id stringlengths 10 13 | content stringlengths 424 1.17M |
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app_data_2100 | One foggy Stockholm morning, Karlsson decided to snack on some jam in his friend Lillebror Svantenson's house. Fortunately for Karlsson, there wasn't anybody in his friend's house. Karlsson was not going to be hungry any longer, so he decided to get some food in the house.
Karlsson's gaze immediately fell on n wooden ... |
app_data_2101 | You are given three multisets of pairs of colored sticks: $R$ pairs of red sticks, the first pair has length $r_1$, the second pair has length $r_2$, $\dots$, the $R$-th pair has length $r_R$; $G$ pairs of green sticks, the first pair has length $g_1$, the second pair has length $g_2$, $\dots$, the $G$-th pair has l... |
app_data_2102 | After battling Shikamaru, Tayuya decided that her flute is too predictable, and replaced it with a guitar. The guitar has $6$ strings and an infinite number of frets numbered from $1$. Fretting the fret number $j$ on the $i$-th string produces the note $a_{i} + j$.
Tayuya wants to play a melody of $n$ notes. Each note... |
app_data_2103 | Given an array $a$ of length $n$, find another array, $b$, of length $n$ such that:
for each $i$ $(1 \le i \le n)$ $MEX(\{b_1$, $b_2$, $\ldots$, $b_i\})=a_i$.
The $MEX$ of a set of integers is the smallest non-negative integer that doesn't belong to this set.
If such array doesn't exist, determine this.
-----In... |
app_data_2104 | You are given a set of all integers from $l$ to $r$ inclusive, $l < r$, $(r - l + 1) \le 3 \cdot 10^5$ and $(r - l)$ is always odd.
You want to split these numbers into exactly $\frac{r - l + 1}{2}$ pairs in such a way that for each pair $(i, j)$ the greatest common divisor of $i$ and $j$ is equal to $1$. Each number ... |
app_data_2105 | Happy new year! The year 2020 is also known as Year Gyeongja (경자년, gyeongja-nyeon) in Korea. Where did the name come from? Let's briefly look at the Gapja system, which is traditionally used in Korea to name the years.
There are two sequences of $n$ strings $s_1, s_2, s_3, \ldots, s_{n}$ and $m$ strings $t_1, t_2, t_3... |
app_data_2106 | There are n cities in the country where the Old Peykan lives. These cities are located on a straight line, we'll denote them from left to right as c_1, c_2, ..., c_{n}. The Old Peykan wants to travel from city c_1 to c_{n} using roads. There are (n - 1) one way roads, the i-th road goes from city c_{i} to city c_{i} + ... |
app_data_2107 | Dima loves Inna very much. He decided to write a song for her. Dima has a magic guitar with n strings and m frets. Dima makes the guitar produce sounds like that: to play a note, he needs to hold one of the strings on one of the frets and then pull the string. When Dima pulls the i-th string holding it on the j-th fret... |
app_data_2108 | You are given an undirected graph without self-loops or multiple edges which consists of $n$ vertices and $m$ edges. Also you are given three integers $n_1$, $n_2$ and $n_3$.
Can you label each vertex with one of three numbers 1, 2 or 3 in such way, that: Each vertex should be labeled by exactly one number 1, 2 or 3... |
app_data_2109 | Vitaly has an array of n distinct integers. Vitaly wants to divide this array into three non-empty sets so as the following conditions hold:
The product of all numbers in the first set is less than zero ( < 0). The product of all numbers in the second set is greater than zero ( > 0). The product of all numbers in... |
app_data_2110 | There are many freight trains departing from Kirnes planet every day. One day on that planet consists of $h$ hours, and each hour consists of $m$ minutes, where $m$ is an even number. Currently, there are $n$ freight trains, and they depart every day at the same time: $i$-th train departs at $h_i$ hours and $m_i$ minut... |
app_data_2111 | Andrewid the Android is a galaxy-known detective. Now he does not investigate any case and is eating chocolate out of boredom.
