question large_stringlengths 265 13.2k |
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Recently, the Fair Nut has written k strings of length n, consisting of letters "a" and "b". He calculated c — the number of strings that are prefixes of at least one of the written strings. Every string was counted only one time.
Then, he lost his she... |
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Two people are playing a game with a string s, consisting of lowercase latin letters.
On a player's turn, he should choose two consecutive equal letters in the string and delete them.
For example, if the string is equal to "xaax" than there is only ... |
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Neko loves divisors. During the latest number theory lesson, he got an interesting exercise from his math teacher.
Neko has two integers a and b. His goal is to find a non-negative integer k such that the least common multiple of a+k and b+k is the sma... |
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You're given an array a of length 2n. Is it possible to reorder it in such way so that the sum of the first n elements isn't equal to the sum of the last n elements?
Input
The first line contains an integer n (1 ≤ n ≤ 1000), where 2n is the number of ... |
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There are n points on the plane, the i-th of which is at (x_i, y_i). Tokitsukaze wants to draw a strange rectangular area and pick all the points in the area.
The strange area is enclosed by three lines, x = l, y = a and x = r, as its left side, its bo... |
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Anadi has a set of dominoes. Every domino has two parts, and each part contains some dots. For every a and b such that 1 ≤ a ≤ b ≤ 6, there is exactly one domino with a dots on one half and b dots on the other half. The set contains exactly 21 dominoes.... |
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At first, let's define function f(x) as follows: $$$ \begin{matrix} f(x) & = & \left\{ \begin{matrix} x/2 & \mbox{if } x is even \\\ x - 1 & \mbox{otherwise } \end{matrix} \right. \end{matrix} $$$
We can see that if we choose some value v and will app... |
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Kana was just an ordinary high school girl before a talent scout discovered her. Then, she became an idol. But different from the stereotype, she is also a gameholic.
One day Kana gets interested in a new adventure game called Dragon Quest. In this ga... |
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Polycarpus has postcards and photos hung in a row on the wall. He decided to put them away to the closet and hang on the wall a famous painter's picture. Polycarpus does it like that: he goes from the left to the right and removes the objects consecutiv... |
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Little Petya likes numbers a lot. He found that number 123 in base 16 consists of two digits: the first is 7 and the second is 11. So the sum of digits of 123 in base 16 is equal to 18.
Now he wonders what is an average value of sum of digits of the nu... |
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The Bubble Cup hypothesis stood unsolved for 130 years. Who ever proves the hypothesis will be regarded as one of the greatest mathematicians of our time! A famous mathematician Jerry Mao managed to reduce the hypothesis to this problem:
Given a number... |
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Petya is preparing for his birthday. He decided that there would be n different dishes on the dinner table, numbered from 1 to n. Since Petya doesn't like to cook, he wants to order these dishes in restaurants.
Unfortunately, all dishes are prepared in... |
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Suppose you have a sequence of k integers A = [a_1, a_2, ... , a_k] where each a_i ≥ 2. A sequence of prime integers P = [p_1, p_2, ..., p_k] is called suitable for the sequence A if a_1 is divisible by p_1, a_2 is divisible by p_2 and so on.
A sequen... |
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This is an interactive problem.
There exists a matrix a of size n × m (n rows and m columns), you know only numbers n and m. The rows of the matrix are numbered from 1 to n from top to bottom, and columns of the matrix are numbered from 1 to m from lef... |
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Baby Ehab was toying around with arrays. He has an array a of length n. He defines an array to be good if there's no way to partition it into 2 subsequences such that the sum of the elements in the first is equal to the sum of the elements in the second... |
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This is the easy version of the problem. The only difference is that here k=2. You can make hacks only if both the versions of the problem are solved.
This is an interactive problem.
Every decimal number has a base k equivalent. The individual digits ... |
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They say that Berland has exactly two problems, fools and roads. Besides, Berland has n cities, populated by the fools and connected by the roads. All Berland roads are bidirectional. As there are many fools in Berland, between each pair of cities there... |
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Little penguin Polo adores strings. But most of all he adores strings of length n.
One day he wanted to find a string that meets the following conditions:
1. The string consists of n lowercase English letters (that is, the string's length equals n),... |
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Ilya is a very clever lion, he lives in an unusual city ZooVille. In this city all the animals have their rights and obligations. Moreover, they even have their own bank accounts. The state of a bank account is an integer. The state of a bank account ca... |
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Dima liked the present he got from Inna very much. He liked the present he got from Seryozha even more.
