[Solution] Concat Sort CodeChef Solution 2022

Problem

JJ has an array $A$. He can perform the following operation on $A$:

• Divide $A$ into two subsequences $P$ and $Q$ such that each $A_i$ belongs to either $P$ or $Q$.
• Set $A := P\ \texttt{concat}\ Q$

Here $\texttt{concat}$ denotes the concatenation operation. For e.g. $[2, 1, 5] \texttt{ concat } [4, 3] = [2, 1, 5, 4, 3]$.

Is it possible to make $A$ sorted in non-decreasing order after applying the above operation at most once?

Note: An array $X$ is a subsequence of an array $Y$ if $X$ can be obtained by deletion of several (possibly, zero or all) elements from $Y$.

Input Format

• The first line contains a single integer $T$ — the number of test cases. Then the test cases follow.
• The first line of each test case contains an integer $N$ — the size of the array $A$.

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• The second line of each test case contains $N$ space-separated integers $A_1, A_2, \ldots, A_N$ denoting the array $A$.

Output Format

For each test case, output YES if it is possible to make the array $A$ sorted after applying the given operation at most once. Otherwise, output NO.

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You may print each character of YES and NO in uppercase or lowercase (for example, yes, yEs, Yes will be considered identical).

Explanation:

Test case $1$: We can select $P = [1, 2, 3]$ and $Q = [4, 5, 6]$. Therefore $A$ will become $[1, 2, 3, 4, 5, 6]$ which is sorted.

Test case $2$: It can be proven that it is not possible to sort $A$ by using the given operation at most once.

Test case $3$: We can select $P = [5, 7, 9]$ and $Q = [10, 11]$. Therefore $A$ will become $[5, 7, 9, 10, 11]$ which is sorted.