A bar of chocolate can be presented as an n × n table, where each cell represents one piece of chocolate. The columns of the table are numbered from 1 to n from left to right and the rows are ... |
app_data_2112 | There are $n$ warriors in a row. The power of the $i$-th warrior is $a_i$. All powers are pairwise distinct.
You have two types of spells which you may cast: Fireball: you spend $x$ mana and destroy exactly $k$ consecutive warriors; Berserk: you spend $y$ mana, choose two consecutive warriors, and the warrior with ... |
app_data_2113 | Mahmoud and Ehab continue their adventures! As everybody in the evil land knows, Dr. Evil likes bipartite graphs, especially trees.
A tree is a connected acyclic graph. A bipartite graph is a graph, whose vertices can be partitioned into 2 sets in such a way, that for each edge (u, v) that belongs to the graph, u and ... |
app_data_2114 | Egor wants to achieve a rating of 1600 points on the well-known chess portal ChessForces and he needs your help!
Before you start solving the problem, Egor wants to remind you how the chess pieces move. Chess rook moves along straight lines up and down, left and right, as many squares as it wants. And when it wants, i... |
app_data_2115 | You are given a sequence of positive integers a_1, a_2, ..., a_{n}.
While possible, you perform the following operation: find a pair of equal consecutive elements. If there are more than one such pair, find the leftmost (with the smallest indices of elements). If the two integers are equal to x, delete both and inser... |
app_data_2116 | Ayush is a cashier at the shopping center. Recently his department has started a ''click and collect" service which allows users to shop online.
The store contains k items. n customers have already used the above service. Each user paid for m items. Let a_{ij} denote the j-th item in the i-th person's order.
Due to ... |
app_data_2117 | The Resistance is trying to take control over as many planets of a particular solar system as possible. Princess Heidi is in charge of the fleet, and she must send ships to some planets in order to maximize the number of controlled planets.
The Galaxy contains N planets, connected by bidirectional hyperspace tunnels i... |
app_data_2118 | Merge sort is a well-known sorting algorithm. The main function that sorts the elements of array a with indices from [l, r) can be implemented as follows: If the segment [l, r) is already sorted in non-descending order (that is, for any i such that l ≤ i < r - 1 a[i] ≤ a[i + 1]), then end the function call; Let $\ope... |
app_data_2119 | Vasya owns three big integers — $a, l, r$. Let's define a partition of $x$ such a sequence of strings $s_1, s_2, \dots, s_k$ that $s_1 + s_2 + \dots + s_k = x$, where $+$ is a concatanation of strings. $s_i$ is the $i$-th element of the partition. For example, number $12345$ has the following partitions: ["1", "2", "3"... |
app_data_2120 | On Children's Day, the child got a toy from Delayyy as a present. However, the child is so naughty that he can't wait to destroy the toy.
The toy consists of n parts and m ropes. Each rope links two parts, but every pair of parts is linked by at most one rope. To split the toy, the child must remove all its parts. The... |
app_data_2121 | For his computer science class, Jacob builds a model tree with sticks and balls containing n nodes in the shape of a tree. Jacob has spent a_{i} minutes building the i-th ball in the tree.
Jacob's teacher will evaluate his model and grade Jacob based on the effort he has put in. However, she does not have enough time ... |
app_data_2122 | Whereas humans nowadays read fewer and fewer books on paper, book readership among marmots has surged. Heidi has expanded the library and is now serving longer request sequences.
-----Input-----
Same as the easy version, but the limits have changed: 1 ≤ n, k ≤ 400 000.
-----Output-----
Same as the easy version.
... |
app_data_2123 | Caisa solved the problem with the sugar and now he is on the way back to home.
Caisa is playing a mobile game during his path. There are (n + 1) pylons numbered from 0 to n in this game. The pylon with number 0 has zero height, the pylon with number i (i > 0) has height h_{i}. The goal of the game is to reach n-th py... |
app_data_2124 | Recently Vladik discovered a new entertainment — coding bots for social networks. He would like to use machine learning in his bots so now he want to prepare some learning data for them.
