GATE CS 2016 Set 2 — Question 49
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.NAT+2 / -0HardMaster TheoremAsymptotic AnalysisAlgorithmsRecursion Tree Method
Algorithms → Asymptotic Analysis → Master Theorem
Last updated
Question
The given diagram shows the flowchart for a recursive function . Assume that all statements, except for the recursive calls, have time complexity. If the worst case time complexity of this function is , then the least possible value (accurate up to two decimal positions) of is ______.
Correct answer
2.2 to 2.4
Solution
The worst-case time complexity is determined by the path in the flowchart that generates the maximum number of recursive calls.Tracing the longest path:
Recurrence relation: .
Using Master Theorem: .
.
Rounded to two decimal places: 2.32.
1.Start (1st call)
2.Right branch (2nd call) (3rd call)
3.Down branch (4th call)
4.Left branch (5th call) Return
Total recursive calls per step: 5.Recurrence relation: .
Using Master Theorem: .
.
Rounded to two decimal places: 2.32.
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…