/*
 * @(#)Arrays.java	1.59 04/04/01
 *
 * Copyright 2004 Sun Microsystems, Inc. All rights reserved.
 * SUN PROPRIETARY/CONFIDENTIAL. Use is subject to license terms.
 */

package java.util;

import java.lang.reflect.*;

/**
 * This class contains various methods for manipulating arrays (such as
 * sorting and searching).  This class also contains a static factory 
 * that allows arrays to be viewed as lists.
 *
 * <p>The methods in this class all throw a <tt>NullPointerException</tt> if
 * the specified array reference is null, except where noted.
 *
 * <p>The documentation for the methods contained in this class includes
 * briefs description of the <i>implementations</i>.  Such descriptions should
 * be regarded as <i>implementation notes</i>, rather than parts of the
 * <i>specification</i>.  Implementors should feel free to substitute other
 * algorithms, so long as the specification itself is adhered to.  (For
 * example, the algorithm used by <tt>sort(Object[])</tt> does not have to be
 * a mergesort, but it does have to be <i>stable</i>.)
 *
 * <p>This class is a member of the 
 * <a href="{@docRoot}/../guide/collections/index.html">
 * Java Collections Framework</a>.
 *
 * @author  Josh Bloch
 * @author  Neal Gafter
 * @version 1.59, 04/01/04
 * @see     Comparable
 * @see     Comparator
 * @since   1.2
 */

public class Arrays {
    // Suppresses default constructor, ensuring non-instantiability.
    private Arrays() {
    }

    // Sorting

    /**
     * Sorts the specified array of longs into ascending numerical order.
     * The sorting algorithm is a tuned quicksort, adapted from Jon
     * L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
     * Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
     * 1993).  This algorithm offers n*log(n) performance on many data sets
     * that cause other quicksorts to degrade to quadratic performance.
     *
     * @param a the array to be sorted.
     */
    public static void sort(long[] a) {
	sort1(a, 0, a.length);
    }

    /**
     * Sorts the specified range of the specified array of longs into
     * ascending numerical order.  The range to be sorted extends from index
     * <tt>fromIndex</tt>, inclusive, to index <tt>toIndex</tt>, exclusive.
     * (If <tt>fromIndex==toIndex</tt>, the range to be sorted is empty.)
     *
     * <p>The sorting algorithm is a tuned quicksort, adapted from Jon
     * L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
     * Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
     * 1993).  This algorithm offers n*log(n) performance on many data sets
     * that cause other quicksorts to degrade to quadratic performance.
     *
     * @param a the array to be sorted.
     * @param fromIndex the index of the first element (inclusive) to be
     *        sorted.
     * @param toIndex the index of the last element (exclusive) to be sorted.
     * @throws IllegalArgumentException if <tt>fromIndex > toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
     * <tt>toIndex > a.length</tt>
     */
    public static void sort(long[] a, int fromIndex, int toIndex) {
        rangeCheck(a.length, fromIndex, toIndex);
	sort1(a, fromIndex, toIndex-fromIndex);
    }

    /**
     * Sorts the specified array of ints into ascending numerical order.
     * The sorting algorithm is a tuned quicksort, adapted from Jon
     * L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
     * Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
     * 1993).  This algorithm offers n*log(n) performance on many data sets
     * that cause other quicksorts to degrade to quadratic performance.
     *
     * @param a the array to be sorted.
     */
    public static void sort(int[] a) {
	sort1(a, 0, a.length);
    }

    /**
     * Sorts the specified range of the specified array of ints into
     * ascending numerical order.  The range to be sorted extends from index
     * <tt>fromIndex</tt>, inclusive, to index <tt>toIndex</tt>, exclusive.
     * (If <tt>fromIndex==toIndex</tt>, the range to be sorted is empty.)<p>
     *
     * The sorting algorithm is a tuned quicksort, adapted from Jon
     * L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
     * Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
     * 1993).  This algorithm offers n*log(n) performance on many data sets
     * that cause other quicksorts to degrade to quadratic performance.
     *
     * @param a the array to be sorted.
     * @param fromIndex the index of the first element (inclusive) to be
     *        sorted.
     * @param toIndex the index of the last element (exclusive) to be sorted.
     * @throws IllegalArgumentException if <tt>fromIndex > toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
     *	       <tt>toIndex > a.length</tt>
     */
    public static void sort(int[] a, int fromIndex, int toIndex) {
        rangeCheck(a.length, fromIndex, toIndex);
	sort1(a, fromIndex, toIndex-fromIndex);
    }

    /**
     * Sorts the specified array of shorts into ascending numerical order.
     * The sorting algorithm is a tuned quicksort, adapted from Jon
     * L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
     * Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
     * 1993).  This algorithm offers n*log(n) performance on many data sets
     * that cause other quicksorts to degrade to quadratic performance.
     *
     * @param a the array to be sorted.
     */
    public static void sort(short[] a) {
	sort1(a, 0, a.length);
    }

    /**
     * Sorts the specified range of the specified array of shorts into
     * ascending numerical order.  The range to be sorted extends from index
     * <tt>fromIndex</tt>, inclusive, to index <tt>toIndex</tt>, exclusive.
     * (If <tt>fromIndex==toIndex</tt>, the range to be sorted is empty.)<p>
     *
     * The sorting algorithm is a tuned quicksort, adapted from Jon
     * L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
     * Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
     * 1993).  This algorithm offers n*log(n) performance on many data sets
     * that cause other quicksorts to degrade to quadratic performance.
     *
     * @param a the array to be sorted.
     * @param fromIndex the index of the first element (inclusive) to be
     *        sorted.
     * @param toIndex the index of the last element (exclusive) to be sorted.
     * @throws IllegalArgumentException if <tt>fromIndex > toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
     *	       <tt>toIndex > a.length</tt>
     */
    public static void sort(short[] a, int fromIndex, int toIndex) {
        rangeCheck(a.length, fromIndex, toIndex);
	sort1(a, fromIndex, toIndex-fromIndex);
    }

    /**
     * Sorts the specified array of chars into ascending numerical order.
     * The sorting algorithm is a tuned quicksort, adapted from Jon
     * L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
     * Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
     * 1993).  This algorithm offers n*log(n) performance on many data sets
     * that cause other quicksorts to degrade to quadratic performance.
     *
     * @param a the array to be sorted.
     */
    public static void sort(char[] a) {
	sort1(a, 0, a.length);
    }

    /**
     * Sorts the specified range of the specified array of chars into
     * ascending numerical order.  The range to be sorted extends from index
     * <tt>fromIndex</tt>, inclusive, to index <tt>toIndex</tt>, exclusive.
     * (If <tt>fromIndex==toIndex</tt>, the range to be sorted is empty.)<p>
     *
     * The sorting algorithm is a tuned quicksort, adapted from Jon
     * L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
     * Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
     * 1993).  This algorithm offers n*log(n) performance on many data sets
     * that cause other quicksorts to degrade to quadratic performance.
     *
     * @param a the array to be sorted.
     * @param fromIndex the index of the first element (inclusive) to be
     *        sorted.
     * @param toIndex the index of the last element (exclusive) to be sorted.
     * @throws IllegalArgumentException if <tt>fromIndex > toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
     *	       <tt>toIndex > a.length</tt>
     */
    public static void sort(char[] a, int fromIndex, int toIndex) {
        rangeCheck(a.length, fromIndex, toIndex);
	sort1(a, fromIndex, toIndex-fromIndex);
    }

    /**
     * Sorts the specified array of bytes into ascending numerical order.
     * The sorting algorithm is a tuned quicksort, adapted from Jon
     * L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
     * Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
     * 1993).  This algorithm offers n*log(n) performance on many data sets
     * that cause other quicksorts to degrade to quadratic performance.
     *
     * @param a the array to be sorted.
     */
    public static void sort(byte[] a) {
	sort1(a, 0, a.length);
    }

    /**
     * Sorts the specified range of the specified array of bytes into
     * ascending numerical order.  The range to be sorted extends from index
     * <tt>fromIndex</tt>, inclusive, to index <tt>toIndex</tt>, exclusive.
     * (If <tt>fromIndex==toIndex</tt>, the range to be sorted is empty.)<p>
     *
     * The sorting algorithm is a tuned quicksort, adapted from Jon
     * L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
     * Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
     * 1993).  This algorithm offers n*log(n) performance on many data sets
     * that cause other quicksorts to degrade to quadratic performance.
     *
     * @param a the array to be sorted.
     * @param fromIndex the index of the first element (inclusive) to be
     *        sorted.
     * @param toIndex the index of the last element (exclusive) to be sorted.
     * @throws IllegalArgumentException if <tt>fromIndex > toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
     *	       <tt>toIndex > a.length</tt>
     */
    public static void sort(byte[] a, int fromIndex, int toIndex) {
        rangeCheck(a.length, fromIndex, toIndex);
	sort1(a, fromIndex, toIndex-fromIndex);
    }

    /**
     * Sorts the specified array of doubles into ascending numerical order.
     * <p>
     * The <code><</code> relation does not provide a total order on
     * all floating-point values; although they are distinct numbers
     * <code>-0.0 == 0.0</code> is <code>true</code> and a NaN value
     * compares neither less than, greater than, nor equal to any
     * floating-point value, even itself.  To allow the sort to
     * proceed, instead of using the <code><</code> relation to
     * determine ascending numerical order, this method uses the total
     * order imposed by {@link Double#compareTo}.  This ordering
     * differs from the <code><</code> relation in that
     * <code>-0.0</code> is treated as less than <code>0.0</code> and
     * NaN is considered greater than any other floating-point value.
     * For the purposes of sorting, all NaN values are considered
     * equivalent and equal.
     * <p>
     * The sorting algorithm is a tuned quicksort, adapted from Jon
     * L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
     * Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
     * 1993).  This algorithm offers n*log(n) performance on many data sets
     * that cause other quicksorts to degrade to quadratic performance.
     *
     * @param a the array to be sorted.
     */
    public static void sort(double[] a) {
	sort2(a, 0, a.length);
    }

    /**
     * Sorts the specified range of the specified array of doubles into
     * ascending numerical order.  The range to be sorted extends from index
     * <tt>fromIndex</tt>, inclusive, to index <tt>toIndex</tt>, exclusive.
     * (If <tt>fromIndex==toIndex</tt>, the range to be sorted is empty.)
     * <p>
     * The <code><</code> relation does not provide a total order on
     * all floating-point values; although they are distinct numbers
     * <code>-0.0 == 0.0</code> is <code>true</code> and a NaN value
     * compares neither less than, greater than, nor equal to any
     * floating-point value, even itself.  To allow the sort to
     * proceed, instead of using the <code><</code> relation to
     * determine ascending numerical order, this method uses the total
     * order imposed by {@link Double#compareTo}.  This ordering
     * differs from the <code><</code> relation in that
     * <code>-0.0</code> is treated as less than <code>0.0</code> and
     * NaN is considered greater than any other floating-point value.
     * For the purposes of sorting, all NaN values are considered
     * equivalent and equal.
     * <p>
     * The sorting algorithm is a tuned quicksort, adapted from Jon
     * L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
     * Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
     * 1993).  This algorithm offers n*log(n) performance on many data sets
     * that cause other quicksorts to degrade to quadratic performance.
     *
     * @param a the array to be sorted.
     * @param fromIndex the index of the first element (inclusive) to be
     *        sorted.
     * @param toIndex the index of the last element (exclusive) to be sorted.
     * @throws IllegalArgumentException if <tt>fromIndex > toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
     *	       <tt>toIndex > a.length</tt>
     */
    public static void sort(double[] a, int fromIndex, int toIndex) {
        rangeCheck(a.length, fromIndex, toIndex);
	sort2(a, fromIndex, toIndex);
    }

    /**
     * Sorts the specified array of floats into ascending numerical order.
     * <p>
     * The <code><</code> relation does not provide a total order on
     * all floating-point values; although they are distinct numbers
     * <code>-0.0f == 0.0f</code> is <code>true</code> and a NaN value
     * compares neither less than, greater than, nor equal to any
     * floating-point value, even itself.  To allow the sort to
     * proceed, instead of using the <code><</code> relation to
     * determine ascending numerical order, this method uses the total
     * order imposed by {@link Float#compareTo}.  This ordering
     * differs from the <code><</code> relation in that
     * <code>-0.0f</code> is treated as less than <code>0.0f</code> and
     * NaN is considered greater than any other floating-point value.
     * For the purposes of sorting, all NaN values are considered
     * equivalent and equal.
     * <p>
     * The sorting algorithm is a tuned quicksort, adapted from Jon
     * L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
     * Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
     * 1993).  This algorithm offers n*log(n) performance on many data sets
     * that cause other quicksorts to degrade to quadratic performance.
     *
     * @param a the array to be sorted.
     */
    public static void sort(float[] a) {
	sort2(a, 0, a.length);
    }

