GCD (greatest common divisor)【求最大公约数】

The following snippet is copied from the book(Structure and Interpretation of Computer Programs 1.2.5)

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The greatest common divisor (GCD) of two integers a and b is defined to be the largest integer that divides both a and b with no remainder.
The idea of the algorithm is based on the observation that, if r is the remainder when a is divided by b, then the common divisors of a and b are precisely the same as the common divisors of b and r. Thus, we can use the equation

GCD(a,b) = GCD(b,r)

to successively reduce the problem of computing a GCD to the problem of computing the GCD of smaller and smaller pairs of integers. For example,

GCD(246,40) = GCD(40,6)
            = GCD(6，4)
            = GCD(4，2)
            = GCD(2，0)
            = 2
reduces GCD(206,40) to GCD(2,0), which is 2. It is possible to show that starting with any two positive integers and performing repeated reductions will always eventually produce a pair where the second number is 0. Then the GCD is the other number in the pair. This method for computing the GCD is known as Euclid's Algorithm.42

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The following code works in VC2005

 

#include "stdafx.h"
#include

/*

function: gcd

input:     a,b

output:  the gcd of integer a and b

*/

int gcd(int a, int b)
{
 if(0 == b)
 {
  return a;
 }
 else
 {
  return gcd(b, a%b);
 }
}

 

int _tmain(int argc, _TCHAR* argv[])
{
 int r = gcd(206, 40);
 printf("r=%d", r);

 r  = gcd(40, 206);
 printf("r=%d", r);
 return 0;
}

 

remark: Euclid's Algorithm: 欧几里得算法