Computes the median of an array. - Java Collection Framework

Description

Computes the median of an array.

Demo Code

//package com.java2s;

public class Main {
    public static void main(String[] argv) throws Exception {
        double[] v = new double[] { 34.45, 35.45, 36.67, 37.78, 37.0000,
                37.1234, 67.2344, 68.34534, 69.87700 };
        System.out.println(median(v));
    }//from w  w w  .j  a  v a  2  s . c  o  m

    /**
     * Computes the median of an array.
     * If the array contains an even number of elements,
     * then the mean of the lower and upper medians is returned.
     */
    public static double median(double[] v) {
        if (v.length == 3) {
            return median3(copy(v));
        } else if (v.length == 5) {
            return median5(copy(v));
        } else if (v.length == 7) {
            return median7(copy(v));
        } else if (v.length % 2 == 1) { // odd
            return quickSelect(copy(v), false);
        } else { // even
            double[] tmp = copy(v);
            double lowerMedian = quickSelect(tmp, false);
            double upperMedian = quickSelect(tmp, true);
            return (lowerMedian + upperMedian) / 2.0;
        }
    }

    /**
     * Computes the median of an array.
     * If the array contains an even number of elements,
     * the lower median is returned.
     */
    public static int median(int[] v) {
        if (v.length == 3) {
            return median3(copy(v));
        } else if (v.length == 5) {
            return median5(copy(v));
        } else if (v.length == 7) {
            return median7(copy(v));
        } else {
            return quickSelect(copy(v));
        }
    }

    private static double median3(double[] v) {
        sortInPlace(v, 0, 1);
        sortInPlace(v, 1, 2);
        sortInPlace(v, 0, 1);
        return v[1];
    }

    private static int median3(int[] v) {
        sortInPlace(v, 0, 1);
        sortInPlace(v, 1, 2);
        sortInPlace(v, 0, 1);
        return v[1];
    }

    /**
     * Returns a copy of the array.
     */
    //a call to array.clone() may also work although this is a primitive type. I haven't checked
    //it even may be faster
    public static int[] copy(int[] array) {
        int[] result;
        result = new int[array.length];
        System.arraycopy(array, 0, result, 0, array.length);
        return result;
    }

    /**
     * Returns a copy of the array.
     */
    //a call to array.clone() may also work although this is a primitive type. I haven't checked
    //it even may be faster
    public static long[] copy(long[] array) {
        long[] result;
        result = new long[array.length];
        System.arraycopy(array, 0, result, 0, array.length);
        return result;
    }

    /**
     * Returns a copy of the array.
     */
    //a call to array.clone() may also work although this is a primitive type. I haven't checked
    //it even may be faster
    public static float[] copy(float[] array) {
        float[] result;
        result = new float[array.length];
        System.arraycopy(array, 0, result, 0, array.length);
        return result;
    }

    /**
     * Returns a copy of the array.
     */
    //a call to array.clone() may also work although this is a primitive type. I haven't checked
    //it even may be faster
    public static double[] copy(double[] array) {
        double[] result;
        result = new double[array.length];
        System.arraycopy(array, 0, result, 0, array.length);
        return result;
    }

    /**
     * Returns a copy of the array.
     */
    public static double[][] copy(double[][] v) {
        double[][] ans = new double[v.length][];
        for (int k = 0; k < v.length; k++)
            ans[k] = copy(v[k]);
        return (ans);
    }

    /**
     * Returns a copy of the array.
     */
    public static int[][] copy(int[][] v) {
        int[][] ans = new int[v.length][];
        for (int k = 0; k < v.length; k++)
            ans[k] = copy(v[k]);
        return (ans);
    }

    private static double median5(double[] v) {
        sortInPlace(v, 0, 1);
        sortInPlace(v, 3, 4);
        sortInPlace(v, 0, 3);
        sortInPlace(v, 1, 4);
        sortInPlace(v, 1, 2);
        sortInPlace(v, 2, 3);
        sortInPlace(v, 1, 2);
        return v[2];
    }

    private static int median5(int[] v) {
        sortInPlace(v, 0, 1);
        sortInPlace(v, 3, 4);
        sortInPlace(v, 0, 3);
        sortInPlace(v, 1, 4);
        sortInPlace(v, 1, 2);
        sortInPlace(v, 2, 3);
        sortInPlace(v, 1, 2);
        return v[2];
    }

