Algorithms | Analysis of Algorithms | Question 16
Consider the following three claims
I (n + k)^m = (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 =(n^k) (II) 2^(n+1) = 2*2^n = O(2^n)