At first, he need to download t chats. Vladik coded a script which should have downloaded the chats, however, something went wrong. ... |
app_data_2125 | Innokenty works at a flea market and sells some random stuff rare items. Recently he found an old rectangular blanket. It turned out that the blanket is split in $n \cdot m$ colored pieces that form a rectangle with $n$ rows and $m$ columns.
The colored pieces attracted Innokenty's attention so he immediately came up... |
app_data_2126 | Luckily, Serval got onto the right bus, and he came to the kindergarten on time. After coming to kindergarten, he found the toy bricks very funny.
He has a special interest to create difficult problems for others to solve. This time, with many $1 \times 1 \times 1$ toy bricks, he builds up a 3-dimensional object. We c... |
app_data_2127 | Polycarp has recently got himself a new job. He now earns so much that his old wallet can't even store all the money he has.
Berland bills somehow come in lots of different sizes. However, all of them are shaped as rectangles (possibly squares). All wallets are also produced in form of rectangles (possibly squares).
... |
app_data_2128 | Creatnx has $n$ mirrors, numbered from $1$ to $n$. Every day, Creatnx asks exactly one mirror "Am I beautiful?". The $i$-th mirror will tell Creatnx that he is beautiful with probability $\frac{p_i}{100}$ for all $1 \le i \le n$.
Creatnx asks the mirrors one by one, starting from the $1$-st mirror. Every day, if he as... |
app_data_2129 | There are n cities and m two-way roads in Berland, each road connects two cities. It is known that there is no more than one road connecting each pair of cities, and there is no road which connects the city with itself. It is possible that there is no way to get from one city to some other city using only these roads.
... |
app_data_2130 | Vitya has learned that the answer for The Ultimate Question of Life, the Universe, and Everything is not the integer 54 42, but an increasing integer sequence $a_1, \ldots, a_n$. In order to not reveal the secret earlier than needed, Vitya encrypted the answer and obtained the sequence $b_1, \ldots, b_n$ using the foll... |
app_data_2131 | Ramesses knows a lot about problems involving trees (undirected connected graphs without cycles)!
He created a new useful tree decomposition, but he does not know how to construct it, so he asked you for help!
The decomposition is the splitting the edges of the tree in some simple paths in such a way that each two pa... |
app_data_2132 | Polycarp has just attempted to pass the driving test. He ran over the straight road with the signs of four types.
speed limit: this sign comes with a positive integer number — maximal speed of the car after the sign (cancel the action of the previous sign of this type); overtake is allowed: this sign means that aft... |
app_data_2133 | Anton is growing a tree in his garden. In case you forgot, the tree is a connected acyclic undirected graph.
There are n vertices in the tree, each of them is painted black or white. Anton doesn't like multicolored trees, so he wants to change the tree such that all vertices have the same color (black or white).
To c... |
app_data_2134 | Marcin is a coach in his university. There are $n$ students who want to attend a training camp. Marcin is a smart coach, so he wants to send only the students that can work calmly with each other.
Let's focus on the students. They are indexed with integers from $1$ to $n$. Each of them can be described with two intege... |
app_data_2135 | They say "years are like dominoes, tumbling one after the other". But would a year fit into a grid? I don't think so.
Limak is a little polar bear who loves to play. He has recently got a rectangular grid with h rows and w columns. Each cell is a square, either empty (denoted by '.') or forbidden (denoted by '#'). Row... |
app_data_2136 | Pink Floyd are pulling a prank on Roger Waters. They know he doesn't like walls, he wants to be able to walk freely, so they are blocking him from exiting his room which can be seen as a grid.
Roger Waters has a square grid of size $n\times n$ and he wants to traverse his grid from the upper left ($1,1$) corner to the... |
app_data_2137 | Ghosts live in harmony and peace, they travel the space without any purpose other than scare whoever stands in their way.
