GATE CS 2021 Set 2 — Question 18
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Algorithms → Asymptotic Analysis → Best, Worst, Average Case
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Question
What is the worst-case number of arithmetic operations performed by recursive binary search on a sorted array of size ?
Correct answer
(B) Θ(₂(n))
Solution
The recursive binary search algorithm works by comparing the target value to the middle element of the array. The recurrence relation for the number of operations is:where represents the constant number of arithmetic operations (like calculating the mid index and comparisons) performed at each step.Using the Master Theorem for :
Since , we fall into Case 2 of the Master Theorem:Thus, the worst-case time complexity (and number of operations) is .
Since , we fall into Case 2 of the Master Theorem:Thus, the worst-case time complexity (and number of operations) is .
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