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Algorithms | Analysis of Algorithms | Question 16

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Consider the following three claims:

(n+k)^m = \Theta(n^m) where k and m are constants

II 2^{n+1} = O(2^n) 

 III 2^{2n+1} = O(2^n)

Which of these claims is correct? (GATE CS 2003)


I and II


I and III


II and III


I, II and III

Answer: (A)


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

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Last Updated : 28 Jun, 2021
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