GATE DA 2026 Set 1 — Question 31
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Programming, Data Structures & Algorithms → Complexity Analysis → Best, Average & Worst Case
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Question
Let A be a sorted array containing 1000 distinct integers. You perform a recursive binary search on A to find an element y. Suppose each comparison checks whether the middle element computed during the current recursive step is equal to, less than, or greater than y.The maximum number of comparisons that may have to be performed if y is not an element of A is _______ . (Answer in integer)
Correct answer
10 to 10
Solution
The binary search algorithm divides the search space by half in each step. The number of comparisons required in the worst case (when the element is not found) is given by the height of the recursion tree, which is .Given :Alternatively, we can trace the reduction of the array size:
1.1000 elements 1 comparison
2.500 elements 1 comparison
3.250 elements 1 comparison
4.125 elements 1 comparison
5.62 elements 1 comparison
6.31 elements 1 comparison
7.15 elements 1 comparison
8.7 elements 1 comparison
9.3 elements 1 comparison
10.1 element 1 comparison
After the 10th comparison, if the element is not found, the search space becomes empty. Thus, the maximum number of comparisons is 10.Continue learning with Success Tracker
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