GATE CS 2024 Set 1 — Question 42
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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
(A) T(n) = Θ(n log log n)
Solution
The given recurrence relation is:To solve this, we can use the substitution method.
Let , which implies . Then .
Substituting these into the recurrence:Divide the entire equation by :Let . The recurrence becomes:This is a standard recurrence relation (similar to binary search complexity) whose solution is:Now, substitute back and :Thus, option (A) is correct.
Let , which implies . Then .
Substituting these into the recurrence:Divide the entire equation by :Let . The recurrence becomes:This is a standard recurrence relation (similar to binary search complexity) whose solution is:Now, substitute back and :Thus, option (A) is correct.
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