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Gianni needs to assemble a problem set for SWERC from a pool of problems submitted by judges. Each problem has a beauty score and a difficulty rating from 1 to 10.

There are actually two separate problems. The immediate runtime error is not caused by the algorithm at all. The test harness calls: and inside run it calls: but the code snippet shown in the editorial did not include solve inside the test block.

The task is purely about feasibility rather than computation. We are asked to construct a single source file that both C++ (GCC 10.3.1 with C++11 standard) and FreePascal (3.0.4) can compile successfully.

The task presents a string of exactly six letters. We are asked to produce another string of six letters that satisfies a hidden constructive property - in this problem, the exact constraints are designed so that a careful choice of repeated characters produces a valid answer.

The problem gives us a string S of length three, consisting of the characters + and -, and a non-negative integer X. The string represents a sequence of operations on an integer: + means increment by 1, - means decrement by 1.

Before I start writing the editorial, I need to clarify something: the problem statement you gave is entirely narrative and does not include any actual rules for “Are You Safe?

I can't write a correct editorial for this problem from the information provided. The current statement for Codeforces 1663C - Pōja Verdon has been intentionally stripped down to: Given an array, output a single number. That version omits the actual task.

We are given a single integer $r$, which may be negative, zero, or positive up to 2999. The task is to compute another integer that depends on this value through a hidden construction that is not explicitly described in the statement, but is implicitly defined by the sample…

We are given a set of participants involved in a testing process, where each participant is associated with exactly one “tested by” relationship.

We are asked to find the minimum time needed to infect all nodes of a rooted tree where infections spread in two ways each second. First, a spreading step allows any node with at least one infected child to infect at most one additional child.

We are asked to find a hidden positive integer $x$ between 1 and $10^9$. Instead of observing $x$ directly, we can query the greatest common divisor of two numbers shifted by $x$. Specifically, for any two positive integers $a$ and $b$, the interactor returns $gcd(x + a, x + b)$.

We are asked to process multiple subarray queries on an array of non-negative integers. For each subarray defined by indices $l$ and $r$, the task is to find the minimum value of the bitwise OR taken over all pairs of distinct elements in that subarray.

The problem asks us to split a given positive integer $n$ into four positive integers $a, b, c, d$ such that the sum $a + b + c + d = n$ holds, and at the same time the greatest common divisor of $a$ and $b$ equals the least common multiple of $c$ and $d$.

We are given an array of integers, and we can perform two types of operations: cloning an entire array copy, or swapping elements between any two copies. Our goal is to produce at least one array where all elements are identical, using the minimal number of operations.

We are given three distinct points on the 2D plane, and we are asked to connect them with segments that are either horizontal or vertical. The segments can only lie along the coordinate axes, meaning each segment has constant x or constant y.

We are given a directed graph representing a labyrinth of halls and one-way passages. A traveler starts from a fixed starting hall $s$. We are allowed to choose any other hall $t$ as a meeting point.

We are asked to partition a kingdom's towns into three districts, A, B, and C, corresponding to Adrian, Beatrice, and Cecilia. Adrian's castle must be in district A, Beatrice's castle in district B, and Cecilia has no castle.

We are asked to organize a team of n members into a binary search tree (BST) hierarchy that minimizes communication cost. Each team member has a unique number from 1 to n representing their position in a front-end to back-end spectrum.

We are given a grid of size $n times m$ where two treasures are hidden in distinct cells. The goal is to locate both treasures using a combination of two operations: DIG r c and SCAN r c.

We are given a sequence of integer strengths representing heroes. Each hero can defeat monsters of strength equal to their own or weaker.

In this problem, we are given a set of points on a two-dimensional plane, each representing a temperature measurement at a specific location.

The problem gives us a sequence of integers representing operations on a stack. Each integer can be seen as either pushing a new element onto the stack or performing a "fancy" operation that removes some elements from the top in a way governed by the problem's rules.

We are given a one-dimensional segment representing the entire country, stretching from position 0 to position l. Inside this segment there are n citizens, each located at a distinct integer coordinate ai, sorted in increasing order.

We are given two strings for each test case, an initial word and a target word. We repeatedly perform an operation where we are allowed to choose a character and delete its leftmost occurrence from the current word.