    /**
     * Sorts the specified range of the specified array of floats into
     * ascending numerical order.  The range to be sorted extends from index
     * <tt>fromIndex</tt>, inclusive, to index <tt>toIndex</tt>, exclusive.
     * (If <tt>fromIndex==toIndex</tt>, the range to be sorted is empty.)
     * <p>
     * The <code><</code> relation does not provide a total order on
     * all floating-point values; although they are distinct numbers
     * <code>-0.0f == 0.0f</code> is <code>true</code> and a NaN value
     * compares neither less than, greater than, nor equal to any
     * floating-point value, even itself.  To allow the sort to
     * proceed, instead of using the <code><</code> relation to
     * determine ascending numerical order, this method uses the total
     * order imposed by {@link Float#compareTo}.  This ordering
     * differs from the <code><</code> relation in that
     * <code>-0.0f</code> is treated as less than <code>0.0f</code> and
     * NaN is considered greater than any other floating-point value.
     * For the purposes of sorting, all NaN values are considered
     * equivalent and equal.
     * <p>
     * The sorting algorithm is a tuned quicksort, adapted from Jon
     * L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
     * Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
     * 1993).  This algorithm offers n*log(n) performance on many data sets
     * that cause other quicksorts to degrade to quadratic performance.
     *
     * @param a the array to be sorted.
     * @param fromIndex the index of the first element (inclusive) to be
     *        sorted.
     * @param toIndex the index of the last element (exclusive) to be sorted.
     * @throws IllegalArgumentException if <tt>fromIndex > toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
     *	       <tt>toIndex > a.length</tt>
     */
    public static void sort(float[] a, int fromIndex, int toIndex) {
        rangeCheck(a.length, fromIndex, toIndex);
	sort2(a, fromIndex, toIndex);
    }

    private static void sort2(double a[], int fromIndex, int toIndex) {
        final long NEG_ZERO_BITS = Double.doubleToLongBits(-0.0d);
        /*
         * The sort is done in three phases to avoid the expense of using
         * NaN and -0.0 aware comparisons during the main sort.
         */

        /*
         * Preprocessing phase:  Move any NaN's to end of array, count the
         * number of -0.0's, and turn them into 0.0's. 
         */
        int numNegZeros = 0;
        int i = fromIndex, n = toIndex;
        while(i < n) {
            if (a[i] != a[i]) {
		double swap = a[i];
                a[i] = a[--n];
                a[n] = swap;
            } else {
                if (a[i]==0 && Double.doubleToLongBits(a[i])==NEG_ZERO_BITS) {
                    a[i] = 0.0d;
                    numNegZeros++;
                }
                i++;
            }
        }

        // Main sort phase: quicksort everything but the NaN's
	sort1(a, fromIndex, n-fromIndex);

        // Postprocessing phase: change 0.0's to -0.0's as required
        if (numNegZeros != 0) {
            int j = binarySearch(a, 0.0d, fromIndex, n-1); // posn of ANY zero
            do {
                j--;
            } while (j>=0 && a[j]==0.0d);

            // j is now one less than the index of the FIRST zero
            for (int k=0; k<numNegZeros; k++)
                a[++j] = -0.0d;
        }
    }


    private static void sort2(float a[], int fromIndex, int toIndex) {
        final int NEG_ZERO_BITS = Float.floatToIntBits(-0.0f);
        /*
         * The sort is done in three phases to avoid the expense of using
         * NaN and -0.0 aware comparisons during the main sort.
         */

        /*
         * Preprocessing phase:  Move any NaN's to end of array, count the
         * number of -0.0's, and turn them into 0.0's. 
         */
        int numNegZeros = 0;
        int i = fromIndex, n = toIndex;
        while(i < n) {
            if (a[i] != a[i]) {
		float swap = a[i];
                a[i] = a[--n];
                a[n] = swap;
            } else {
                if (a[i]==0 && Float.floatToIntBits(a[i])==NEG_ZERO_BITS) {
                    a[i] = 0.0f;
                    numNegZeros++;
                }
                i++;
            }
        }

        // Main sort phase: quicksort everything but the NaN's
	sort1(a, fromIndex, n-fromIndex);

        // Postprocessing phase: change 0.0's to -0.0's as required
        if (numNegZeros != 0) {
            int j = binarySearch(a, 0.0f, fromIndex, n-1); // posn of ANY zero
            do {
                j--;
            } while (j>=0 && a[j]==0.0f);

            // j is now one less than the index of the FIRST zero
            for (int k=0; k<numNegZeros; k++)
                a[++j] = -0.0f;
        }
    }


    /*
     * The code for each of the seven primitive types is largely identical.
     * C'est la vie.
     */

    /**
     * Sorts the specified sub-array of longs into ascending order.
     */
    private static void sort1(long x[], int off, int len) {
	// Insertion sort on smallest arrays
	if (len < 7) {
	    for (int i=off; i<len+off; i++)
		for (int j=i; j>off && x[j-1]>x[j]; j--)
		    swap(x, j, j-1);
	    return;
	}

	// Choose a partition element, v
	int m = off + (len >> 1);       // Small arrays, middle element
	if (len > 7) {
	    int l = off;
	    int n = off + len - 1;
	    if (len > 40) {        // Big arrays, pseudomedian of 9
		int s = len8;
		l = med3(x, l,     l+s, l+2*s);
		m = med3(x, m-s,   m,   m+s);
		n = med3(x, n-2*s, n-s, n);
	    }
	    m = med3(x, l, m, n); // Mid-size, med of 3
	}
	long v = x[m];

	// Establish Invariant: v* (<v)* (>v)* v*
	int a = off, b = a, c = off + len - 1, d = c;
	while(true) {
	    while (b <= c && x[b] <= v) {
		if (x[b] == v)
		    swap(x, a++, b);
		b++;
	    }
	    while (c >= b && x[c] >= v) {
		if (x[c] == v)
		    swap(x, c, d--);
		c--;
	    }
	    if (b > c)
		break;
	    swap(x, b++, c--);
	}

	// Swap partition elements back to middle
	int s, n = off + len;
	s = Math.min(a-off, b-a  );  vecswap(x, off, b-s, s);
	s = Math.min(d-c,   n-d-1);  vecswap(x, b,   n-s, s);

	// Recursively sort non-partition-elements
	if ((s = b-a) > 1)
	    sort1(x, off, s);
	if ((s = d-c) > 1)
	    sort1(x, n-s, s);
    }

    /**
     * Swaps x[a] with x[b].
     */
    private static void swap(long x[], int a, int b) {
	long t = x[a];
	x[a] = x[b];
	x[b] = t;
    }

    /**
     * Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].
     */
    private static void vecswap(long x[], int a, int b, int n) {
	for (int i=0; i<n; i++, a++, b++)
	    swap(x, a, b);
    }

    /**
     * Returns the index of the median of the three indexed longs.
     */
    private static int med3(long x[], int a, int b, int c) {
	return (x[a] < x[b] ?
		(x[b] < x[c] ? b : x[a] < x[c] ? c : a) :
		(x[b] > x[c] ? b : x[a] > x[c] ? c : a));
    }

    /**
     * Sorts the specified sub-array of integers into ascending order.
     */
    private static void sort1(int x[], int off, int len) {
	// Insertion sort on smallest arrays
	if (len < 7) {
	    for (int i=off; i<len+off; i++)
		for (int j=i; j>off && x[j-1]>x[j]; j--)
		    swap(x, j, j-1);
	    return;
	}

	// Choose a partition element, v
	int m = off + (len >> 1);       // Small arrays, middle element
	if (len > 7) {
	    int l = off;
	    int n = off + len - 1;
	    if (len > 40) {        // Big arrays, pseudomedian of 9
		int s = len8;
		l = med3(x, l,     l+s, l+2*s);
		m = med3(x, m-s,   m,   m+s);
		n = med3(x, n-2*s, n-s, n);
	    }
	    m = med3(x, l, m, n); // Mid-size, med of 3
	}
	int v = x[m];

	// Establish Invariant: v* (<v)* (>v)* v*
	int a = off, b = a, c = off + len - 1, d = c;
	while(true) {
	    while (b <= c && x[b] <= v) {
		if (x[b] == v)
		    swap(x, a++, b);
		b++;
	    }
	    while (c >= b && x[c] >= v) {
		if (x[c] == v)
		    swap(x, c, d--);
		c--;
	    }
	    if (b > c)
		break;
	    swap(x, b++, c--);
	}

	// Swap partition elements back to middle
	int s, n = off + len;
	s = Math.min(a-off, b-a  );  vecswap(x, off, b-s, s);
	s = Math.min(d-c,   n-d-1);  vecswap(x, b,   n-s, s);

	// Recursively sort non-partition-elements
	if ((s = b-a) > 1)
	    sort1(x, off, s);
	if ((s = d-c) > 1)
	    sort1(x, n-s, s);
    }

    /**
     * Swaps x[a] with x[b].
     */
    private static void swap(int x[], int a, int b) {
	int t = x[a];
	x[a] = x[b];
	x[b] = t;
    }

    /**
     * Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].
     */
    private static void vecswap(int x[], int a, int b, int n) {
	for (int i=0; i<n; i++, a++, b++)
	    swap(x, a, b);
    }

    /**
     * Returns the index of the median of the three indexed integers.
     */
    private static int med3(int x[], int a, int b, int c) {
	return (x[a] < x[b] ?
		(x[b] < x[c] ? b : x[a] < x[c] ? c : a) :
		(x[b] > x[c] ? b : x[a] > x[c] ? c : a));
    }

    /**
     * Sorts the specified sub-array of shorts into ascending order.
     */
    private static void sort1(short x[], int off, int len) {
	// Insertion sort on smallest arrays
	if (len < 7) {
	    for (int i=off; i<len+off; i++)
		for (int j=i; j>off && x[j-1]>x[j]; j--)
		    swap(x, j, j-1);
	    return;
	}

	// Choose a partition element, v
	int m = off + (len >> 1);       // Small arrays, middle element
	if (len > 7) {
	    int l = off;
	    int n = off + len - 1;
	    if (len > 40) {        // Big arrays, pseudomedian of 9
		int s = len8;
		l = med3(x, l,     l+s, l+2*s);
		m = med3(x, m-s,   m,   m+s);
		n = med3(x, n-2*s, n-s, n);
	    }
	    m = med3(x, l, m, n); // Mid-size, med of 3
	}
	short v = x[m];

	// Establish Invariant: v* (<v)* (>v)* v*
	int a = off, b = a, c = off + len - 1, d = c;
	while(true) {
	    while (b <= c && x[b] <= v) {
		if (x[b] == v)
		    swap(x, a++, b);
		b++;
	    }
	    while (c >= b && x[c] >= v) {
		if (x[c] == v)
		    swap(x, c, d--);
		c--;
	    }
	    if (b > c)
		break;
	    swap(x, b++, c--);
	}

	// Swap partition elements back to middle
	int s, n = off + len;
	s = Math.min(a-off, b-a  );  vecswap(x, off, b-s, s);
	s = Math.min(d-c,   n-d-1);  vecswap(x, b,   n-s, s);

	// Recursively sort non-partition-elements
	if ((s = b-a) > 1)
	    sort1(x, off, s);
	if ((s = d-c) > 1)
	    sort1(x, n-s, s);
    }

    /**
     * Swaps x[a] with x[b].
     */
    private static void swap(short x[], int a, int b) {
	short t = x[a];
	x[a] = x[b];
	x[b] = t;
    }

    /**
     * Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].
     */
    private static void vecswap(short x[], int a, int b, int n) {
	for (int i=0; i<n; i++, a++, b++)
	    swap(x, a, b);
    }

    /**
     * Returns the index of the median of the three indexed shorts.
     */
    private static int med3(short x[], int a, int b, int c) {
	return (x[a] < x[b] ?
		(x[b] < x[c] ? b : x[a] < x[c] ? c : a) :
		(x[b] > x[c] ? b : x[a] > x[c] ? c : a));
    }


    /**
     * Sorts the specified sub-array of chars into ascending order.
     */
    private static void sort1(char x[], int off, int len) {
	// Insertion sort on smallest arrays
	if (len < 7) {
	    for (int i=off; i<len+off; i++)
		for (int j=i; j>off && x[j-1]>x[j]; j--)
		    swap(x, j, j-1);
	    return;
	}

	// Choose a partition element, v
	int m = off + (len >> 1);       // Small arrays, middle element
	if (len > 7) {
	    int l = off;
	    int n = off + len - 1;
	    if (len > 40) {        // Big arrays, pseudomedian of 9
		int s = len8;
		l = med3(x, l,     l+s, l+2*s);
		m = med3(x, m-s,   m,   m+s);
		n = med3(x, n-2*s, n-s, n);
	    }
	    m = med3(x, l, m, n); // Mid-size, med of 3
	}
	char v = x[m];

	// Establish Invariant: v* (<v)* (>v)* v*
	int a = off, b = a, c = off + len - 1, d = c;
	while(true) {
	    while (b <= c && x[b] <= v) {
		if (x[b] == v)
		    swap(x, a++, b);
		b++;
	    }
	    while (c >= b && x[c] >= v) {
		if (x[c] == v)
		    swap(x, c, d--);
		c--;
	    }
	    if (b > c)
		break;
	    swap(x, b++, c--);
	}

	// Swap partition elements back to middle
	int s, n = off + len;
	s = Math.min(a-off, b-a  );  vecswap(x, off, b-s, s);
	s = Math.min(d-c,   n-d-1);  vecswap(x, b,   n-s, s);

	// Recursively sort non-partition-elements
	if ((s = b-a) > 1)
	    sort1(x, off, s);
	if ((s = d-c) > 1)
	    sort1(x, n-s, s);
    }

    /**
     * Swaps x[a] with x[b].
     */
    private static void swap(char x[], int a, int b) {
	char t = x[a];
	x[a] = x[b];
	x[b] = t;
    }

