Median of Medians in Java

Question

I am trying to implement Median of Medians in Java for a method like this:

Select(Comparable[] list, int pos, int colSize, int colMed)

Answer 1

The question asked for Java, so here it is

import java.util.*;

public class MedianOfMedians {
    private MedianOfMedians() {

    }

    /**
     * Returns median of list in linear time.
     * 
     * @param list list to search, which may be reordered on return
     * @return median of array in linear time.
     */
    public static Comparable getMedian(ArrayList list) {
        int s = list.size();
        if (s < 1)
            throw new IllegalArgumentException();
        int pos = select(list, 0, s, s / 2);
        return list.get(pos);
    }

    /**
     * Returns position of k'th largest element of sub-list.
     * 
     * @param list list to search, whose sub-list may be shuffled before
     *            returning
     * @param lo first element of sub-list in list
     * @param hi just after last element of sub-list in list
     * @param k
     * @return position of k'th largest element of (possibly shuffled) sub-list.
     */
    public static int select(ArrayList list, int lo, int hi, int k) {
        if (lo >= hi || k < 0 || lo + k >= hi)
            throw new IllegalArgumentException();
        if (hi - lo < 10) {
            Collections.sort(list.subList(lo, hi));
            return lo + k;
        }
        int s = hi - lo;
        int np = s / 5; // Number of partitions
        for (int i = 0; i < np; i++) {
            // For each partition, move its median to front of our sublist
            int lo2 = lo + i * 5;
            int hi2 = (i + 1 == np) ? hi : (lo2 + 5);
            int pos = select(list, lo2, hi2, 2);
            Collections.swap(list, pos, lo + i);
        }

        // Partition medians were moved to front, so we can recurse without making another list.
        int pos = select(list, lo, lo + np, np / 2);

        // Re-partition list to [pivot]
        int m = triage(list, lo, hi, pos);
        int cmp = lo + k - m;
        if (cmp > 0)
            return select(list, m + 1, hi, k - (m - lo) - 1);
        else if (cmp < 0)
            return select(list, lo, m, k);
        return lo + k;
    }

    /**
     * Partition sub-list into 3 parts [pivot].
     * 
     * @param list
     * @param lo
     * @param hi
     * @param pos input position of pivot value
     * @return output position of pivot value
     */
    private static int triage(ArrayList list, int lo, int hi,
            int pos) {
        Comparable pivot = list.get(pos);
        int lo3 = lo;
        int hi3 = hi;
        while (lo3 < hi3) {
            Comparable e = list.get(lo3);
            int cmp = e.compareTo(pivot);
            if (cmp < 0)
                lo3++;
            else if (cmp > 0)
                Collections.swap(list, lo3, --hi3);
            else {
                while (hi3 > lo3 + 1) {
                    assert (list.get(lo3).compareTo(pivot) == 0);
                    e = list.get(--hi3);
                    cmp = e.compareTo(pivot);
                    if (cmp <= 0) {
                        if (lo3 + 1 == hi3) {
                            Collections.swap(list, lo3, lo3 + 1);
                            lo3++;
                            break;
                        }
                        Collections.swap(list, lo3, lo3 + 1);
                        assert (list.get(lo3 + 1).compareTo(pivot) == 0);
                        Collections.swap(list, lo3, hi3);
                        lo3++;
                        hi3++;
                    }
                }
                break;
            }
        }
        assert (list.get(lo3).compareTo(pivot) == 0);
        return lo3;
    }

}

Here is a Unit test to check it works...

import java.util.*;

import junit.framework.TestCase;

public class MedianOfMedianTest extends TestCase {
    public void testMedianOfMedianTest() {
        Random r = new Random(1);
        int n = 87;
        for (int trial = 0; trial < 1000; trial++) {
            ArrayList list = new ArrayList();
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                int v = r.nextInt(256);
                a[i] = v;
                list.add(v);
            }
            int m1 = (Integer)MedianOfMedians.getMedian(list);
            Arrays.sort(a);
            int m2 = a[n/2];
            assertEquals(m1, m2);
        }
    }
}

However, the above code is too slow for practical use.

Here is a simpler way to get the k'th element that does not guarantee performance, but is much faster in practice:

/**
 * Returns position of k'th largest element of sub-list.
 * 
 * @param list list to search, whose sub-list may be shuffled before
 *            returning
 * @param lo first element of sub-list in list
 * @param hi just after last element of sub-list in list
 * @param k
 * @return position of k'th largest element of (possibly shuffled) sub-list.
 */
static int select(double[] list, int lo, int hi, int k) {
    int n = hi - lo;
    if (n < 2)
        return lo;

    double pivot = list[lo + (k * 7919) % n]; // Pick a random pivot

    // Triage list to [pivot]
    int nLess = 0, nSame = 0, nMore = 0;
    int lo3 = lo;
    int hi3 = hi;
    while (lo3 < hi3) {
        double e = list[lo3];
        int cmp = compare(e, pivot);
        if (cmp < 0) {
            nLess++;
            lo3++;
        } else if (cmp > 0) {
            swap(list, lo3, --hi3);
            if (nSame > 0)
                swap(list, hi3, hi3 + nSame);
            nMore++;
        } else {
            nSame++;
            swap(list, lo3, --hi3);
        }
    }
    assert (nSame > 0);
    assert (nLess + nSame + nMore == n);
    assert (list[lo + nLess] == pivot);
    assert (list[hi - nMore - 1] == pivot);
    if (k >= n - nMore)
        return select(list, hi - nMore, hi, k - nLess - nSame);
    else if (k < nLess)
        return select(list, lo, lo + nLess, k);
    return lo + k;
}