Consider the array: A=[10,7,8,19,41,35,25,31] Suppose merge sort is executed…

To find the number of void merge operations, we trace the Merge Sort algorithm on the array A = [10, 7, 8, 19, 41, 35, 25, 31].

Step 1: Divide the Array

The array is recursively divided until sub-arrays of size 1 are reached:

• Level 0: [10, 7, 8, 19, 41, 35, 25, 31]

• Level 1: [10, 7, 8, 19] and [41, 35, 25, 31]

• Level 2: [10, 7], [8, 19], [41, 35], [25, 31]

• Level 3 (Base): [10], [7], [8], [19], [41], [35], [25], [31]

Step 2: Perform Merges (Bottom-Up)

A merge is 'void' if the largest element of the left sub-array is less than or equal to the smallest element of the right sub-array. In this case, the output is just the left elements followed by the right elements.

• Merge 1: [10] and [7]. Left max (10) > Right min (7). Result: [7, 10]. (Not void)

• Merge 2: [8] and [19]. Left max (8) < Right min (19). Result: [8, 19]. (Void)

• Merge 3: [41] and [35]. Left max (41) > Right min (35). Result: [35, 41]. (Not void)

• Merge 4: [25] and [31]. Left max (25) < Right min (31). Result: [25, 31]. (Void)

• Merge 5: [7, 10] and [8, 19]. Left max (10) > Right min (8). Result: [7, 8, 10, 19]. (Not void)

• Merge 6: [35, 41] and [25, 31]. Left max (41) > Right min (25). Result: [25, 31, 35, 41]. (Not void)

• Merge 7: [7, 8, 10, 19] and [25, 31, 35, 41]. Left max (19) < Right min (25). Result: [7, 8, 10, 19, 25, 31, 35, 41]. (Void)

Step 3: Count Void Merges

The void merges occurred in Merge 2, Merge 4, and Merge 7.

Total void merge operations = 3.