id stringlengths 19 19 | problem stringlengths 445 3.52k | tests stringlengths 41 746 |
|---|---|---|
cf-7523ff0de46ffb62 |
You are given two integers $x$ and $y$.
Output two integers: the minimum of $x$ and $y$, followed by the maximum of $x$ and $y$.
Input Format:
The first line contains a single integer $t$ ($1 \leq t \leq 100$) — the number of test cases.
The only line of each test case contains two space-separated integers $x$ and ... | [{"input": "10\n1 9\n8 4\n1 4\n3 4\n2 0\n2 4\n6 9\n3 3\n0 0\n9 9", "output": "1 9\n4 8\n1 4\n3 4\n0 2\n2 4\n6 9\n3 3\n0 0\n9 9"}] |
cf-c02443ec23f88353 |
You are given a string $s$ consisting of lowercase English letters.
Rearrange the characters of $s$ to form a new string $r$ that is not equal to $s$, or report that it's impossible.
Input Format:
The first line contains a single integer $t$ ($1 \leq t \leq 1000$) — the number of test cases.
The only line of each t... | [{"input": "8\ncodeforces\naaaaa\nxxxxy\nco\nd\nnutdealer\nmwistht\nhhhhhhhhhh", "output": "YES\nforcodesec\nNO\nYES\nxxyxx\nYES\noc\nNO\nYES\nundertale\nYES\nthtsiwm\nNO"}] |
cf-7ac66687aa5eab54 |
There is a clock labeled with the numbers $1$ through $12$ in clockwise order, as shown below.
In this example, $(a,b,c,d)=(2,9,10,6)$, and the strings intersect.
Alice and Bob have four distinct integers $a$, $b$, $c$, $d$ not more than $12$. Alice ties a red stri... | [{"input": "15\n2 9 10 6\n3 8 9 1\n1 2 3 4\n5 3 4 12\n1 8 2 10\n3 12 11 8\n9 10 12 1\n12 1 10 2\n3 12 6 9\n1 9 8 4\n6 7 9 12\n7 12 9 6\n10 12 11 1\n3 9 6 12\n1 4 3 5", "output": "YES\nNO\nNO\nYES\nYES\nNO\nNO\nNO\nNO\nNO\nNO\nYES\nYES\nYES\nYES"}] |
cf-e76762ee2f865346 |
You are given a binary string$^{\dagger}$. Please find the minimum number of pieces you need to cut it into, so that the resulting pieces can be rearranged into a sorted binary string.
Note that:
* each character must lie in exactly one of the pieces; * the pi... | [{"input": "6\n11010\n00000000\n1\n10\n0001111\n0110", "output": "3\n1\n1\n2\n1\n2"}] |
cf-8a7b37d147fff9f2 |
Timur is in a car traveling on the number line from point $0$ to point $n$. The car starts moving from point $0$ at minute $0$.
There are $k+1$ signs on the line at points $0, a_1, a_2, \dots, a_k$, and Timur knows that the car will arrive there at minutes $0, b_1, b_2, \dots, b_k$, respectively. The sequences $a$ an... | [{"input": "4\n10 1 3\n10\n10\n0\n6\n7\n10 2 4\n4 10\n4 7\n6\n4\n2\n7\n1000000000 1 1\n1000000000\n1000000000\n99999999\n6 1 3\n6\n5\n2\n6\n5", "output": "0 6 7 \n5 4 2 5 \n99999999 \n1 5 4"}] |
cf-d64ea36c259258bd |
Given an integer $r$, find the number of lattice points that have a Euclidean distance from $(0, 0)$ greater than or equal to $r$ but strictly less than $r+1$.
A lattice point is a point with integer coordinates. The Euclidean distance from $(0, 0)$ to the point $(x,y)$ is $\sqrt{x^2 + y^2}$.
Input Format:
The first... | [{"input": "6\n1\n2\n3\n4\n5\n1984", "output": "8\n16\n20\n24\n40\n12504"}] |
cf-71cdab7c3ed2a9e3 |
You are given an array $a$ consisting of $n$ nonnegative integers.
You can swap the elements at positions $i$ and $j$ if $a_i~\mathsf{XOR}~a_j < 4$, where $\mathsf{XOR}$ is the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).
Find the lexicographically smallest array that can be made wit... | [{"input": "4\n4\n1 0 3 2\n5\n2 7 1 5 6\n8\n1 2 1 2 1 2 1 2\n4\n16 4 1 64", "output": "0 1 2 3 \n1 5 2 6 7 \n1 1 1 1 2 2 2 2 \n16 4 1 64"}] |
cf-d5bc0040e507c601 |
Bob has a grid with $3$ rows and $n$ columns, each of which contains either $a_i$ or $-a_i$ for some integer $1 \leq i \leq n$. For example, one possible grid for $n=4$ is shown below:
$$\begin{bmatrix} a_1 & -a_2 & -a_3 & -a_2 \\\ -a_4 & a_4 & -a_1 & -a_3 \\\ a_1 & a_2 & -a_2 & a_4 \end{bmatrix}$$
Alice and Bob pla... | [{"input": "4\n4\n1 -2 -3 -2\n-4 4 -1 -3\n1 2 -2 4\n2\n1 2\n-1 -2\n2 -2\n5\n1 2 3 4 5\n-2 3 -4 -5 -1\n3 -5 1 2 2\n6\n1 3 -6 2 5 2\n1 3 -2 -3 -6 -5\n-2 -1 -3 2 3 1", "output": "YES\nNO\nYES\nNO"}] |
cf-c9dc2fe6951af63c |
A contest contains $n$ problems and the difficulty of the $i$-th problem is expected to be at most $b_i$. There are already $n$ problem proposals and the difficulty of the $i$-th problem is $a_i$. Initially, both $a_1, a_2, \ldots, a_n$ and $b_1, b_2, \ldots, b_n$ are sorted in non-decreasing order.
Some of the probl... | [{"input": "2\n6\n1000 1400 2000 2000 2200 2700\n800 1200 1500 1800 2200 3000\n6\n4 5 6 7 8 9\n1 2 3 4 5 6", "output": "2\n3"}] |
cf-f022f97a83aecd81 |
There are $n$ coins on the table forming a circle, and each coin is either facing up or facing down. Alice and Bob take turns to play the following game, and Alice goes first.
In each operation, the player chooses a facing-up coin, removes the coin, and flips the two coins that are adjacent to it. If (before the oper... | [{"input": "3\n5\nUUDUD\n5\nUDDUD\n2\nUU", "output": "YES\nNO\nNO"}] |
cf-03989708ba80f434 |
You have some cards. An integer between $1$ and $n$ is written on each card: specifically, for each $i$ from $1$ to $n$, you have $a_i$ cards which have the number $i$ written on them.
There is also a shop which contains unlimited cards of each type. You have $k$ coins, so you can buy $k$ new cards in total, and the ... | [{"input": "8\n1 10\n1\n2 4\n8 4\n3 4\n6 1 8\n3 9\n7 6 2\n5 3\n6 6 7 4 6\n9 7\n7 6 1 7 6 2 4 3 3\n10 10\n1 3 1 2 1 9 3 5 7 5\n9 8\n5 8 7 5 1 3 2 9 8", "output": "11\n15\n15\n22\n28\n32\n28\n36"}] |
cf-6b96f12da81e3aa6 |
The two versions are different problems. You may want to read both versions. You can make hacks only if both versions are solved.
You are given two positive integers $n$, $m$.
Calculate the number of ordered pairs $(a, b)$ satisfying the following conditions:
* $1\le a\le n$, $1\le b\le m$; * $a+b$ is a multip... | [{"input": "6\n1 1\n2 3\n3 5\n10 8\n100 1233\n1000000 1145141", "output": "1\n3\n4\n14\n153\n1643498"}] |
cf-27257141f88d7919 |
The two versions are different problems. You may want to read both versions. You can make hacks only if both versions are solved.
You are given two positive integers $n$, $m$.
Calculate the number of ordered pairs $(a, b)$ satisfying the following conditions:
* $1\le a\le n$, $1\le b\le m$; * $b \cdot \gcd(a,b... | [{"input": "6\n1 1\n2 3\n3 5\n10 8\n100 1233\n1000000 1145141", "output": "0\n1\n1\n6\n423\n5933961"}] |
cf-0c54c4db17b4a002 |
Let $\operatorname{lowbit}(x)$ denote the value of the lowest binary bit of $x$, e.g. $\operatorname{lowbit}(12)=4$, $\operatorname{lowbit}(8)=8$.
