question large_stringlengths 265 13.2k |
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Alice has just learnt about primeStrings. A string is a primeString if the number of distinct alphabets used in the string is a prime and also the number of occurrences of each alphabet in the string is also a prime.
Given a String you need to tell if i... |
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Ali baba did a trick on the forty thieves and was able to trap them inside a big cave which was the home of wild wolves. The thieves are without any weapons, only the chief of the thieves has knife. With no weapons they will not be able to fight with th... |
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You have a sequence A composed of N positive integers: A_{1}, A_{2}, \cdots, A_{N}.
You will now successively do the following Q operations:
* In the i-th operation, you replace every element whose value is B_{i} with C_{i}.
For each i (1 \leq i \l... |
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If there is an integer not less than 0 satisfying the following conditions, print the smallest such integer; otherwise, print `-1`.
* The integer has exactly N digits in base ten. (We assume 0 to be a 1-digit integer. For other integers, leading zeros ... |
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We have N switches with "on" and "off" state, and M bulbs. The switches are numbered 1 to N, and the bulbs are numbered 1 to M.
Bulb i is connected to k_i switches: Switch s_{i1}, s_{i2}, ..., and s_{ik_i}. It is lighted when the number of switches tha... |
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Let S(n) denote the sum of the digits in the decimal notation of n. For example, S(123) = 1 + 2 + 3 = 6.
We will call an integer n a Snuke number when, for all positive integers m such that m > n, \frac{n}{S(n)} \leq \frac{m}{S(m)} holds.
Given an int... |
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The postal code in Atcoder Kingdom is A+B+1 characters long, its (A+1)-th character is a hyphen `-`, and the other characters are digits from `0` through `9`.
You are given a string S. Determine whether it follows the postal code format in Atcoder King... |
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We have a sequence of length N, a = (a_1, a_2, ..., a_N). Each a_i is a positive integer.
Snuke's objective is to permute the element in a so that the following condition is satisfied:
* For each 1 ≤ i ≤ N - 1, the product of a_i and a_{i + 1} is a mu... |
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There is a tree T with N vertices, numbered 1 through N. For each 1 ≤ i ≤ N - 1, the i-th edge connects vertices a_i and b_i.
Snuke is constructing a directed graph T' by arbitrarily assigning direction to each edge in T. (There are 2^{N - 1} different... |
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There are N balls placed in a row. AtCoDeer the deer is painting each of these in one of the K colors of his paint cans. For aesthetic reasons, any two adjacent balls must be painted in different colors.
Find the number of the possible ways to paint th... |
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Assume that a, b, and n are all positive integers. Let f (i) be the i-th fraction of the fraction a / b (0 ≤ f (i) ≤ 9). At this time, let s be the sum of f (i) from i = 1 to n.
s = f (1) + f (2) + ... + f (n)
Create a program that reads a, b, n, out... |
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Tsuruga Castle, a symbol of Aizuwakamatsu City, was named "Tsuruga Castle" after Gamo Ujisato built a full-scale castle tower. You can overlook the Aizu basin from the castle tower. On a clear day, you can see Tsuruga Castle from the summit of Mt. Iimor... |
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The educational program (AHK Education) of the Aiz Broadcasting Association broadcasts a handicraft program for children, "Play with Tsukuro". Today is the time to make a rectangle with sticks, but I would like to see if I can make a rectangle using the... |
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problem
In the area where Kazakhstan is now located, there used to be a trade route called the "Silk Road".
There are N + 1 cities on the Silk Road, numbered from west as city 0, city 1, ..., city N. The distance between city i -1 and city i (1 ≤ i ≤ ... |
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In the good old Hachioji railroad station located in the west of Tokyo, there are several parking lines, and lots of freight trains come and go every day.
All freight trains travel at night, so these trains containing various types of cars are settled ... |
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Shortest Common Non-Subsequence
A subsequence of a sequence $P$ is a sequence that can be derived from the original sequence $P$ by picking up some or no elements of $P$ preserving the order. For example, "ICPC" is a subsequence of "MICROPROCESSOR".
A... |
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A Garden with Ponds
Mr. Gardiner is a modern garden designer who is excellent at utilizing the terrain features. His design method is unique: he first decides the location of ponds and design them with the terrain features intact.