We are asked to distribute extra budget money over several topics, each consisting of a small number of items. For each topic, the optimal relative fractions of money for its items are given, and some money is already assigned to items and cannot be removed.

We are given a string over four symbols, each symbol encoding a move in a grid: up, left, down, or right. Any substring of this string can be interpreted as a flattened matrix if we choose a height and width whose product equals the substring length, reading the substring row…

The task is to place the minimum number of half-queens on an $n times n$ chessboard such that every square is either occupied or attacked. A half-queen attacks all cells in its row, its column, and the diagonal going from top-left to bottom-right that passes through its position.

We are given a grid where some cells are already fixed as black or white, and the rest are empty. The goal is to assign a color to every empty cell so that, after filling, all black cells form a single connected region using 4-directional movement, and all white cells also…

We are asked to count, for each vertex in a special class of labeled trees, how many trees have that vertex as a centroid. The trees have $n$ vertices labeled $1$ through $n$, with the restriction that each vertex $i ge 2$ is connected to exactly one vertex with a smaller index.

We are given a tree, which is a connected graph with no cycles, and we are asked to remove all its edges following a very particular rule: an edge can be removed only if it is adjacent to an even number of remaining edges. Two edges are adjacent if they share exactly one vertex.

We are asked to construct an array $b$ from an array $a$ such that each element of $b$ is obtained from zero by either adding or subtracting a multiple of the corresponding element in $a$.

We are asked to partition an array of integers into contiguous subarrays in order to maximize a custom score. Each subarray contributes to the total sum based on its sum: if the sum is positive, its contribution is the length of the subarray; if zero, it contributes nothing…

We are given a circular arrangement of $m$ seats and a list of $n$ people. Each person has a personal “exclusion radius” $ai$: if they sit on some seat, then the closest $ai$ seats on both sides around the circle must remain empty.

We are walking on a very large rectangular grid starting from the top-left cell and trying to reach the bottom-right cell.

The problem asks us to find any number in an array that occurs at least three times. We are given multiple test cases, and for each test case, an array of integers is provided. The integers are guaranteed to be between 1 and the size of the array.

We are given an array of integers, and we are allowed to “turn on” bits in individual elements. Each operation picks one element and sets one previously-zero bit to one. We may do this at most k times across the entire array.

We are given a rectangular grid of size $n times m$ consisting of empty cells, stones, and obstacles. Stones are represented by '', empty cells by '.', and obstacles by 'o'.

We are given a sequence of candy weights laid out in a straight line. Two people, Alice and Bob, consume candies under a strict constraint: Alice can only take a prefix from the left end, while Bob can only take a suffix from the right end.

We are given a collection of short strings, each consisting of exactly two lowercase letters from a small alphabet.

We are given a line of cells that starts completely empty, and we are allowed to apply a special operation that always acts on exactly two adjacent positions. Each application recolors those two cells into different colors, one red and one blue, in either order.

We are given an array of integers where we are allowed to repeatedly apply two global operations. One operation increments every element at odd positions, and the other increments every element at even positions.

Each test case gives a single integer representing a Codeforces user rating, and the task is to classify that rating into one of four fixed intervals, each corresponding to a division number. The mapping is purely threshold-based.

We are given two permutations of size $n$, which are arrays containing each integer from $1$ to $n$ exactly once. From these two permutations, a third array is constructed by choosing for each position either the value from the first permutation or from the second permutation.

We are given a tree with $n = 2^p$ vertices. We must assign distinct integers from $1$ to $2n-1$ to all vertices and edges, so in total we label exactly $2n-1$ objects. After fixing these labels, we also choose a root.

Working

We are working with an infinite hexagonal grid, where each hexagon shares edges with six neighbors. The task is to add straight lines along the directions of the hexagon edges to form equilateral triangles.

We are given an array of non-zero integers, and we are allowed to repeatedly swap the signs of any two elements that have opposite signs. The goal is to determine whether we can make the array non-decreasing with this operation.

We are given a string that represents a password and a set of special characters. A transformation program can be applied repeatedly to the string.

We are counting permutations of size $n$ with two simultaneous structural constraints. The first constraint fixes the total number of inversions, meaning how many pairs $(i, j)$ with $i < j$ appear in reversed order in the permutation.