For an array $a$ of length $n$, if an array $s$ of length $n$ satisfies $s_k=\left(\sum\limits_{i=k-\operatorname{lowbit}(k)+1}^{k}a_i\right)\bmod 998\,244\,353$ for all $... | [{"input": "2\n8 1\n1 2 1 4 1 2 1 8\n6 2\n1 4 3 17 5 16", "output": "1 1 1 1 1 1 1 1\n1 2 3 4 5 6"}] |
cf-d269d3c95353659a |
Little R is a magician who likes non-decreasing arrays. She has an array of length $n$, initially as $a_1, \ldots, a_n$, in which each element is an integer between $[1, m]$. She wants it to be non-decreasing, i.e., $a_1 \leq a_2 \leq \ldots \leq a_n$.
To do this, she can perform several magic tricks. Little R has a ... | [{"input": "3\n5 8\n1 6 3 7 1\n2 3 5 8 7 1 5 6\n3 3\n1 3 2\n2 1 3\n10 10\n2 8 5 4 8 4 1 5 10 10\n6 7 2 6 3 4 1 1 3 5", "output": "3\n-1\n3"}] |
cf-2846ab5c0f8efc0a |
Three friends gathered to play a few games of chess together.
In every game, two of them play against each other. The winner gets $2$ points while the loser gets $0$, and in case of a draw, both players get $1$ point each. Note that the same pair of players could have played any non-negative number of times (possibly... | [{"input": "7\n0 0 0\n0 1 1\n1 1 1\n1 1 2\n3 3 3\n3 4 5\n1 1 10", "output": "0\n1\n-1\n2\n-1\n6\n2"}] |
cf-7ae26c5706fd4fd1 |
Today, Cat and Fox found an array $a$ consisting of $n$ non-negative integers.
Define the loneliness of $a$ as the smallest positive integer $k$ ($1 \le k \le n$) such that for any two positive integers $i$ and $j$ ($1 \leq i, j \leq n - k +1$), the following holds: $$a_i | a_{i+1} | \ldots | a_{i+k-1} = a_j | a_{j+1... | [{"input": "7\n1\n0\n3\n2 2 2\n3\n1 0 2\n5\n3 0 1 4 2\n5\n2 0 4 0 2\n7\n0 0 0 0 1 2 4\n8\n0 1 3 2 2 1 0 3", "output": "1\n1\n3\n4\n4\n7\n3"}] |
cf-3a92d2c8dbf1ac59 |
Fox loves permutations! She came up with the following problem and asked Cat to solve it:
You are given an even positive integer $n$ and a permutation$^\dagger$ $p$ of length $n$.
The score of another permutation $q$ of length $n$ is the number of local maximums in the array $a$ of length $n$, where $a_i = p_i + q_i... | [{"input": "4\n4\n1 2 3 4\n4\n4 3 1 2\n6\n6 5 1 4 2 3\n8\n1 2 4 5 7 6 8 3", "output": "2 4 1 3\n3 1 4 2\n2 5 1 4 3 6\n5 4 8 2 7 1 6 3"}] |
cf-d894a01fb8ac77eb |
This is an interactive problem.
Fox gave Cat two positive integers $n$ and $k$. She has a hidden array $a_1, \ldots , a_n$ of length $n$, such that $1 \leq a_i \leq n$ for every $i$. Now they are going to play the following game:
For any two integers $l, r$ such that $1 \leq l \leq r \leq n$, define $f(l, r) = (r - ... | [{"input": "3\n1 1\n\n1\n2 2\n\n1\n\n3\n\n1\n6 3\n\n7\n\n2\n\n3\n\n6\n\n1", "output": "! 1\n\n\n? 1 1\n\n? 2 1\n\n! -1\n\n\n? 1 9\n\n? 1 6\n\n? 3 6\n\n? 4 6\n\n! 6"}] |
cf-6d4279adcb1fad9f |
Fox has found an array $p_1, p_2, \ldots, p_n$, that is a permutation of length $n^\dagger$ of the numbers $1, 2, \ldots, n$. She wants to sort the elements in increasing order. Cat wants to help her — he is able to swap any two numbers $x$ and $y$ in the array, but only if $l \leq x + y \leq r$ (note that the constra... | [{"input": "7\n2\n2 1\n3\n3 1 2\n4\n3 2 1 4\n5\n5 3 1 2 4\n5\n1 2 3 4 5\n6\n3 2 1 5 4 6\n6\n1 3 2 4 5 6", "output": "6\n11\n23\n29\n55\n46\n58"}] |
cf-d0e6b6fcda95bed7 |
For $k$ positive integers $x_1, x_2, \ldots, x_k$, the value $\gcd(x_1, x_2, \ldots, x_k)$ is the greatest common divisor of the integers $x_1, x_2, \ldots, x_k$ — the largest integer $z$ such that all the integers $x_1, x_2, \ldots, x_k$ are divisible by $z$.
You are given three arrays $a_1, a_2, \ldots, a_n$, $b_1,... | [{"input": "3 4\n1 2 3\n4 5 6\n1 1 1\n0 1 2 3", "output": "2 3 3 3"}, {"input": "5 5\n3 4 6 8 4\n8 3 4 9 3\n10 20 30 40 50\n5 55 13 1000 113", "output": "2 7 3 7 7"}, {"input": "1 1\n3\n4\n5\n0", "output": "7"}] |
cf-aa9efedb39810f70 |
Little Rosie has a phone with a desktop (or launcher, as it is also called). The desktop can consist of several screens. Each screen is represented as a grid of size $5 \times 3$, i.e., five rows and three columns.
There are $x$ applications with an icon size of $1 \times 1$ cells; such an icon occupies only one cell... | [{"input": "11\n1 1\n7 2\n12 4\n0 3\n1 0\n8 1\n0 0\n2 0\n15 0\n8 2\n0 9", "output": "1\n1\n2\n2\n1\n1\n0\n1\n1\n2\n5"}] |
cf-2900b66654b363c3 |
Polycarp has a string $s$, which consists of lowercase Latin letters. He encodes this string using the following algorithm:
* first, he constructs a new auxiliary string $r$, which consists of all distinct letters of the string $s$, written in alphabetical order; * then the encoding happens as follows: each char... | [{"input": "5\n10\nserofedsoc\n3\nttf\n9\ntlrhgmaoi\n1\nw\n15\nhnndledmnhlttin", "output": "codeforces\nfft\nalgorithm\nw\nmeetinthemiddle"}] |
cf-d3d645b73b59c21d |
Polycarp was given an array $a$ of $n$ integers. He really likes triples of numbers, so for each $j$ ($1 \le j \le n - 2$) he wrote down a triple of elements $[a_j, a_{j + 1}, a_{j + 2}]$.
Polycarp considers a pair of triples $b$ and $c$ beautiful if they differ in exactly one position, that is, one of the following ... | [{"input": "8\n5\n3 2 2 2 3\n5\n1 2 1 2 1\n8\n1 2 3 2 2 3 4 2\n4\n2 1 1 1\n8\n2 1 1 2 1 1 1 1\n7\n2 1 1 1 1 1 1\n6\n2 1 1 1 1 1\n5\n2 1 1 1 1", "output": "2\n0\n3\n1\n8\n4\n3\n2"}] |
cf-5500d3fcb5e5722a |
Let's imagine the surface of Mars as an infinite coordinate plane. Initially, the rover Perseverance-2 and the helicopter Ingenuity-2 are located at the point with coordinates $(0, 0)$. A set of instructions $s$ consisting of $n$ instructions of the following types was specially developed for them:
* N: move one me... | [{"input": "10\n6\nNENSNE\n3\nWWW\n6\nNESSWS\n2\nSN\n2\nWE\n4\nSSNN\n4\nWESN\n2\nSS\n4\nEWNN\n4\nWEWE", "output": "RRHRRH\nNO\nHRRHRH\nNO\nNO\nRHRH\nRRHH\nRH\nRRRH\nRRHH"}] |
cf-1aa2747d93916bb1 |
Being a physicist, Charlie likes to plan his life in simple and precise terms.
For the next $m$ months, starting with no money, Charlie will work hard and earn $x$ pounds per month. For the $i$-th month $(1 \le i \le m)$, there'll be a single opportunity of paying cost $c_i$ pounds to obtain happiness $h_i$.
Borrowi... | [{"input": "7\n1 10\n1 5\n2 80\n0 10\n200 100\n3 100\n70 100\n100 200\n150 150\n5 8\n3 1\n5 3\n3 4\n1 5\n5 3\n2 5\n1 5\n2 1\n5 3\n2 5\n2 4\n4 1\n5 1\n3 4\n5 2\n2 1\n1 2\n3 5\n3 2\n3 2", "output": "0\n10\n200\n15\n1\n9\n9"}] |
cf-faae40af5e76d60b |
Alice and Bob were playing a game again. They have a grid of size $a \times b$ ($1 \le a, b \le 10^9$), on which there are $n$ chips, with at most one chip in each cell. The cell at the intersection of the $x$-th row and the $y$-th column has coordinates $(x, y)$.
