I just found this algorithm to compute the greatest common divisor in my lecture notes:
public static int gcd( int a, int b ) {
while (b != 0) {
final int r = a % b;
a = b;
b = r;
}
return a;
}
So r is the remainder when dividing b into a (get the mod). Then b is assigned to a, and the remainder is assigned to b, and a is returned. I can't for the life of my see how this works!
And then, apparently this algorithm doesn't work for all cases, and this one must then be used:
public static int gcd( int a, int b ) {
final int gcd;
if (b != 0) {
final int q = a / b;
final int r = a % b; // a == r + q * b AND r == a - q * b.
gcd = gcd( b, r );
} else {
gcd = a;
}
return gcd;
}
I don't understand the reasoning behind this. I generally get recursion and am good at Java but this is eluding me. Help please?
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