Java gcd gcd(int a, int b)

Description

Greatest common divisor. http://en.wikipedia.org/wiki/Greatest_common_divisor gcd( 6, 9 ) = 3 gcd( 4, 9 ) = 1 gcd( 0, 9 ) = 9 - see: http://math.stackexchange.com/questions/27719/what-is-gcd0-a-where-a-is-a-positive-integer gcd( 0, 0 ) = 0 - this is the only situation when the result is zero. gcd( 0, Integer.MIN_VALUE ) = Integer.MIN_VALUE gcd( Integer.MIN_VALUE, 0 ) = Integer.MIN_VALUE gcd( Integer.MIN_VALUE, Integer.MIN_VALUE ) = Integer.MIN_VALUE - these are the only situations when the result is negative, because abs( Integer.MIN_VALUE ) cannot fit in int. gcd( a, b ) = gcd( -a, b ) = gcd( a, -b ) = gcd( -a, -b ) = gcd( b, a ) The result is always positive except four exceptional situations described above.

License

Open Source License

Parameter

Parameter	Description
a	first number
b	second number

Return

greatest common divisor of a and b

Declaration

public static int gcd(int a, int b)

Method Source Code

//package com.java2s;
//License from project: Open Source License 

public class Main {
    /**//from   w w  w  . j ava2  s  .  c om
     * Greatest common divisor.<br>
     * http://en.wikipedia.org/wiki/Greatest_common_divisor<br>
     * gcd( 6, 9 ) = 3<br>
     * gcd( 4, 9 ) = 1<br>
     * gcd( 0, 9 ) = 9 - see: http://math.stackexchange.com/questions/27719/what-is-gcd0-a-where-a-is-a-positive-integer<br>
     * gcd( 0, 0 ) = 0 - this is the only situation when the result is zero.<br>
     * gcd( 0, Integer.MIN_VALUE ) = Integer.MIN_VALUE<br>
     * gcd( Integer.MIN_VALUE, 0 ) = Integer.MIN_VALUE<br>
     * gcd( Integer.MIN_VALUE, Integer.MIN_VALUE ) = Integer.MIN_VALUE
     * - these are the only situations when the result is negative,
     * because abs( Integer.MIN_VALUE ) cannot fit in int.<br>
     * gcd( a, b ) = gcd( -a, b ) = gcd( a, -b ) = gcd( -a, -b ) = gcd( b, a )<br>
     * The result is always positive except four exceptional situations described above.
     * @param a first number
     * @param b second number
     * @return greatest common divisor of a and b
     */
    public static int gcd(int a, int b) {
        if (a == 0)
            return b < 0 ? -b : b;
        if (b == 0)
            return a < 0 ? -a : a;
        if (a < 0) {
            // Integer.MIN_VALUE is power of two, so greatest common divisor is lowest set bit of second argument.
            // See: Integer.lowestOneBit.
            if (a == Integer.MIN_VALUE)
                return b & -b;
            a = -a;
        }
        if (b < 0) {
            if (b == Integer.MIN_VALUE)
                return a & -a;
            b = -b;
        }
        // Euclidean algorithm.
        // Binary algorithm seems to be slower on modern computers.
        // Both algorithms have the same asymptotics.
        while (b > 0) {
            int c = a % b;
            a = b;
            b = c;
        }
        return a;
    }

    /**
     * Greatest common divisor.<br>
     * http://en.wikipedia.org/wiki/Greatest_common_divisor<br>
     * gcd( 6, 9 ) = 3<br>
     * gcd( 4, 9 ) = 1<br>
     * gcd( 0, 9 ) = 9 - see: http://math.stackexchange.com/questions/27719/what-is-gcd0-a-where-a-is-a-positive-integer<br>
     * gcd( 0, 0 ) = 0 - this is the only situation when the result is zero.<br>
     * gcd( 0, Long.MIN_VALUE ) = Long.MIN_VALUE<br>
     * gcd( Long.MIN_VALUE, 0 ) = Long.MIN_VALUE<br>
     * gcd( Long.MIN_VALUE, Long.MIN_VALUE ) = Long.MIN_VALUE
     * - these are the only situations when the result is negative,
     * because abs( Long.MIN_VALUE ) cannot fit in long.<br>
     * gcd( a, b ) = gcd( -a, b ) = gcd( a, -b ) = gcd( -a, -b ) = gcd( b, a )<br>
     * The result is always positive except four exceptional situations described above.
     * @param a first number
     * @param b second number
     * @return greatest common divisor of a and b
     */
    public static long gcd(long a, long b) {
        if (a == 0L)
            return b < 0L ? -b : b;
        if (b == 0L)
            return a < 0L ? -a : a;
        if (a < 0L) {
            // Long.MIN_VALUE is power of two, so greatest common divisor is lowest set bit of second argument.
            // See: Long.lowestOneBit.
            if (a == Long.MIN_VALUE)
                return b & -b;
            a = -a;
        }
        if (b < 0L) {
            if (b == Long.MIN_VALUE)
                return a & -a;
            b = -b;
        }
        if (a <= Integer.MAX_VALUE && b <= Integer.MAX_VALUE) {
            int aa = (int) a;
            int bb = (int) b;
            while (bb > 0) {
                int c = aa % bb;
                aa = bb;
                bb = c;
            }
            return aa;
        }
        while (b > 0L) {
            long c = a % b;
            a = b;
            b = c;
        }
        return a;
    }
}