    /**
     * Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].
     */
    private static void vecswap(char x[], int a, int b, int n) {
	for (int i=0; i<n; i++, a++, b++)
	    swap(x, a, b);
    }

    /**
     * Returns the index of the median of the three indexed chars.
     */
    private static int med3(char x[], int a, int b, int c) {
	return (x[a] < x[b] ?
		(x[b] < x[c] ? b : x[a] < x[c] ? c : a) :
		(x[b] > x[c] ? b : x[a] > x[c] ? c : a));
    }


    /**
     * Sorts the specified sub-array of bytes into ascending order.
     */
    private static void sort1(byte x[], int off, int len) {
	// Insertion sort on smallest arrays
	if (len < 7) {
	    for (int i=off; i<len+off; i++)
		for (int j=i; j>off && x[j-1]>x[j]; j--)
		    swap(x, j, j-1);
	    return;
	}

	// Choose a partition element, v
	int m = off + (len >> 1);       // Small arrays, middle element
	if (len > 7) {
	    int l = off;
	    int n = off + len - 1;
	    if (len > 40) {        // Big arrays, pseudomedian of 9
		int s = len8;
		l = med3(x, l,     l+s, l+2*s);
		m = med3(x, m-s,   m,   m+s);
		n = med3(x, n-2*s, n-s, n);
	    }
	    m = med3(x, l, m, n); // Mid-size, med of 3
	}
	byte v = x[m];

	// Establish Invariant: v* (<v)* (>v)* v*
	int a = off, b = a, c = off + len - 1, d = c;
	while(true) {
	    while (b <= c && x[b] <= v) {
		if (x[b] == v)
		    swap(x, a++, b);
		b++;
	    }
	    while (c >= b && x[c] >= v) {
		if (x[c] == v)
		    swap(x, c, d--);
		c--;
	    }
	    if (b > c)
		break;
	    swap(x, b++, c--);
	}

	// Swap partition elements back to middle
	int s, n = off + len;
	s = Math.min(a-off, b-a  );  vecswap(x, off, b-s, s);
	s = Math.min(d-c,   n-d-1);  vecswap(x, b,   n-s, s);

	// Recursively sort non-partition-elements
	if ((s = b-a) > 1)
	    sort1(x, off, s);
	if ((s = d-c) > 1)
	    sort1(x, n-s, s);
    }

    /**
     * Swaps x[a] with x[b].
     */
    private static void swap(byte x[], int a, int b) {
	byte t = x[a];
	x[a] = x[b];
	x[b] = t;
    }

    /**
     * Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].
     */
    private static void vecswap(byte x[], int a, int b, int n) {
	for (int i=0; i<n; i++, a++, b++)
	    swap(x, a, b);
    }

    /**
     * Returns the index of the median of the three indexed bytes.
     */
    private static int med3(byte x[], int a, int b, int c) {
	return (x[a] < x[b] ?
		(x[b] < x[c] ? b : x[a] < x[c] ? c : a) :
		(x[b] > x[c] ? b : x[a] > x[c] ? c : a));
    }


    /**
     * Sorts the specified sub-array of doubles into ascending order.
     */
    private static void sort1(double x[], int off, int len) {
	// Insertion sort on smallest arrays
	if (len < 7) {
	    for (int i=off; i<len+off; i++)
		for (int j=i; j>off && x[j-1]>x[j]; j--)
		    swap(x, j, j-1);
	    return;
	}

	// Choose a partition element, v
	int m = off + (len >> 1);       // Small arrays, middle element
	if (len > 7) {
	    int l = off;
	    int n = off + len - 1;
	    if (len > 40) {        // Big arrays, pseudomedian of 9
		int s = len8;
		l = med3(x, l,     l+s, l+2*s);
		m = med3(x, m-s,   m,   m+s);
		n = med3(x, n-2*s, n-s, n);
	    }
	    m = med3(x, l, m, n); // Mid-size, med of 3
	}
	double v = x[m];

	// Establish Invariant: v* (<v)* (>v)* v*
	int a = off, b = a, c = off + len - 1, d = c;
	while(true) {
	    while (b <= c && x[b] <= v) {
		if (x[b] == v)
		    swap(x, a++, b);
		b++;
	    }
	    while (c >= b && x[c] >= v) {
		if (x[c] == v)
		    swap(x, c, d--);
		c--;
	    }
	    if (b > c)
		break;
	    swap(x, b++, c--);
	}

	// Swap partition elements back to middle
	int s, n = off + len;
	s = Math.min(a-off, b-a  );  vecswap(x, off, b-s, s);
	s = Math.min(d-c,   n-d-1);  vecswap(x, b,   n-s, s);

	// Recursively sort non-partition-elements
	if ((s = b-a) > 1)
	    sort1(x, off, s);
	if ((s = d-c) > 1)
	    sort1(x, n-s, s);
    }

    /**
     * Swaps x[a] with x[b].
     */
    private static void swap(double x[], int a, int b) {
	double t = x[a];
	x[a] = x[b];
	x[b] = t;
    }

    /**
     * Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].
     */
    private static void vecswap(double x[], int a, int b, int n) {
	for (int i=0; i<n; i++, a++, b++)
	    swap(x, a, b);
    }

    /**
     * Returns the index of the median of the three indexed doubles.
     */
    private static int med3(double x[], int a, int b, int c) {
	return (x[a] < x[b] ?
		(x[b] < x[c] ? b : x[a] < x[c] ? c : a) :
		(x[b] > x[c] ? b : x[a] > x[c] ? c : a));
    }


    /**
     * Sorts the specified sub-array of floats into ascending order.
     */
    private static void sort1(float x[], int off, int len) {
	// Insertion sort on smallest arrays
	if (len < 7) {
	    for (int i=off; i<len+off; i++)
		for (int j=i; j>off && x[j-1]>x[j]; j--)
		    swap(x, j, j-1);
	    return;
	}

	// Choose a partition element, v
	int m = off + (len >> 1);       // Small arrays, middle element
	if (len > 7) {
	    int l = off;
	    int n = off + len - 1;
	    if (len > 40) {        // Big arrays, pseudomedian of 9
		int s = len8;
		l = med3(x, l,     l+s, l+2*s);
		m = med3(x, m-s,   m,   m+s);
		n = med3(x, n-2*s, n-s, n);
	    }
	    m = med3(x, l, m, n); // Mid-size, med of 3
	}
	float v = x[m];

	// Establish Invariant: v* (<v)* (>v)* v*
	int a = off, b = a, c = off + len - 1, d = c;
	while(true) {
	    while (b <= c && x[b] <= v) {
		if (x[b] == v)
		    swap(x, a++, b);
		b++;
	    }
	    while (c >= b && x[c] >= v) {
		if (x[c] == v)
		    swap(x, c, d--);
		c--;
	    }
	    if (b > c)
		break;
	    swap(x, b++, c--);
	}

	// Swap partition elements back to middle
	int s, n = off + len;
	s = Math.min(a-off, b-a  );  vecswap(x, off, b-s, s);
	s = Math.min(d-c,   n-d-1);  vecswap(x, b,   n-s, s);

	// Recursively sort non-partition-elements
	if ((s = b-a) > 1)
	    sort1(x, off, s);
	if ((s = d-c) > 1)
	    sort1(x, n-s, s);
    }

    /**
     * Swaps x[a] with x[b].
     */
    private static void swap(float x[], int a, int b) {
	float t = x[a];
	x[a] = x[b];
	x[b] = t;
    }

    /**
     * Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].
     */
    private static void vecswap(float x[], int a, int b, int n) {
	for (int i=0; i<n; i++, a++, b++)
	    swap(x, a, b);
    }

    /**
     * Returns the index of the median of the three indexed floats.
     */
    private static int med3(float x[], int a, int b, int c) {
	return (x[a] < x[b] ?
		(x[b] < x[c] ? b : x[a] < x[c] ? c : a) :
		(x[b] > x[c] ? b : x[a] > x[c] ? c : a));
    }


    /**
     * Sorts the specified array of objects into ascending order, according to
     * the <i>natural ordering</i> of its elements.  All elements in the array
     * must implement the <tt>Comparable</tt> interface.  Furthermore, all
     * elements in the array must be <i>mutually comparable</i> (that is,
     * <tt>e1.compareTo(e2)</tt> must not throw a <tt>ClassCastException</tt>
     * for any elements <tt>e1</tt> and <tt>e2</tt> in the array).<p>
     *
     * This sort is guaranteed to be <i>stable</i>:  equal elements will
     * not be reordered as a result of the sort.<p>
     *
     * The sorting algorithm is a modified mergesort (in which the merge is
     * omitted if the highest element in the low sublist is less than the
     * lowest element in the high sublist).  This algorithm offers guaranteed
     * n*log(n) performance.
     * 
     * @param a the array to be sorted.
     * @throws  ClassCastException if the array contains elements that are not
     *		<i>mutually comparable</i> (for example, strings and integers).
     * @see Comparable
     */
    public static void sort(Object[] a) {
        Object[] aux = (Object[])a.clone();
        mergeSort(aux, a, 0, a.length, 0);
    }

    /**
     * Sorts the specified range of the specified array of objects into
     * ascending order, according to the <i>natural ordering</i> of its
     * elements.  The range to be sorted extends from index
     * <tt>fromIndex</tt>, inclusive, to index <tt>toIndex</tt>, exclusive.
     * (If <tt>fromIndex==toIndex</tt>, the range to be sorted is empty.)  All
     * elements in this range must implement the <tt>Comparable</tt>
     * interface.  Furthermore, all elements in this range must be <i>mutually
     * comparable</i> (that is, <tt>e1.compareTo(e2)</tt> must not throw a
     * <tt>ClassCastException</tt> for any elements <tt>e1</tt> and
     * <tt>e2</tt> in the array).<p>
     *
     * This sort is guaranteed to be <i>stable</i>:  equal elements will
     * not be reordered as a result of the sort.<p>
     *
     * The sorting algorithm is a modified mergesort (in which the merge is
     * omitted if the highest element in the low sublist is less than the
     * lowest element in the high sublist).  This algorithm offers guaranteed
     * n*log(n) performance.
     * 
     * @param a the array to be sorted.
     * @param fromIndex the index of the first element (inclusive) to be
     *        sorted.
     * @param toIndex the index of the last element (exclusive) to be sorted.
     * @throws IllegalArgumentException if <tt>fromIndex > toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
     *	       <tt>toIndex > a.length</tt>
     * @throws    ClassCastException if the array contains elements that are
     *		  not <i>mutually comparable</i> (for example, strings and
     *		  integers).
     * @see Comparable
     */
    public static void sort(Object[] a, int fromIndex, int toIndex) {
        rangeCheck(a.length, fromIndex, toIndex);
	Object[] aux = cloneSubarray(a, fromIndex, toIndex);
        mergeSort(aux, a, fromIndex, toIndex, -fromIndex);
    }

    /**
     * Tuning parameter: list size at or below which insertion sort will be
     * used in preference to mergesort or quicksort.
     */
    private static final int INSERTIONSORT_THRESHOLD = 7;

    /**
     * Clones an array within the specified bounds.
     * This method assumes that a is an array.
     */
    private static <T> T[] cloneSubarray(T[] a, int from, int to) {
        int n = to - from;
	T[] result = (T[])Array.newInstance(a.getClass().getComponentType(), n);
        System.arraycopy(a, from, result, 0, n);
        return result;
    }

    /**
     * Src is the source array that starts at index 0
     * Dest is the (possibly larger) array destination with a possible offset
     * low is the index in dest to start sorting
     * high is the end index in dest to end sorting
     * off is the offset to generate corresponding low, high in src
     */
    private static void mergeSort(Object[] src,
				  Object[] dest,
				  int low,
				  int high,
				  int off) {
	int length = high - low;

	// Insertion sort on smallest arrays
        if (length < INSERTIONSORT_THRESHOLD) {
            for (int i=low; i<high; i++)
                for (int j=i; j>low &&
			 ((Comparable) dest[j-1]).compareTo(dest[j])>0; j--)
                    swap(dest, j, j-1);
            return;
        }

        // Recursively sort halves of dest into src
        int destLow  = low;
        int destHigh = high;
        low  += off;
        high += off;
        int mid = (low + high) >> 1;
        mergeSort(dest, src, low, mid, -off);
        mergeSort(dest, src, mid, high, -off);

        // If list is already sorted, just copy from src to dest.  This is an
        // optimization that results in faster sorts for nearly ordered lists.
        if (((Comparable)src[mid-1]).compareTo(src[mid]) <= 0) {
            System.arraycopy(src, low, dest, destLow, length);
            return;
        }

        // Merge sorted halves (now in src) into dest
        for(int i = destLow, p = low, q = mid; i < destHigh; i++) {
            if (q >= high || p < mid && ((Comparable)src[p]).compareTo(src[q])<=0)
                dest[i] = src[p++];
            else
                dest[i] = src[q++];
        }
    }

    /**
     * Swaps x[a] with x[b].
     */
    private static void swap(Object[] x, int a, int b) {
	Object t = x[a];
	x[a] = x[b];
	x[b] = t;
    }

