[Solution] Interesting Subarray CodeChef Solution

Problem

You are given an array $A$ of length $N$.

The interesting value of a subarray is defined as the product of the maximum and minimum elements of the subarray.

Find the minimum and maximum interesting value over all subarrays for the given array.

Note: A subarray is obtained by deletion of several (possibly zero) elements from the beginning of the array and several (possibly zero) elements from the end of the array.

Input Format

• The first line of input will contain a single integer $T$, denoting the number of test cases.
• The first line of each test case contains an integer $N$ - the length of the array $A$.
• The second line of each test case contains $N$ space-separated integers $A_1,A_2,\ldots,A_N$.

Output Format

For each test case, output two space-separated integers on a new line the minimum and maximum interesting value over all subarrays for the given array.

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Explanation:

Test case $1$: The minimum interesting value possible is $4$. A subarray with interesting value equal to $4$ is $[2,2]$. Here, both minimum and maximum elements of the subarray are $2$. It can be proven that no subarray of the array has interesting value less than $4$.
The maximum interesting value possible is $4$. A subarray with interesting value equal to $4$ is $[2,2]$. Here, both minimum and maximum elements of the subarray are $2$. It can be proven that no subarray of the array has interesting value greater than $4$.

Test case $2$: The minimum interesting value possible is $0$. A subarray with interesting value equal to $0$ is $[5, 0, 9]$. Here, minimum element is $0$ and maximum element is $9$. It can be proven that no subarray of the array has interesting value less than $0$.
The maximum interesting value possible is $81$. A subarray with interesting value equal to $81$ is $[9]$. Here, both minimum and maximum elements of the subarray are $9$. It can be proven that no subarray of the array has interesting value more than $81$.