A16325. Ones and Twos
编程题
普及/提高-
知识点
题目描述
You are given a $1$ -indexed array $a$ of length $n$ where each element is $1$ or $2$ .
Process $q$ queries of the following two types:
- "1 s": check if there exists a subarray $^{\dagger}$ of $a$ whose sum equals to $s$ .
- "2 i v": change $a_i$ to $v$ .
$^{\dagger}$ An array $b$ is a subarray of an array $a$ if $b$ can be obtained from $a$ by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end. In particular, an array is a subarray of itself.
Process $q$ queries of the following two types:
- "1 s": check if there exists a subarray $^{\dagger}$ of $a$ whose sum equals to $s$ .
- "2 i v": change $a_i$ to $v$ .
$^{\dagger}$ An array $b$ is a subarray of an array $a$ if $b$ can be obtained from $a$ by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end. In particular, an array is a subarray of itself.
输入格式
Each test contains multiple test cases. The first line contains a single integer $t$ ( $1 \le t \le 10^4$ ) — the number of test cases. The description of the test cases follows.
The first line of each test case contains two integers $n$ and $q$ ( $1\le n,q\le 10^5$ ) — the length of array $a$ and the number of queries.
The second line of each test case contains $n$ integers $a_1,a_2,\ldots,a_n$ ( $a_i$ is $1$ or $2$ ) — the elements of array $a$ .
Each of the following $q$ lines of each test case contains some integers. The first integer $\mathrm{op}$ is either $1$ or $2$ .
- If $\mathrm{op}$ is $1$ , it is followed by one integer $s$ ( $1 \leq s \leq 2n$ ).
- If $\mathrm{op}$ is $2$ , it is followed by two integers $i$ and $v$ ( $1 \leq i \leq n$ , $v$ is $1$ or $2$ ).
It is guaranteed that the sum of $n$ and the sum of $q$ over all test cases both do not exceed $10^5$ .
The first line of each test case contains two integers $n$ and $q$ ( $1\le n,q\le 10^5$ ) — the length of array $a$ and the number of queries.
The second line of each test case contains $n$ integers $a_1,a_2,\ldots,a_n$ ( $a_i$ is $1$ or $2$ ) — the elements of array $a$ .
Each of the following $q$ lines of each test case contains some integers. The first integer $\mathrm{op}$ is either $1$ or $2$ .
- If $\mathrm{op}$ is $1$ , it is followed by one integer $s$ ( $1 \leq s \leq 2n$ ).
- If $\mathrm{op}$ is $2$ , it is followed by two integers $i$ and $v$ ( $1 \leq i \leq n$ , $v$ is $1$ or $2$ ).
It is guaranteed that the sum of $n$ and the sum of $q$ over all test cases both do not exceed $10^5$ .
输出格式
For each query with $\mathrm{op}=1$ , output "YES" in one line if there exists a subarray of $a$ whose sum is equals to $s$ , otherwise output "NO".
You can output the answer in any case (upper or lower). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive responses.
You can output the answer in any case (upper or lower). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive responses.
输入输出样例
输入 #1
2 5 5 2 1 2 1 2 1 5 1 6 1 7 2 4 2 1 7 3 2 2 2 2 1 6 1 5
输出 #1
YES YES NO YES YES NO
说明/提示
Consider the first example:
- The answer for the first query is "YES" because $a_1+a_2+a_3=2+1+2=5$ .
- The answer for the second query is "YES" because $a_1+a_2+a_3+a_4=2+1+2+1=6$ .
- The answer for the third query is "NO" because we cannot find any subarray of $a$ whose sum is $7$ .
- After the fourth query, the array $a$ becomes $[2,1,2,2,2]$ .
- The answer for the fifth query is "YES" because $a_2+a_3+a_4+a_5=1+2+2+2=7$ .
- The answer for the first query is "YES" because $a_1+a_2+a_3=2+1+2=5$ .
- The answer for the second query is "YES" because $a_1+a_2+a_3+a_4=2+1+2+1=6$ .
- The answer for the third query is "NO" because we cannot find any subarray of $a$ whose sum is $7$ .
- After the fourth query, the array $a$ becomes $[2,1,2,2,2]$ .
- The answer for the fifth query is "YES" because $a_2+a_3+a_4+a_5=1+2+2+2=7$ .