GATE CS 2016 Set 1 — Question 23
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+1 / -0.33EasyBubble, Insertion, Selection SortSortingAlgorithmsMerge SortQuick SortBest, Worst, Average CaseAsymptotic Analysis
Algorithms → Asymptotic Analysis → Best, Worst, Average Case
Last updated
Question
The worst case running times of Insertion sort, Merge sort and Quick sort, respectively, are:
Correct answer
(D) Θ(n²), Θ(n log n), and Θ(n²)
Solution
1.Insertion Sort: In the worst case (e.g., reverse sorted array), the time complexity is .
2.Merge Sort: The recurrence relation is , which solves to in the worst case.
3.Quick Sort: In the worst case (e.g., already sorted array with first/last element as pivot), the recurrence is , which solves to .
Therefore, the respective worst-case running times are , , and .Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE CS question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Asymptotic Analysis
2026 Set 1 Q17Consider the following recurrence relations: For all ,…2026 Set 2 Q24Consider the following functions, where is a positive integer.…2026 Set 2 Q25Which of the following can be recurrence relation(s) corresponding to an algorithm with time…2026 Set 2 Q32Consider an array . Suppose the merge sort algorithm is…2026 Set 2 Q37Let be a weighted directed acyclic graph with edges and vertices. Given and a…