Alice made the first move, and the players took turns... | [{"input": "6\n4 4 3 2\n4 1\n3 3\n2 4\nD 2\nR 1\n4 4 3 3\n4 1\n3 2\n2 3\nD 1\nL 1\nU 2\n3 5 3 2\n1 3\n2 2\n3 3\nR 2\nR 2\n6 4 4 2\n1 4\n2 3\n5 3\n1 1\nR 1\nU 1\n9 3 2 1\n6 1\n3 3\nD 8\n10 10 2 5\n7 5\n9 1\nR 1\nL 2\nD 1\nU 4\nD 1", "output": "2 1\n2 0\n0 3\n1 1\n2 0\n0 1"}] |
cf-5bdc7b104350f60f |
You can never buy enough happiness, so here we go again! In this version, you can only buy $h_i = 1$ unit of happiness each month, but the number of months is hugely increased. We are in the realm of quantum happiness and time dilation.
Being a physicist, Charlie likes to plan his life in simple and precise terms.
F... | [{"input": "6\n3 3\n2 2 2\n6 5\n2 2 8 2 6 8\n6 4\n4 10 3 8 6 10\n2 1\n1 1\n4 1\n4 1 3 1\n4 2\n1 3 4 3", "output": "2\n4\n3\n1\n2\n1"}] |
cf-4dcb5afc4dd0896d |
Mocha likes arrays, so before her departure, Bazoka gave her an array $a$ consisting of $n$ positive integers as a gift.
Now Mocha wants to know whether array $a$ could become sorted in non- decreasing order after performing the following operation some (possibly, zero) times:
* Split the array into two parts — a ... | [{"input": "3\n6\n1 1 4 5 1 4\n5\n7 9 2 2 3\n3\n1 2 3", "output": "No\nYes\nYes"}] |
cf-eb141c5086038eac |
Mocha likes arrays, so before her departure, 378QAQ gave her an array $a$ consisting of $n$ positive integers as a gift.
Mocha thinks that $a$ is beautiful if there exist two numbers $i$ and $j$ ($1\leq i,j\leq n$, $i\neq j$) such that for all $k$ ($1 \leq k \leq n$), $a_k$ is divisible$^\dagger$ by either $a_i$ or $... | [{"input": "4\n3\n7 3 8\n5\n7 1 9 3 5\n5\n4 12 2 6 3\n5\n7 49 9 3 1000000000", "output": "No\nYes\nYes\nNo"}] |
cf-56bd4e1044a4fc5a |
Mocha likes arrays, so before her departure, Chamo gave her an array $a$ consisting of $n$ positive integers as a gift.
Mocha doesn't like arrays containing different numbers, so Mocha decides to use magic to change the array. Mocha can perform the following three-step operation some (possibly, zero) times:
1. Cho... | [{"input": "2\n2\n1 2\n5\n1 2 3 4 5", "output": "1\n4"}] |
cf-241362537a821837 |
378QAQ has a tree with $n$ vertices. Initially, all vertices are white.
There are two chess pieces called $P_A$ and $P_B$ on the tree. $P_A$ and $P_B$ are initially located on vertices $a$ and $b$ respectively. In one step, 378QAQ will do the following in order:
1. Move $P_A$ to a neighboring vertex. If the target... | [{"input": "3\n2\n1 2\n1 2\n5\n1 2\n1 2\n1 3\n1 4\n1 5\n8\n5 4\n7 1\n1 5\n1 8\n8 3\n7 2\n8 6\n3 4", "output": "2\n8\n13"}] |
cf-2504211e2da6bf85 |
You are given a tree of $n$ vertices numbered from $1$ to $n$. Initially, all vertices are colored white or black.
You are asked to perform $q$ queries:
* "u" — toggle the color of vertex $u$ (if it was white, change it to black and vice versa).
After each query, you should answer whether all the black vertices ... | [{"input": "2\n2 1\n1 0\n1 2\n1\n5 4\n1 0 0 0 0\n1 2\n1 3\n1 5\n3 4\n4\n3\n2\n5", "output": "No\nNo\nYes\nYes\nNo"}, {"input": "4\n5 3\n1 1 1 1 1\n3 5\n2 5\n3 4\n1 5\n1\n1\n1\n4 4\n0 0 0 0\n1 2\n2 3\n1 4\n1\n2\n3\n2\n1 1\n1\n1\n1 1\n0\n1", "output": "Yes\nNo\nYes\nYes\nYes\nYes\nNo\nNo\nYes"}] |
cf-fe72bd8119780ec8 |
Define the binary encoding of a finite set of natural numbers $T \subseteq \\{0,1,2,\ldots\\}$ as $f(T) = \sum\limits_{i \in T} 2^i$. For example, $f(\\{0,2\\}) = 2^0 + 2^2 = 5$ and $f(\\{\\}) = 0$. Notice that $f$ is a bijection from all such sets to all non-negative integers. As such, $f^{-1}$ is also defined.
You ... | [{"input": "3\n15 15 15 15 15 15 12", "output": "4\n3\n5\n6\n7"}, {"input": "5\n63 63 63 63 6 63 63 63 63 63 63 5 63 63 63 63 63 63 8 63 63 63 63 2 63 63 63 63 63 63 63", "output": "1\n19"}] |
cf-1ca08b48bd892578 |
One day, Zimpha casually came up with a problem. As a member of "Zimpha fan club", you decided to solve that problem. You are given two strings $s$ and $t$ of length $n$ and $m$, respectively. Both strings only consist of lowercase English letters, - and *.
You need to replace all occurrences of * and -, observi... | [{"input": "10 10\njustmonika\nj-stsayori", "output": "No"}, {"input": "7 8\nttk-wxx\n*tt-l-xx", "output": "Yes"}, {"input": "13 11\nasoulwangziji\n-soulg*z-y-", "output": "No"}, {"input": "7 3\nabc*cba\na*c", "output": "No"}, {"input": "20 18\nbulijiojio-dibuliduo\n*li*ji-*ox*i*-du*-", "output": "Yes"}] |
cf-7f5b6e4b96fcd311 |
378QAQ has a string $s$ of length $n$. Define the core of a string as the substring$^\dagger$ with maximum lexicographic$^\ddagger$ order.
For example, the core of "$\mathtt{bazoka}$" is "$\mathtt{zoka}$", and the core of "$\mathtt{aaa}$" is "$\mathtt{aaa}$".
378QAQ wants to rearrange the string $s$ so that the core... | [{"input": "6\n3\nqaq\n4\ncccc\n6\nbazoka\n6\nzazzzz\n7\nababbbb\n7\nccbabcc", "output": "qaq\ncccc\nz\nzzz\nbbababb\ncbcacbc"}] |
cf-79fa4a4184718719 |
This is the way it always was.
This is the way it always will be.
All will be forgotten again soon...
Jellyfish is playing a one-player card game called "Slay the Spire". There are $n$ cards in total numbered from $1$ to $n$. The $i$-th card has power $c_i$.
There is a binary string $s$ of length $n$. If $s_i = \t... | [{"input": "4\n5\n0 1 1 1 2\n00100\n3\n2 3 3\n000\n10\n0 0 0 0 0 0 0 1 1 1\n1111011111\n20\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 2 3 3 4\n00000000001000101010", "output": "500000004\n0\n0\n675898154"}] |
cf-11cfb743bc719098 |
Monocarp is working on his new site, and the current challenge is to make the users pick strong passwords.
Monocarp decided that strong passwords should satisfy the following conditions:
* password should consist only of lowercase Latin letters and digits; * there should be no digit that comes after a letter (s... | [{"input": "5\n4\n12ac\n5\n123wa\n9\nallllmost\n5\nac123\n6\n011679", "output": "YES\nNO\nYES\nNO\nYES"}] |
cf-80c6887ef976a83f |
You are given two integer arrays: array $a$ of length $n$ and array $b$ of length $n+1$.
You can perform the following operations any number of times in any order:
* choose any element of the array $a$ and increase it by $1$; * choose any element of the array $a$ and decrease it by $1$; * choose any element ... | [{"input": "3\n1\n2\n1 3\n2\n3 3\n3 3 3\n4\n4 2 1 2\n2 1 5 2 3", "output": "3\n1\n8"}] |
cf-0ca0714ae890d497 |
Monocarp is opening his own IT company. He wants to hire $n$ programmers and $m$ testers.
