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What is the running time of insertion sort if all elements are equal? Please illustrate the process of sorting the sequence 3, 1, 4, 5, 9, 2, 6, 5 using bubble sort. Please illustrate the process of sorting the sequence 3, 1, 4, 1, 5, 9, 2, 6 using merge sort.
Expert Answer
(1) The running time of insertion sort if all elements are equal : O(n)
Let A denote the array being sorted. For each element A[i], you check the preceding element A[i-1] and find they are equal. And you do not check further. Thus, you perform exactly n-1 comparisons, which makes the algorithm run in O(n) time.
(2) Bubble sort
(3)