According to his uni... |
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A convex polygon consisting of N vertices is given. The coordinates of each vertex are represented counterclockwise by (X1, Y1), (X2, Y2), ……, (XN, YN). No matter what straight line passes through the point P, find the coordinates of the point P so that... |
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Problem Statement
Let's consider operations on monochrome images that consist of hexagonal pixels, each of which is colored in either black or white. Because of the shape of pixels, each of them has exactly six neighbors (e.g. pixels that share an edge... |
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C: Namo .. Cut
problem
-Defeat the mysterious giant jellyfish, codenamed "Nari"-
"Nari" has a very strong vitality, so if you don't keep cutting quickly, it will be revived in a blink of an eye. We are making trial and error every day to find out how... |
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Problem
The popular video posting site "ZouTube" is now in the midst of an unprecedented "virtual ZouTuber" boom. Among them, the one that has been attracting particular attention recently is the junior virtual ZouTuber "Aizumarim (commonly known as Az... |
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You are given $n$ integers $w_i (i = 0, 1, ..., n-1)$ to be sorted in ascending order. You can swap two integers $w_i$ and $w_j$. Each swap operation has a cost, which is the sum of the two integers $w_i + w_j$. You can perform the operations any number... |
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A state with $n$ flags of ON or OFF can be represented by a sequence of bits where $0, 1, ..., n-1$ -th flag corresponds to 1 (ON) or 0 (OFF). The state can be managed by the corresponding decimal integer, because the sequence of bits is a binary repres... |
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You are given a rectangular parallelepiped with sides of positive integer lengths A, B and C.
Find the number of different groups of three integers (a, b, c) such that 1≤ a≤ b≤ c and parallelepiped A× B× C can be paved with parallelepipeds a× b× c. No... |
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When Masha came to math classes today, she saw two integer sequences of length n - 1 on the blackboard. Let's denote the elements of the first sequence as a_i (0 ≤ a_i ≤ 3), and the elements of the second sequence as b_i (0 ≤ b_i ≤ 3).
Masha became int... |
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Initially Ildar has an empty array. He performs n steps. On each step he takes a subset of integers already added to the array and appends the mex of this subset to the array.
The mex of an multiset of integers is the smallest non-negative integer not... |
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You are given an integer number n. The following algorithm is applied to it:
1. if n = 0, then end algorithm;
2. find the smallest prime divisor d of n;
3. subtract d from n and go to step 1.
Determine the number of subtrations the algorith... |
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Petr has just bought a new car. He's just arrived at the most known Petersburg's petrol station to refuel it when he suddenly discovered that the petrol tank is secured with a combination lock! The lock has a scale of 360 degrees and a pointer which ini... |
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You are given a connected undirected graph consisting of n vertices and m edges. There are no self-loops or multiple edges in the given graph.
You have to direct its edges in such a way that the obtained directed graph does not contain any paths of len... |
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You are given two arrays a and b, both of length n.
Let's define a function f(l, r) = ∑_{l ≤ i ≤ r} a_i ⋅ b_i.
Your task is to reorder the elements (choose an arbitrary order of elements) of the array b to minimize the value of ∑_{1 ≤ l ≤ r ≤ n} f(l, ... |
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The Third Doctor Who once correctly said that travel between parallel universes is "like travelling sideways". However, he incorrectly thought that there were infinite parallel universes, whereas in fact, as we now all know, there will never be more tha... |
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Demonstrative competitions will be held in the run-up to the 20NN Berlatov Olympic Games. Today is the day for the running competition!
Berlatov team consists of 2n runners which are placed on two running tracks; n runners are placed on each track. The... |
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Now that Kuroni has reached 10 years old, he is a big boy and doesn't like arrays of integers as presents anymore. This year he wants a Bracket sequence as a Birthday present. More specifically, he wants a bracket sequence so complex that no matter how ... |
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Slime and his n friends are at a party. Slime has designed a game for his friends to play.
At the beginning of the game, the i-th player has a_i biscuits. At each second, Slime will choose a biscuit randomly uniformly among all a_1 + a_2 + … + a_n bisc... |
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Little Petya very much likes computers. Recently he has received a new "Ternatron IV" as a gift from his mother. Unlike other modern computers, "Ternatron IV" operates with ternary and not binary logic. Petya immediately wondered how the xor operation i... |
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Being stuck at home, Ray became extremely bored. To pass time, he asks Lord Omkar to use his time bending power: Infinity Clock! However, Lord Omkar will only listen to mortals who can solve the following problem:
You are given an array a of n integers... |
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There are n piranhas with sizes a_1, a_2, …, a_n in the aquarium. Piranhas are numbered from left to right in order they live in the aquarium.
Scientists of the Berland State University want to find if there is dominant piranha in the aquarium. The pir... |
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There are n glasses on the table numbered 1, …, n. The glass i can hold up to a_i units of water, and currently contains b_i units of water.