There are $n+m+1$ candidates, numbered from $1$ to $n+m+1$ in chronological order of their arriving time. The $i$-th candidate has programming skill $a_i$ and testing skill $b_i$ (a person's programming skill is different from t... | [{"input": "4\n1 0\n2 1\n1 2\n0 2\n4 5 5\n5 4 1\n1 2\n2 1 5 4\n5 2 3 1\n3 1\n4 3 3 4 1\n5 5 4 5 2", "output": "1 2 \n5 6 9 \n8 11 11 12 \n13 13 13 12 15"}] |
cf-ee1166e86da8a5bc |
A regular bracket sequence is a bracket sequence that can be transformed into a correct arithmetic expression by inserting characters '1' and '+' between the original characters of the sequence. For example:
* bracket sequences "()()" and "(())" are regular (the resulting expressions are: "(1)+(1)" and "((1+1)+1)")... | [{"input": "4\n(())\n()\n()()()\n(()())(())", "output": "1\n0\n3\n13"}] |
cf-01dda202b0218b62 |
Initially, we had one array, which was a permutation of size $n$ (an array of size $n$ where each integer from $1$ to $n$ appears exactly once).
We performed $q$ operations. During the $i$-th operation, we did the following:
* choose any array we have with at least $2$ elements; * split it into two non-empty ar... | [{"input": "6 3\n6 4 4\n5 5 2", "output": "30"}, {"input": "10 1\n10\n9", "output": "1814400"}, {"input": "4 1\n2\n4", "output": "8"}] |
cf-94ba82d61a989906 |
You are given a rooted tree, consisting of $n$ vertices, numbered from $1$ to $n$. Vertex $1$ is the root. Additionally, the root only has one child.
You are asked to add exactly $k$ edges to the tree (possibly, multiple edges and/or edges already existing in the tree).
Recall that a bridge is such an edge that, aft... | [{"input": "4\n2\n1 2\n12\n4 10\n5 12\n12 11\n3 6\n9 6\n1 6\n12 7\n11 6\n2 11\n10 9\n10 8\n8\n1 2\n2 3\n2 4\n3 5\n3 6\n4 7\n4 8\n5\n1 2\n2 3\n3 4\n4 5", "output": "0 \n7 3 1 0 0 0 0 0 0 0 0 \n4 1 0 0 0 0 0 \n0 0 0 0"}] |
cf-686973a2ba447968 |
The little boy Nikita was given some cubes as a present. He decided to build a tower out of them.
Initially, the tower doesn't have any cubes. In one move, Nikita either puts exactly $1$ cube on top of the tower or removes exactly $1$ cube from the top of the tower. Is it possible that after $n$ moves, the resulting ... | [{"input": "3\n3 3\n2 4\n5 3", "output": "Yes\nNo\nYes"}] |
cf-1087f5de081a27de |
You are given a positive integer $x$. Find any array of integers $a_0, a_1, \ldots, a_{n-1}$ for which the following holds:
* $1 \le n \le 32$, * $a_i$ is $1$, $0$, or $-1$ for all $0 \le i \le n - 1$, * $x = \displaystyle{\sum_{i=0}^{n - 1}{a_i \cdot 2^i}}$, * There does not exist an index $0 \le i \le n ... | [{"input": "7\n1\n14\n24\n15\n27\n11\n19", "output": "1\n1\n5\n0 -1 0 0 1\n6\n0 0 0 -1 0 1\n5\n-1 0 0 0 1\n6\n-1 0 -1 0 0 1\n5\n-1 0 -1 0 1\n5\n-1 0 1 0 1"}] |
cf-bf629747f8647fbd |
Nikita is a student passionate about number theory and algorithms. He faces an interesting problem related to an array of numbers.
Suppose Nikita has an array of integers $a$ of length $n$. He will call a subsequence$^\dagger$ of the array special if its [least common multiple (LCM)](https://en.wikipedia.org/wiki/Lea... | [{"input": "6\n5\n1 2 4 8 16\n6\n3 2 10 20 60 1\n7\n2 3 4 6 12 100003 1200036\n9\n2 42 7 3 6 7 7 1 6\n8\n4 99 57 179 10203 2 11 40812\n1\n1", "output": "0\n4\n4\n5\n8\n0"}] |
cf-200064be45810647 |
You are given a binary (consisting only of 0s and 1s) $n \times m$ matrix. You are also given a XORificator, using which you can invert all the values in a chosen row (i.e. replace 0 with 1 and 1 with 0).
A column in the matrix is considered special if it contains exactly one 1. Your task is to find the maximum numbe... | [{"input": "5\n3 4\n1010\n0110\n0100\n1 1\n1\n1 1\n0\n2 5\n00101\n10110\n3 3\n101\n111\n000", "output": "3\n010\n1\n0\n1\n1\n3\n00\n2\n010"}] |
cf-978389c1f63e8c56 |
This is an interactive problem.
You are given an integer $n$.
The jury has hidden from you a directed graph with $n$ vertices (numbered from $1$ to $n$) and some number of edges. You additionally know that:
* The graph only contains edges of the form $i \leftarrow j$, where $1 \le i < j \le n$. * For any three... | [{"input": "2\n4\n\nYES\n\nYES\n\nYES\n\nNO\n\nNO\n\nNO\n\n5", "output": "? 1 2\n\n? 2 3\n\n? 1 3\n\n? 1 4\n\n? 2 4\n\n? 3 4\n\n! 0 0 0 1\n\n! 1 1 0 1 0"}] |
cf-53bbfadfc69af54a |
Alice has $n$ books. The $1$-st book contains $a_1$ pages, the $2$-nd book contains $a_2$ pages, $\ldots$, the $n$-th book contains $a_n$ pages. Alice does the following:
* She divides all the books into two non-empty piles. Thus, each book ends up in exactly one of the two piles. * Alice reads one book with the ... | [{"input": "5\n2\n1 1\n4\n2 3 3 1\n5\n2 2 3 2 2\n2\n10 3\n3\n1 2 3", "output": "2\n4\n5\n13\n5"}] |
cf-b15b42ca21d6498c |
Bob decided to open a bakery. On the opening day, he baked $n$ buns that he can sell. The usual price of a bun is $a$ coins, but to attract customers, Bob organized the following promotion:
* Bob chooses some integer $k$ ($0 \le k \le \min(n, b)$). * Bob sells the first $k$ buns at a modified price. In this case,... | [{"input": "7\n4 4 5\n5 5 9\n10 10 5\n5 5 11\n1000000000 1000000000 1000000000\n1000000000 1000000000 1\n1000 1 1000", "output": "17\n35\n100\n45\n1000000000000000000\n1000000000000000000\n500500"}] |
cf-09d4b3eee7968b29 |
Let's call the Manhattan value of a permutation$^{\dagger}$ $p$ the value of the expression $|p_1 - 1| + |p_2 - 2| + \ldots + |p_n - n|$.
For example, for the permutation $[1, 2, 3]$, the Manhattan value is $|1 - 1| + |2 - 2| + |3 - 3| = 0$, and for the permutation $[3, 1, 2]$, the Manhattan value is $|3 - 1| + |1 - ... | [{"input": "8\n3 4\n4 5\n7 0\n1 1000000000000\n8 14\n112 777\n5 12\n5 2", "output": "Yes\n3 1 2\nNo\nYes\n1 2 3 4 5 6 7\nNo\nYes\n8 2 3 4 5 6 1 7\nNo\nYes\n5 4 3 1 2\nYes\n2 1 3 4 5"}] |
cf-97100ad837e06861 |
Elections are taking place in Berland. There are $n$ candidates participating in the elections, numbered from $1$ to $n$. The $i$-th candidate has $a_i$ fans who will vote for him. Additionally, there are $c$ people who are undecided about their favorite candidate, let's call them undecided. Undecided people will vote... | [{"input": "5\n3 1\n2 0 3\n2 3\n0 10\n5 3\n5 4 3 2 1\n4 5\n3 10 7 1\n6 0\n2 2 2 3 3 3", "output": "0 1 2\n1 0\n0 1 2 3 4\n1 0 2 3\n1 1 2 0 4 5"}] |
cf-cc1dd97084442fd7 |
Sasha has two binary strings $s$ and $t$ of the same length $n$, consisting of the characters 0 and 1.