Dima felt so grateful to Inna about the present that he decided to buy her n hares. Inna was very happy. She lined up the hares in a row, numbered ... |
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Sereja loves number sequences very much. That's why he decided to make himself a new one following a certain algorithm.
Sereja takes a blank piece of paper. Then he starts writing out the sequence in m stages. Each time he either adds a new number to t... |
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The Queen of England has n trees growing in a row in her garden. At that, the i-th (1 ≤ i ≤ n) tree from the left has height ai meters. Today the Queen decided to update the scenery of her garden. She wants the trees' heights to meet the condition: for ... |
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Right now you are to solve a very, very simple problem — to crack the safe. Four positive integers stand one by one on a circle protecting the safe. You know that to unlock this striking safe you have to make all four numbers equal to one. Operations ar... |
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You are organizing a cycling race on the streets of the city. The city contains n junctions, some pairs of them are connected by roads; on each road you can move in any direction. No two roads connect the same pair of intersections, and no road connects... |
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A restaurant received n orders for the rental. Each rental order reserve the restaurant for a continuous period of time, the i-th order is characterized by two time values — the start time li and the finish time ri (li ≤ ri).
Restaurant management can ... |
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A group of n cities is connected by a network of roads. There is an undirected road between every pair of cities, so there are <image> roads in total. It takes exactly y seconds to traverse any single road.
A spanning tree is a set of roads containing ... |
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A tree is a connected undirected graph consisting of n vertices and n - 1 edges. Vertices are numbered 1 through n.
Limak is a little polar bear and Radewoosh is his evil enemy. Limak once had a tree but Radewoosh stolen it. Bear is very sad now becaus... |
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Today Sonya learned about long integers and invited all her friends to share the fun. Sonya has an initially empty multiset with integers. Friends give her t queries, each of one of the following type:
1. + ai — add non-negative integer ai to the mu... |
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The academic year has just begun, but lessons and olympiads have already occupied all the free time. It is not a surprise that today Olga fell asleep on the Literature. She had a dream in which she was on a stairs.
The stairs consists of n steps. The ... |
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Igor found out discounts in a shop and decided to buy n items. Discounts at the store will last for a week and Igor knows about each item that its price now is ai, and after a week of discounts its price will be bi.
Not all of sellers are honest, so no... |
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The Floral Clock has been standing by the side of Mirror Lake for years. Though unable to keep time, it reminds people of the passage of time and the good old days.
On the rim of the Floral Clock are 2n flowers, numbered from 1 to 2n clockwise, each of... |
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You are given several queries. In the i-th query you are given a single positive integer ni. You are to represent ni as a sum of maximum possible number of composite summands and print this maximum number, or print -1, if there are no such splittings.
... |
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— Thanks a lot for today.
— I experienced so many great things.
— You gave me memories like dreams... But I have to leave now...
— One last request, can you...
— Help me solve a Codeforces problem?
— ......
— What?
Chtholly has been thinking abou... |
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As Will is stuck in the Upside Down, he can still communicate with his mom, Joyce, through the Christmas lights (he can turn them on and off with his mind). He can't directly tell his mom where he is, because the monster that took him to the Upside Down... |
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And where the are the phone numbers?
You are given a string s consisting of lowercase English letters and an integer k. Find the lexicographically smallest string t of length k, such that its set of letters is a subset of the set of letters of s and s ... |
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Rachel, being an awesome android programmer, just finished an App that will let us draw a triangle by selecting three points on the touch-plane.Now She asks her friend Bruce to draw a Right-Angled Triangle (we'll call it RAT) by selecting 3 integral poi... |
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Today, you have been given the task of handling the entire Taxi Network of Berland City. Berland city has a huge number of taxi travellers, and you need to help them in transportation in the most efficient manner.
To be precise, this city consists of ... |
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Max feels lonely after shifting to a new locality, as he does not have any friend there. So his parents bought him a new number from the Integers SuperMarket! Every child in the locality has bought a number from the same market.
He takes the number t... |
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How many strings can be obtained by applying the following operation on a string S exactly K times: "choose one lowercase English letter and insert it somewhere"?
The answer can be enormous, so print it modulo (10^9+7).
Constraints
* K is an integer ... |
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N friends of Takahashi has come to a theme park.
To ride the most popular roller coaster in the park, you must be at least K centimeters tall.
The i-th friend is h_i centimeters tall.
How many of the Takahashi's friends can ride the roller coaster?
... |
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There are N men and N women, both numbered 1, 2, \ldots, N.
