(programming required) Modify your implementations from Exercise 6.69 to count the number of swaps and comparisons each algorithm performs. Then run all three algorithms on each of the 8! = 40,320...

(programming required) Modify your implementations from Exercise 6.69 to count the number of swaps and comparisons each algorithm performs. Then run all three algorithms on each of the 8! = 40,320 different orderings of the elements {1, 2, . . . , 8}. How do the algorithms’ performances compare, on average?

Exercise 6.69

prove this claim, explicitly describe an array A[1 . . . n] for which early-stopping-bubbleSort performs poorly—that is, in Ω(n 2 ) time—on both A and the reverse of A.

(programming required) Implement the three versions of Bubble Sort (including the two in Figure 6.23) in a programming language of your choice.

Figure 6.23: Bubble Sort, improved.