There is also a computing machine that can perform two types of operations on binary strings $a$ and $b$ of the same length $k$:
1. If $a_{i} = a_{i + 2} =$ 0, then you can assign $b_{i + 1} :=$ 1 ($1 \le i \le k... | [{"input": "3\n4\n1111\n0000\n2\n1 2\n2 4\n4\n1010\n1101\n2\n1 3\n1 4\n6\n010101\n011010\n5\n2 3\n1 6\n2 5\n4 4\n3 6", "output": "2\n3\n2\n3\n1\n4\n3\n1\n2"}] |
cf-61505319ac981d75 |
Given an array $a$ of length $n$. Let's construct a square matrix $b$ of size $n \times n$, in which the $i$-th row contains the array $a$ cyclically shifted to the right by $(i - 1)$. For example, for the array $a = [3, 4, 5]$, the obtained matrix is
$$b = \begin{bmatrix} 3 & 4 & 5 \\\ 5 & 3 & 4 \\\ 4 & 5 & 3 \end{b... | [{"input": "6\n3 3\n3 4 5\n3 3\n3 4 9\n3 2\n3 4 9\n2 2\n2 8\n5 3\n8 27 5 4 3\n4 10\n2 2 2 2", "output": "3\n2\n3\n1\n4\n1"}] |
cf-2e5b5d04f1d95a7f |
Alice and Bob came up with a rather strange game. They have an array of integers $a_1, a_2,\ldots, a_n$. Alice chooses a certain integer $k$ and tells it to Bob, then the following happens:
* Bob chooses two integers $i$ and $j$ ($1 \le i < j \le n$), and then finds the maximum among the integers $a_i, a_{i + 1},\l... | [{"input": "6\n4\n2 4 1 7\n5\n1 2 3 4 5\n2\n1 1\n3\n37 8 16\n5\n10 10 10 10 9\n10\n3 12 9 5 2 3 2 9 8 2", "output": "3\n1\n0\n15\n9\n2"}] |
cf-336a44a84724d94f |
You are given two distinct non-negative integers $x$ and $y$. Consider two infinite sequences $a_1, a_2, a_3, \ldots$ and $b_1, b_2, b_3, \ldots$, where
* $a_n = n \oplus x$; * $b_n = n \oplus y$.
Here, $x \oplus y$ denotes the [bitwise XOR](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) operation of int... | [{"input": "4\n0 1\n12 4\n57 37\n316560849 14570961", "output": "1\n8\n4\n33554432"}] |
cf-1bc44fec8f5fbeb5 |
You have been offered to play a game. In this game, there are $n$ possible outcomes, and for each of them, you must bet a certain integer amount of coins. In the event that the $i$-th outcome turns out to be winning, you will receive back the amount of coins equal to your bet on that outcome, multiplied by $k_i$. Note... | [{"input": "6\n3\n3 2 7\n2\n3 3\n5\n5 5 5 5 5\n6\n7 9 3 17 9 13\n3\n6 3 2\n5\n9 4 6 8 3", "output": "27 41 12 \n1 1 \n-1\n1989 1547 4641 819 1547 1071 \n-1\n8 18 12 9 24"}] |
cf-4857ca2b46ac76e5 |
You are given a binary string $s$ of length $n$, consisting of zeros and ones. You can perform the following operation exactly once:
1. Choose an integer $p$ ($1 \le p \le n$). 2. Reverse the substring $s_1 s_2 \ldots s_p$. After this step, the string $s_1 s_2 \ldots s_n$ will become $s_p s_{p-1} \ldots s_1 s_{p... | [{"input": "7\n8 4\n11100001\n4 2\n1110\n12 3\n111000100011\n5 5\n00000\n6 1\n101001\n8 4\n01110001\n12 2\n110001100110", "output": "3\n-1\n7\n5\n4\n-1\n3"}] |
cf-83c9c92eee2f2fad |
The Manhattan distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is defined as: $$|x_1 - x_2| + |y_1 - y_2|.$$
We call a Manhattan triangle three points on the plane, the Manhattan distances between each pair of which are equal.
You are given a set of pairwise distinct points and an even integer $d$. Your tas... | [{"input": "6\n6 4\n3 1\n0 0\n0 -2\n5 -3\n3 -5\n2 -2\n5 4\n0 0\n0 -2\n5 -3\n3 -5\n2 -2\n6 6\n3 1\n0 0\n0 -2\n5 -3\n3 -5\n2 -2\n4 4\n3 0\n0 3\n-3 0\n0 -3\n10 8\n2 1\n-5 -1\n-4 -1\n-5 -3\n0 1\n-2 5\n-4 4\n-4 2\n0 0\n-4 1\n4 400000\n100000 100000\n-100000 100000\n100000 -100000\n-100000 -100000", "output": "2 6 1\n4 3 5\n... |
cf-546e2bfd848ad791 |
This is an interactive problem.
Kostyanych has chosen a complete undirected graph$^{\dagger}$ with $n$ vertices, and then removed exactly $(n - 2)$ edges from it. You can ask queries of the following type:
* "? $d$" — Kostyanych tells you the number of vertex $v$ with a degree at least $d$. Among all possible such... | [{"input": "3\n4\n\n0 0\n\n1 4\n\n2 3\n\n4\n\n1 0\n\n4 2\n\n2\n\n1 0", "output": "? 3\n\n? 2\n\n? 1\n\n! 4 3 1 2\n\n? 3\n\n? 0\n\n! 4 1 2 3\n\n? 0\n\n! 2 1"}] |
cf-c5781db3fd9b0c93 |
Vlad is planning to hold $m$ rounds next month. Each round should contain one problem of difficulty levels 'A', 'B', 'C', 'D', 'E', 'F', and 'G'.
Vlad already has a bank of $n$ problems, where the $i$-th problem has a difficulty level of $a_i$. There may not be enough of these problems, so he may have to come up with... | [{"input": "3\n10 1\nBGECDCBDED\n10 2\nBGECDCBDED\n9 1\nBBCDEFFGG", "output": "2\n5\n1"}] |
cf-6b1da5c26358bb68 |
Dmitry has $n$ cubes, numbered from left to right from $1$ to $n$. The cube with index $f$ is his favorite.
Dmitry threw all the cubes on the table, and the $i$-th cube showed the value $a_i$ ($1 \le a_i \le 100$). After that, he arranged the cubes in non-increasing order of their values, from largest to smallest. If... | [{"input": "12\n5 2 2\n4 3 3 2 3\n5 5 3\n4 2 1 3 5\n5 5 2\n5 2 4 1 3\n5 5 5\n1 2 5 4 3\n5 5 4\n3 1 2 4 5\n5 5 5\n4 3 2 1 5\n6 5 3\n1 2 3 1 2 3\n10 1 1\n1 1 1 1 1 1 1 1 1 1\n1 1 1\n42\n5 2 3\n2 2 1 1 2\n2 1 1\n2 1\n5 3 1\n3 3 2 3 2", "output": "MAYBE\nYES\nNO\nYES\nYES\nYES\nMAYBE\nMAYBE\nYES\nYES\nYES\nNO"}] |
cf-bc5062c8c3e0ab6e |
Sofia had an array of $n$ integers $a_1, a_2, \ldots, a_n$. One day she got bored with it, so she decided to sequentially apply $m$ modification operations to it.
Each modification operation is described by a pair of numbers $\langle c_j, d_j \rangle$ and means that the element of the array with index $c_j$ should be... | [{"input": "7\n3\n1 2 1\n1 3 2\n4\n1 3 1 2\n4\n1 2 3 5\n2 1 3 5\n2\n2 3\n5\n7 6 1 10 10\n3 6 1 11 11\n3\n4 3 11\n4\n3 1 7 8\n2 2 7 10\n5\n10 3 2 2 1\n5\n5 7 1 7 9\n4 10 1 2 9\n8\n1 1 9 8 7 2 10 4\n4\n1000000000 203 203 203\n203 1000000000 203 1000000000\n2\n203 1000000000\n1\n1\n1\n5\n1 3 4 5 1", "output": "YES\nNO\nNO... |
cf-d0c531ba295dc35b |
GCD (Greatest Common Divisor) of two integers $x$ and $y$ is the maximum integer $z$ by which both $x$ and $y$ are divisible. For example, $GCD(36, 48) = 12$, $GCD(5, 10) = 5$, and $GCD(7,11) = 1$.
Kristina has an array $a$ consisting of exactly $n$ positive integers. She wants to count the GCD of each neighbouring p... | [{"input": "12\n6\n20 6 12 3 48 36\n4\n12 6 3 4\n3\n10 12 3\n5\n32 16 8 4 2\n5\n100 50 2 10 20\n4\n2 4 8 1\n10\n7 4 6 2 4 5 1 4 2 8\n7\n5 9 6 8 5 9 2\n6\n11 14 8 12 9 3\n9\n5 7 3 10 6 3 12 6 3\n3\n4 2 4\n8\n1 6 11 12 6 12 3 6", "output": "YES\nNO\nYES\nNO\nYES\nYES\nNO\nYES\nYES\nYES\nYES\nYES"}] |
cf-7ab2686a86e7e11b |
You have been given a matrix $a$ of size $n$ by $m$, containing a permutation of integers from $1$ to $n \cdot m$.