For each i, j (1 \leq i, j \leq N), the compatibility of Man i and Woman j is given as an integer a_{i, j}. If a_{i, j} = 1, Man i and Woman j are compatible; if a_{i, j} = 0, they are not.
T... |
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In Takahashi's mind, there is always an integer sequence of length 2 \times 10^9 + 1: A = (A_{-10^9}, A_{-10^9 + 1}, ..., A_{10^9 - 1}, A_{10^9}) and an integer P.
Initially, all the elements in the sequence A in Takahashi's mind are 0, and the value o... |
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We say that a odd number N is similar to 2017 when both N and (N+1)/2 are prime.
You are given Q queries.
In the i-th query, given two odd numbers l_i and r_i, find the number of odd numbers x similar to 2017 such that l_i ≤ x ≤ r_i.
Constraints
* 1... |
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Snuke, who loves animals, built a zoo.
There are N animals in this zoo. They are conveniently numbered 1 through N, and arranged in a circle. The animal numbered i (2≤i≤N-1) is adjacent to the animals numbered i-1 and i+1. Also, the animal numbered 1 i... |
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AtCoDeer the deer and his friend TopCoDeer is playing a game. The game consists of N turns. In each turn, each player plays one of the two gestures, Rock and Paper, as in Rock-paper-scissors, under the following condition:
(※) After each turn, (the num... |
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With the motto "Creating your own path," a shrine created a fortune-telling fortune with its own hands. Ask the person who draws the lottery to throw six stones first, then the line segment connecting the first and second of the thrown stones, the line ... |
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N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula
$ \ Frac {A + B} {C --D} $
I want to find the maximum value of.
Given N different natural numbers, choose ... |
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Carving the cake 2 (Cake 2)
JOI-kun and IOI-chan are twin brothers and sisters. JOI has been enthusiastic about making sweets lately, and JOI tried to bake a cake and eat it today, but when it was baked, IOI who smelled it came, so we decided to divide... |
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There are many caves deep in mountains found in the countryside. In legend, each cave has a treasure hidden within the farthest room from the cave's entrance. The Shogun has ordered his Samurais to explore these caves with Karakuri dolls (robots) and to... |
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In the year 2020, a race of atomically energized cars will be held. Unlike today’s car races, fueling is not a concern of racing teams. Cars can run throughout the course without any refueling. Instead, the critical factor is tire (tyre). Teams should c... |
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Fair Chocolate-Cutting
You are given a flat piece of chocolate of convex polygon shape. You are to cut it into two pieces of precisely the same amount with a straight knife.
Write a program that computes, for a given convex polygon, the maximum and mi... |
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Boolean Expression Compressor
You are asked to build a compressor for Boolean expressions that transforms expressions to the shortest form keeping their meaning.
The grammar of the Boolean expressions has terminals `0` `1` `a` `b` `c` `d` `-` `^` `*` ... |
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Ikta has an extraordinary feeling for undirected graphs. Ikta likes the undirected graph G and its two-point s, t pair (G, s, t) that has the greatest "beauty". The "beauty" of a pair (G, s, t) is the edge e = \\ {u, v \\} (u and v are two different poi... |
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A: Isono, let's do that! --Sendame -
story
Nakajima "Isono ~, let's do that!"
Isono "What is that, Nakajima"
Nakajima "Look, that's that. It's hard to explain because I have to express it in letters for some reason."
Isono "No, it seems that you ca... |
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Print all subsets of a set $S$, which contains $0, 1, ... n-1$ as elements. Note that we represent $0, 1, ... n-1$ as 00...0001, 00...0010, 00...0100, ..., 10...0000 in binary respectively and the integer representation of a subset is calculated by bitw... |
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Asmany strings are strings of '0's and '1's that have as many 00 as 11. A string such as 00110001 consists of 3 "00" and
1 "11". Of course this is not an Asmany string. 0011, 1100, 000111000111 are Asmany strings. An L'th Asmany number is the number of
... |
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Let's start from some definitions.
Strings A and B are called anagrams if it's possible to rearrange the letters of string A using all the original letters exactly once and achieve string B; in other words A and B are permutations of each other. For ex... |
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Bob and Alice are often participating in various programming competitions. Like many competitive programmers, Alice and Bob have good and bad days. They noticed, that their lucky and unlucky days are repeating with some period. For example, for Alice da... |
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Miyako came to the flea kingdom with a ukulele. She became good friends with local flea residents and played beautiful music for them every day.
In return, the fleas made a bigger ukulele for her: it has n strings, and each string has (10^{18} + 1) fre... |
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Alice has a string s. She really likes the letter "a". She calls a string good if strictly more than half of the characters in that string are "a"s. For example "aaabb", "axaa" are good strings, and "baca", "awwwa", "" (empty string) are not.