There are $n$ ghosts in the universe, they move in the $OXY$ plane, each one of them has its own velocity that does not change in time: $\overrightarrow{V} = V_{x}\overrightarrow{i} + V_{y}\overrig... |
app_data_2138 | You are given a sequence of n positive integers d_1, d_2, ..., d_{n} (d_1 < d_2 < ... < d_{n}). Your task is to construct an undirected graph such that:
there are exactly d_{n} + 1 vertices; there are no self-loops; there are no multiple edges; there are no more than 10^6 edges; its degree set is equal to d.
V... |
app_data_2139 | The bear has a string s = s_1s_2... s_{|}s| (record |s| is the string's length), consisting of lowercase English letters. The bear wants to count the number of such pairs of indices i, j (1 ≤ i ≤ j ≤ |s|), that string x(i, j) = s_{i}s_{i} + 1... s_{j} contains at least one string "bear" as a substring.
String x(i, j) ... |
app_data_2140 | Pasha got a very beautiful string s for his birthday, the string consists of lowercase Latin letters. The letters in the string are numbered from 1 to |s| from left to right, where |s| is the length of the given string.
Pasha didn't like his present very much so he decided to change it. After his birthday Pasha spent ... |
app_data_2141 | You are given a chess board with $n$ rows and $n$ columns. Initially all cells of the board are empty, and you have to put a white or a black knight into each cell of the board.
A knight is a chess piece that can attack a piece in cell ($x_2$, $y_2$) from the cell ($x_1$, $y_1$) if one of the following conditions is m... |
app_data_2142 | You are given two arrays of integers $a_1,\ldots,a_n$ and $b_1,\ldots,b_m$.
Your task is to find a non-empty array $c_1,\ldots,c_k$ that is a subsequence of $a_1,\ldots,a_n$, and also a subsequence of $b_1,\ldots,b_m$. If there are multiple answers, find one of the smallest possible length. If there are still multiple... |
app_data_2143 | Mike decided to teach programming to children in an elementary school. He knows that it is not an easy task to interest children in that age to code. That is why he decided to give each child two sweets.
Mike has $n$ sweets with sizes $a_1, a_2, \ldots, a_n$. All his sweets have different sizes. That is, there is no s... |
app_data_2144 | You are given two integers $a$ and $m$. Calculate the number of integers $x$ such that $0 \le x < m$ and $\gcd(a, m) = \gcd(a + x, m)$.
Note: $\gcd(a, b)$ is the greatest common divisor of $a$ and $b$.
-----Input-----
The first line contains the single integer $T$ ($1 \le T \le 50$) — the number of test cases.
Nex... |
app_data_2145 | Recently Petya walked in the forest and found a magic stick.
Since Petya really likes numbers, the first thing he learned was spells for changing numbers. So far, he knows only two spells that can be applied to a positive integer: If the chosen number $a$ is even, then the spell will turn it into $\frac{3a}{2}$; If... |
app_data_2146 | Recently, Mike was very busy with studying for exams and contests. Now he is going to chill a bit by doing some sight seeing in the city.
City consists of n intersections numbered from 1 to n. Mike starts walking from his house located at the intersection number 1 and goes along some sequence of intersections. Walking... |
app_data_2147 | A Large Software Company develops its own social network. Analysts have found that during the holidays, major sporting events and other significant events users begin to enter the network more frequently, resulting in great load increase on the infrastructure.
As part of this task, we assume that the social network is... |
app_data_2148 | Carol is currently curling.
She has n disks each with radius r on the 2D plane.
Initially she has all these disks above the line y = 10^100.
She then will slide the disks towards the line y = 0 one by one in order from 1 to n.
When she slides the i-th disk, she will place its center at the point (x_{i}, 10^100). ... |
app_data_2149 | Your program fails again. This time it gets "Wrong answer on test 233".
This is the easier version of the problem. In this version $1 \le n \le 2000$. You can hack this problem only if you solve and lock both problems.
The problem is about a test containing $n$ one-choice-questions. Each of the questions contains $k$... |
app_data_2150 | Alicia has an array, $a_1, a_2, \ldots, a_n$, of non-negative integers. For each $1 \leq i \leq n$, she has found a non-negative integer $x_i = max(0, a_1, \ldots, a_{i-1})$. Note that for $i=1$, $x_i = 0$.