A permutation of $n$ integers is an array containing all numbers from $1$ to $n$ exactly once. For example, the arrays $[1]$, $[2, 1, 3]$, $[5, 4, 3, 2, 1]$ are permutations, while the arrays $[1, 1]$, $... | [{"input": "7\n1 1\n1\n1\n2 2\n1 2\n3 4\n4 3\n2 1\n2 2\n1 2\n3 4\n4 3\n1 2\n3 4\n1 5 9 6\n12 10 4 8\n7 11 3 2\n1 5 9 6\n12 10 4 8\n7 11 3 2\n3 3\n1 5 9\n6 4 2\n3 8 7\n9 5 1\n2 4 6\n7 8 3\n2 3\n1 2 6\n5 4 3\n6 1 2\n3 4 5\n1 5\n5 1 2 3 4\n4 2 5 1 3", "output": "YES\nYES\nNO\nYES\nYES\nNO\nYES"}] |
cf-46b5d0f266fb5973 |
This is an easy version of the problem; it differs from the hard version only by the question. The easy version only needs you to print whether some values are non-zero or not. The hard version needs you to print the exact values.
Alice and Bob are dividing the field. The field is a rectangle of size $n \times m$ ($2... | [{"input": "5\n2 2 3\n1 1\n1 2\n2 2\n5 5 4\n1 2\n2 2\n3 4\n4 3\n2 5 9\n1 2\n1 5\n1 1\n2 2\n2 4\n2 5\n1 4\n2 3\n1 3\n6 4 4\n6 2\n1 3\n1 4\n1 2\n3 4 5\n2 1\n3 2\n1 4\n1 3\n2 4", "output": "1\n1 0 1 \n11\n0 1 0 1 \n1\n0 0 1 1 0 0 0 0 0 \n6\n1 0 0 0 \n1\n1 1 0 0 0"}] |
cf-575a7dd3dacefcac |
This is a hard version of the problem; it differs from the easy version only by the question. The easy version only needs you to print whether some values are non-zero or not. The hard version needs you to print the exact values.
Alice and Bob are dividing the field. The field is a rectangle of size $n \times m$ ($2 ... | [{"input": "5\n2 2 3\n1 1\n1 2\n2 2\n5 5 4\n1 2\n2 2\n3 4\n4 3\n2 5 9\n1 2\n1 5\n1 1\n2 2\n2 4\n2 5\n1 4\n2 3\n1 3\n6 4 4\n6 2\n1 3\n1 4\n1 2\n3 4 5\n2 1\n3 2\n1 4\n1 3\n2 4", "output": "1\n1 0 1 \n11\n0 1 0 4 \n1\n0 0 1 1 0 0 0 0 0 \n6\n15 0 0 0 \n1\n2 3 0 0 0"}] |
cf-62950c42317da0ea |
Yasya was walking in the forest and accidentally found a tree with $n$ vertices. A tree is a connected undirected graph with no cycles.
Next to the tree, the girl found an ancient manuscript with $m$ queries written on it. The queries can be of two types.
The first type of query is described by the integer $y$. The ... | [{"input": "2\n3 7\n1 2 1\n3 1 8\n^ 5\n? 2 9\n^ 1\n? 1 10\n^ 6\n? 3 1\n? 2 9\n5 6\n1 2 777\n3 2 2812\n4 1 16\n5 3 1000000000\n^ 4\n? 3 123\n? 5 1000000000\n^ 1000000000\n? 1 908070\n? 2 1", "output": "13 15 11 10 \n1000000127 2812 999756331 999999756"}, {"input": "3\n8 4\n8 6 3\n6 3 4\n2 5 4\n7 6 2\n7 1 10\n4 1 4\n5 1 ... |
cf-4035efd555f39da9 |
Turtle and Piggy are playing a number game.
First, Turtle will choose an integer $x$, such that $l \le x \le r$, where $l, r$ are given. It's also guaranteed that $2l \le r$.
Then, Piggy will keep doing the following operation until $x$ becomes $1$:
* Choose an integer $p$ such that $p \ge 2$ and $p \mid x$ (i.e.... | [{"input": "5\n2 4\n3 6\n2 15\n6 22\n114514 1919810", "output": "2\n2\n3\n4\n20"}] |
cf-71583b418f5b422f |
There is a sequence $a_0, a_1, a_2, \ldots$ of infinite length. Initially $a_i = i$ for every non-negative integer $i$.
After every second, each element of the sequence will simultaneously change. $a_i$ will change to $a_{i - 1} \mid a_i \mid a_{i + 1}$ for every positive integer $i$. $a_0$ will change to $a_0 \mid a... | [{"input": "9\n0 0\n0 1\n0 2\n1 0\n5 2\n10 1\n20 3\n1145 14\n19198 10", "output": "0\n1\n3\n1\n7\n11\n23\n1279\n19455"}] |
cf-d9a92f5b1ca467a7 |
Turtle was playing with a sequence $a_1, a_2, \ldots, a_n$ consisting of positive integers. Unfortunately, some of the integers went missing while playing.
Now the sequence becomes incomplete. There may exist an arbitrary number of indices $i$ such that $a_i$ becomes $-1$. Let the new sequence be $a'$.
Turtle is sad... | [{"input": "9\n8\n-1 -1 -1 2 -1 -1 1 -1\n4\n-1 -1 -1 -1\n6\n3 -1 -1 -1 9 -1\n4\n-1 5 -1 6\n4\n2 -1 -1 3\n4\n1 2 3 4\n2\n4 2\n5\n-1 3 -1 3 6\n13\n-1 -1 3 -1 -1 -1 -1 7 -1 -1 3 -1 -1", "output": "4 9 4 2 4 2 1 2\n7 3 6 13\n3 1 2 4 9 18\n-1\n-1\n-1\n4 2\n6 3 1 3 6\n3 1 3 1 3 7 3 7 3 1 3 1 3"}] |
cf-ee148c8d94fef8f0 |
Turtle just learned how to multiply two integers in his math class, and he was very excited.
Then Piggy gave him an integer $n$, and asked him to construct a sequence $a_1, a_2, \ldots, a_n$ consisting of integers which satisfied the following conditions:
* For all $1 \le i \le n$, $1 \le a_i \le 3 \cdot 10^5$. ... | [{"input": "3\n2\n3\n4", "output": "114514 114514\n1 2 2\n3 3 4 4"}] |
cf-12ded724e7b4e8ce |
Turtle just received $n$ segments and a sequence $a_1, a_2, \ldots, a_n$. The $i$-th segment is $[l_i, r_i]$.
Turtle will create an undirected graph $G$. If segment $i$ and segment $j$ intersect, then Turtle will add an undirected edge between $i$ and $j$ with a weight of $|a_i - a_j|$, for every $i \ne j$.
Turtle w... | [{"input": "4\n5\n1 7 3\n2 4 6\n3 5 5\n6 7 9\n3 4 4\n5\n2 7 3\n1 3 6\n4 5 5\n6 7 9\n1 1 4\n4\n1 4 3\n1 2 1\n3 4 5\n1 4 4\n3\n1 3 1\n2 3 3\n4 5 8", "output": "9\n13\n4\n-1"}] |
cf-e3b3e78d8d33ea08 |
Note the unusual definition of $\text{MEX}$ in this problem.
Piggy gave Turtle a binary tree$^{\dagger}$ with $n$ vertices and a sequence $a_1, a_2, \ldots, a_n$ on his birthday. The binary tree is rooted at vertex $1$.
If a set of paths $P = \\{(x_i, y_i)\\}$ in the tree covers each edge exactly once, then Turtle w... | [{"input": "5\n5\n3 2 2 1 1\n1 1 2 2\n5\n3 2 1 1 1\n1 1 2 2\n6\n1 2 1 2 1 3\n1 2 3 3 4\n7\n2 1 2 3 1 2 1\n1 1 2 2 3 3\n10\n1 2 2 1 4 2 3 1 2 1\n1 1 2 2 3 3 4 5 5", "output": "4\n6\n6\n6\n7"}] |
cf-6948ecd6286e913c |
Dima loves watching soccer. In such a game, the score on the scoreboard is represented as $x$ : $y$, where $x$ is the number of goals of the first team, and $y$ is the number of goals of the second team. At any given time, only one team can score a goal, so the score $x$ : $y$ can change to either $(x + 1)$ : $y$, or ... | [{"input": "6\n1 0\n5 0\n1 2\n3 2\n1 2\n4 5\n1 2\n4 3\n1 2\n1 2\n998244353 0\n1000000000 999999999", "output": "YES\nNO\nYES\nNO\nYES\nYES"}] |
cf-5fdd0e04ea336294 |
Recently, the first-year student Maxim learned about the Collatz conjecture, but he didn't pay much attention during the lecture, so he believes that the following process is mentioned in the conjecture:
There is a variable $x$ and a constant $y$. The following operation is performed $k$ times:
* increase $x$ by $... | [{"input": "13\n1 3 1\n2 3 1\n24 5 5\n16 3 2\n2 2 1\n1337 18 1\n1 2 144133\n12345678 3 10\n998244353 2 998244353\n998244353 123456789 998244352\n998244354 998241111 998244352\n998244355 2 9982443\n1000000000 1000000000 1000000000", "output": "2\n1\n1\n2\n3\n1338\n1\n16936\n1\n21180097\n6486\n1\n2"}] |
cf-50b61b3d8c1fef5e |
On another boring day, Egor got bored and decided to do something. But since he has no friends, he came up with a game to play.
