Java Binomial Coefficients binomialCoefficientDouble(final int n, final int k)

Description

Returns a <code>double</code> representation of the <a href="http://mathworld.wolfram.com/BinomialCoefficient.html"> Binomial Coefficient</a>, "<code>n choose k</code>", the number of <code>k</code>-element subsets that can be selected from an <code>n</code>-element set.

License

Apache License

Parameter

Parameter	Description
n	the size of the set
k	the size of the subsets to be counted

Exception

Parameter	Description
IllegalArgumentException	if preconditions are not met.

Return

n choose k

Declaration

public static double binomialCoefficientDouble(final int n, final int k)

Method Source Code

//package com.java2s;
/*//from  w w  w .j a  v  a 2  s .  c om
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

public class Main {
    /**
     * Returns a <code>double</code> representation of the <a
     * href="http://mathworld.wolfram.com/BinomialCoefficient.html"> Binomial
     * Coefficient</a>, "<code>n choose k</code>", the number of
     * <code>k</code>-element subsets that can be selected from an
     * <code>n</code>-element set.
     * <p>
     * <Strong>Preconditions</strong>:
     * <ul>
     * <li> <code>0 <= k <= n </code> (otherwise
     * <code>IllegalArgumentException</code> is thrown)</li>
     * <li> The result is small enough to fit into a <code>double</code>. The
     * largest value of <code>n</code> for which all coefficients are <
     * Double.MAX_VALUE is 1029. If the computed value exceeds Double.MAX_VALUE,
     * Double.POSITIVE_INFINITY is returned</li>
     * </ul></p>
     * 
     * @param n the size of the set
     * @param k the size of the subsets to be counted
     * @return <code>n choose k</code>
     * @throws IllegalArgumentException if preconditions are not met.
     */
    public static double binomialCoefficientDouble(final int n, final int k) {
        return Math.floor(Math.exp(binomialCoefficientLog(n, k)) + 0.5);
    }

    /**
     * Returns the natural <code>log</code> of the <a
     * href="http://mathworld.wolfram.com/BinomialCoefficient.html"> Binomial
     * Coefficient</a>, "<code>n choose k</code>", the number of
     * <code>k</code>-element subsets that can be selected from an
     * <code>n</code>-element set.
     * <p>
     * <Strong>Preconditions</strong>:
     * <ul>
     * <li> <code>0 <= k <= n </code> (otherwise
     * <code>IllegalArgumentException</code> is thrown)</li>
     * </ul></p>
     * 
     * @param n the size of the set
     * @param k the size of the subsets to be counted
     * @return <code>n choose k</code>
     * @throws IllegalArgumentException if preconditions are not met.
     */
    public static double binomialCoefficientLog(final int n, final int k) {
        if (n < k) {
            throw new IllegalArgumentException("must have n >= k for binomial coefficient (n,k)");
        }
        if (n < 0) {
            throw new IllegalArgumentException("must have n >= 0 for binomial coefficient (n,k)");
        }
        if ((n == k) || (k == 0)) {
            return 0;
        }
        if ((k == 1) || (k == n - 1)) {
            return Math.log((double) n);
        }
        double logSum = 0;

        // n!/k!
        for (int i = k + 1; i <= n; i++) {
            logSum += Math.log((double) i);
        }

        // divide by (n-k)!
        for (int i = 2; i <= n - k; i++) {
            logSum -= Math.log((double) i);
        }

        return logSum;
    }

    /** 
     * <p>Returns the 
     * <a href="http://mathworld.wolfram.com/Logarithm.html">logarithm</a>
     * for base <code>b</code> of <code>x</code>.
     * </p>
     * <p>Returns <code>NaN<code> if either argument is negative.  If 
     * <code>base</code> is 0 and <code>x</code> is positive, 0 is returned.
     * If <code>base</code> is positive and <code>x</code> is 0, 
     * <code>Double.NEGATIVE_INFINITY</code> is returned.  If both arguments
     * are 0, the result is <code>NaN</code>.</p>
     * 
     * @param base the base of the logarithm, must be greater than 0
     * @param x argument, must be greater than 0
     * @return the value of the logarithm - the number y such that base^y = x.
     * @since 1.2
     */
    public static double log(double base, double x) {
        return Math.log(x) / Math.log(base);
    }
}