    /**
     * Sorts the specified array of objects according to the order induced by
     * the specified comparator.  All elements in the array must be
     * <i>mutually comparable</i> by the specified comparator (that is,
     * <tt>c.compare(e1, e2)</tt> must not throw a <tt>ClassCastException</tt>
     * for any elements <tt>e1</tt> and <tt>e2</tt> in the array).<p>
     *
     * This sort is guaranteed to be <i>stable</i>:  equal elements will
     * not be reordered as a result of the sort.<p>
     *
     * The sorting algorithm is a modified mergesort (in which the merge is
     * omitted if the highest element in the low sublist is less than the
     * lowest element in the high sublist).  This algorithm offers guaranteed
     * n*log(n) performance. 
     *
     * @param a the array to be sorted.
     * @param c the comparator to determine the order of the array.  A
     *        <tt>null</tt> value indicates that the elements' <i>natural
     *        ordering</i> should be used.
     * @throws  ClassCastException if the array contains elements that are
     *		not <i>mutually comparable</i> using the specified comparator.
     * @see Comparator
     */
    public static <T> void sort(T[] a, Comparator<? super T> c) {
	T[] aux = (T[])a.clone();
        if (c==null)
            mergeSort(aux, a, 0, a.length, 0);
        else
            mergeSort(aux, a, 0, a.length, 0, c);
    }

    /**
     * Sorts the specified range of the specified array of objects according
     * to the order induced by the specified comparator.  The range to be
     * sorted extends from index <tt>fromIndex</tt>, inclusive, to index
     * <tt>toIndex</tt>, exclusive.  (If <tt>fromIndex==toIndex</tt>, the
     * range to be sorted is empty.)  All elements in the range must be
     * <i>mutually comparable</i> by the specified comparator (that is,
     * <tt>c.compare(e1, e2)</tt> must not throw a <tt>ClassCastException</tt>
     * for any elements <tt>e1</tt> and <tt>e2</tt> in the range).<p>
     *
     * This sort is guaranteed to be <i>stable</i>:  equal elements will
     * not be reordered as a result of the sort.<p>
     *
     * The sorting algorithm is a modified mergesort (in which the merge is
     * omitted if the highest element in the low sublist is less than the
     * lowest element in the high sublist).  This algorithm offers guaranteed
     * n*log(n) performance. 
     *
     * @param a the array to be sorted.
     * @param fromIndex the index of the first element (inclusive) to be
     *        sorted.
     * @param toIndex the index of the last element (exclusive) to be sorted.
     * @param c the comparator to determine the order of the array.  A
     *        <tt>null</tt> value indicates that the elements' <i>natural
     *        ordering</i> should be used.
     * @throws ClassCastException if the array contains elements that are not
     *	       <i>mutually comparable</i> using the specified comparator.
     * @throws IllegalArgumentException if <tt>fromIndex > toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
     *	       <tt>toIndex > a.length</tt>
     * @see Comparator
     */
    public static <T> void sort(T[] a, int fromIndex, int toIndex,
				Comparator<? super T> c) {
        rangeCheck(a.length, fromIndex, toIndex);
	T[] aux = (T[])cloneSubarray(a, fromIndex, toIndex);
        if (c==null)
            mergeSort(aux, a, fromIndex, toIndex, -fromIndex);
        else
            mergeSort(aux, a, fromIndex, toIndex, -fromIndex, c);
    }

    /**
     * Src is the source array that starts at index 0
     * Dest is the (possibly larger) array destination with a possible offset
     * low is the index in dest to start sorting
     * high is the end index in dest to end sorting
     * off is the offset into src corresponding to low in dest
     */
    private static void mergeSort(Object[] src,
				  Object[] dest,
				  int low, int high, int off,
				  Comparator c) {
	int length = high - low;

	// Insertion sort on smallest arrays
	if (length < INSERTIONSORT_THRESHOLD) {
	    for (int i=low; i<high; i++)
		for (int j=i; j>low && c.compare(dest[j-1], dest[j])>0; j--)
		    swap(dest, j, j-1);
	    return;
	}

        // Recursively sort halves of dest into src
        int destLow  = low;
        int destHigh = high;
        low  += off;
        high += off;
        int mid = (low + high) >> 1;
        mergeSort(dest, src, low, mid, -off, c);
        mergeSort(dest, src, mid, high, -off, c);

        // If list is already sorted, just copy from src to dest.  This is an
        // optimization that results in faster sorts for nearly ordered lists.
        if (c.compare(src[mid-1], src[mid]) <= 0) {
           System.arraycopy(src, low, dest, destLow, length);
           return;
        }

        // Merge sorted halves (now in src) into dest
        for(int i = destLow, p = low, q = mid; i < destHigh; i++) {
            if (q >= high || p < mid && c.compare(src[p], src[q]) <= 0)
                dest[i] = src[p++];
            else
                dest[i] = src[q++];
        }
    }

    /**
     * Check that fromIndex and toIndex are in range, and throw an
     * appropriate exception if they aren't.
     */
    private static void rangeCheck(int arrayLen, int fromIndex, int toIndex) {
        if (fromIndex > toIndex)
            throw new IllegalArgumentException("fromIndex(" + fromIndex +
                       ") > toIndex(" + toIndex+")");
        if (fromIndex < 0)
            throw new ArrayIndexOutOfBoundsException(fromIndex);
        if (toIndex > arrayLen)
            throw new ArrayIndexOutOfBoundsException(toIndex);
    }

    // Searching

    /**
     * Searches the specified array of longs for the specified value using the
     * binary search algorithm.  The array <strong>must</strong> be sorted (as
     * by the <tt>sort</tt> method, above) prior to making this call.  If it
     * is not sorted, the results are undefined.  If the array contains
     * multiple elements with the specified value, there is no guarantee which
     * one will be found.
     *
     * @param a the array to be searched.
     * @param key the value to be searched for.
     * @return index of the search key, if it is contained in the list;
     *	       otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The
     *	       <i>insertion point</i> is defined as the point at which the
     *	       key would be inserted into the list: the index of the first
     *	       element greater than the key, or <tt>list.size()</tt>, if all
     *	       elements in the list are less than the specified key.  Note
     *	       that this guarantees that the return value will be >= 0 if
     *	       and only if the key is found.
     * @see #sort(long[])
     */
    public static int binarySearch(long[] a, long key) {
	int low = 0;
	int high = a.length-1;

	while (low <= high) {
	    int mid = (low + high) >> 1;
	    long midVal = a[mid];

	    if (midVal < key)
		low = mid + 1;
	    else if (midVal > key)
		high = mid - 1;
	    else
		return mid; // key found
	}
	return -(low + 1);  // key not found.
    }


    /**
     * Searches the specified array of ints for the specified value using the
     * binary search algorithm.  The array <strong>must</strong> be sorted (as
     * by the <tt>sort</tt> method, above) prior to making this call.  If it
     * is not sorted, the results are undefined.  If the array contains
     * multiple elements with the specified value, there is no guarantee which
     * one will be found.
     *
     * @param a the array to be searched.
     * @param key the value to be searched for.
     * @return index of the search key, if it is contained in the list;
     *	       otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The
     *	       <i>insertion point</i> is defined as the point at which the
     *	       key would be inserted into the list: the index of the first
     *	       element greater than the key, or <tt>list.size()</tt>, if all
     *	       elements in the list are less than the specified key.  Note
     *	       that this guarantees that the return value will be >= 0 if
     *	       and only if the key is found.
     * @see #sort(int[])
     */
    public static int binarySearch(int[] a, int key) {
	int low = 0;
	int high = a.length-1;

	while (low <= high) {
	    int mid = (low + high) >> 1;
	    int midVal = a[mid];

	    if (midVal < key)
		low = mid + 1;
	    else if (midVal > key)
		high = mid - 1;
	    else
		return mid; // key found
	}
	return -(low + 1);  // key not found.
    }

    /**
     * Searches the specified array of shorts for the specified value using
     * the binary search algorithm.  The array <strong>must</strong> be sorted
     * (as by the <tt>sort</tt> method, above) prior to making this call.  If
     * it is not sorted, the results are undefined.  If the array contains
     * multiple elements with the specified value, there is no guarantee which
     * one will be found.
     *
     * @param a the array to be searched.
     * @param key the value to be searched for.
     * @return index of the search key, if it is contained in the list;
     *	       otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The
     *	       <i>insertion point</i> is defined as the point at which the
     *	       key would be inserted into the list: the index of the first
     *	       element greater than the key, or <tt>list.size()</tt>, if all
     *	       elements in the list are less than the specified key.  Note
     *	       that this guarantees that the return value will be >= 0 if
     *	       and only if the key is found.
     * @see #sort(short[])
     */
    public static int binarySearch(short[] a, short key) {
	int low = 0;
	int high = a.length-1;

	while (low <= high) {
	    int mid = (low + high) >> 1;
	    short midVal = a[mid];

	    if (midVal < key)
		low = mid + 1;
	    else if (midVal > key)
		high = mid - 1;
	    else
		return mid; // key found
	}
	return -(low + 1);  // key not found.
    }

    /**
     * Searches the specified array of chars for the specified value using the
     * binary search algorithm.  The array <strong>must</strong> be sorted (as
     * by the <tt>sort</tt> method, above) prior to making this call.  If it
     * is not sorted, the results are undefined.  If the array contains
     * multiple elements with the specified value, there is no guarantee which
     * one will be found.
     *
     * @param a the array to be searched.
     * @param key the value to be searched for.
     * @return index of the search key, if it is contained in the list;
     *	       otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The
     *	       <i>insertion point</i> is defined as the point at which the
     *	       key would be inserted into the list: the index of the first
     *	       element greater than the key, or <tt>list.size()</tt>, if all
     *	       elements in the list are less than the specified key.  Note
     *	       that this guarantees that the return value will be >= 0 if
     *	       and only if the key is found.
     * @see #sort(char[])
     */
    public static int binarySearch(char[] a, char key) {
	int low = 0;
	int high = a.length-1;

	while (low <= high) {
	    int mid = (low + high) >> 1;
	    char midVal = a[mid];

	    if (midVal < key)
		low = mid + 1;
	    else if (midVal > key)
		high = mid - 1;
	    else
		return mid; // key found
	}
	return -(low + 1);  // key not found.
    }

    /**
     * Searches the specified array of bytes for the specified value using the
     * binary search algorithm.  The array <strong>must</strong> be sorted (as
     * by the <tt>sort</tt> method, above) prior to making this call.  If it
     * is not sorted, the results are undefined.  If the array contains
     * multiple elements with the specified value, there is no guarantee which
     * one will be found.
     *
     * @param a the array to be searched.
     * @param key the value to be searched for.
     * @return index of the search key, if it is contained in the list;
     *	       otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The
     *	       <i>insertion point</i> is defined as the point at which the
     *	       key would be inserted into the list: the index of the first
     *	       element greater than the key, or <tt>list.size()</tt>, if all
     *	       elements in the list are less than the specified key.  Note
     *	       that this guarantees that the return value will be >= 0 if
     *	       and only if the key is found.
     * @see #sort(byte[])
     */
    public static int binarySearch(byte[] a, byte key) {
	int low = 0;
	int high = a.length-1;

	while (low <= high) {
	    int mid = (low + high) >> 1;
	    byte midVal = a[mid];

	    if (midVal < key)
		low = mid + 1;
	    else if (midVal > key)
		high = mid - 1;
	    else
		return mid; // key found
	}
	return -(low + 1);  // key not found.
    }

    /**
     * Searches the specified array of doubles for the specified value using
     * the binary search algorithm.  The array <strong>must</strong> be sorted
     * (as by the <tt>sort</tt> method, above) prior to making this call.  If
     * it is not sorted, the results are undefined.  If the array contains
     * multiple elements with the specified value, there is no guarantee which
     * one will be found.  This method considers all NaN values to be 
     * equivalent and equal.
     *
     * @param a the array to be searched.
     * @param key the value to be searched for.
     * @return index of the search key, if it is contained in the list;
     *	       otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The
     *	       <i>insertion point</i> is defined as the point at which the
     *	       key would be inserted into the list: the index of the first
     *	       element greater than the key, or <tt>list.size()</tt>, if all
     *	       elements in the list are less than the specified key.  Note
     *	       that this guarantees that the return value will be >= 0 if
     *	       and only if the key is found.
     * @see #sort(double[])
     */
    public static int binarySearch(double[] a, double key) {
        return binarySearch(a, key, 0, a.length-1);
    }

    private static int binarySearch(double[] a, double key, int low,int high) {
	while (low <= high) {
	    int mid = (low + high) >> 1;
	    double midVal = a[mid];

            int cmp;
            if (midVal < key) {
                cmp = -1;   // Neither val is NaN, thisVal is smaller
            } else if (midVal > key) {
                cmp = 1;    // Neither val is NaN, thisVal is larger
            } else {
                long midBits = Double.doubleToLongBits(midVal);
                long keyBits = Double.doubleToLongBits(key);
                cmp = (midBits == keyBits ?  0 : // Values are equal
                       (midBits < keyBits ? -1 : // (-0.0, 0.0) or (!NaN, NaN)
                        1));                     // (0.0, -0.0) or (NaN, !NaN)
            }

	    if (cmp < 0)
		low = mid + 1;
	    else if (cmp > 0)
		high = mid - 1;
	    else
		return mid; // key found
	}
	return -(low + 1);  // key not found.
    }

