GATE CS 2021 Set 1 — Question 40
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Algorithms → Asymptotic Analysis → Recursion Tree Method
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Question
Consider the following recurrence relation.Which one of the following options is correct?
Correct answer
(C) T(n) = Θ(n)
Solution
The given recurrence relation is for . This is a divide-and-conquer recurrence of the form .
1.Identify parameters: Here, and . The work done at each level is .
2.Check the sum of coefficients:
3.Apply Generalized Master Theorem / Akra-Bazzi: Since the sum of the coefficients , the work done at the root level, , dominates the recurrence. Specifically, if and , then .
4.Conclusion: Since , the complexity is .
Alternatively, using the substitution method, we can show that for some constant , proving . Since is trivial due to the term, we have .Continue learning with Success Tracker
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