For example, if Alicia had the array $a = \{0, 1, 2, 0, 3\}$, then $x = \{0, 0, 1, 2, 2\}$.
Then, she calculate... |
app_data_2151 | You are given a sequence $s$ consisting of $n$ digits from $1$ to $9$.
You have to divide it into at least two segments (segment — is a consecutive sequence of elements) (in other words, you have to place separators between some digits of the sequence) in such a way that each element belongs to exactly one segment and... |
app_data_2152 | Duff is addicted to meat! Malek wants to keep her happy for n days. In order to be happy in i-th day, she needs to eat exactly a_{i} kilograms of meat. [Image]
There is a big shop uptown and Malek wants to buy meat for her from there. In i-th day, they sell meat for p_{i} dollars per kilogram. Malek knows all numbers... |
app_data_2153 | There are $n$ beautiful skyscrapers in New York, the height of the $i$-th one is $h_i$. Today some villains have set on fire first $n - 1$ of them, and now the only safety building is $n$-th skyscraper.
Let's call a jump from $i$-th skyscraper to $j$-th ($i < j$) discrete, if all skyscrapers between are strictly lower... |
app_data_2154 | You can perfectly predict the price of a certain stock for the next N days. You would like to profit on this knowledge, but only want to transact one share of stock per day. That is, each day you will either buy one share, sell one share, or do nothing. Initially you own zero shares, and you cannot sell shares when you... |
app_data_2155 | Since Sonya has just learned the basics of matrices, she decided to play with them a little bit.
Sonya imagined a new type of matrices that she called rhombic matrices. These matrices have exactly one zero, while all other cells have the Manhattan distance to the cell containing the zero. The cells with equal numbers ... |
app_data_2156 | Consider a sequence of digits of length $2^k$ $[a_1, a_2, \ldots, a_{2^k}]$. We perform the following operation with it: replace pairs $(a_{2i+1}, a_{2i+2})$ with $(a_{2i+1} + a_{2i+2})\bmod 10$ for $0\le i<2^{k-1}$. For every $i$ where $a_{2i+1} + a_{2i+2}\ge 10$ we get a candy! As a result, we will get a sequence of ... |
app_data_2157 | The little girl loves the problems on array queries very much.
One day she came across a rather well-known problem: you've got an array of n elements (the elements of the array are indexed starting from 1); also, there are q queries, each one is defined by a pair of integers l_{i}, r_{i} (1 ≤ l_{i} ≤ r_{i} ≤ n). You n... |
app_data_2158 | Heidi's friend Jenny is asking Heidi to deliver an important letter to one of their common friends. Since Jenny is Irish, Heidi thinks that this might be a prank. More precisely, she suspects that the message she is asked to deliver states: "Send the fool further!", and upon reading it the recipient will ask Heidi to d... |
app_data_2159 | Bear Limak has n colored balls, arranged in one long row. Balls are numbered 1 through n, from left to right. There are n possible colors, also numbered 1 through n. The i-th ball has color t_{i}.
For a fixed interval (set of consecutive elements) of balls we can define a dominant color. It's a color occurring the big... |
app_data_2160 | Alice and Bob are playing a game on a line with $n$ cells. There are $n$ cells labeled from $1$ through $n$. For each $i$ from $1$ to $n-1$, cells $i$ and $i+1$ are adjacent.
Alice initially has a token on some cell on the line, and Bob tries to guess where it is.
Bob guesses a sequence of line cell numbers $x_1, x_... |
app_data_2161 | Vasya has several phone books, in which he recorded the telephone numbers of his friends. Each of his friends can have one or several phone numbers.