    /**
     * Searches the specified array of floats for the specified value using
     * the binary search algorithm.  The array <strong>must</strong> be sorted
     * (as by the <tt>sort</tt> method, above) prior to making this call.  If
     * it is not sorted, the results are undefined.  If the array contains
     * multiple elements with the specified value, there is no guarantee which
     * one will be found.  This method considers all NaN values to be 
     * equivalent and equal.
     *
     * @param a the array to be searched.
     * @param key the value to be searched for.
     * @return index of the search key, if it is contained in the list;
     *	       otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The
     *	       <i>insertion point</i> is defined as the point at which the
     *	       key would be inserted into the list: the index of the first
     *	       element greater than the key, or <tt>list.size()</tt>, if all
     *	       elements in the list are less than the specified key.  Note
     *	       that this guarantees that the return value will be >= 0 if
     *	       and only if the key is found.
     * @see #sort(float[])
     */
    public static int binarySearch(float[] a, float key) {
        return binarySearch(a, key, 0, a.length-1);
    }

    private static int binarySearch(float[] a, float key, int low,int high) {
	while (low <= high) {
	    int mid = (low + high) >> 1;
	    float midVal = a[mid];

            int cmp;
            if (midVal < key) {
                cmp = -1;   // Neither val is NaN, thisVal is smaller
            } else if (midVal > key) {
                cmp = 1;    // Neither val is NaN, thisVal is larger
            } else {
                int midBits = Float.floatToIntBits(midVal);
                int keyBits = Float.floatToIntBits(key);
                cmp = (midBits == keyBits ?  0 : // Values are equal
                       (midBits < keyBits ? -1 : // (-0.0, 0.0) or (!NaN, NaN)
                        1));                     // (0.0, -0.0) or (NaN, !NaN)
            }

	    if (cmp < 0)
		low = mid + 1;
	    else if (cmp > 0)
		high = mid - 1;
	    else
		return mid; // key found
	}
	return -(low + 1);  // key not found.
    }


    /**
     * Searches the specified array for the specified object using the binary
     * search algorithm.  The array must be sorted into ascending order
     * according to the <i>natural ordering</i> of its elements (as by
     * <tt>Sort(Object[]</tt>), above) prior to making this call.  If it is
     * not sorted, the results are undefined.
     * (If the array contains elements that are not  mutually comparable (for
     * example,strings and integers), it <i>cannot</i> be sorted according 
     * to the natural order of its elements, hence results are undefined.)
     *  If the array contains multiple
     * elements equal to the specified object, there is no guarantee which
     * one will be found.
     *
     * @param a the array to be searched.
     * @param key the value to be searched for.
     * @return index of the search key, if it is contained in the list;
     *	       otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The
     *	       <i>insertion point</i> is defined as the point at which the
     *	       key would be inserted into the list: the index of the first
     *	       element greater than the key, or <tt>list.size()</tt>, if all
     *	       elements in the list are less than the specified key.  Note
     *	       that this guarantees that the return value will be >= 0 if
     *	       and only if the key is found.
     * @throws ClassCastException if the search key in not comparable to the
     *         elements of the array.
     * @see Comparable
     * @see #sort(Object[])
     */
    public static int binarySearch(Object[] a, Object key) {
	int low = 0;
	int high = a.length-1;

	while (low <= high) {
	    int mid = (low + high) >> 1;
	    Comparable midVal = (Comparable)a[mid];
	    int cmp = midVal.compareTo(key);

	    if (cmp < 0)
		low = mid + 1;
	    else if (cmp > 0)
		high = mid - 1;
	    else
		return mid; // key found
	}
	return -(low + 1);  // key not found.
    }

    /**
     * Searches the specified array for the specified object using the binary
     * search algorithm.  The array must be sorted into ascending order
     * according to the specified comparator (as by the <tt>Sort(Object[],
     * Comparator)</tt> method, above), prior to making this call.  If it is
     * not sorted, the results are undefined. 
     * If the array contains multiple
     * elements equal to the specified object, there is no guarantee which one
     * will be found.
     *
     * @param a the array to be searched.
     * @param key the value to be searched for.
     * @param c the comparator by which the array is ordered.  A
     *        <tt>null</tt> value indicates that the elements' <i>natural
     *        ordering</i> should be used.
     * @return index of the search key, if it is contained in the list;
     *	       otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The
     *	       <i>insertion point</i> is defined as the point at which the
     *	       key would be inserted into the list: the index of the first
     *	       element greater than the key, or <tt>list.size()</tt>, if all
     *	       elements in the list are less than the specified key.  Note
     *	       that this guarantees that the return value will be >= 0 if
     *	       and only if the key is found.
     * @throws ClassCastException if the array contains elements that are not
     *	       <i>mutually comparable</i> using the specified comparator,
     *	       or the search key in not mutually comparable with the
     *	       elements of the array using this comparator.
     * @see Comparable
     * @see #sort(Object[], Comparator)
     */
    public static <T> int binarySearch(T[] a, T key, Comparator<? super T> c) {
        if (c==null) {
            return binarySearch(a, key);
	}

	int low = 0;
	int high = a.length-1;

	while (low <= high) {
	    int mid = (low + high) >> 1;
	    T midVal = a[mid];
	    int cmp = c.compare(midVal, key);

	    if (cmp < 0)
		low = mid + 1;
	    else if (cmp > 0)
		high = mid - 1;
	    else
		return mid; // key found
	}
	return -(low + 1);  // key not found.
    }


    // Equality Testing

    /**
     * Returns <tt>true</tt> if the two specified arrays of longs are
     * <i>equal</i> to one another.  Two arrays are considered equal if both
     * arrays contain the same number of elements, and all corresponding pairs
     * of elements in the two arrays are equal.  In other words, two arrays
     * are equal if they contain the same elements in the same order.  Also,
     * two array references are considered equal if both are <tt>null</tt>.<p>
     *
     * @param a one array to be tested for equality.
     * @param a2 the other array to be tested for equality.
     * @return <tt>true</tt> if the two arrays are equal.
     */
    public static boolean equals(long[] a, long[] a2) {
        if (a==a2)
            return true;
        if (a==null || a2==null)
            return false;

        int length = a.length;
        if (a2.length != length)
            return false;

        for (int i=0; i<length; i++)
            if (a[i] != a2[i])
                return false;

        return true;
    }

    /**
     * Returns <tt>true</tt> if the two specified arrays of ints are
     * <i>equal</i> to one another.  Two arrays are considered equal if both
     * arrays contain the same number of elements, and all corresponding pairs
     * of elements in the two arrays are equal.  In other words, two arrays
     * are equal if they contain the same elements in the same order.  Also,
     * two array references are considered equal if both are <tt>null</tt>.<p>
     *
     * @param a one array to be tested for equality.
     * @param a2 the other array to be tested for equality.
     * @return <tt>true</tt> if the two arrays are equal.
     */
    public static boolean equals(int[] a, int[] a2) {
        if (a==a2)
            return true;
        if (a==null || a2==null)
            return false;

        int length = a.length;
        if (a2.length != length)
            return false;

        for (int i=0; i<length; i++)
            if (a[i] != a2[i])
                return false;

        return true;
    }

    /**
     * Returns <tt>true</tt> if the two specified arrays of shorts are
     * <i>equal</i> to one another.  Two arrays are considered equal if both
     * arrays contain the same number of elements, and all corresponding pairs
     * of elements in the two arrays are equal.  In other words, two arrays
     * are equal if they contain the same elements in the same order.  Also,
     * two array references are considered equal if both are <tt>null</tt>.<p>
     *
     * @param a one array to be tested for equality.
     * @param a2 the other array to be tested for equality.
     * @return <tt>true</tt> if the two arrays are equal.
     */
    public static boolean equals(short[] a, short a2[]) {
        if (a==a2)
            return true;
        if (a==null || a2==null)
            return false;

        int length = a.length;
        if (a2.length != length)
            return false;

        for (int i=0; i<length; i++)
            if (a[i] != a2[i])
                return false;

        return true;
    }

    /**
     * Returns <tt>true</tt> if the two specified arrays of chars are
     * <i>equal</i> to one another.  Two arrays are considered equal if both
     * arrays contain the same number of elements, and all corresponding pairs
     * of elements in the two arrays are equal.  In other words, two arrays
     * are equal if they contain the same elements in the same order.  Also,
     * two array references are considered equal if both are <tt>null</tt>.<p>
     *
     * @param a one array to be tested for equality.
     * @param a2 the other array to be tested for equality.
     * @return <tt>true</tt> if the two arrays are equal.
     */
    public static boolean equals(char[] a, char[] a2) {
        if (a==a2)
            return true;
        if (a==null || a2==null)
            return false;

        int length = a.length;
        if (a2.length != length)
            return false;

        for (int i=0; i<length; i++)
            if (a[i] != a2[i])
                return false;

        return true;
    }

    /**
     * Returns <tt>true</tt> if the two specified arrays of bytes are
     * <i>equal</i> to one another.  Two arrays are considered equal if both
     * arrays contain the same number of elements, and all corresponding pairs
     * of elements in the two arrays are equal.  In other words, two arrays
     * are equal if they contain the same elements in the same order.  Also,
     * two array references are considered equal if both are <tt>null</tt>.<p>
     *
     * @param a one array to be tested for equality.
     * @param a2 the other array to be tested for equality.
     * @return <tt>true</tt> if the two arrays are equal.
     */
    public static boolean equals(byte[] a, byte[] a2) {
        if (a==a2)
            return true;
        if (a==null || a2==null)
            return false;

        int length = a.length;
        if (a2.length != length)
            return false;

        for (int i=0; i<length; i++)
            if (a[i] != a2[i])
                return false;

        return true;
    }

    /**
     * Returns <tt>true</tt> if the two specified arrays of booleans are
     * <i>equal</i> to one another.  Two arrays are considered equal if both
     * arrays contain the same number of elements, and all corresponding pairs
     * of elements in the two arrays are equal.  In other words, two arrays
     * are equal if they contain the same elements in the same order.  Also,
     * two array references are considered equal if both are <tt>null</tt>.<p>
     *
     * @param a one array to be tested for equality.
     * @param a2 the other array to be tested for equality.
     * @return <tt>true</tt> if the two arrays are equal.
     */
    public static boolean equals(boolean[] a, boolean[] a2) {
        if (a==a2)
            return true;
        if (a==null || a2==null)
            return false;

        int length = a.length;
        if (a2.length != length)
            return false;

        for (int i=0; i<length; i++)
            if (a[i] != a2[i])
                return false;

        return true;
    }

    /**
     * Returns <tt>true</tt> if the two specified arrays of doubles are
     * <i>equal</i> to one another.  Two arrays are considered equal if both
     * arrays contain the same number of elements, and all corresponding pairs
     * of elements in the two arrays are equal.  In other words, two arrays
     * are equal if they contain the same elements in the same order.  Also,
     * two array references are considered equal if both are <tt>null</tt>.<p>
     *
     * Two doubles <tt>d1</tt> and <tt>d2</tt> are considered equal if:
     * <pre>    <tt>new Double(d1).equals(new Double(d2))</tt></pre>
     * (Unlike the <tt>==</tt> operator, this method considers
     * <tt>NaN</tt> equals to itself, and 0.0d unequal to -0.0d.)
     *
     * @param a one array to be tested for equality.
     * @param a2 the other array to be tested for equality.
     * @return <tt>true</tt> if the two arrays are equal.
     * @see Double#equals(Object)
     */
    public static boolean equals(double[] a, double[] a2) {
        if (a==a2)
            return true;
        if (a==null || a2==null)
            return false;

        int length = a.length;
        if (a2.length != length)
            return false;

        for (int i=0; i<length; i++)
	    if (Double.doubleToLongBits(a[i])!=Double.doubleToLongBits(a2[i]))
                return false;

        return true;
    }

    /**
     * Returns <tt>true</tt> if the two specified arrays of floats are
     * <i>equal</i> to one another.  Two arrays are considered equal if both
     * arrays contain the same number of elements, and all corresponding pairs
     * of elements in the two arrays are equal.  In other words, two arrays
     * are equal if they contain the same elements in the same order.  Also,
     * two array references are considered equal if both are <tt>null</tt>.<p>
     *
     * Two floats <tt>f1</tt> and <tt>f2</tt> are considered equal if:
     * <pre>    <tt>new Float(f1).equals(new Float(f2))</tt></pre>
     * (Unlike the <tt>==</tt> operator, this method considers
     * <tt>NaN</tt> equals to itself, and 0.0f unequal to -0.0f.)
     *
     * @param a one array to be tested for equality.
     * @param a2 the other array to be tested for equality.
     * @return <tt>true</tt> if the two arrays are equal.
     * @see Float#equals(Object)
     */
    public static boolean equals(float[] a, float[] a2) {
        if (a==a2)
            return true;
        if (a==null || a2==null)
            return false;

        int length = a.length;
        if (a2.length != length)
            return false;

        for (int i=0; i<length; i++)
	    if (Float.floatToIntBits(a[i])!=Float.floatToIntBits(a2[i]))
                return false;

        return true;
    }


    /**
     * Returns <tt>true</tt> if the two specified arrays of Objects are
     * <i>equal</i> to one another.  The two arrays are considered equal if
     * both arrays contain the same number of elements, and all corresponding
     * pairs of elements in the two arrays are equal.  Two objects <tt>e1</tt>
     * and <tt>e2</tt> are considered <i>equal</i> if <tt>(e1==null ? e2==null
     * : e1.equals(e2))</tt>.  In other words, the two arrays are equal if
     * they contain the same elements in the same order.  Also, two array
     * references are considered equal if both are <tt>null</tt>.<p>
     *
     * @param a one array to be tested for equality.
     * @param a2 the other array to be tested for equality.
     * @return <tt>true</tt> if the two arrays are equal.
     */
    public static boolean equals(Object[] a, Object[] a2) {
        if (a==a2)
            return true;
        if (a==null || a2==null)
            return false;

        int length = a.length;
        if (a2.length != length)
            return false;

        for (int i=0; i<length; i++) {
            Object o1 = a[i];
            Object o2 = a2[i];
            if (!(o1==null ? o2==null : o1.equals(o2)))
                return false;
        }

        return true;
    }


    // Filling

    /**
     * Assigns the specified long value to each element of the specified array
     * of longs.
     *
     * @param a the array to be filled.
     * @param val the value to be stored in all elements of the array.
     */
    public static void fill(long[] a, long val) {
        fill(a, 0, a.length, val);
    }

