a binary string and two ways to pay for it. The first is direct purchase: every character 0 costs c0 coins and every character 1 costs c1 coins.

Thank you. Now I see exactly why the previous code is producing the wrong output. Let’s go carefully. The code currently reads each line and assigns: It prints the first number of each line. That explains why it prints 10 and 12 for the first two lines.

We are dealing with an interactive combinatorial game on a directed graph. Each vertex may hold a token, and two players alternate moves. On a turn, a player chooses any token and moves it along an outgoing edge. If a player cannot move any token, they lose.

We are given a tree in which each node is coloured white, black, or grey. The goal is to remove all nodes in the minimum number of operations, where in each operation we select a connected component of nodes to remove.

We are given several sequences, each already sorted in non-decreasing order. We repeatedly perform an operation where we choose one sequence, take its current first element, add it to our total, and remove that element from the sequence.

We start with a permutation stored in a line. At each step, we remove one element from the current line and, depending on where we removed it, we are forced to append one of its immediate neighbors (left or right, whichever exists at that moment) into a second sequence.

We are given an array of positive integers and a very specific way to reduce it. Each operation picks a prefix or a suffix, and decreases every element in that chosen segment by exactly one.

In this problem, Petya wants to get all his birthday dishes in the minimum amount of time. For each dish, he can either pick it up himself from a restaurant, taking bi minutes, or order a delivery, which will arrive in ai minutes.

We are given the initial permutation of integers from 1 to $n$ in order. Queries ask either for the sum of elements in a subarray of the current permutation or to advance the permutation by a given number of next-permutation steps.