You would like to choose k glasses and collect as much water in them as possible. To that effect you can pour w... |
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After reaching your destination, you want to build a new colony on the new planet. Since this planet has many mountains and the colony must be built on a flat surface you decided to flatten the mountains using boulders (you are still dreaming so this ma... |
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As a teacher, Riko Hakozaki often needs to help her students with problems from various subjects. Today, she is asked a programming task which goes as follows.
You are given an undirected complete graph with n nodes, where some edges are pre-assigned w... |
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This is an interactive problem.
Little Dormi was faced with an awkward problem at the carnival: he has to guess the edges of an unweighted tree of n nodes! The nodes of the tree are numbered from 1 to n.
The game master only allows him to ask one type... |
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You are given n points on a plane. All points are different.
Find the number of different groups of three points (A, B, C) such that point B is the middle of segment AC.
The groups of three points are considered unordered, that is, if point B is the ... |
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The Little Elephant has found a ragged old black-and-white string s on the attic.
The characters of string s are numbered from the left to the right from 1 to |s|, where |s| is the length of the string. Let's denote the i-th character of string s as si... |
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There are n boys and m girls studying in the class. They should stand in a line so that boys and girls alternated there as much as possible. Let's assume that positions in the line are indexed from left to right by numbers from 1 to n + m. Then the numb... |
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Coming up with a new problem isn't as easy as many people think. Sometimes it is hard enough to name it. We'll consider a title original if it doesn't occur as a substring in any titles of recent Codeforces problems.
You've got the titles of n last pr... |
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There are n kangaroos with pockets. Each kangaroo has a size (integer number). A kangaroo can go into another kangaroo's pocket if and only if the size of kangaroo who hold the kangaroo is at least twice as large as the size of kangaroo who is held.
Ea... |
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Imagine you have an infinite 2D plane with Cartesian coordinate system. Some of the integral points are blocked, and others are not. Two integral points A and B on the plane are 4-connected if and only if:
* the Euclidean distance between A and B is ... |
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Polycarpus develops an interesting theory about the interrelation of arithmetic progressions with just everything in the world. His current idea is that the population of the capital of Berland changes over time like an arithmetic progression. Well, or ... |
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Kolya got string s for his birthday, the string consists of small English letters. He immediately added k more characters to the right of the string.
Then Borya came and said that the new string contained a tandem repeat of length l as a substring. How... |
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Paul hates palindromes. He assumes that string s is tolerable if each its character is one of the first p letters of the English alphabet and s doesn't contain any palindrome contiguous substring of length 2 or more.
Paul has found a tolerable string s... |
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The Berland State University is hosting a ballroom dance in celebration of its 100500-th anniversary! n boys and m girls are already busy rehearsing waltz, minuet, polonaise and quadrille moves.
We know that several boy&girl pairs are going to be invit... |
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Two players play a simple game. Each player is provided with a box with balls. First player's box contains exactly n1 balls and second player's box contains exactly n2 balls. In one move first player can take from 1 to k1 balls from his box and throw th... |
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Developing tools for creation of locations maps for turn-based fights in a new game, Petya faced the following problem.
A field map consists of hexagonal cells. Since locations sizes are going to be big, a game designer wants to have a tool for quick f... |
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And while Mishka is enjoying her trip...
Chris is a little brown bear. No one knows, where and when he met Mishka, but for a long time they are together (excluding her current trip). However, best friends are important too. John is Chris' best friend.
... |
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Let’s define a grid to be a set of tiles with 2 rows and 13 columns. Each tile has an English letter written in it. The letters don't have to be unique: there might be two or more tiles with the same letter written on them. Here is an example of a grid:... |
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There are n servers in a laboratory, each of them can perform tasks. Each server has a unique id — integer from 1 to n.
It is known that during the day q tasks will come, the i-th of them is characterized with three integers: ti — the moment in seconds... |
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Oleg the client and Igor the analyst are good friends. However, sometimes they argue over little things. Recently, they started a new company, but they are having trouble finding a name for the company.
To settle this problem, they've decided to play a... |
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Karen has just arrived at school, and she has a math test today!
<image>
The test is about basic addition and subtraction. Unfortunately, the teachers were too busy writing tasks for Codeforces rounds, and had no time to make an actual test. So, they ... |
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The All-Berland National Olympiad in Informatics has just ended! Now Vladimir wants to upload the contest from the Olympiad as a gym to a popular Codehorses website.
Unfortunately, the archive with Olympiad's data is a mess. For example, the files with... |
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Absent-minded Masha got set of n cubes for her birthday.
At each of 6 faces of each cube, there is exactly one digit from 0 to 9. Masha became interested what is the largest natural x such she can make using her new cubes all integers from 1 to x.
