GATE CS 2024 Set 1 — Question 17
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Question
Given an integer array of size , we want to check if the array is sorted (in either ascending or descending order). An algorithm solves this problem by making a single pass through the array and comparing each element of the array only with its adjacent elements. The worst-case time complexity of this algorithm is
Correct answer
(A) both O(N) and Ω(N)
Solution
To determine if an array of size is sorted (either ascending or descending), an algorithm must examine every element at least once to ensure no pair violates the sorting order. A single-pass algorithm that compares each element with its adjacent neighbor will perform exactly comparisons in the worst case (e.g., when the array is indeed sorted or the violation occurs at the very end). Since the number of operations is proportional to , the time complexity is . By the definitions of asymptotic notation, implies that and . Therefore, the worst-case time complexity is both
O(N) and .Continue learning with Success Tracker
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