# Returns a double representation of the (http://mathworld.wolfram.com/BinomialCoefficient.html) Binomial Coefficient : Math « Development Class « Java

Returns a double representation of the (http://mathworld.wolfram.com/BinomialCoefficient.html) Binomial Coefficient

import java.io.File;

/*
* Licensed to the Apache Software Foundation (ASF) under one or more
*  contributor license agreements.  See the NOTICE file distributed with
*  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
*
*
*  Unless required by applicable law or agreed to in writing, software
*  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
*  See the License for the specific language governing permissions and
*
*
*/
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;
}
}

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