Alice can... |
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A telephone number is a sequence of exactly 11 digits, where the first digit is 8. For example, the sequence 80011223388 is a telephone number, but the sequences 70011223388 and 80000011223388 are not.
You are given a string s of length n, consisting o... |
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Mislove had an array a_1, a_2, ⋅⋅⋅, a_n of n positive integers, but he has lost it. He only remembers the following facts about it:
* The number of different numbers in the array is not less than l and is not greater than r;
* For each array's elem... |
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You are working for the Gryzzl company, headquartered in Pawnee, Indiana.
The new national park has been opened near Pawnee recently and you are to implement a geolocation system, so people won't get lost. The concept you developed is innovative and mi... |
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Bob is a competitive programmer. He wants to become red, and for that he needs a strict training regime. He went to the annual meeting of grandmasters and asked n of them how much effort they needed to reach red.
"Oh, I just spent x_i hours solving pro... |
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Bessie the cow has just intercepted a text that Farmer John sent to Burger Queen! However, Bessie is sure that there is a secret message hidden inside.
The text is a string s of lowercase Latin letters. She considers a string t as hidden in string s if... |
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For the multiset of positive integers s=\\{s_1,s_2,...,s_k\}, define the Greatest Common Divisor (GCD) and Least Common Multiple (LCM) of s as follow:
* \gcd(s) is the maximum positive integer x, such that all integers in s are divisible on x.
* lc... |
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This year in Equestria was a year of plenty, so Applejack has decided to build some new apple storages. According to the advice of the farm designers, she chose to build two storages with non-zero area: one in the shape of a square and another one in th... |
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You are playing a very popular game called Cubecraft. Initially, you have one stick and want to craft k torches. One torch can be crafted using one stick and one coal.
Hopefully, you've met a very handsome wandering trader who has two trade offers:
... |
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Petya loves lucky numbers very much. Everybody knows that lucky numbers are positive integers whose decimal record contains only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.
Petya has sequence a consisting... |
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You are given n - 1 integers a_2, ..., a_n and a tree with n vertices rooted at vertex 1. The leaves are all at the same distance d from the root.
Recall that a tree is a connected undirected graph without cycles. The distance between two vertices is ... |
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Omkar has received a message from Anton saying "Your story for problem A is confusing. Just make a formal statement." Because of this, Omkar gives you an array a = [a_1, a_2, …, a_n] of n distinct integers. An array b = [b_1, b_2, …, b_k] is called nice... |
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Sensation, sensation in the two-dimensional kingdom! The police have caught a highly dangerous outlaw, member of the notorious "Pihters" gang. The law department states that the outlaw was driving from the gang's headquarters in his car when he crashed ... |
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We know that prime numbers are positive integers that have exactly two distinct positive divisors. Similarly, we'll call a positive integer t Т-prime, if t has exactly three distinct positive divisors.
You are given an array of n positive integers. For... |
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Gena loves sequences of numbers. Recently, he has discovered a new type of sequences which he called an almost arithmetical progression. A sequence is an almost arithmetical progression, if its elements can be represented as:
* a1 = p, where p is som... |
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«Polygon» is a system which allows to create programming tasks in a simple and professional way. When you add a test to the problem, the corresponding form asks you for the test index. As in most cases it is clear which index the next test will have, th... |
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You are an adventurer currently journeying inside an evil temple. After defeating a couple of weak zombies, you arrived at a square room consisting of tiles forming an n × n grid. The rows are numbered 1 through n from top to bottom, and the columns are... |
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There are n cities in Berland. Each city has its index — an integer number from 1 to n. The capital has index r1. All the roads in Berland are two-way. The road system is such that there is exactly one path from the capital to each city, i.e. the road m... |
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Let's assume that
* v(n) is the largest prime number, that does not exceed n;
* u(n) is the smallest prime number strictly greater than n.
Find <image>.
Input
The first line contains integer t (1 ≤ t ≤ 500) — the number of testscases.
Each... |
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While resting on the ship after the "Russian Code Cup" a boy named Misha invented an interesting game. He promised to give his quadrocopter to whoever will be the first one to make a rectangular table of size n × m, consisting of positive integers such ... |
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DZY loves chessboard, and he enjoys playing with it.
He has a chessboard of n rows and m columns. Some cells of the chessboard are bad, others are good. For every good cell, DZY wants to put a chessman on it. Each chessman is either white or black. Aft... |
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After you had helped George and Alex to move in the dorm, they went to help their friend Fedor play a new computer game «Call of Soldiers 3».