Egor has a deck of $n$ cards, the $i$-th card from the top has a number $a_i$ written on it. Egor wants to play a certain number of rounds until the cards run out. In each round, he takes a ... | [{"input": "8\n5 3 10\n2 1 11 3 7\n10 1 5\n17 8 12 11 7 11 21 13 10 8\n3 4 5\n3 4 2\n8 12 25\n10 7 5 13 8 9 12 7\n2 3 3\n5 2\n9 7 9\n2 10 5 1 3 7 6 2 3\n1 8 10\n9\n5 5 6\n1 4 2 6 4", "output": "3\n0\n1\n4\n0\n3\n1\n2"}] |
cf-895ee117276fc985 |
Nikita loves mountains and has finally decided to visit the Berlyand mountain range! The range was so beautiful that Nikita decided to capture it on a map. The map is a table of $n$ rows and $m$ columns, with each cell containing a non-negative integer representing the height of the mountain.
He also noticed that mou... | [{"input": "8\n3 3 2\n7 11 3\n4 2 3\n0 1 15\n100\n010\n000\n4 4 3\n123 413 24 233\n123 42 0 216\n22 1 1 53\n427 763 22 6\n0101\n1111\n1010\n0101\n3 3 2\n2 1 1\n1 1 2\n1 5 4\n010\n101\n010\n3 3 2\n2 1 1\n1 1 2\n1 5 3\n010\n101\n010\n3 4 3\n46 49 50 1\n19 30 23 12\n30 25 1 46\n1000\n0100\n0010\n5 4 4\n39 30 0 17\n22 42 3... |
cf-b9be4f453fa811fd |
Let $bit(x)$ denote the number of ones in the binary representation of a non-negative integer $x$.
A subarray of an array is called $k$-good if it consists only of numbers with no more than $k$ ones in their binary representation, i.e., a subarray $(l, r)$ of array $a$ is good if for any $i$ such that $l \le i \le r$... | [{"input": "10\n6 1\n16 2\n1 1\n3 1\n31 3\n14 1\n1337 5\n100000 20\n795569939321040850 56\n576460752303423268 59", "output": "7\n35\n1\n6\n155\n8\n7323\n49965\n741136395\n66679884"}] |
cf-35558baff322d158 |
You have an array $a$ of $n$ elements. There are also $q$ modifications of the array. Before the first modification and after each modification, you would like to know the following:
What is the minimum length subarray that needs to be sorted in non-decreasing order in order for the array $a$ to be completely sorted ... | [{"input": "2\n5\n2 2 3 4 5\n3\n2 1\n4 1\n1 1\n5\n1 2 3 4 5\n9\n1 4\n2 3\n5 2\n3 1\n1 1\n5 1\n4 1\n3 1\n2 1", "output": "-1 -1\n1 2\n1 4\n3 4\n-1 -1\n1 3\n1 3\n1 5\n1 5\n2 5\n2 5\n2 5\n2 5\n-1 -1"}] |
cf-39dc6d797ec012dc |
An array of integers $a_1,a_2,\cdots,a_n$ is beautiful subject to an integer $k$ if it satisfies the following:
* The sum of $a_{j}$ over all $j$ such that $j$ is a multiple of $k$ and $1 \le j \le n $, itself, is a multiple of $k$. * More formally, if $\sum_{k | j} a_{j}$ is divisible by $k$ for all $1 \le j \l... | [{"input": "3\n3\n6\n7", "output": "4 22 18\n10 6 15 32 125 54\n23 18 27 36 5 66 7"}] |
cf-26164dd358b25b03 |
You are given two grids of numbers $a$ and $b$, with $n$ rows and $m$ columns. All the values in the grid are $0$, $1$ or $2$.
You can perform the following operation on $a$ any number of times:
* Pick any subrectangle in the grid with length and width $\ge 2$. You are allowed to choose the entire grid as a subrec... | [{"input": "7\n3 3\n000\n000\n000\n111\n111\n111\n4 4\n0000\n0000\n0000\n0000\n2100\n1200\n0012\n0021\n4 4\n1020\n1200\n1210\n0000\n0000\n1200\n2200\n0000\n3 3\n012\n012\n012\n010\n111\n011\n8 8\n00000000\n00000000\n00000000\n00000000\n00000000\n00000000\n00000000\n10000000\n00000000\n01200000\n02010000\n00102000\n0002... |
cf-85d614b42c653847 |
Alice, Bob and Charlie want to share a rectangular cake cut into $n$ pieces. Each person considers every piece to be worth a different value. The $i$-th piece is considered to be of value $a_i$ by Alice, $b_i$ by Bob and $c_i$ by Charlie.
The sum over all $a_i$, all $b_i$ and all $c_i$ individually is the same, equal... | [{"input": "10\n5\n5 1 1 1 1\n1 1 5 1 1\n1 1 1 1 5\n6\n1 2 3 4 5 6\n5 6 1 2 3 4\n3 4 5 6 1 2\n4\n4 4 4 4\n4 4 4 4\n4 4 4 4\n5\n5 10 5 2 10\n9 6 9 7 1\n10 7 10 2 3\n3\n4 5 2\n6 1 4\n1 8 2\n3\n10 4 10\n8 7 9\n10 4 10\n7\n57113 65383 19795 53580 74452 3879 23255\n12917 16782 89147 93107 27365 15044 43095\n33518 63581 3356... |
cf-3b24035b37b7e3d0 |
Given two arrays of distinct positive integers $a$ and $b$ of length $n$, we would like to make both the arrays the same. Two arrays $x$ and $y$ of length $k$ are said to be the same when for all $1 \le i \le k$, $x_i = y_i$.
Now in one move, you can choose some index $l$ and $r$ in $a$ ($l \le r$) and swap $a_l$ and... | [{"input": "6\n4\n1 2 3 4\n1 2 3 4\n5\n1 3 4 2 5\n7 1 2 5 4\n4\n1 2 3 4\n4 3 2 1\n3\n1 2 3\n1 3 2\n5\n1 5 7 1000 4\n4 1 7 5 1000\n3\n1 4 2\n1 3 2", "output": "YES\nNO\nYES\nNO\nNO\nNO"}] |
cf-5f489f6285179bc0 |
Alice and Bob are playing a game. There are $n$ balls, out of which $k$ are special. Each ball has a value associated with it.
The players play turn by turn. In each turn, the player randomly picks a ball and adds the value of the ball to their score, which is $0$ at the beginning of the game. The selected ball is re... | [{"input": "1\n5 2\n10 20 5 15 25", "output": "45 30"}, {"input": "5\n1 1\n732507\n2 2\n5817860 5398510\n5 1\n2122894 4951549 2750585 7821535 3214167\n8 4\n1405323 5069867 6883092 6972029 328406 2478975 7628890 9973340\n4 2\n9662050 3566134 3996473 9872255", "output": "732507 0\n11216370 0\n810642660 210218077\n7224029... |
cf-4d8452a6dc8692ee |
You have an array of non-negative integers $a_1, a_2, \ldots, a_n$.
The value of a sub-array of length $\ge 2$, $a[l, r] = [a_l, a_{l+1}, \ldots, a_r]$ is the minimum value of $a_i \oplus a_j$ such that $l \le i < j \le r$, where $\oplus$ is the xor (exclusive-or) operator.
You have to find the $k$-th smallest value... | [{"input": "4\n5 2\n1 2 3 4 5\n2 1\n4 3\n4 6\n1 2 4 8\n5 9\n1 2 3 4 5", "output": "1\n7\n12\n3"}] |
cf-3210cc15125b1902 |
You are given a tree with $n$ nodes numbered from $1$ to $n$, along with an array of size $n$. The value of $i$-th node is $a_{i}$. There are $q$ queries. In each query, you are given 2 nodes numbered as $x$ and $y$.
Consider the path from the node numbered as $x$ to the node numbered as $y$. Let the path be represen... | [{"input": "1\n4\n1 2\n2 3\n3 4\n2 3 6 5\n3\n1 4\n3 4\n1 1", "output": "14\n10\n2"}] |
cf-68791d88924e8208 |
Define the range of a non-empty array to be the maximum value minus the minimum value. For example, the range of $[1,4,2]$ is $4-1=3$.
