$1.$ Determine the running time $($big$-$Oh notation$)$ in each of the following cases :$($a$)$ Mergesort for sorted input.$($b$)$ Insertion sort for reverse$-$ordered input.$($c$)$ Mergesort for random input.$($d$)$ Quicksort for reverse$-$ordered input when the pivot is chosen as the larger of the firsttwo non distinct elements.$($e$)$ Quicksort for random input when the pivot is chosen as a random element.$($f$)$ Insertion sort for random input