Vasya decided to organize information about the phone numbers of friends. You will be given n strings — all entries from Vasya's phone books. Each entry starts with a fri... |
app_data_2162 | A team of three programmers is going to play a contest. The contest consists of $n$ problems, numbered from $1$ to $n$. Each problem is printed on a separate sheet of paper. The participants have decided to divide the problem statements into three parts: the first programmer took some prefix of the statements (some num... |
app_data_2163 | For a sequence a of n integers between 1 and m, inclusive, denote f(a) as the number of distinct subsequences of a (including the empty subsequence).
You are given two positive integers n and m. Let S be the set of all sequences of length n consisting of numbers from 1 to m. Compute the sum f(a) over all a in S modulo... |
app_data_2164 | This is the easy version of the problem. The difference is the constraint on the sum of lengths of strings and the number of test cases. You can make hacks only if you solve all versions of this task.
You are given a string $s$, consisting of lowercase English letters. Find the longest string, $t$, which satisfies the... |
app_data_2165 | Consider a system of n water taps all pouring water into the same container. The i-th water tap can be set to deliver any amount of water from 0 to a_{i} ml per second (this amount may be a real number). The water delivered by i-th tap has temperature t_{i}.
If for every $i \in [ 1, n ]$ you set i-th tap to deliver ex... |
app_data_2166 | Iahub is so happy about inventing bubble sort graphs that he's staying all day long at the office and writing permutations. Iahubina is angry that she is no more important for Iahub. When Iahub goes away, Iahubina comes to his office and sabotage his research work.
The girl finds an important permutation for the resea... |
app_data_2167 | Polycarpus has an array, consisting of n integers a_1, a_2, ..., a_{n}. Polycarpus likes it when numbers in an array match. That's why he wants the array to have as many equal numbers as possible. For that Polycarpus performs the following operation multiple times:
he chooses two elements of the array a_{i}, a_{j} (... |
app_data_2168 | A conglomerate consists of $n$ companies. To make managing easier, their owners have decided to merge all companies into one. By law, it is only possible to merge two companies, so the owners plan to select two companies, merge them into one, and continue doing so until there is only one company left.
But anti-monopol... |
app_data_2169 | We have a grid with H rows and W columns. The square at the i-th row and the j-th column will be called Square (i,j).
The integers from 1 through H×W are written throughout the grid, and the integer written in Square (i,j) is A_{i,j}.
You, a magical girl, can teleport a piece placed on Square (i,j) to Square (x,y) by c... |
app_data_2170 | Count the pairs of length-N sequences consisting of integers between 1 and M (inclusive), A_1, A_2, \cdots, A_{N} and B_1, B_2, \cdots, B_{N}, that satisfy all of the following conditions:
- A_i \neq B_i, for every i such that 1\leq i\leq N.
- A_i \neq A_j and B_i \neq B_j, for every (i, j) such that 1\leq i < j\leq ... |
app_data_2171 | This morning Chef wants to jump a little. In a few minutes he will arrive at the point 0. Then he will perform a lot of jumps in such a sequence: 1-jump, 2-jump, 3-jump, 1-jump, 2-jump, 3-jump, 1-jump, and so on.
1-jump means that if Chef is at the point x, he will jump to the point x+1.
2-jump means that if Chef is a... |
app_data_2172 | You have a new professor of graph theory and he speaks very quickly. You come up with the following plan to keep up with his lecture and make notes.
You know two languages, and the professor is giving the lecture in the first one. The words in both languages consist of lowercase English characters, each language consi... |
app_data_2173 | One very well-known internet resource site (let's call it X) has come up with a New Year adventure. Specifically, they decided to give ratings to all visitors.
There are n users on the site, for each user we know the rating value he wants to get as a New Year Present. We know that user i wants to get at least a_{i} ra... |
app_data_2174 | Permutation p is an ordered set of integers p_1, p_2, ..., p_{n}, consisting of n distinct positive integers, each of them doesn't exceed n. We'll denote the i-th element of permutation p as p_{i}. We'll call number n the size or the length of permutation p_1, p_2, ..., p_{n}.