    /**
     * Assigns the specified long value to each element of the specified 
     * range of the specified array of longs.  The range to be filled
     * extends from index <tt>fromIndex</tt>, inclusive, to index
     * <tt>toIndex</tt>, exclusive.  (If <tt>fromIndex==toIndex</tt>, the 
     * range to be filled is empty.)
     *
     * @param a the array to be filled.
     * @param fromIndex the index of the first element (inclusive) to be
     *        filled with the specified value.
     * @param toIndex the index of the last element (exclusive) to be
     *        filled with the specified value.
     * @param val the value to be stored in all elements of the array.
     * @throws IllegalArgumentException if <tt>fromIndex > toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
     *	       <tt>toIndex > a.length</tt>
     */
    public static void fill(long[] a, int fromIndex, int toIndex, long val) {
        rangeCheck(a.length, fromIndex, toIndex);
        for (int i=fromIndex; i<toIndex; i++)
            a[i] = val;
    }

    /**
     * Assigns the specified int value to each element of the specified array
     * of ints.
     *
     * @param a the array to be filled.
     * @param val the value to be stored in all elements of the array.
     */
    public static void fill(int[] a, int val) {
        fill(a, 0, a.length, val);
    }

    /**
     * Assigns the specified int value to each element of the specified 
     * range of the specified array of ints.  The range to be filled
     * extends from index <tt>fromIndex</tt>, inclusive, to index
     * <tt>toIndex</tt>, exclusive.  (If <tt>fromIndex==toIndex</tt>, the 
     * range to be filled is empty.)
     *
     * @param a the array to be filled.
     * @param fromIndex the index of the first element (inclusive) to be
     *        filled with the specified value.
     * @param toIndex the index of the last element (exclusive) to be
     *        filled with the specified value.
     * @param val the value to be stored in all elements of the array.
     * @throws IllegalArgumentException if <tt>fromIndex > toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
     *	       <tt>toIndex > a.length</tt>
     */
    public static void fill(int[] a, int fromIndex, int toIndex, int val) {
        rangeCheck(a.length, fromIndex, toIndex);
        for (int i=fromIndex; i<toIndex; i++)
            a[i] = val;
    }

    /**
     * Assigns the specified short value to each element of the specified array
     * of shorts.
     *
     * @param a the array to be filled.
     * @param val the value to be stored in all elements of the array.
     */
    public static void fill(short[] a, short val) {
        fill(a, 0, a.length, val);
    }

    /**
     * Assigns the specified short value to each element of the specified 
     * range of the specified array of shorts.  The range to be filled
     * extends from index <tt>fromIndex</tt>, inclusive, to index
     * <tt>toIndex</tt>, exclusive.  (If <tt>fromIndex==toIndex</tt>, the 
     * range to be filled is empty.)
     *
     * @param a the array to be filled.
     * @param fromIndex the index of the first element (inclusive) to be
     *        filled with the specified value.
     * @param toIndex the index of the last element (exclusive) to be
     *        filled with the specified value.
     * @param val the value to be stored in all elements of the array.
     * @throws IllegalArgumentException if <tt>fromIndex > toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
     *	       <tt>toIndex > a.length</tt>
     */
    public static void fill(short[] a, int fromIndex, int toIndex, short val) {
        rangeCheck(a.length, fromIndex, toIndex);
        for (int i=fromIndex; i<toIndex; i++)
            a[i] = val;
    }

    /**
     * Assigns the specified char value to each element of the specified array
     * of chars.
     *
     * @param a the array to be filled.
     * @param val the value to be stored in all elements of the array.
     */
    public static void fill(char[] a, char val) {
        fill(a, 0, a.length, val);
    }

    /**
     * Assigns the specified char value to each element of the specified 
     * range of the specified array of chars.  The range to be filled
     * extends from index <tt>fromIndex</tt>, inclusive, to index
     * <tt>toIndex</tt>, exclusive.  (If <tt>fromIndex==toIndex</tt>, the 
     * range to be filled is empty.)
     *
     * @param a the array to be filled.
     * @param fromIndex the index of the first element (inclusive) to be
     *        filled with the specified value.
     * @param toIndex the index of the last element (exclusive) to be
     *        filled with the specified value.
     * @param val the value to be stored in all elements of the array.
     * @throws IllegalArgumentException if <tt>fromIndex > toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
     *	       <tt>toIndex > a.length</tt>
     */
    public static void fill(char[] a, int fromIndex, int toIndex, char val) {
        rangeCheck(a.length, fromIndex, toIndex);
        for (int i=fromIndex; i<toIndex; i++)
            a[i] = val;
    }

    /**
     * Assigns the specified byte value to each element of the specified array
     * of bytes.
     *
     * @param a the array to be filled.
     * @param val the value to be stored in all elements of the array.
     */
    public static void fill(byte[] a, byte val) {
        fill(a, 0, a.length, val);
    }

    /**
     * Assigns the specified byte value to each element of the specified 
     * range of the specified array of bytes.  The range to be filled
     * extends from index <tt>fromIndex</tt>, inclusive, to index
     * <tt>toIndex</tt>, exclusive.  (If <tt>fromIndex==toIndex</tt>, the 
     * range to be filled is empty.)
     *
     * @param a the array to be filled.
     * @param fromIndex the index of the first element (inclusive) to be
     *        filled with the specified value.
     * @param toIndex the index of the last element (exclusive) to be
     *        filled with the specified value.
     * @param val the value to be stored in all elements of the array.
     * @throws IllegalArgumentException if <tt>fromIndex > toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
     *	       <tt>toIndex > a.length</tt>
     */
    public static void fill(byte[] a, int fromIndex, int toIndex, byte val) {
        rangeCheck(a.length, fromIndex, toIndex);
        for (int i=fromIndex; i<toIndex; i++)
            a[i] = val;
    }

    /**
     * Assigns the specified boolean value to each element of the specified
     * array of booleans.
     *
     * @param a the array to be filled.
     * @param val the value to be stored in all elements of the array.
     */
    public static void fill(boolean[] a, boolean val) {
        fill(a, 0, a.length, val);
    }

    /**
     * Assigns the specified boolean value to each element of the specified 
     * range of the specified array of booleans.  The range to be filled
     * extends from index <tt>fromIndex</tt>, inclusive, to index
     * <tt>toIndex</tt>, exclusive.  (If <tt>fromIndex==toIndex</tt>, the 
     * range to be filled is empty.)
     *
     * @param a the array to be filled.
     * @param fromIndex the index of the first element (inclusive) to be
     *        filled with the specified value.
     * @param toIndex the index of the last element (exclusive) to be
     *        filled with the specified value.
     * @param val the value to be stored in all elements of the array.
     * @throws IllegalArgumentException if <tt>fromIndex > toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
     *	       <tt>toIndex > a.length</tt>
     */
    public static void fill(boolean[] a, int fromIndex, int toIndex,
                            boolean val) {
        rangeCheck(a.length, fromIndex, toIndex);
        for (int i=fromIndex; i<toIndex; i++)
            a[i] = val;
    }

    /**
     * Assigns the specified double value to each element of the specified
     * array of doubles.
     *
     * @param a the array to be filled.
     * @param val the value to be stored in all elements of the array.
     */
    public static void fill(double[] a, double val) {
        fill(a, 0, a.length, val);
    }

    /**
     * Assigns the specified double value to each element of the specified 
     * range of the specified array of doubles.  The range to be filled
     * extends from index <tt>fromIndex</tt>, inclusive, to index
     * <tt>toIndex</tt>, exclusive.  (If <tt>fromIndex==toIndex</tt>, the 
     * range to be filled is empty.)
     *
     * @param a the array to be filled.
     * @param fromIndex the index of the first element (inclusive) to be
     *        filled with the specified value.
     * @param toIndex the index of the last element (exclusive) to be
     *        filled with the specified value.
     * @param val the value to be stored in all elements of the array.
     * @throws IllegalArgumentException if <tt>fromIndex > toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
     *	       <tt>toIndex > a.length</tt>
     */
    public static void fill(double[] a, int fromIndex, int toIndex,double val){
        rangeCheck(a.length, fromIndex, toIndex);
        for (int i=fromIndex; i<toIndex; i++)
            a[i] = val;
    }

    /**
     * Assigns the specified float value to each element of the specified array
     * of floats.
     *
     * @param a the array to be filled.
     * @param val the value to be stored in all elements of the array.
     */
    public static void fill(float[] a, float val) {
        fill(a, 0, a.length, val);
    }

    /**
     * Assigns the specified float value to each element of the specified 
     * range of the specified array of floats.  The range to be filled
     * extends from index <tt>fromIndex</tt>, inclusive, to index
     * <tt>toIndex</tt>, exclusive.  (If <tt>fromIndex==toIndex</tt>, the 
     * range to be filled is empty.)
     *
     * @param a the array to be filled.
     * @param fromIndex the index of the first element (inclusive) to be
     *        filled with the specified value.
     * @param toIndex the index of the last element (exclusive) to be
     *        filled with the specified value.
     * @param val the value to be stored in all elements of the array.
     * @throws IllegalArgumentException if <tt>fromIndex > toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
     *	       <tt>toIndex > a.length</tt>
     */
    public static void fill(float[] a, int fromIndex, int toIndex, float val) {
        rangeCheck(a.length, fromIndex, toIndex);
        for (int i=fromIndex; i<toIndex; i++)
            a[i] = val;
    }

    /**
     * Assigns the specified Object reference to each element of the specified
     * array of Objects.
     *
     * @param a the array to be filled.
     * @param val the value to be stored in all elements of the array.
     */
    public static void fill(Object[] a, Object val) {
        Arrays.fill(a, 0, a.length, val);
    }

    /**
     * Assigns the specified Object reference to each element of the specified 
     * range of the specified array of Objects.  The range to be filled
     * extends from index <tt>fromIndex</tt>, inclusive, to index
     * <tt>toIndex</tt>, exclusive.  (If <tt>fromIndex==toIndex</tt>, the 
     * range to be filled is empty.)
     *
     * @param a the array to be filled.
     * @param fromIndex the index of the first element (inclusive) to be
     *        filled with the specified value.
     * @param toIndex the index of the last element (exclusive) to be
     *        filled with the specified value.
     * @param val the value to be stored in all elements of the array.
     * @throws IllegalArgumentException if <tt>fromIndex > toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
     *	       <tt>toIndex > a.length</tt>
     */
    public static void fill(Object[] a, int fromIndex, int toIndex, Object val) {
        rangeCheck(a.length, fromIndex, toIndex);
        for (int i=fromIndex; i<toIndex; i++)
            a[i] = val;
    }


    // Misc

    /**
     * Returns a fixed-size list backed by the specified array.  (Changes to
     * the returned list "write through" to the array.)  This method acts
     * as bridge between array-based and collection-based APIs, in
     * combination with <tt>Collection.toArray</tt>.  The returned list is
     * serializable and implements {@link RandomAccess}.
     *
     * <p>This method also provides a convenient way to create a fixed-size
     * list initialized to contain several elements:
     * <pre>
     *     List<String> stooges = Arrays.asList("Larry", "Moe", "Curly");
     * </pre>
     *
     * @param a the array by which the list will be backed.
     * @return a list view of the specified array.
     * @see Collection#toArray()
     */
    public static <T> List<T> asList(T... a) {
	return new ArrayList<T>(a);
    }

    /**
     * @serial include
     */
    private static class ArrayList<E> extends AbstractList<E>
	implements RandomAccess, java.io.Serializable
    {
        private static final long serialVersionUID = -2764017481108945198L;
	private Object[] a;

	ArrayList(E[] array) {
            if (array==null)
                throw new NullPointerException();
	    a = array;
	}

	public int size() {
	    return a.length;
	}

	public Object[] toArray() {
	    return (Object[])a.clone();
	}

	public E get(int index) {
	    return (E)a[index];
	}

	public E set(int index, E element) {
	    Object oldValue = a[index];
	    a[index] = element;
	    return (E)oldValue;
	}

        public int indexOf(Object o) {
            if (o==null) {
                for (int i=0; i<a.length; i++)
                    if (a[i]==null)
                        return i;
            } else {
                for (int i=0; i<a.length; i++)
                    if (o.equals(a[i]))
                        return i;
            }
            return -1;
        }

        public boolean contains(Object o) {
            return indexOf(o) != -1;
        }
    }