To ... |
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Vasya and Kolya play a game with a string, using the following rules. Initially, Kolya creates a string s, consisting of small English letters, and uniformly at random chooses an integer k from a segment [0, len(s) - 1]. He tells Vasya this string s, an... |
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Mishka received a gift of multicolored pencils for his birthday! Unfortunately he lives in a monochrome world, where everything is of the same color and only saturation differs. This pack can be represented as a sequence a1, a2, ..., an of n integer num... |
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Rhezo and his friend Vanya love problem solving. They have a problem set containing N problems, with points assigned to each. Rhezo wants to solve problems in such a way that he gets the maximum number of points. Rhezo has a weird habit of solving only ... |
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N persons are standing in a row. The height of the i-th person from the front is A_i.
We want to have each person stand on a stool of some heights - at least zero - so that the following condition is satisfied for every person:
Condition: Nobody in fr... |
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There are N children standing in a line from left to right. The activeness of the i-th child from the left is A_i.
You can rearrange these children just one time in any order you like.
When a child who originally occupies the x-th position from the le... |
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We have N integers. The i-th integer is A_i.
Find \sum_{i=1}^{N-1}\sum_{j=i+1}^{N} (A_i \mbox{ XOR } A_j), modulo (10^9+7).
What is \mbox{ XOR }?
The XOR of integers A and B, A \mbox{ XOR } B, is defined as follows:
* When A \mbox{ XOR } B is writte... |
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You are given three strings A, B and C. Check whether they form a word chain.
More formally, determine whether both of the following are true:
* The last character in A and the initial character in B are the same.
* The last character in B and the ini... |
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You are given a permutation P_1 ... P_N of the set {1, 2, ..., N}.
You can apply the following operation to this permutation, any number of times (possibly zero):
* Choose two indices i,j (1 ≦ i < j ≦ N), such that j - i ≧ K and |P_i - P_j| = 1. Then,... |
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Dr .: Peter. I did.
Peter: See you again? What kind of silly invention is this time?
Dr .: You invented the detector for that phantom elementary particle axion.
Peter: Speaking of Axion, researchers such as the European Organization for Nuclear Resea... |
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I decided to move and decided to leave this place. There is nothing wrong with this land itself, but there is only one thing to worry about. It's a plum tree planted in the garden. I was looking forward to this plum blooming every year. After leaving he... |
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problem
Given two strings, find the longest of the strings contained in both strings and write a program that answers that length.
Here, the string s included in the string t means that s appears consecutively in t. An empty string, that is, a string ... |
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Problem Statement
There is a maze which can be described as a W \times H grid. The upper-left cell is denoted as (1, 1), and the lower-right cell is (W, H). You are now at the cell (1, 1) and have to go to the cell (W, H). However, you can only move to... |
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Problem statement
There is a positive integer sequence $ a_1, a_2, \ ldots, a_N $ of length $ N $.
Consider the following game, which uses this sequence and is played by $ 2 $ players on the play and the play.
* Alternately select one of the followin... |
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You are given n segments on a coordinate line; each endpoint of every segment has integer coordinates. Some segments can degenerate to points. Segments can intersect with each other, be nested in each other or even coincide.
Your task is the following:... |
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Dima the hamster enjoys nibbling different things: cages, sticks, bad problemsetters and even trees!
Recently he found a binary search tree and instinctively nibbled all of its edges, hence messing up the vertices. Dima knows that if Andrew, who has be... |
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Ivan places knights on infinite chessboard. Initially there are n knights. If there is free cell which is under attack of at least 4 knights then he places new knight in this cell. Ivan repeats this until there are no such free cells. One can prove that... |
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Petya loves lucky numbers. We all know that lucky numbers are the positive integers whose decimal representations contain only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.
Petya recently learned to determi... |
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There are n students and m clubs in a college. The clubs are numbered from 1 to m. Each student has a potential p_i and is a member of the club with index c_i. Initially, each student is a member of exactly one club. A technical fest starts in the colle... |
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You are given two arrays a and b, both of length n. All elements of both arrays are from 0 to n-1.
You can reorder elements of the array b (if you want, you may leave the order of elements as it is). After that, let array c be the array of length n, th... |
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You are given a graph with 3 ⋅ n vertices and m edges. You are to find a matching of n edges, or an independent set of n vertices.
A set of edges is called a matching if no two edges share an endpoint.
A set of vertices is called an independent set if... |
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You are given a sequence a_1, a_2, ..., a_n consisting of n non-zero integers (i.e. a_i ≠ 0).
