QuickX.java

Below is the syntax highlighted version of QuickX.java from §2.3 Quicksort.

/*************************************************************************
 *  Compilation:  javac QuickX.java
 *  Execution:    java QuickX N
 *  
 *  Uses the Bentley-McIlroy 3-way partitioning scheme,
 *  chooses the partitioning element using Tukey's ninther,
 *  and cuts off to insertion sort.
 *
 *  Reference: Engineering a Sort Function by Jon L. Bentley
 *  and M. Douglas McIlroy. Softwae-Practice and Experience,
 *  Vol. 23 (11), 1249-1265 (November 1993).
 *
 *************************************************************************/

public class QuickX {
    private static final int CUTOFF = 8;  // cutoff to insertion sort, must be >= 1

    public static void sort(Comparable[] a) {
        sort(a, 0, a.length - 1);
    }

    private static void sort(Comparable[] a, int lo, int hi) { 
        int N = hi - lo + 1;

        // cutoff to insertion sort
        if (N <= CUTOFF) {
            insertionSort(a, lo, hi);
            return;
        }

        // use median-of-3 as partitioning element
        else if (N <= 40) {
            int m = median3(a, lo, lo + N/2, hi);
            exch(a, m, lo);
        }

        // use Tukey ninther as partitioning element
        else  {
            int eps = N/8;
            int mid = lo + N/2;
            int m1 = median3(a, lo, lo + eps, lo + eps + eps);
            int m2 = median3(a, mid - eps, mid, mid + eps);
            int m3 = median3(a, hi - eps - eps, hi - eps, hi); 
            int ninther = median3(a, m1, m2, m3);
            exch(a, ninther, lo);
        }

        // Bentley-McIlroy 3-way partitioning
        int i = lo, j = hi+1;
        int p = lo, q = hi+1;
        while (true) {
            Comparable v = a[lo];
            while (less(a[++i], v))
                if (i == hi) break;
            while (less(v, a[--j]))
                if (j == lo) break;
            if (i >= j) break;
            exch(a, i, j);
            if (eq(a[i], v)) exch(a, ++p, i);
            if (eq(a[j], v)) exch(a, --q, j);
        }
        exch(a, lo, j);

        i = j + 1;
        j = j - 1;
        for (int k = lo+1; k <= p; k++) exch(a, k, j--);
        for (int k = hi  ; k >= q; k--) exch(a, k, i++);

        sort(a, lo, j);
        sort(a, i, hi);
    }


    // sort from a[lo] to a[hi] using insertion sort
    private static void insertionSort(Comparable[] a, int lo, int hi) {
        for (int i = lo; i <= hi; i++)
            for (int j = i; j > lo && less(a[j], a[j-1]); j--)
                exch(a, j, j-1);
    }


    // return the index of the median element among a[i], a[j], and a[k]
    private static int median3(Comparable[] a, int i, int j, int k) {
        return (less(a[i], a[j]) ?
               (less(a[j], a[k]) ? j : less(a[i], a[k]) ? k : i) :
               (less(a[k], a[j]) ? j : less(a[k], a[i]) ? k : i));
    }

   /***********************************************************************
    *  Helper sorting functions
    ***********************************************************************/
    
    // is v < w ?
    private static boolean less(Comparable v, Comparable w) {
        return (v.compareTo(w) < 0);
    }

    // does v == w ?
    private static boolean eq(Comparable v, Comparable w) {
        return (v.compareTo(w) == 0);
    }
        
    // exchange a[i] and a[j]
    private static void exch(Object[] a, int i, int j) {
        Object swap = a[i];
        a[i] = a[j];
        a[j] = swap;
    }


   /***********************************************************************
    *  Check if array is sorted - useful for debugging
    ***********************************************************************/
    private static boolean isSorted(Comparable[] a) {
        for (int i = 1; i < a.length; i++)
            if (less(a[i], a[i-1])) return false;
        return true;
    }



    // test client
    public static void main(String[] args) {

        // generate array of N random reals between 0 and 1
        int N = Integer.parseInt(args[0]);
        Double[] a = new Double[N];
        for (int i = 0; i < N; i++) {
            a[i] = Math.random();
        }
        
        // sort the array
        sort(a);

        // display results
        for (int i = 0; i < N; i++) {
            StdOut.println(a[i]);
        }
        StdOut.println("isSorted = " + isSorted(a));

    }

}