You are given an array $a_1, a_2, \ldots, a_n$ of length $n \geq 3$. It is guaranteed $a$ is sorted.
You have to color each element of $a$ red or blue so that:
* the range of the ... | [{"input": "7\n4\n1 1 2 2\n5\n1 2 3 4 5\n3\n3 3 3\n4\n1 2 2 2\n3\n1 2 2\n3\n1 1 2\n3\n1 9 84", "output": "YES\nRBRR\nYES\nBBRBB\nNO\nYES\nRBBR\nYES\nRRB\nYES\nBRR\nYES\nBRB"}] |
cf-d81d9c8ba952a505 |
A digit is large if it is between $5$ and $9$, inclusive. A positive integer is large if all of its digits are large.
You are given an integer $x$. Can it be the sum of two large positive integers with the same number of digits?
Input Format:
The first line contains a single integer $t$ ($1 \leq t \leq 10^4$) — the ... | [{"input": "11\n1337\n200\n1393938\n1434\n98765432123456789\n11111111111111111\n420\n1984\n10\n69\n119", "output": "YES\nNO\nYES\nYES\nNO\nYES\nNO\nYES\nYES\nNO\nNO"}] |
cf-5fa3fb3b49dbd702 |
The two versions of the problem are different. You may want to read both versions. You can make hacks only if both versions are solved.
You are given an array $a$ of length $n$. Start with $c = 0$. Then, for each $i$ from $1$ to $n$ (in increasing order) do exactly one of the following:
* Option $1$: set $c$ to $c... | [{"input": "5\n4\n10 -9 -3 4\n8\n1 4 3 4 1 4 3 4\n3\n-1 -2 -3\n4\n-1000000000 1000000000 1000000000 1000000000\n4\n1 9 8 4", "output": "6\n24\n6\n4000000000\n22"}] |
cf-a7fa9759eff61255 |
The two versions of the problem are different. You may want to read both versions. You can make hacks only if both versions are solved.
You are given an array $a$ of length $n$. Start with $c = 0$. Then, for each $i$ from $1$ to $n$ (in increasing order) do exactly one of the following:
* Option $1$: set $c$ to $c... | [{"input": "5\n4\n2 -5 3 -3\n8\n1 4 3 4 1 4 3 4\n3\n-1 -2 -3\n4\n-1000000000 1000000000 1000000000 1000000000\n4\n1 9 8 4", "output": "12\n256\n1\n8\n16"}] |
cf-5118104022fa64fe |
You are given a string $s$ consisting of lowercase Latin characters. Count the number of nonempty strings $t \neq$ "$\texttt{a}$" such that it is possible to partition$^{\dagger}$ $s$ into some substrings satisfying the following conditions:
* each substring either equals $t$ or "$\texttt{a}$", and * at least on... | [{"input": "8\naaaaa\nbaba\ncabacb\naaabaaa\nbitset\nab\nabbaaaabbb\nyearnineteeneightyfour", "output": "4\n4\n1\n16\n1\n2\n3\n1"}] |
cf-7d90be3588221da2 |
Two hungry red pandas, Oscar and Lura, have a tree $T$ with $n$ nodes. They are willing to perform the following shuffle procedure on the whole tree $T$ exactly once. With this shuffle procedure, they will create a new tree out of the nodes of the old tree.
1. Choose any node $V$ from the original tree $T$. Create ... | [{"input": "4\n5\n1 2\n1 3\n2 4\n2 5\n5\n1 2\n2 3\n3 4\n4 5\n6\n1 2\n1 3\n1 4\n1 5\n1 6\n10\n9 3\n8 1\n10 6\n8 5\n7 8\n4 6\n1 3\n10 1\n2 7", "output": "4\n3\n5\n6"}] |
cf-650d93f12b4cd5ba |
There is a hidden array $a_1, a_2, \ldots, a_n$ of length $n$ whose elements are integers between $-m$ and $m$, inclusive.
You are given an array $b_1, b_2, \ldots, b_n$ of length $n$ and a string $s$ of length $n$ consisting of the characters $\texttt{P}$, $\texttt{S}$, and $\texttt{?}$.
For each $i$ from $1$ to $n... | [{"input": "6\n4 10\nPSPP\n1 9 8 10\n4 1000000000\n????\n1 1 1 4000000000\n8 1000000000\n?P?SSP?P\n-857095623 -1424391899 -851974476 673437144 471253851 -543483033 364945701 -178537332\n4 7\nPPSS\n4 2 1 3\n9 20\n?????????\n1 2 3 4 5 6 7 8 9\n3 1000000000\nP??\n-145463248 -974068460 -1287458396", "output": "1\n0\n2\n1\n... |
cf-2034d12ca0220544 |
The secret behind Oscar's first magic trick has been revealed! Because he still wants to impress Lura, he comes up with a new idea: he still wants to sort a permutation $p_1, p_2, \ldots, p_n$ of $[1, 2, \ldots, n]$.
This time, he chooses an integer $k$. He wants to sort the permutation in non-decreasing order using ... | [{"input": "3\n5\n5 1 2 3 4\n5\n2 3 5 4 1\n6\n1 2 3 4 5 6", "output": "4\n1\n2 1\n3\n2\n1 3\n2 1\n6\n0"}] |
cf-8a750ad6391674a9 |
There are $n$ towers at $n$ distinct points $(x_1, y_1), (x_2, y_2), \ldots, (x_n, y_n)$, such that no three are collinear and no four are concyclic. Initially, you own towers $(x_1, y_1)$ and $(x_2, y_2)$, and you want to capture all of them. To do this, you can do the following operation any number of times:
* Pi... | [{"input": "3\n5\n1 1\n2 5\n3 3\n4 2\n5 4\n6\n1 1\n3 3\n1 2\n2 1\n3 10000\n19 84\n7\n2 7\n-4 -3\n-3 6\n3 1\n-5 2\n1 -4\n-1 7", "output": "1\n0\n10"}] |
cf-1f0b89e27db09b4b |
Matthew is given two strings $a$ and $b$, both of length $3$. He thinks it's particularly funny to create two new words by swapping the first character of $a$ with the first character of $b$. He wants you to output $a$ and $b$ after the swap.
Note that the new words may not necessarily be different.
Input Format:
Th... | [{"input": "6\nbit set\ncat dog\nhot dog\nuwu owo\ncat cat\nzzz zzz", "output": "sit bet\ndat cog\ndot hog\nowu uwo\ncat cat\nzzz zzz"}] |
cf-f90a85e39db3bde3 |
Given an integer $n$, find an integer $x$ such that:
* $2 \leq x \leq n$. * The sum of multiples of $x$ that are less than or equal to $n$ is maximized. Formally, $x + 2x + 3x + \dots + kx$ where $kx \leq n$ is maximized over all possible values of $x$.
Input Format:
The first line contains $t$ ($1 \leq t \leq ... | [{"input": "2\n3\n15", "output": "3\n2"}] |
cf-9474cceabd190d0e |
Alex thinks some array is good if there exists some element that can be represented as the sum of all other elements (the sum of all other elements is $0$ if there are no other elements). For example, the array $[1,6,3,2]$ is good since $1+3+2=6$. Furthermore, the array $[0]$ is also good. However, the arrays $[1,2,3,... | [{"input": "7\n1\n0\n1\n1\n4\n1 1 2 0\n5\n0 1 2 1 4\n7\n1 1 0 3 5 2 12\n7\n1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 294967296\n10\n0 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 589934592", "output": "1\n0\n3\n3\n4\n1\n2"}] |
cf-10c296908f2b0a5f |
Given a $n$ by $m$ grid consisting of '.' and '#' characters, there exists a whole manhattan circle on the grid. The top left corner of the grid has coordinates $(1,1)$, and the bottom right corner has coordinates $(n, m)$.
Point ($a, b$) belongs to the manhattan circle centered at ($h, k$) if $|h - a| + |k - b| < r$... | [{"input": "6\n5 5\n.....\n.....\n..#..\n.....\n.....\n5 5\n..#..\n.###.\n#####\n.###.\n..#..\n5 6\n......\n......\n.#....\n###...\n.#....\n1 1\n#\n5 6\n...#..\n..###.\n.#####\n..###.\n...#..\n2 10\n..........\n...#......", "output": "3 3\n3 3\n4 2\n1 1\n3 4\n2 4"}] |
End of preview. Expand in Data Studio
DeepCoder Codeforces test 408 independent val for zero-code-l1. Source agentica-org/DeepCoder-Preview-Dataset codeforces/test plus id. See also Tommysha/zero-code-l1-val.
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