Algorithms | Analysis of Algorithms | Question 14

In the following C function, let n >= m. 

C

int gcd(n, m)
{
    if (n % m == 0)
        return m;
    n = n % m;
    return gcd(m, n);
}

How many recursive calls are made by this function?
(A) (log(n))
(B) (n)
(C) (log(log(n)))
(D) (sqrt(n))

(A)

A

(B)

B

(C)

C

(D)

D

Answer: (A)

Explanation:

Above code is implementation of the Euclidean algorithm for finding Greatest Common Divisor (GCD). Please see http://mathworld.wolfram.com/EuclideanAlgorithm.html for time complexity.

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