GATE CS 2026 Set 2 — Question 25
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Algorithms → Asymptotic Analysis → Master Theorem
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Question
Which of the following can be recurrence relation(s) corresponding to an algorithm with time complexity ?
Correct answer
(A) T(n) = T(n-1) + 1, T(1) = 1; (B) T(n) = 2T((n)/(2)) + 1, T(1) = 1
Solution
We solve each recurrence relation:(A)
This represents a simple loop or recursion depth of with constant work per step.
.
This is correct.(B)
Using Master Theorem: .
.
Since , Case 1 applies.
.
This is correct.(C)
Using Master Theorem: .
.
Since , Case 2 applies.
.
This is incorrect.(D)
This is the sum of the first integers.
.
This is incorrect.Thus, options (A) and (B) are correct.
This represents a simple loop or recursion depth of with constant work per step.
.
This is correct.(B)
Using Master Theorem: .
.
Since , Case 1 applies.
.
This is correct.(C)
Using Master Theorem: .
.
Since , Case 2 applies.
.
This is incorrect.(D)
This is the sum of the first integers.
.
This is incorrect.Thus, options (A) and (B) are correct.
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