What is the complexity of the following recurrence: T'п) — 4T (п/2) +п, T(1) —D1 %3D
What is the complexity of the following recurrence: T'п) — 4T (п/2) +п, T(1) —D1 %3D
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Step 1
The recursion tree can be formed of the given recurrence as follows:
T(n) = 4T(n/2) + n
= n + 4(n/2 + 4T(n/22))
= … + (4i – 1/2i -1 )n + 4iT (n/22))
= n + 2n + 4n + … + 4log n T(1)
log2 n-1
= Σ + Θ (4 log n)
i=0
= n (2log n- 1) / (2 -1 ) + Θ (2log n)2 { (22)log n = ( 2log n)2 }
= Θ (n2) + Θ(n2)
= Θ(n2)
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