GATE | GATE-CS-2003 | Question 66

The cube root of a natural number n is defined as the largest natural number m such that m3 ≤ n. The complexity of computing the cube root of n (n is represented in binary notation) is:
(A) O(n) but not O(n0.5)
(B) O(n0.5) but not O((log n)k) for any constant k > 0
(C) O((log n)k) for some constant k > 0, but not O ((log log n)m) for any constant m > 0
(D) O((log log n)m) for some constant k > 0.5, but not O((log log n)0.5)

Answer: (C)

Explanation: Refer

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