data structures

Exercise 4() : This is part of Problem 22 in the book: Bubblesort is a popular, but inefficient, sorting algorithm. It works by repeatedly swapping adjacent elements that are out of order. The procedure BUBBLESORT sorts array A[1:n]. BUBBLESORT (A,n) (a) Let A denote the array A after BuBBLESORT (A,n) is executed. To prove that BUBBLESORT is correct, you need to prove that it terminates and that Department of Mathematics and Computer Science 21L50 Data Structures Eindhoven University of Technology A[1]A[2]A[n] In order to show that BuBesont actually sorts, what else do you need to prove? (b) State precisely a loop invariant for the for loop in lines 24, and prove that this loop invariant holds. Your proof should use the structure of the loop invariant proof in the lecture. (c) Using the termination condition of the loop invariant proved in (b), state a loop invariant for the for loop in lines 14 that allows you to prove the inequality above. Your proof should use the structure of the loop invariant proof in the lecture