Main.java Source code

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Here is the source code for Main.java

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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 an exact 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>long</code>. The
     * largest value of <code>n</code> for which all coefficients are
     * <code> < Long.MAX_VALUE</code> is 66. If the computed value exceeds
     * <code>Long.MAX_VALUE</code> an <code>ArithMeticException
     *      </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.
     * @throws ArithmeticException if the result is too large to be represented
     *         by a long integer.
     */
    public static long binomialCoefficient(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 1;
        }
        if ((k == 1) || (k == n - 1)) {
            return n;
        }

        long result = Math.round(binomialCoefficientDouble(n, k));
        if (result == Long.MAX_VALUE) {
            throw new ArithmeticException("result too large to represent in a long integer");
        }
        return result;
    }

    /**
     * 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;
    }
}