A15650. Quick Sort
编程题
普及/提高-
知识点
题目描述
You are given a permutation $^\dagger$ $p$ of length $n$ and a positive integer $k \le n$ .
In one operation, you:
- Choose $k$ distinct elements $p_{i_1}, p_{i_2}, \ldots, p_{i_k}$ .
- Remove them and then add them sorted in increasing order to the end of the permutation.
For example, if $p = [2,5,1,3,4]$ and $k = 2$ and you choose $5$ and $3$ as the elements for the operation, then $[2, \color{red}{5}, 1, \color{red}{3}, 4] \rightarrow [2, 1, 4, \color{red}{3},\color{red}{5}]$ .
Find the minimum number of operations needed to sort the permutation in increasing order. It can be proven that it is always possible to do so.
$^\dagger$ A permutation of length $n$ is an array consisting of $n$ distinct integers from $1$ to $n$ in arbitrary order. For example, $[2,3,1,5,4]$ is a permutation, but $[1,2,2]$ is not a permutation ( $2$ appears twice in the array), and $[1,3,4]$ is also not a permutation ( $n=3$ but there is $4$ in the array).
In one operation, you:
- Choose $k$ distinct elements $p_{i_1}, p_{i_2}, \ldots, p_{i_k}$ .
- Remove them and then add them sorted in increasing order to the end of the permutation.
For example, if $p = [2,5,1,3,4]$ and $k = 2$ and you choose $5$ and $3$ as the elements for the operation, then $[2, \color{red}{5}, 1, \color{red}{3}, 4] \rightarrow [2, 1, 4, \color{red}{3},\color{red}{5}]$ .
Find the minimum number of operations needed to sort the permutation in increasing order. It can be proven that it is always possible to do so.
$^\dagger$ A permutation of length $n$ is an array consisting of $n$ distinct integers from $1$ to $n$ in arbitrary order. For example, $[2,3,1,5,4]$ is a permutation, but $[1,2,2]$ is not a permutation ( $2$ appears twice in the array), and $[1,3,4]$ is also not a permutation ( $n=3$ but there is $4$ in the array).
输入格式
The first line contains a single integer $t$ ( $1 \le t \le 10^4$ ) — the number of test cases. The description of test cases follows.
The first line of each test case contains two integers $n$ and $k$ ( $2 \le n \le 10^5$ , $1 \le k \le n$ ).
The second line of each test case contains $n$ integers $p_1,p_2,\ldots, p_n$ ( $1 \le p_i \le n$ ). It is guaranteed that $p$ is a permutation.
It is guaranteed that the sum of $n$ over all test cases does not exceed $10^5$ .
The first line of each test case contains two integers $n$ and $k$ ( $2 \le n \le 10^5$ , $1 \le k \le n$ ).
The second line of each test case contains $n$ integers $p_1,p_2,\ldots, p_n$ ( $1 \le p_i \le n$ ). It is guaranteed that $p$ is a permutation.
It is guaranteed that the sum of $n$ over all test cases does not exceed $10^5$ .
输出格式
For each test case output a single integer — the minimum number of operations needed to sort the permutation. It can be proven that it is always possible to do so.
输入输出样例
输入 #1
4 3 2 1 2 3 3 1 3 1 2 4 2 1 3 2 4 4 2 2 3 1 4
输出 #1
0 1 1 2
说明/提示
In the first test case, the permutation is already sorted.
In the second test case, you can choose element $3$ , and the permutation will become sorted as follows: $[\color{red}{3}, 1, 2] \rightarrow [1, 2, \color{red}{3}]$ .
In the third test case, you can choose elements $3$ and $4$ , and the permutation will become sorted as follows: $[1, \color{red}{3}, 2, \color{red}{4}] \rightarrow [1, 2, \color{red}{3},\color{red}{4}]$ .
In the fourth test case, it can be shown that it is impossible to sort the permutation in $1$ operation. However, if you choose elements $2$ and $1$ in the first operation, and choose elements $3$ and $4$ in the second operation, the permutation will become sorted as follows: $[\color{red}{2}, 3, \color{red}{1}, 4] \rightarrow [\color{blue}{3}, \color{blue}{4}, \color{red}{1}, \color{red}{2}] \rightarrow [1,2, \color{blue}{3}, \color{blue}{4}]$ .
In the second test case, you can choose element $3$ , and the permutation will become sorted as follows: $[\color{red}{3}, 1, 2] \rightarrow [1, 2, \color{red}{3}]$ .
In the third test case, you can choose elements $3$ and $4$ , and the permutation will become sorted as follows: $[1, \color{red}{3}, 2, \color{red}{4}] \rightarrow [1, 2, \color{red}{3},\color{red}{4}]$ .
In the fourth test case, it can be shown that it is impossible to sort the permutation in $1$ operation. However, if you choose elements $2$ and $1$ in the first operation, and choose elements $3$ and $4$ in the second operation, the permutation will become sorted as follows: $[\color{red}{2}, 3, \color{red}{1}, 4] \rightarrow [\color{blue}{3}, \color{blue}{4}, \color{red}{1}, \color{red}{2}] \rightarrow [1,2, \color{blue}{3}, \color{blue}{4}]$ .