GATE CS 2026 Set 2 — Question 32
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Algorithms → Divide & Conquer → Merge Sort (D&C)
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Question
Consider an array . Suppose the merge sort algorithm is executed on array 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 and sorted right array is said to be void if the output of the merge operation is the elements of array followed by the elements of array .The number of void merge operations among these 7 merge operations is __________.
Correct answer
3 to 3
Solution
We perform Merge Sort on the array .Step 1: Splitting
A merge is void if all elements of are less than or equal to all elements of (i.e., ), resulting in the concatenation then .
- Level 0:
- Level 1: and
- Level 2: , , ,
- Level 3: , , , , , , ,
A merge is void if all elements of are less than or equal to all elements of (i.e., ), resulting in the concatenation then .
1.Merge([10], [7]):
- .
- Result: .
- Is it then ? No (). Not void.
- .
- Result: .
- Is it then ? Yes (). Void (1).
- .
- Result: .
- Is it then ? No (). Not void.
- .
- Result: .
- Is it then ? Yes (). Void (2).
- .
- Result: .
- Is it then ? No (). Not void.
- .
- Result: .
- Is it then ? No (). Not void.
- .
- , .
- Since , the result is simply concatenated with : .
- Is it then ? Yes. Void (3).
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