    /**
     * Returns a hash code based on the contents of the specified array.
     * For any two <tt>long</tt> arrays <tt>a</tt> and <tt>b</tt>
     * such that <tt>Arrays.equals(a, b)</tt>, it is also the case that
     * <tt>Arrays.hashCode(a) == Arrays.hashCode(b)</tt>.
     *
     * <p>The value returned by this method is the same value that would be
     * obtained by invoking the {@link List#hashCode() <tt>hashCode</tt>}
     * method on a {@link List} containing a sequence of {@link Long}
     * instances representing the elements of <tt>a</tt> in the same order.
     * If <tt>a</tt> is <tt>null</tt>, this method returns 0.
     *
     * @param a the array whose hash value to compute
     * @return a content-based hash code for <tt>a</tt>
     * @since 1.5
     */
    public static int hashCode(long a[]) {
        if (a == null)
            return 0;
 
        int result = 1;
        for (long element : a) {
            int elementHash = (int)(element ^ (element >>> 32));
            result = 31 * result + elementHash;
        }
 
        return result;
    }
 
    /**
     * Returns a hash code based on the contents of the specified array.
     * For any two non-null <tt>int</tt> arrays <tt>a</tt> and <tt>b</tt>
     * such that <tt>Arrays.equals(a, b)</tt>, it is also the case that
     * <tt>Arrays.hashCode(a) == Arrays.hashCode(b)</tt>.
     *
     * <p>The value returned by this method is the same value that would be
     * obtained by invoking the {@link List#hashCode() <tt>hashCode</tt>}
     * method on a {@link List} containing a sequence of {@link Integer}
     * instances representing the elements of <tt>a</tt> in the same order.
     * If <tt>a</tt> is <tt>null</tt>, this method returns 0.
     *
     * @param a the array whose hash value to compute
     * @return a content-based hash code for <tt>a</tt>
     * @since 1.5
     */
    public static int hashCode(int a[]) {
        if (a == null)
            return 0;
 
        int result = 1;
        for (int element : a)
            result = 31 * result + element;
 
        return result;
    }
 
    /**
     * Returns a hash code based on the contents of the specified array.
     * For any two <tt>short</tt> arrays <tt>a</tt> and <tt>b</tt>
     * such that <tt>Arrays.equals(a, b)</tt>, it is also the case that
     * <tt>Arrays.hashCode(a) == Arrays.hashCode(b)</tt>.
     *
     * <p>The value returned by this method is the same value that would be
     * obtained by invoking the {@link List#hashCode() <tt>hashCode</tt>}
     * method on a {@link List} containing a sequence of {@link Short}
     * instances representing the elements of <tt>a</tt> in the same order.
     * If <tt>a</tt> is <tt>null</tt>, this method returns 0.
     *
     * @param a the array whose hash value to compute
     * @return a content-based hash code for <tt>a</tt>
     * @since 1.5
     */
    public static int hashCode(short a[]) {
        if (a == null)
            return 0;
 
        int result = 1;
        for (short element : a)
            result = 31 * result + element;
 
        return result;
    }
 
    /**
     * Returns a hash code based on the contents of the specified array.
     * For any two <tt>char</tt> arrays <tt>a</tt> and <tt>b</tt>
     * such that <tt>Arrays.equals(a, b)</tt>, it is also the case that
     * <tt>Arrays.hashCode(a) == Arrays.hashCode(b)</tt>.
     *
     * <p>The value returned by this method is the same value that would be
     * obtained by invoking the {@link List#hashCode() <tt>hashCode</tt>}
     * method on a {@link List} containing a sequence of {@link Character}
     * instances representing the elements of <tt>a</tt> in the same order.
     * If <tt>a</tt> is <tt>null</tt>, this method returns 0.
     *
     * @param a the array whose hash value to compute
     * @return a content-based hash code for <tt>a</tt>
     * @since 1.5
     */
    public static int hashCode(char a[]) {
        if (a == null)
            return 0;
 
        int result = 1;
        for (char element : a)
            result = 31 * result + element;
 
        return result;
    }
 
    /**
     * Returns a hash code based on the contents of the specified array.
     * For any two <tt>byte</tt> arrays <tt>a</tt> and <tt>b</tt>
     * such that <tt>Arrays.equals(a, b)</tt>, it is also the case that
     * <tt>Arrays.hashCode(a) == Arrays.hashCode(b)</tt>.
     *
     * <p>The value returned by this method is the same value that would be
     * obtained by invoking the {@link List#hashCode() <tt>hashCode</tt>}
     * method on a {@link List} containing a sequence of {@link Byte}
     * instances representing the elements of <tt>a</tt> in the same order.
     * If <tt>a</tt> is <tt>null</tt>, this method returns 0.
     *
     * @param a the array whose hash value to compute
     * @return a content-based hash code for <tt>a</tt>
     * @since 1.5
     */
    public static int hashCode(byte a[]) {
        if (a == null)
            return 0;
 
        int result = 1;
        for (byte element : a)
            result = 31 * result + element;
 
        return result;
    }
 
    /**
     * Returns a hash code based on the contents of the specified array.
     * For any two <tt>boolean</tt> arrays <tt>a</tt> and <tt>b</tt>
     * such that <tt>Arrays.equals(a, b)</tt>, it is also the case that
     * <tt>Arrays.hashCode(a) == Arrays.hashCode(b)</tt>.
     *
     * <p>The value returned by this method is the same value that would be
     * obtained by invoking the {@link List#hashCode() <tt>hashCode</tt>}
     * method on a {@link List} containing a sequence of {@link Boolean}
     * instances representing the elements of <tt>a</tt> in the same order.
     * If <tt>a</tt> is <tt>null</tt>, this method returns 0.
     *
     * @param a the array whose hash value to compute
     * @return a content-based hash code for <tt>a</tt>
     * @since 1.5
     */
    public static int hashCode(boolean a[]) {
        if (a == null)
            return 0;
 
        int result = 1;
        for (boolean element : a)
            result = 31 * result + (element ? 1231 : 1237);
 
        return result;
    }
 
    /**
     * Returns a hash code based on the contents of the specified array.
     * For any two <tt>float</tt> arrays <tt>a</tt> and <tt>b</tt>
     * such that <tt>Arrays.equals(a, b)</tt>, it is also the case that
     * <tt>Arrays.hashCode(a) == Arrays.hashCode(b)</tt>.
     *
     * <p>The value returned by this method is the same value that would be
     * obtained by invoking the {@link List#hashCode() <tt>hashCode</tt>}
     * method on a {@link List} containing a sequence of {@link Float}
     * instances representing the elements of <tt>a</tt> in the same order.
     * If <tt>a</tt> is <tt>null</tt>, this method returns 0.
     *
     * @param a the array whose hash value to compute
     * @return a content-based hash code for <tt>a</tt>
     * @since 1.5
     */
    public static int hashCode(float a[]) {
        if (a == null)
            return 0;
 
        int result = 1;
        for (float element : a)
            result = 31 * result + Float.floatToIntBits(element);
 
        return result;
    }
 
    /**
     * Returns a hash code based on the contents of the specified array.
     * For any two <tt>double</tt> arrays <tt>a</tt> and <tt>b</tt>
     * such that <tt>Arrays.equals(a, b)</tt>, it is also the case that
     * <tt>Arrays.hashCode(a) == Arrays.hashCode(b)</tt>.
     *
     * <p>The value returned by this method is the same value that would be
     * obtained by invoking the {@link List#hashCode() <tt>hashCode</tt>}
     * method on a {@link List} containing a sequence of {@link Double}
     * instances representing the elements of <tt>a</tt> in the same order.
     * If <tt>a</tt> is <tt>null</tt>, this method returns 0.
     *
     * @param a the array whose hash value to compute
     * @return a content-based hash code for <tt>a</tt>
     * @since 1.5
     */
    public static int hashCode(double a[]) {
        if (a == null)
            return 0;
 
        int result = 1;
        for (double element : a) {
            long bits = Double.doubleToLongBits(element);
            result = 31 * result + (int)(bits ^ (bits >>> 32));
        }
        return result;
    }
 
    /**
     * Returns a hash code based on the contents of the specified array.  If
     * the array contains other arrays as elements, the hash code is based on
     * their identities rather than their contents.  It is therefore
     * acceptable to invoke this method on an array that contains itself as an
     * element,  either directly or indirectly through one or more levels of
     * arrays.
     *
     * <p>For any two arrays <tt>a</tt> and <tt>b</tt> such that
     * <tt>Arrays.equals(a, b)</tt>, it is also the case that
     * <tt>Arrays.hashCode(a) == Arrays.hashCode(b)</tt>.
     *
     * <p>The value returned by this method is equal to the value that would
     * be returned by <tt>Arrays.asList(a).hashCode()</tt>, unless <tt>a</tt>
     * is <tt>null</tt>, in which case <tt>0</tt> is returned.
     *
     * @param a the array whose content-based hash code to compute
     * @return a content-based hash code for <tt>a</tt>
     * @see #deepHashCode(Object[])
     * @since 1.5
     */
    public static int hashCode(Object a[]) {
        if (a == null)
            return 0;
 
        int result = 1;
 
        for (Object element : a)
            result = 31 * result + (element == null ? 0 : element.hashCode());
 
        return result;
    }
 
    /**
     * Returns a hash code based on the "deep contents" of the specified
     * array.  If the array contains other arrays as elements, the
     * hash code is based on their contents and so on, ad infinitum.
     * It is therefore unacceptable to invoke this method on an array that
     * contains itself as an element, either directly or indirectly through
     * one or more levels of arrays.  The behavior of such an invocation is
     * undefined.
     *
     * <p>For any two arrays <tt>a</tt> and <tt>b</tt> such that
     * <tt>Arrays.deepEquals(a, b)</tt>, it is also the case that
     * <tt>Arrays.deepHashCode(a) == Arrays.deepHashCode(b)</tt>.
     *
     * <p>The computation of the value returned by this method is similar to
     * that of the value returned by {@link List#hashCode()} on a list
     * containing the same elements as <tt>a</tt> in the same order, with one
     * difference: If an element <tt>e</tt> of <tt>a</tt> is itself an array,
     * its hash code is computed not by calling <tt>e.hashCode()</tt>, but as
     * by calling the appropriate overloading of <tt>Arrays.hashCode(e)</tt>
     * if <tt>e</tt> is an array of a primitive type, or as by calling
     * <tt>Arrays.deepHashCode(e)</tt> recursively if <tt>e</tt> is an array
     * of a reference type.  If <tt>a</tt> is <tt>null</tt>, this method
     * returns 0.
     *
     * @param a the array whose deep-content-based hash code to compute
     * @return a deep-content-based hash code for <tt>a</tt>
     * @see #hashCode(Object[])
     * @since 1.5
     */
    public static int deepHashCode(Object a[]) {
        if (a == null)
            return 0;
 
        int result = 1;
 
        for (Object element : a) {
            int elementHash = 0;
            if (element instanceof Object[])
                elementHash = deepHashCode((Object[]) element);
            else if (element instanceof byte[])
                elementHash = hashCode((byte[]) element);
            else if (element instanceof short[])
                elementHash = hashCode((short[]) element);
            else if (element instanceof int[])
                elementHash = hashCode((int[]) element);
            else if (element instanceof long[])
                elementHash = hashCode((long[]) element);
            else if (element instanceof char[])
                elementHash = hashCode((char[]) element);
            else if (element instanceof float[])
                elementHash = hashCode((float[]) element);
            else if (element instanceof double[])
                elementHash = hashCode((double[]) element);
            else if (element instanceof boolean[])
                elementHash = hashCode((boolean[]) element);
            else if (element != null)
                elementHash = element.hashCode();
 
            result = 31 * result + elementHash;
        }
 
        return result;
    }
 
    /**
     * Returns <tt>true</tt> if the two specified arrays are <i>deeply
     * equal</i> to one another.  Unlike the @link{#equals{Object[],Object[])
     * method, this method is appropriate for use with nested arrays of
     * arbitrary depth.
     *
     * <p>Two array references are considered deeply equal if both
     * are <tt>null</tt>, or if they refer to arrays that contain the same
     * number of elements and all corresponding pairs of elements in the two
     * arrays are deeply equal.
     *
     * <p>Two possibly <tt>null</tt> elements <tt>e1</tt> and <tt>e2</tt> are
     * deeply equal if any of the following conditions hold:
     * <ul>
     *    <li> <tt>e1</tt> and <tt>e2</tt> are both arrays of object reference
     *         types, and <tt>Arrays.deepEquals(e1, e2) would return true</tt>
     *    <li> <tt>e1</tt> and <tt>e2</tt> are arrays of the same primitive
     *         type, and the appropriate overloading of
     *         <tt>Arrays.equals(e1, e2)</tt> would return true.
     *    <li> <tt>e1 == e2</tt>
     *    <li> <tt>e1.equals(e2)</tt> would return true.
     * </ul>
     * Note that this definition permits <tt>null</tt> elements at any depth.
     *
     * <p>If either of the specified arrays contain themselves as elements
     * either directly or indirectly through one or more levels of arrays,
     * the behavior of this method is undefined.
     *
     * @param a1 one array to be tested for equality
     * @param a2 the other array to be tested for equality
     * @return <tt>true</tt> if the two arrays are equal
     * @see #equals(Object[],Object[])
     * @since 1.5
     */
    public static boolean deepEquals(Object[] a1, Object[] a2) {
        if (a1 == a2)
            return true;
        if (a1 == null || a2==null)
            return false;
        int length = a1.length;
        if (a2.length != length)
            return false;
 
        for (int i = 0; i < length; i++) {
            Object e1 = a1[i];
            Object e2 = a2[i];
 
            if (e1 == e2)
                continue;
            if (e1 == null)
                return false;
 
