Consider an array A = [10, 7, 8, 19, 41, 35, 25, 31]. Suppose the merge sort algorithm is executed o

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Question

Consider an array A = [10, 7, 8, 19, 41, 35, 25, 31]. Suppose the merge sort algorithm is executed on array A to sort it in increasing order. The merge sort algorithm will carry out a total of 7 merge operations.A merge operation on sorted left array L and sorted right array R is said to be void if the output of the merge operation is the elements of array L followed by the elements of array R.The number of void merge operations among these 7 merge operations is __________. (answer in integer)

Accepted Answer

Answer: 3Concept -- Merge Sort and Void Merges: A void merge occurs when max(L) ≤ min(R), so concatenation works without comparisons. Trace merges:Initial array: [10,7,8,19,41,35,25,31]Level 1 (size1):Merge [10] and [7]: max(10)=10, min(7)=7 → 10>7 → not void.Merge [8] and [19]: 8≤19 → void (1).Merge [41] and [35]: 41>35 → not void.Merge [25] and [31]: 25≤31 → void (2).Level 2 (size2):Merge [7,10] and [8,19]: max(7,10)=10, min(8,19)=8 → 10>8 → not void.Merge [35,41] and [25,31]: max(35,41)=41, min(25,31)=25 → 41>25 → not void.Level 3 (size4):Merge [7,8,10,19] and [25,31,35,41]: max=19, min=25 → 19≤25 → void (3).Total void = 3.Note: In merge sort, a void merge occurs when the two subarrays are already in order relative to each other, which can happen if the array is already sorted or has large sorted segments. This reduces the number of comparisons but not the number of moves.

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