#GYM104787L. Yet Another Maximize Permutation Subarrays
Yet Another Maximize Permutation Subarrays
Description
You are given a permutation $p$ of size $n$. You want to maximize the number of subarrays of $p$ that are permutations. In order to do so, you must perform the following operation exactly once:
- Select integers $i$, $j$, where $1\le i,j\le n$, then
- Swap $p_i$ and $p_j$.
For example, if $p=[5,1,4,2,3]$ and we choose $i=2$, $j=3$, the resulting array will be $[5,4,1,2,3]$. If instead we choose $i=j=5$, the resulting array will be $[5,1,4,2,3]$.
Which choice of $i$ and $j$ will maximize the number of subarrays that are permutations?
NOTE:
- A permutation of length $n$ is an array 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).
- An array $a$ is a subarray of an array $b$ if $a$ can be obtained from $b$ by deleting several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.
The first line of the input contains a single integer $t\ (1\le t\le 10)$ — the number of test cases. The description of the test cases follows.
The first line of each test case contains a single integer $n\ (1\le n\le 10^6)$ — the size of the permutation.
The next line of each test case contains $n$ integers $p_1,p_2,\cdots p_n$ ($1\le p_i\le n$, all $p_i$ are distinct) — the elements of the permutation p.
For each test case, output two integers $i$ and $j$ ($1\le i,j \le n$) — the indices to swap in $p$.
If there are multiple solutions, print any of them.
Input
The first line of the input contains a single integer $t\ (1\le t\le 10)$ — the number of test cases. The description of the test cases follows.
The first line of each test case contains a single integer $n\ (1\le n\le 10^6)$ — the size of the permutation.
The next line of each test case contains $n$ integers $p_1,p_2,\cdots p_n$ ($1\le p_i\le n$, all $p_i$ are distinct) — the elements of the permutation p.
Output
For each test case, output two integers $i$ and $j$ ($1\le i,j \le n$) — the indices to swap in $p$.
If there are multiple solutions, print any of them.
8
3
1 2 3
3
1 3 2
5
1 3 2 5 4
6
4 5 6 1 2 3
9
8 7 6 3 2 1 4 5 9
10
7 10 5 1 9 8 3 2 6 4
10
8 5 10 9 2 1 3 4 6 7
10
2 3 5 7 10 1 8 6 4 9
3 3
1 2
1 4
1 3
9 9
4 9
2 4
1 5