Java BigInteger LCM lcm(BigInteger... values)

Description

Calculates the least common multiple of the specified BigInteger big integer numbers.

License

BSD License

Parameter

Parameter	Description
values	values for which the lcm is to be computed

Return

lcm of all values, negative for uneven number of negative values, one for no values or if all values are zero and positive otherwise

Declaration

public static BigInteger lcm(BigInteger... values)

Method Source Code

//package com.java2s;
/*/*from  w ww  . j ava  2s  .c  o  m*/
 * =============================================================================
 * Simplified BSD License, see http://www.opensource.org/licenses/
 * -----------------------------------------------------------------------------
 * Copyright (c) 2008-2009, Marco Terzer, Zurich, Switzerland
 * All rights reserved.
 * 
 * Redistribution and use in source and binary forms, with or without 
 * modification, are permitted provided that the following conditions are met:
 * 
 *     * Redistributions of source code must retain the above copyright notice, 
 *       this list of conditions and the following disclaimer.
 *     * Redistributions in binary form must reproduce the above copyright 
 *       notice, this list of conditions and the following disclaimer in the 
 *       documentation and/or other materials provided with the distribution.
 *     * Neither the name of the Swiss Federal Institute of Technology Zurich 
 *       nor the names of its contributors may be used to endorse or promote 
 *       products derived from this software without specific prior written 
 *       permission.
 * 
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" 
 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 
 * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE 
 * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR 
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 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN 
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 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE 
 * POSSIBILITY OF SUCH DAMAGE.
 * =============================================================================
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import java.math.BigInteger;

public class Main {
    /**
     * Calculates the least common multiple of the specified {@link BigInteger 
     * big integer} numbers.
     * This method might be useful to scale up a vector of fractions to convert
     * them to integers.
     * <p>
     * The result is negative if an uneven number of single values is negative,
     * one for no values or if all values are zero and positive otherwise.
     * 
     * @param values   values for which the lcm is to be computed
     * @return         lcm of all values, negative for uneven number of 
     *                negative values, one for no values or if all values are zero 
     *                and positive otherwise
     */
    public static BigInteger lcm(BigInteger... values) {
        if (values.length == 0)
            return BigInteger.ONE;
        BigInteger lcm = values[0];
        for (int i = 1; i < values.length; i++) {
            if (values[i].signum() != 0) {
                final BigInteger gcd = lcm.gcd(values[i]);
                if (gcd.equals(BigInteger.ONE)) {
                    lcm = lcm.multiply(values[i]);
                } else {
                    if (!values[i].equals(gcd)) {
                        lcm = lcm.multiply(values[i].divide(gcd));
                    }
                }
            }
        }
        return lcm;
    }

    /**
     * Calculates the greatest common divisor of the specified {@link BigInteger 
     * big integer} numbers.
     * This method might be useful to scale down a vector of big integers. 
     * <p>
     * If all numbers are negative, the resulting gcd is also negative. If all 
     * numbers are zero, the result is zero. Otherwise, the result is positive.
     * 
     * @param values   values for which the gcd is to be computed
     * @return         gcd of all values, negative if all values negative, zero
     *                if all values zero, positive otherwise
     */
    public static BigInteger gcd(BigInteger... values) {
        if (values.length == 0)
            return BigInteger.ONE;
        int allSgn = values[0].signum();
        BigInteger gcd = values[0];
        for (int i = 1; i < values.length; i++) {
            if (allSgn != values[i].signum())
                allSgn = 1;
            if (gcd.signum() == 0 || gcd.equals(BigInteger.ONE))
                break;
            if (values[i].signum() != 0) {
                gcd = gcd.gcd(values[i]);
            }
        }
        if (allSgn == 0)
            return BigInteger.ZERO;
        if (allSgn < 0) {
            return gcd.negate();
        }
        return gcd;
    }
}