UH ID: Consider the in-place sorting algorithm MySort. Algorithm MySort 1: function MYSORT(arr) Input An array arr of n elements. Output > None for i+1 to n- 1 do j+i-1 2: 3: while j 20 and arr[j] > arr[j+ 1] do 4: temp + arrlj) arrlj] + arrlj + 1] + 1] + temp j+j-1 5: 6: 7: 8: (1) Consider your 7-digit UH ID. How many comparisons (among array elements) does MySort perform to sort the digits in your UH ID? Justify your answer. (ii) If the input array has n elements, how many comparisons does the algorithm perform in the worst case? What is the input that achieves this worst case? Justify your answer. (iii) If the input array has n elements, how many comparisons does the algorithm perform in the best case? What is the input that achieves this best case? Justify your answer. (iv) A stable sorting algorithm is one in which elements with the same value remain in the same relative order after the sort is complete. For example, if A = [2,5, 4, 5, 1). a stable sort would output [1, 2, 4, 5, 5]. Notice that the red 5 and the blue 5 occur in the same relative order before and after the array is sorted. Is MySort a stable sorting algorithm? Justify your answer. (v) Prove the correctness of MySort using mathematical induction.

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