Please show all steps in detail on how to solve the problem.

8. Consider the bubble-sort algorithm described below void bubble (dtype Al], int n) int i,j for (i = n-1; i>0; i--) for (j = 0; j A SWAP(AL), Aj 1) (a) Analyze the time complexity, T(n), of the bubble-sort algorithm (b) Rewrite the algorithm using recursion (c) Let f(n) be the worst-case number of key-comparisons used by this algorithm to sort n cle- ments. Write a recurrence for f(n). Solve the recurrence by repeated substitution (i.e, iteration method)