The game has (m + 1) players and n types of soldiers in total. Players «Call of Soldiers 3» are numbered form ... |
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Berland has n cities, the capital is located in city s, and the historic home town of the President is in city t (s ≠ t). The cities are connected by one-way roads, the travel time for each of the road is a positive integer.
Once a year the President v... |
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The Department of economic development of IT City created a model of city development till year 2100.
To prepare report about growth perspectives it is required to get growth estimates from the model.
To get the growth estimates it is required to solv... |
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Alyona decided to go on a diet and went to the forest to get some apples. There she unexpectedly found a magic rooted tree with root in the vertex 1, every vertex and every edge of which has a number written on.
The girl noticed that some of the tree's... |
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Captain Bill the Hummingbird and his crew recieved an interesting challenge offer. Some stranger gave them a map, potion of teleportation and said that only this potion might help them to reach the treasure.
Bottle with potion has two values x and y w... |
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Kirill plays a new computer game. He came to the potion store where he can buy any potion. Each potion is characterized by two integers — amount of experience and cost. The efficiency of a potion is the ratio of the amount of experience to the cost. Eff... |
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Let quasi-palindromic number be such number that adding some leading zeros (possible none) to it produces a palindromic string.
String t is called a palindrome, if it reads the same from left to right and from right to left.
For example, numbers 131 ... |
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You are given an array a consisting of n integers, and additionally an integer m. You have to choose some sequence of indices b1, b2, ..., bk (1 ≤ b1 < b2 < ... < bk ≤ n) in such a way that the value of <image> is maximized. Chosen sequence can be empty... |
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Mishka is decorating the Christmas tree. He has got three garlands, and all of them will be put on the tree. After that Mishka will switch these garlands on.
When a garland is switched on, it periodically changes its state — sometimes it is lit, someti... |
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A dragon symbolizes wisdom, power and wealth. On Lunar New Year's Day, people model a dragon with bamboo strips and clothes, raise them with rods, and hold the rods high and low to resemble a flying dragon.
A performer holding the rod low is represente... |
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Petya loves volleyball very much. One day he was running late for a volleyball match. Petya hasn't bought his own car yet, that's why he had to take a taxi. The city has n junctions, some of which are connected by two-way roads. The length of each road ... |
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You took a peek on Thanos wearing Infinity Gauntlet. In the Gauntlet there is a place for six Infinity Gems:
* the Power Gem of purple color,
* the Time Gem of green color,
* the Space Gem of blue color,
* the Soul Gem of orange color,
* ... |
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Lily Aldrin, as the slap bet commissioner, needs to resolve issues regarding slap bets due with Barney and Marshall. She has mandated that there be a fixed period of time in which the slaps may be used.
So, she draws two lines representing the given t... |
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DG (Departmental Gathering) is coming….
As one of the most famous girls in the college everybody is smitten with Harshada and wants to give
her roses. But Harshada is only into coders , therefore she sends out word that she would accept
roses from ... |
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Problem :
The Starks(S),Lannisters(L) and the Baratheons(B) are fighting for the
Iron Throne. These three houses are fighting from ages to capture the
throne.
The N th battle goes on for N days before a winner
emerges. Interestingly,the battles follow... |
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Karan has decided to give stickers to all the attendees of the last day of Google Week. The stickers will be given such that the last person to enter the hall gets a single sticker. The second last person entering the hall gets two stickers and so on.
... |
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We have N strings of lowercase English letters: S_1, S_2, \cdots, S_N.
Takahashi wants to make a string that is a palindrome by choosing one or more of these strings - the same string can be chosen more than once - and concatenating them in some order ... |
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We have held a popularity poll for N items on sale. Item i received A_i votes.
From these N items, we will select M as popular items. However, we cannot select an item with less than \dfrac{1}{4M} of the total number of votes.
If M popular items can b... |
Solve the programming task below in a Python markdown code block.
There are N mountains in a circle, called Mountain 1, Mountain 2, ..., Mountain N in clockwise order. N is an odd number.
Between these mountains, there are N dams, called Dam 1, Dam 2, ..., Dam N. Dam i (1 \leq i \leq N) is located between Mountain i ... |
Solve the programming task below in a Python markdown code block.
You are given integers N and K. Find the number of triples (a,b,c) of positive integers not greater than N such that a+b,b+c and c+a are all multiples of K. The order of a,b,c does matter, and some of them can be the same.
Constraints
* 1 \leq N,K \le... |
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