Codeforces题解｜1385C - Make It Good

题目信息 📚

【题目描述】

You are given an array $a$ consisting of $n$ integers. You have to find the length of the smallest (shortest) prefix of elements you need to erase from $a$ to make it a good array. Recall that the prefix of the array $a = [a_1, a_2, \ldots, a_n]$ is a subarray consisting of several first elements: the prefix of the array $a$ of length $k$ is the array $[a_1, a_2, \ldots, a_k]$ $(0 \leq k \leq n)$.

The array $b$ of length $m$ is called good, if you can obtain a non-decreasing array $c$ ($c_1 \leq c_2 \leq \cdots \leq c_m$) from it, repeating the following operation $m$ times (initially, $c$ is empty):

Select either the first or the last element of $b$, remove it from $b$, and append it to the end of the array $c$.

For example, if we do 4 operations: take $b_1$, then $b_m$, then $b_{m-1}$ and at last $b_2$, then $b$ becomes $[b_3, b_4, \ldots, b_{m-3}]$ and $c = [b_1, b_m, b_{m-1}, b_2]$.

Consider the following example: $b = [1, 2, 3, 4, 4, 2, 1]$. This array is good because we can obtain a non-decreasing array $c$ from it by the following sequence of operations:

Take the first element of $b$, so $b = [2, 3, 4, 4, 2, 1]$, $c = [1]$.
Take the last element of $b$, so $b = [2, 3, 4, 4, 2]$, $c = [1, 1]$.
Take the last element of $b$, so $b = [2, 3, 4, 4]$, $c = [1, 1, 2]$.
Take the first element of $b$, so $b = [3, 4, 4]$, $c = [1, 1, 2, 2]$.
Take the first element of $b$, so $b = [4, 4]$, $c = [1, 1, 2, 2, 3]$.
Take the last element of $b$, so $b = [4]$, $c = [1, 1, 2, 2, 3, 4]$.
Take the only element of $b$, so $b = []$, $c = [1, 1, 2, 2, 3, 4, 4]$ — $c$ is non-decreasing.

Note that the array consisting of one element is good.

Print the length of the shortest prefix of $a$ to delete (erase), to make $a$ a good array. Note that the required length can be $0$.

You have to answer $t$ independent test cases.

【输入】

The first line of the input contains one integer $t$ $(1 \leq t \leq 2 \times 10^4)$ — the number of test cases. Then $t$ test cases follow.

The first line of each test case contains one integer $n$ $(1 \leq n \leq 2 \times 10^5)$ — the length of $a$. The second line of the test case contains $n$ integers $a_1, a_2, \ldots, a_n$ $(1 \leq a_i \leq 2 \times 10^5)$, where $a_i$ is the $i$-th element of $a$.

It is guaranteed that the sum of $n$ does not exceed $2 \times 10^5$ $(\sum n \leq 2 \times 10^5)$.

【输出】

For each test case, print the answer: the length of the shortest prefix of elements you need to erase from $a$ to make it a good array.

【输入样例1】

5
4
1 2 3 4
7
4 3 3 8 4 5 2
3
1 1 1
7
1 3 1 4 5 3 2
5
5 4 3 2 3

【输出样例1】

【提示】

In the first test case of the example, the array $a$ is already good, so we don’t need to erase any prefix.

In the second test case of the example, the initial array $a$ is not good. Let’s erase the first 4 elements of $a$; the result is $[4, 5, 2]$. The resulting array is good. You can prove that if you erase a fewer number of first elements, the result will not be good.