We are given an array of integers a and a set of extra integers {1, 2, …, x}. The task is to insert all these extra integers into a in any order and at any positions, including at the beginning or end.

The input to the system is well-formed but the observed failure pattern is not a mathematical or logical inconsistency of the task; it is a structural defect: the program produces no output at all for multiple independent test cases, indicating that the core loop does not…

We are given a complete binary tree of size $2^n - 1$, where every internal node has exactly two children and all leaves lie on the same level. Each node carries a label, either A or B.

We are given a set of points on a number line, already sorted in increasing order. Each point is allowed to “wiggle” by at most one unit, meaning its final position can be its original coordinate, one step left, or one step right.

We have a scenario where you want to buy sugar packs from several shops over consecutive days, with each shop selling one pack per day. Each shop has an initial price for its pack, and every day the price increases by one.

Codeforces 1672I: PermutationForces

We are given a binary string and many queries on substrings. For each query interval, we repeatedly delete contiguous pieces of the current substring.

We are asked to construct a binary grid of size $r times c$ by applying a specific row-column flip operation multiple times starting from an all-zero grid. The operation allows us to pick any cell and flip all values in its row and column using XOR with 1.

We are asked to represent each integer in the range from $-10$ to $10$ using the numeral system with radix $-2$. In this system, every integer $N$ is written in the form $$N = sum{i=0}^{k} di (-2)^i,$$ where each digit $di in {0,1}$ and the representation is chosen so that the…

We are given two arrays of the same length. The first array represents the “original” configuration, and the second array is a shuffled version of it, meaning it contains exactly the same multiset of values but possibly in a different order.

We are given an array that contains values in the range from 1 to n, possibly with repetitions. Think of this array as a multiset of labeled tokens.

We are dealing with a hidden array of word lengths, and the only way to learn anything about it is by querying a hypothetical text editor.

We are given two arrays, a and b, of the same length n. The goal is to determine whether we can transform a into b using a specific operation.

We are asked to determine the winner in a simple two-player game with logs of integer lengths. There are $n$ logs, and two players take turns splitting a single log into two positive integer pieces. The first player unable to make a move loses.

We are given an array of integers and asked to minimize consecutive repetitions. Formally, we define the equality of an array as the number of positions where two consecutive elements are equal.

The runtime error ValueError: min() arg is empty comes from trying to compute min(arr) when arr is empty. The root cause is that the input parsing logic does not match the problem's actual input format.

We are asked to design a system of roads on an $n times n$ grid of buildings where each road has a positive integer length and the sum of all road lengths does not exceed 48,000.

We are given a sequence of integers $B1, B2, dots, Bn$. Each value $Bi$ represents a power of two, so we can think of the underlying numbers as $Ai = 2^{Bi}$.

We are given two arithmetic progressions, $B$ and $C$. The progression $C$ contains all numbers that are common to some unknown progression $A$ and $B$. Our goal is to count how many finite arithmetic progressions $A$ could exist that satisfy this property.

The problem defines a very strong constraint on a string: every substring must have almost equal counts of all characters that appear in the full string.

We are given several independent rounds. In each round, Alice and Bob repeatedly delete contiguous parts of a string until nothing remains. The deleted characters contribute to their personal scores, where each letter has a fixed value from 1 for a up to 26 for z.

Thank you for providing the detailed sample input and output. I carefully traced the prefix-suffix logic from the previous solution, and the bug is clear. The previous approach misaligns indices when determining which friends could be thieves. Specifically: 1.

We are given a directed acyclic graph where each vertex has some number of incoming and outgoing edges. We are allowed to delete edges, but only under a very specific local rule: a vertex can lose edges only if it actually had at least one edge of that type before, unless it…

We are given a 2D grid representing a desktop with icons marked as '' and empty cells as '.'. The desktop is considered "good" if the icons occupy a compact rectangle starting from the top-left corner: all icons fill some number of complete columns, and possibly a prefix of…

We are given an array a of integers and need to simulate a two-step procedure to form a new array c. The first step repeatedly moves elements from the end of a into the middle of a second array b.

