GATE CS 2017 Set 2 — Question 3
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Algorithms → Arrays & Strings → Asymptotic Notations
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Question
Match the algorithms with their time complexities:
| Algorithm | Time complexity |
|---|---|
| (P) Towers of Hanoi with disks | (i) |
| (Q) Binary search given sorted numbers | (ii) |
| (R) Heap sort given numbers at the worst case | (iii) |
| (S) Addition of two matrices | (iv) |
Correct answer
(C) (P) arrow (iii), (Q) arrow (iv), (R) arrow (ii), (S) arrow (i)
Solution
Matching algorithms to their standard time complexities:
- (P) Towers of Hanoi: The recurrence relation is , which solves to . Thus, (P) matches (iii).
- (Q) Binary search: Searching in a sorted array of size takes time. Thus, (Q) matches (iv).
- (R) Heap sort: The worst-case time complexity of heap sort is . Thus, (R) matches (ii).
- (S) Addition of two matrices: Adding two matrices requires visiting each of the elements once. Thus, the complexity is . Thus, (S) matches (i).
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