You have a sequence of integers a_1... |
app_data_2175 | There is a system of n vessels arranged one above the other as shown in the figure below. Assume that the vessels are numbered from 1 to n, in the order from the highest to the lowest, the volume of the i-th vessel is a_{i} liters. [Image]
Initially, all the vessels are empty. In some vessels water is poured. All the... |
app_data_2176 | You are given a sequence of $n$ pairs of integers: $(a_1, b_1), (a_2, b_2), \dots , (a_n, b_n)$. This sequence is called bad if it is sorted in non-descending order by first elements or if it is sorted in non-descending order by second elements. Otherwise the sequence is good. There are examples of good and bad sequenc... |
app_data_2177 | You are given two integers $A$ and $B$, calculate the number of pairs $(a, b)$ such that $1 \le a \le A$, $1 \le b \le B$, and the equation $a \cdot b + a + b = conc(a, b)$ is true; $conc(a, b)$ is the concatenation of $a$ and $b$ (for example, $conc(12, 23) = 1223$, $conc(100, 11) = 10011$). $a$ and $b$ should not con... |
app_data_2178 | Vasya has got $n$ books, numbered from $1$ to $n$, arranged in a stack. The topmost book has number $a_1$, the next one — $a_2$, and so on. The book at the bottom of the stack has number $a_n$. All numbers are distinct.
Vasya wants to move all the books to his backpack in $n$ steps. During $i$-th step he wants to move... |
app_data_2179 | Little girl Susie accidentally found her elder brother's notebook. She has many things to do, more important than solving problems, but she found this problem too interesting, so she wanted to know its solution and decided to ask you about it. So, the problem statement is as follows.
Let's assume that we are given a c... |
app_data_2180 | Iahub likes chess very much. He even invented a new chess piece named Coder. A Coder can move (and attack) one square horizontally or vertically. More precisely, if the Coder is located at position (x, y), he can move to (or attack) positions (x + 1, y), (x–1, y), (x, y + 1) and (x, y–1).
Iahub wants to know how many ... |
app_data_2181 | Valera takes part in the Berland Marathon. The marathon race starts at the stadium that can be represented on the plane as a square whose lower left corner is located at point with coordinates (0, 0) and the length of the side equals a meters. The sides of the square are parallel to coordinate axes.
As the length of t... |
app_data_2182 | 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 problems", said the $i$-th of them.
Bob wants to train his math ... |
app_data_2183 | Три брата договорились о встрече. Пронумеруем братьев следующим образом: пусть старший брат имеет номер 1, средний брат имеет номер 2, а младший брат — номер 3.
Когда пришло время встречи, один из братьев опоздал. По заданным номерам двух братьев, которые пришли вовремя, вам предстоит определить номер опоздавшего бра... |
app_data_2184 | You are given a boolean function of three variables which is defined by its truth table. You need to find an expression of minimum length that equals to this function. The expression may consist of: Operation AND ('&', ASCII code 38) Operation OR ('|', ASCII code 124) Operation NOT ('!', ASCII code 33) Variables x... |
app_data_2185 | You're given two arrays $a[1 \dots n]$ and $b[1 \dots n]$, both of the same length $n$.
In order to perform a push operation, you have to choose three integers $l, r, k$ satisfying $1 \le l \le r \le n$ and $k > 0$. Then, you will add $k$ to elements $a_l, a_{l+1}, \ldots, a_r$.
For example, if $a = [3, 7, 1, 4, 1, 2... |
app_data_2186 | Watto, the owner of a spare parts store, has recently got an order for the mechanism that can process strings in a certain way. Initially the memory of the mechanism is filled with n strings. Then the mechanism should be able to process queries of the following type: "Given string s, determine if the memory of the mech... |
app_data_2187 | Omkar is building a waterslide in his water park, and he needs your help to ensure that he does it as efficiently as possible.
Omkar currently has $n$ supports arranged in a line, the $i$-th of which has height $a_i$. Omkar wants to build his waterslide from the right to the left, so his supports must be nondecreasing... |
app_data_2188 | You are given $n$ pairs of integers $(a_1, b_1), (a_2, b_2), \ldots, (a_n, b_n)$. All of the integers in the pairs are distinct and are in the range from $1$ to $2 \cdot n$ inclusive.