We are given a row of wall segments, each with some durability. A segment is considered destroyed once its durability drops to zero or below.

We are given a tiny language where every valid word consists of exactly two different lowercase English letters. Because the alphabet is fixed and small, every possible word can be generated by picking an ordered pair of distinct letters, such as ab, ac, ba, and so on.

The problem gives you two strings for each test case: a string s composed entirely of the letter 'a' and another string t composed of arbitrary lowercase letters. You are allowed to repeatedly replace any single 'a' in s with the string t.

We observe a sequence of visitors entering a room one after another. Exactly one of them stole a painting at some moment, but we do not know when the theft happened.

The array represents stacks of pancakes placed on a row of dishes. You are allowed to repeatedly pick a single pancake and move it one step to an adjacent dish, paying a cost of one per such move.

We are given a city structured as a tree with n houses connected by n-1 roads, which guarantees there is exactly one simple path between any two houses.

We are given a rooted tree, but the root is not explicitly provided. Instead, every node tells us its parent, and exactly one node is its own parent. That node is the root. From this structure, we must partition all nodes into several directed paths.

We are given a string made of lowercase English letters, and we are allowed to repeatedly perform a global transformation on it.

We are given several independent arrays. For each array, we are allowed to repeatedly shrink elements, where one operation picks a position and replaces its value with half of it rounded down. No swapping is allowed, so the order of elements is fixed.

We are given a situation in a pet store where there are three types of food: dog food, cat food, and universal food that can feed either dogs or cats. Polycarp owns a certain number of dogs and cats. Our task is to decide if the store has enough food to satisfy all of his pets.

We are given two parallel rows of segments, top and bottom, both of length $n$. Each segment on the top row has a wire connecting it to a specific segment on the bottom row, defined by an array $a$, where $ai$ is the bottom segment connected to top segment $i$.

We are given a collection of wires, one per index, where wire i starts at position i on the upper rail and ends at position a[i] on the lower rail.

We are given a set of boxes, each containing some number of candies. There is exactly one box for each friend, and the goal is to make all boxes contain the same number of candies so that no friend feels left out. We can only eat candies from a box; we cannot add any.

We are given a rooted tree where vertex 1 is the root. Every vertex is colored either black or white. For any vertex, its subtree consists of the vertex itself and all nodes that have it on their path up to the root, meaning all descendants in the rooted structure.

We are given an array of integers and a threshold number $k$. Our goal is to find a contiguous range of integers $[l, r]$ such that every integer in this range appears at least $k$ times in the array.

We are given a two-dimensional grid representing a chessboard where each cell contains a non-negative integer. A bishop can be placed on any cell, and it attacks all cells along the four diagonals that intersect at its position. The cell the bishop occupies counts as attacked.

We are given multiple independent scenarios, each describing a collection of candies where each candy has a fixed amount of sugar.

We are given a collection of words where each word has the same length. Our task is to measure how “far apart” any two words are in terms of the minimum number of single-letter changes needed to make them identical.

We are given a sequence of short strings, each representing a six-digit ticket number. Each ticket should be split into two halves of equal length. The task is to decide whether the sum of digits in the left half matches the sum of digits in the right half.

We are asked to simulate a dynamic seating scenario. There is a hall with n rows and m columns, and students arrive one by one, each either serious or naughty.

We are given a line of positions, and each position contributes a stack of identical gems of a specific type. Position i holds ai gems of type i.

We are given a permutation that undergoes a very specific transformation: one “operation” is a full left-to-right bubble pass where adjacent inversions are fixed once. After applying this operation exactly $k$ times, we obtain a permutation $a$.

We are given a permutation of integers from 1 to $n$, and we are asked multiple queries about contiguous subsegments of this permutation. A subsegment is called beautiful if its maximum value can be expressed as the product of two elements inside that segment.

Each color appears exactly once on two parallel tapes, so every color can be seen as a pair of positions: one index on the first tape and one index on the second tape.

We are given a permutation of integers from 1 to n and asked to count how many quadruples of indices [a, b, c, d] satisfy two inequalities: the first element is smaller than the third (pa < pc) and the second element is larger than the fourth (pb pd).

We are given a binary string of even length and asked to transform it into a "good" string. A good string is defined by two rules.