a$.$ Construct a permutation of $11$ numbers. Sort the numbers using the sorting algorithms: Bubble Sort,

Insertion Sort, Selection Sort and Quick Sort as described in the lecture notes. Note that you should not

use different versions of these algorithms.

Assume that the numbers are stored in an array. You should show the contents of the array after each

iteration for all the algorithms.

b$.$ Given an array of n integers in the locations A$[1],$ A$[2],...,$ A$[$n$],$ describe an O$($n$2)$ time algorithm to

compute the products P$($i$,$j$)=$ A$[$i$]*$A$[$i$+1]*...*$ A$[$j$]$ for all i$,$ j$,1<=$ i $<$ j $<=$ n

$($Hint: First try manually a solution with an array of $6$ elements, then generalize it to an array with any

size n$.)$