Let's call a sequence of integers $x_1, x_2, \ldots, x_{2k}$ good if either $x_1 < x_2 > x_3 < \ldots < x_{2k-2} > x_{2k-1} < x_{2k}$... |
app_data_2189 | You are given a directed acyclic graph with n vertices and m edges. There are no self-loops or multiple edges between any pair of vertices. Graph can be disconnected.
You should assign labels to all vertices in such a way that:
Labels form a valid permutation of length n — an integer sequence such that each integer... |
app_data_2190 | You are given $n$ positive integers $a_1, \ldots, a_n$, and an integer $k \geq 2$. Count the number of pairs $i, j$ such that $1 \leq i < j \leq n$, and there exists an integer $x$ such that $a_i \cdot a_j = x^k$.
-----Input-----
The first line contains two integers $n$ and $k$ ($2 \leq n \leq 10^5$, $2 \leq k \leq ... |
app_data_2191 | Alice and Bob play a game. The game consists of several sets, and each set consists of several rounds. Each round is won either by Alice or by Bob, and the set ends when one of the players has won $x$ rounds in a row. For example, if Bob won five rounds in a row and $x = 2$, then two sets ends.
You know that Alice and... |
app_data_2192 | Chubby Yang is studying linear equations right now. He came up with a nice problem. In the problem you are given an n × n matrix W, consisting of integers, and you should find two n × n matrices A and B, all the following conditions must hold: A_{ij} = A_{ji}, for all i, j (1 ≤ i, j ≤ n); B_{ij} = - B_{ji}, for all... |
app_data_2193 | Egor is a famous Russian singer, rapper, actor and blogger, and finally he decided to give a concert in the sunny Republic of Dagestan.
There are $n$ cities in the republic, some of them are connected by $m$ directed roads without any additional conditions. In other words, road system of Dagestan represents an arbitra... |
app_data_2194 | You are given an array $a$ of length $2^n$. You should process $q$ queries on it. Each query has one of the following $4$ types: $Replace(x, k)$ — change $a_x$ to $k$; $Reverse(k)$ — reverse each subarray $[(i-1) \cdot 2^k+1, i \cdot 2^k]$ for all $i$ ($i \ge 1$); $Swap(k)$ — swap subarrays $[(2i-2) \cdot 2^k+1, (2... |
app_data_2195 | You are given two integers $x$ and $y$. You can perform two types of operations: Pay $a$ dollars and increase or decrease any of these integers by $1$. For example, if $x = 0$ and $y = 7$ there are four possible outcomes after this operation: $x = 0$, $y = 6$; $x = 0$, $y = 8$; $x = -1$, $y = 7$; $x = 1$, $y = 7... |
app_data_2196 | Ivan has got an array of n non-negative integers a_1, a_2, ..., a_{n}. Ivan knows that the array is sorted in the non-decreasing order.
Ivan wrote out integers 2^{a}_1, 2^{a}_2, ..., 2^{a}_{n} on a piece of paper. Now he wonders, what minimum number of integers of form 2^{b} (b ≥ 0) need to be added to the piece of p... |
app_data_2197 | Dexterina and Womandark have been arch-rivals since they’ve known each other. Since both are super-intelligent teenage girls, they’ve always been trying to solve their disputes in a peaceful and nonviolent way. After god knows how many different challenges they’ve given to one another, their score is equal and they’re ... |
app_data_2198 | Daniel has a string s, consisting of lowercase English letters and period signs (characters '.'). Let's define the operation of replacement as the following sequence of steps: find a substring ".." (two consecutive periods) in string s, of all occurrences of the substring let's choose the first one, and replace this su... |
app_data_2199 | You are given a multiset S consisting of positive integers (initially empty). There are two kind of queries: Add a positive integer to S, the newly added integer is not less than any number in it. Find a subset s of the set S such that the value $\operatorname{max}(s) - \operatorname{mean}(s)$ is maximum possible. H... |
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