GATE CS 2025 Set 2 — Question 41
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Question
An array of length with distinct elements is said to be bitonic if there is an index such that is sorted in the non-decreasing order and is sorted in the non-increasing order.Which ONE of the following represents the best possible asymptotic bound for the worst-case number of comparisons by an algorithm that searches for an element in a bitonic array ?
Correct answer
(D) Θ(log n)
Solution
A bitonic array is an array that first increases (non-decreasing) and then decreases (non-increasing). To search for an element in a bitonic array of length :
1.Find the Peak: The peak element (the point where the array transitions from increasing to decreasing) can be found using a modified binary search. By comparing with , we can determine if the peak is to the left or right. This takes comparisons.
2.Binary Search on Segments: Once the peak index is identified, the array is split into two sorted subarrays: (sorted in non-decreasing order) and (sorted in non-increasing order).
3.Search: Perform a standard binary search on the first segment () and a reverse binary search on the second segment ().
The total number of comparisons in the worst case is . Since binary search is the optimal comparison-based search for sorted data, the best possible asymptotic bound for the worst-case is .Continue learning with Success Tracker
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