Algorithms | Analysis of Algorithms | Question 16

Consider the following three claims
I (n + k)^m = \theta(n^m), where k and m are constants
II 2^(n + 1) = 0(2^n)
III 2^(2n + 1) = 0(2^n)
Which of these claims are correct? (GATE CS 2003)

(A) I and II
(B) I and III
(C) II and III
(D) I, II and III


Answer: (A)

Explanation:

(I)  (n+m)^k = n^k + c1*n^(k-1) + ... k^m = \theta(n^k)
(II)  2^(n+1) = 2*2^n = O(2^n)


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