$(20\%)$ Given an array containing the digits $7,4,2,8,1,0,6,3($written as $74281063),$ show how the order of the digits changes during each step of the following algorithms.

$($a$)$ insertion sort

$($b$)$ selection sort

$($c$)$ merge sort

$($d$)$ quick sort

Show the array after each swap, except in insertion sort. For insertion sort, show the array after each insertion.