            // Figure out whether the two elements are equal
            boolean eq;
            if (e1 instanceof Object[] && e2 instanceof Object[])
                eq = deepEquals ((Object[]) e1, (Object[]) e2);
            else if (e1 instanceof byte[] && e2 instanceof byte[])
                eq = equals((byte[]) e1, (byte[]) e2);
            else if (e1 instanceof short[] && e2 instanceof short[])
                eq = equals((short[]) e1, (short[]) e2);
            else if (e1 instanceof int[] && e2 instanceof int[])
                eq = equals((int[]) e1, (int[]) e2);
            else if (e1 instanceof long[] && e2 instanceof long[])
                eq = equals((long[]) e1, (long[]) e2);
            else if (e1 instanceof char[] && e2 instanceof char[])
                eq = equals((char[]) e1, (char[]) e2);
            else if (e1 instanceof float[] && e2 instanceof float[])
                eq = equals((float[]) e1, (float[]) e2);
            else if (e1 instanceof double[] && e2 instanceof double[])
                eq = equals((double[]) e1, (double[]) e2);
            else if (e1 instanceof boolean[] && e2 instanceof boolean[])
                eq = equals((boolean[]) e1, (boolean[]) e2);
            else
                eq = e1.equals(e2);
 
            if (!eq)
                return false;
        }
        return true;
    }
 
    /**
     * Returns a string representation of the contents of the specified array.
     * The string representation consists of a list of the array's elements,
     * enclosed in square brackets (<tt>"[]"</tt>).  Adjacent elements are
     * separated by the characters <tt>", "</tt> (a comma followed by a
     * space).  Elements are converted to strings as by
     * <tt>String.valueOf(long)</tt>.  Returns <tt>"null"</tt> if <tt>a</tt>
     * is <tt>null</tt>.
     *
     * @param a the array whose string representation to return
     * @return a string representation of <tt>a</tt>
     * @since 1.5
     */
    public static String toString(long[] a) {
        if (a == null)
            return "null";
        if (a.length == 0)
            return "[]";
 
        StringBuilder buf = new StringBuilder();
        buf.append('[');
        buf.append(a[0]);
 
        for (int i = 1; i < a.length; i++) {
            buf.append(", ");
            buf.append(a[i]);
        }
 
        buf.append("]");
        return buf.toString();
    }
 
    /**
     * Returns a string representation of the contents of the specified array.
     * The string representation consists of a list of the array's elements,
     * enclosed in square brackets (<tt>"[]"</tt>).  Adjacent elements are
     * separated by the characters <tt>", "</tt> (a comma followed by a
     * space).  Elements are converted to strings as by
     * <tt>String.valueOf(int)</tt>.  Returns <tt>"null"</tt> if <tt>a</tt> is
     * <tt>null</tt>.
     *
     * @param a the array whose string representation to return
     * @return a string representation of <tt>a</tt>
     * @since 1.5
     */
    public static String toString(int[] a) {
        if (a == null)
            return "null";
        if (a.length == 0)
            return "[]";
 
        StringBuilder buf = new StringBuilder();
        buf.append('[');
        buf.append(a[0]);
 
        for (int i = 1; i < a.length; i++) {
            buf.append(", ");
            buf.append(a[i]);
        }
 
        buf.append("]");
        return buf.toString();
    }
 
    /**
     * Returns a string representation of the contents of the specified array.
     * The string representation consists of a list of the array's elements,
     * enclosed in square brackets (<tt>"[]"</tt>).  Adjacent elements are
     * separated by the characters <tt>", "</tt> (a comma followed by a
     * space).  Elements are converted to strings as by
     * <tt>String.valueOf(short)</tt>.  Returns <tt>"null"</tt> if <tt>a</tt>
     * is <tt>null</tt>.
     *
     * @param a the array whose string representation to return
     * @return a string representation of <tt>a</tt>
     * @since 1.5
     */
    public static String toString(short[] a) {
        if (a == null)
            return "null";
        if (a.length == 0)
            return "[]";
 
        StringBuilder buf = new StringBuilder();
        buf.append('[');
        buf.append(a[0]);
 
        for (int i = 1; i < a.length; i++) {
            buf.append(", ");
            buf.append(a[i]);
        }
 
        buf.append("]");
        return buf.toString();
    }
 
    /**
     * Returns a string representation of the contents of the specified array.
     * The string representation consists of a list of the array's elements,
     * enclosed in square brackets (<tt>"[]"</tt>).  Adjacent elements are
     * separated by the characters <tt>", "</tt> (a comma followed by a
     * space).  Elements are converted to strings as by
     * <tt>String.valueOf(char)</tt>.  Returns <tt>"null"</tt> if <tt>a</tt>
     * is <tt>null</tt>.
     *
     * @param a the array whose string representation to return
     * @return a string representation of <tt>a</tt>
     * @since 1.5
     */
    public static String toString(char[] a) {
        if (a == null)
            return "null";
        if (a.length == 0)
            return "[]";
 
        StringBuilder buf = new StringBuilder();
        buf.append('[');
        buf.append(a[0]);
 
        for (int i = 1; i < a.length; i++) {
            buf.append(", ");
            buf.append(a[i]);
        }
 
        buf.append("]");
        return buf.toString();
    }
 
    /**
     * Returns a string representation of the contents of the specified array.
     * The string representation consists of a list of the array's elements,
     * enclosed in square brackets (<tt>"[]"</tt>).  Adjacent elements
     * are separated by the characters <tt>", "</tt> (a comma followed
     * by a space).  Elements are converted to strings as by
     * <tt>String.valueOf(byte)</tt>.  Returns <tt>"null"</tt> if
     * <tt>a</tt> is <tt>null</tt>.
     *
     * @param a the array whose string representation to return
     * @return a string representation of <tt>a</tt>
     * @since 1.5
     */
    public static String toString(byte[] a) {
        if (a == null)
            return "null";
        if (a.length == 0)
            return "[]";
 
        StringBuilder buf = new StringBuilder();
        buf.append('[');
        buf.append(a[0]);
 
        for (int i = 1; i < a.length; i++) {
            buf.append(", ");
            buf.append(a[i]);
        }
 
        buf.append("]");
        return buf.toString();
    }
 
    /**
     * Returns a string representation of the contents of the specified array.
     * The string representation consists of a list of the array's elements,
     * enclosed in square brackets (<tt>"[]"</tt>).  Adjacent elements are
     * separated by the characters <tt>", "</tt> (a comma followed by a
     * space).  Elements are converted to strings as by
     * <tt>String.valueOf(boolean)</tt>.  Returns <tt>"null"</tt> if
     * <tt>a</tt> is <tt>null</tt>.
     *
     * @param a the array whose string representation to return
     * @return a string representation of <tt>a</tt>
     * @since 1.5
     */
    public static String toString(boolean[] a) {
        if (a == null)
            return "null";
        if (a.length == 0)
            return "[]";
 
        StringBuilder buf = new StringBuilder();
        buf.append('[');
        buf.append(a[0]);
 
        for (int i = 1; i < a.length; i++) {
            buf.append(", ");
            buf.append(a[i]);
        }
 
        buf.append("]");
        return buf.toString();
    }
 
    /**
     * Returns a string representation of the contents of the specified array.
     * The string representation consists of a list of the array's elements,
     * enclosed in square brackets (<tt>"[]"</tt>).  Adjacent elements are
     * separated by the characters <tt>", "</tt> (a comma followed by a
     * space).  Elements are converted to strings as by
     * <tt>String.valueOf(float)</tt>.  Returns <tt>"null"</tt> if <tt>a</tt>
     * is <tt>null</tt>.
     *
     * @param a the array whose string representation to return
     * @return a string representation of <tt>a</tt>
     * @since 1.5
     */
    public static String toString(float[] a) {
        if (a == null)
            return "null";
        if (a.length == 0)
            return "[]";
 
        StringBuilder buf = new StringBuilder();
        buf.append('[');
        buf.append(a[0]);
 
        for (int i = 1; i < a.length; i++) {
            buf.append(", ");
            buf.append(a[i]);
        }
 
        buf.append("]");
        return buf.toString();
    }
 
    /**
     * Returns a string representation of the contents of the specified array.
     * The string representation consists of a list of the array's elements,
     * enclosed in square brackets (<tt>"[]"</tt>).  Adjacent elements are
     * separated by the characters <tt>", "</tt> (a comma followed by a
     * space).  Elements are converted to strings as by
     * <tt>String.valueOf(double)</tt>.  Returns <tt>"null"</tt> if <tt>a</tt>
     * is <tt>null</tt>.
     *
     * @param a the array whose string representation to return
     * @return a string representation of <tt>a</tt>
     * @since 1.5
     */
    public static String toString(double[] a) {
        if (a == null)
            return "null";
        if (a.length == 0)
            return "[]";
 
        StringBuilder buf = new StringBuilder();
        buf.append('[');
        buf.append(a[0]);
 
        for (int i = 1; i < a.length; i++) {
            buf.append(", ");
            buf.append(a[i]);
        }
 
        buf.append("]");
        return buf.toString();
    }
 
    /**
     * Returns a string representation of the contents of the specified array.
     * If the array contains other arrays as elements, they are converted to
     * strings by the {@link Object#toString} method inherited from
     * <tt>Object</tt>, which describes their <i>identities</i> rather than
     * their contents.
     *
     * <p>The value returned by this method is equal to the value that would
     * be returned by <tt>Arrays.asList(a).toString()</tt>, unless <tt>a</tt>
     * is <tt>null</tt>, in which case <tt>"null"</tt> is returned.
     *
     * @param a the array whose string representation to return
     * @return a string representation of <tt>a</tt>
     * @see #deepToString(Object[])
     * @since 1.5
    */
    public static String toString(Object[] a) {
        if (a == null)
            return "null";
        if (a.length == 0)
            return "[]";
 
        StringBuilder buf = new StringBuilder();
 
        for (int i = 0; i < a.length; i++) {
            if (i == 0)
                buf.append('[');
            else
                buf.append(", ");
 
            buf.append(String.valueOf(a[i]));
        }
 
        buf.append("]");
        return buf.toString();
    }
 
    /**
     * Returns a string representation of the "deep contents" of the specified
     * array.  If the array contains other arrays as elements, the string
     * representation contains their contents and so on.  This method is
     * designed for converting multidimensional arrays to strings.
     *
     * <p>The string representation consists of a list of the array's
     * elements, enclosed in square brackets (<tt>"[]"</tt>).  Adjacent
     * elements are separated by the characters <tt>", "</tt> (a comma
     * followed  by a space).  Elements are converted to strings as by
     * <tt>String.valueOf(Object)</tt>, unless they are themselves
     * arrays.
     *
     * <p>If an element <tt>e</tt> is an array of a primitive type, it is
     * converted to a string as by invoking the appropriate overloading of
     * <tt>Arrays.toString(e)</tt>.  If an element <tt>e</tt> is an array of a
     * reference type, it is converted to a string as by invoking
     * this method recursively.
     *
     * <p>To avoid infinite recursion, if the specified array contains itself
     * as an element, or contains an indirect reference to itself through one
     * or more levels of arrays, the self-reference is converted to the string
     * <tt>"[...]"</tt>.  For example, an array containing only a reference
     * to itself would be rendered as <tt>"[[...]]"</tt>.
     *
     * <p>This method returns <tt>"null"</tt> if the specified array
     * is <tt>null</tt>.
     *
     * @param a the array whose string representation to return
     * @return a string representation of <tt>a</tt>
     * @see #toString(Object[])
     * @since 1.5
     */
    public static String deepToString(Object[] a) {
        if (a == null)
            return "null";

        int bufLen = 20 * a.length;
        if (a.length != 0 && bufLen <= 0)
            bufLen = Integer.MAX_VALUE;
        StringBuilder buf = new StringBuilder(bufLen);
        deepToString(a, buf, new HashSet());
        return buf.toString();
    }

    private static void deepToString(Object[] a, StringBuilder buf,
                                     Set<Object[]> dejaVu) {
        if (a == null) {
            buf.append("null");
            return;
        }
        dejaVu.add(a);
        buf.append('[');
        for (int i = 0; i < a.length; i++) {
            if (i != 0)
                buf.append(", ");

            Object element = a[i];
            if (element == null) {
                buf.append("null");
            } else {
                Class eClass = element.getClass();

                if (eClass.isArray()) {
                    if (eClass == byte[].class)
                        buf.append(toString((byte[]) element));
                    else if (eClass == short[].class)
                        buf.append(toString((short[]) element));
                    else if (eClass == int[].class)
                        buf.append(toString((int[]) element));
                    else if (eClass == long[].class)
                        buf.append(toString((long[]) element));
                    else if (eClass == char[].class)
                        buf.append(toString((char[]) element));
                    else if (eClass == float[].class)
                        buf.append(toString((float[]) element));
                    else if (eClass == double[].class)
                        buf.append(toString((double[]) element));
                    else if (eClass == boolean[].class)
                        buf.append(toString((boolean[]) element));
                    else { // element is an array of object references
                        if (dejaVu.contains(element))
                            buf.append("[...]");
                        else
                            deepToString((Object[])element, buf, dejaVu);
                    }
                } else {  // element is non-null and not an array
                    buf.append(element.toString());
                }
            }
        }
        buf.append("]");
        dejaVu.remove(a);
    }
}