Top MCQs on Complexity Analysis using Recurrence Relations with Answers

Question 31

For constants a≥1 and b>1, consider the following recurrence defined on the non-negative integers:

T(n) = a⋅T(n/b) + f(n) 

Which one of the following options is correct about the recurrence T(n)?

• A
• B
• C
• D

Question 32

For parameters a and b, both of which are ω(1), T(n)=T(n^1/a)+1, and T(b)=1. Then T(n) is

• Θ(log_alog_bn)
• Θ(log_abn)
• Θ(log_blog_an)
• Θ(log₂log₂n)

Question 33

We can show that the clique problem is NP-hard by proving that

• CLIQUE ≤ P 3-CNF_SAT
• CLIQUE ≤ P VERTEX_COVER
• CLIQUE ≤ P SUBSET_SUM
• None of the above

Question 34

Standard planning algorithms assume environment to be __________.

• Both deterministic and fully observable
• Neither deterministic nor fully observable
• Deterministic but not fully observable
• Not deterministic but fully observable

Question 35

Suppose T(n) = 2T(n/2) + n, T(0) = T(1) = 1 Which one of the following is false. ( GATE CS 2005)
a) T(n) = O(n^2)
b) T(n) = [Tex]\\theta[/Tex](nLogn)
c) T(n) = [Tex]\\Omega[/Tex](n^2)
d) T(n) = O(nLogn)

• A
• B
• C
• D