Algorithms | Analysis of Algorithms (Recurrences) | Question 11
Consider the following recurrence:
Which one of the following is true?
(A) T(n) =
(loglogn)
(B) T(n) =
(logn)
(C) T(n) =
(sqrt(n))
(D) T(n) =
(n)
(A) A
(B) B
(C) C
(D) D
Answer: (B) Explanation: This question can be solved by first change of variable and then Master Method.
Let n = 2^m
T(2^m) = T(2^(m/2)) + 1
Let T(2^m) = S(m)
S(m) = 2S(m/2) + 1
Above expression is a binary tree traversal recursion whose time complexity is
(m). You can also prove using
Master theorem.
S(m) = (m)
= (logn) /* Since n = 2^m */
Now, let us go back to the original recursive function T(n)
T(n) = T(2^m) = S(m)
= (Logn)
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Last Updated :
28 Jun, 2021
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