Codeforces Round 877 (Div. 2) |
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Finished |
You are given a permutation $$$p$$$ of size $$$n$$$. You want to minimize the number of subarrays of $$$p$$$ that are permutations. In order to do so, you must perform the following operation exactly once:
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 minimize the number of subarrays that are permutations?
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).
An array $$$a$$$ is a subarray of an array $$$b$$$ if $$$a$$$ can be obtained from $$$b$$$ by the deletion of 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 $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases. The description of the test cases follows.
The first line of each test case contains a single integer $$$n$$$ ($$$3 \le n \le 2\cdot 10^5$$$) — the size of the permutation.
The next line of each test case contains $$$n$$$ integers $$$p_1, p_2, \ldots p_n$$$ ($$$1 \le p_i \le n$$$, all $$$p_i$$$ are distinct) — the elements of the permutation $$$p$$$.
It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2\cdot 10^5$$$.
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.
831 2 331 3 251 3 2 5 464 5 6 1 2 398 7 6 3 2 1 4 5 9107 10 5 1 9 8 3 2 6 4108 5 10 9 2 1 3 4 6 7102 3 5 7 10 1 8 6 4 9
2 3 1 1 5 2 1 4 9 5 8 8 6 10 5 4
For the first test case, there are four possible arrays after the swap:
For the third sample case, after we swap elements at positions $$$2$$$ and $$$5$$$, the resulting array is $$$[1, 4, 2, 5, 3]$$$. The only subarrays that are permutations are $$$[1]$$$ and $$$[1, 4, 2, 5, 3]$$$. We can show that this is minimal.
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