Let us call an array unsorted if it is not sorted in a nondecreasing order. Consider the problem of

checking whether a given array is unsorted order or not? Note that we do not ask for sorting the

array. The solution should not involve sorting the array. Rather we want to check if it is unsorted.

$($a$)$ Describe the problem formally, i$.$e$.,$ in the Input $-$ Output format.

$($b$)$ What is the input size?

$($c$)$ What is the output size?

$($d$)$ Design an algorithm to solve the problem.

$($e$)$ Consider the following variant of the original problem: Check if the even indexed elements are

sorted in an increasing order. Rewrite this new problem formally and design an algorithm to

solve it$.$