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

1. Java
2. Development Class
3. Math

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
 *  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;
  }
}

   
    
    
    
    
  

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