You have to calculate two following values:
1. the number of pairs of indices (l, r) (l ≤ r) such that a_l ⋅ a_{l + 1} ... a_{r - 1} ⋅ a_r is negative;
... |
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The string t_1t_2 ... t_k is good if each letter of this string belongs to at least one palindrome of length greater than 1.
A palindrome is a string that reads the same backward as forward. For example, the strings A, BAB, ABBA, BAABBBAAB are palindro... |
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After years of hard work scientists invented an absolutely new e-reader display. The new display has a larger resolution, consumes less energy and its production is cheaper. And besides, one can bend it. The only inconvenience is highly unusual manageme... |
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Calculate the number of ways to place n rooks on n × n chessboard so that both following conditions are met:
* each empty cell is under attack;
* exactly k pairs of rooks attack each other.
An empty cell is under attack if there is at least on... |
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You are given a deck of n cards numbered from 1 to n (not necessarily in this order in the deck). You have to sort the deck by repeating the following operation.
* Choose 2 ≤ k ≤ n and split the deck in k nonempty contiguous parts D_1, D_2,..., D_k ... |
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On the competitive programming platform CodeCook, every person has a rating graph described by an array of integers a of length n. You are now updating the infrastructure, so you've created a program to compress these graphs.
The program works as follo... |
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Positive integer x is called divisor of positive integer y, if y is divisible by x without remainder. For example, 1 is a divisor of 7 and 3 is not divisor of 8.
We gave you an integer d and asked you to find the smallest positive integer a, such that ... |
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Sergey attends lessons of the N-ish language. Each lesson he receives a hometask. This time the task is to translate some sentence to the N-ish language. Sentences of the N-ish language can be represented as strings consisting of lowercase Latin letters... |
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The Smart Beaver from ABBYY invented a new message encryption method and now wants to check its performance. Checking it manually is long and tiresome, so he decided to ask the ABBYY Cup contestants for help.
A message is a sequence of n integers a1, a... |
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You've got a list of program warning logs. Each record of a log stream is a string in this format:
"2012-MM-DD HH:MM:SS:MESSAGE" (without the quotes).
String "MESSAGE" consists of spaces, uppercase and lowercase English letters and characters "!", "... |
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Emuskald is an avid horticulturist and owns the world's longest greenhouse — it is effectively infinite in length.
Over the years Emuskald has cultivated n plants in his greenhouse, of m different plant species numbered from 1 to m. His greenhouse is v... |
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Shaass has decided to hunt some birds. There are n horizontal electricity wires aligned parallel to each other. Wires are numbered 1 to n from top to bottom. On each wire there are some oskols sitting next to each other. Oskol is the name of a delicious... |
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Vasya and Petya wrote down all integers from 1 to n to play the "powers" game (n can be quite large; however, Vasya and Petya are not confused by this fact).
Players choose numbers in turn (Vasya chooses first). If some number x is chosen at the curren... |
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Let's call a number k-good if it contains all digits not exceeding k (0, ..., k). You've got a number k and an array a containing n numbers. Find out how many k-good numbers are in a (count each number every time it occurs in array a).
Input
The first... |
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Salve, mi amice.
Et tu quidem de lapis philosophorum. Barba non facit philosophum. Labor omnia vincit. Non potest creatio ex nihilo. Necesse est partibus.
Rp:
I Aqua Fortis
I Aqua Regia
II Amalgama
VII Minium
IV Vitriol
Misce in vitro et æstus, ... |
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Pashmak's homework is a problem about graphs. Although he always tries to do his homework completely, he can't solve this problem. As you know, he's really weak at graph theory; so try to help him in solving the problem.
You are given a weighted direct... |
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Shuseki Kingdom is the world's leading nation for innovation and technology. There are n cities in the kingdom, numbered from 1 to n.
Thanks to Mr. Kitayuta's research, it has finally become possible to construct teleportation pipes between two cities.... |
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There are many anime that are about "love triangles": Alice loves Bob, and Charlie loves Bob as well, but Alice hates Charlie. You are thinking about an anime which has n characters. The characters are labeled from 1 to n. Every pair of two characters c... |
Solve the programming task below in a Python markdown code block.
When Kefa came to the restaurant and sat at a table, the waiter immediately brought him the menu. There were n dishes. Kefa knows that he needs exactly m dishes. But at that, he doesn't want to order the same dish twice to taste as many dishes as possib... |
Solve the programming task below in a Python markdown code block.
In Absurdistan, there are n towns (numbered 1 through n) and m bidirectional railways. There is also an absurdly simple road network — for each pair of different towns x and y, there is a bidirectional road between towns x and y if and only if there is ... |
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