Algorithms | Analysis of Algorithms | Question 14

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

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

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How many recursive calls are made by this function?

(A)	\theta(logn)

(B)	\Omega(n)

(C)	\theta(loglogn)

(D)	\theta(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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