How many void merge operations occur in merge sort for GATE CS 2026 Set-2 Q32?

There are 3 void merge operations. A merge is void when all elements in the left array are less than or equal to all elements in the right array, so the output is simply L concatenated with R. The void merges are: [8]+[19]→[8,19], [25]+[31]→[25,31], and [7,8,10,19]+[25,31,35,41]→[7,8,10,19,25,31,35,41].

What defines a void merge operation in merge sort?

A void merge occurs when merging two sorted arrays L and R such that max(L) is less than or equal to min(R). In this case, the merge operation does not need to compare and interleave elements — it simply outputs all elements of L followed by all elements of R. This is the best-case scenario for a merge operation with minimal comparisons.

Why is the final merge in this example a void operation?

The final merge combines [7,8,10,19] and [25,31,35,41]. The maximum element in the left array is 19, and the minimum element in the right array is 25. Since 19 is less than 25, all elements in the left array are smaller than all elements in the right array. Therefore, the merge is void — the output is simply the left array followed by the right array without any interleaving.

Merge Sort Void Merge Operations Count | GATE CS 2026 Set-2 Q32

Computer Sciences > GATE 2026 SET-2 > Algorithms

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)

Correct : 3

The correct answer is 3.
A void merge occurs when all elements in the left sorted array are less than or equal to all elements in the right sorted array, so the merge simply concatenates L followed by R without interleaving.
Merge sort execution on A = [10, 7, 8, 19, 41, 35, 25, 31]: The algorithm recursively divides until single elements, then merges bottom-up. With 8 elements, there are 7 total merge operations across 3 levels.
Level 1 merges (base case, merging pairs of single elements):
Merge 1: [10] + [7] → [7, 10]. Since 10 > 7, elements interleave. Not void.
Merge 2: [8] + [19] → [8, 19]. Since 8 < 19, output is [8] then [19] directly. Void ✓.
Merge 3: [41] + [35] → [35, 41]. Since 41 > 35, elements interleave. Not void.
Merge 4: [25] + [31] → [25, 31]. Since 25 < 31, output is [25] then [31] directly. Void ✓.
Level 2 merges (merging sorted subarrays of size 2):
Merge 5: [7, 10] + [8, 19] → [7, 8, 10, 19]. Max(L) = 10 > Min(R) = 8, so elements interleave. Not void.
Merge 6: [35, 41] + [25, 31] → [25, 31, 35, 41]. Max(L) = 41 > Min(R) = 25, so elements interleave. Not void.
Level 3 merge (final merge):
Merge 7: [7, 8, 10, 19] + [25, 31, 35, 41] → [7, 8, 10, 19, 25, 31, 35, 41]. Max(L) = 19 < Min(R) = 25, so all of L comes before all of R. Void ✓.
Total void merges = 3.

Similar Questions

Related Topics

Similar Questions

Related Topics

Question Options

Sign in to ExamPrev