    private static double median7(double[] v) {
        sortInPlace(v, 0, 5);
        sortInPlace(v, 0, 3);
        sortInPlace(v, 1, 6);
        sortInPlace(v, 2, 4);
        sortInPlace(v, 0, 1);
        sortInPlace(v, 3, 5);
        sortInPlace(v, 2, 6);
        sortInPlace(v, 2, 3);
        sortInPlace(v, 3, 6);
        sortInPlace(v, 4, 5);
        sortInPlace(v, 1, 4);
        sortInPlace(v, 1, 3);
        sortInPlace(v, 3, 4);
        return v[3];
    }

    private static int median7(int[] v) {
        sortInPlace(v, 0, 5);
        sortInPlace(v, 0, 3);
        sortInPlace(v, 1, 6);
        sortInPlace(v, 2, 4);
        sortInPlace(v, 0, 1);
        sortInPlace(v, 3, 5);
        sortInPlace(v, 2, 6);
        sortInPlace(v, 2, 3);
        sortInPlace(v, 3, 6);
        sortInPlace(v, 4, 5);
        sortInPlace(v, 1, 4);
        sortInPlace(v, 1, 3);
        sortInPlace(v, 3, 4);
        return v[3];
    }

    private static double quickSelect(double[] v, boolean upperMedian) {
        int low = 0, high = v.length - 1;
        final int median = upperMedian ? high / 2 + 1 : high / 2;
        int middle, ll, hh;

        for (;;) {
            if (high <= low) { /* One element only */
                return v[median];
            }

            if (high == low + 1) { /* Two elements only */
                if (v[low] > v[high])
                    swap(v, low, high);
                return v[median];
            }

            /* Find median of low, middle and high items; swap into position low */
            middle = (low + high) / 2;
            if (v[middle] > v[high])
                swap(v, middle, high);
            if (v[low] > v[high])
                swap(v, low, high);
            if (v[middle] > v[low])
                swap(v, middle, low);

            /* Swap low item (now in position middle) into position (low+1) */
            swap(v, middle, low + 1);

            /* Nibble from each end towards middle, swapping items when stuck */
            ll = low + 1;
            hh = high;
            for (;;) {
                do
                    ll++;
                while (v[low] > v[ll]);
                do
                    hh--;
                while (v[hh] > v[low]);

                if (hh < ll)
                    break;

                swap(v, ll, hh);
            }

            /* Swap middle item (in position low) back into correct position */
            swap(v, low, hh);

            /* Re-set active partition */
            if (hh <= median)
                low = ll;
            if (hh >= median)
                high = hh - 1;
        }
    }

    private static int quickSelect(int[] v) {
        int low = 0, high = v.length - 1;
        final int median = high / 2;
        int middle, ll, hh;

        for (;;) {
            if (high <= low) { /* One element only */
                return v[median];
            }

            if (high == low + 1) { /* Two elements only */
                if (v[low] > v[high])
                    swap(v, low, high);
                return v[median];
            }

            /* Find median of low, middle and high items; swap into position low */
            middle = (low + high) / 2;
            if (v[middle] > v[high])
                swap(v, middle, high);
            if (v[low] > v[high])
                swap(v, low, high);
            if (v[middle] > v[low])
                swap(v, middle, low);

            /* Swap low item (now in position middle) into position (low+1) */
            swap(v, middle, low + 1);

            /* Nibble from each end towards middle, swapping items when stuck */
            ll = low + 1;
            hh = high;
            for (;;) {
                do
                    ll++;
                while (v[low] > v[ll]);
                do
                    hh--;
                while (v[hh] > v[low]);

                if (hh < ll)
                    break;

                swap(v, ll, hh);
            }

            /* Swap middle item (in position low) back into correct position */
            swap(v, low, hh);

            /* Re-set active partition */
            if (hh <= median)
                low = ll;
            if (hh >= median)
                high = hh - 1;
        }
    }

    private static void sortInPlace(final double[] v, final int i,
            final int j) {
        if (v[i] > v[j]) {
            final double tmp = v[i];
            v[i] = v[j];
            v[j] = tmp;
        }
    }

    private static void sortInPlace(final int[] v, final int i, final int j) {
        if (v[i] > v[j]) {
            final int tmp = v[i];
            v[i] = v[j];
            v[j] = tmp;
        }
    }

    /**
     * Used by the quick sort and quick select algorithms.
     */
    private static void swap(final int a[], final int i, final int j) {
        final int T;
        T = a[i];
        a[i] = a[j];
        a[j] = T;
    }

    /**
     * Used by the quick sort and quick select algorithms.
     */
    private static void swap(final double a[], final int i, final int j) {
        final double T;
        T = a[i];
        a[i] = a[j];
        a[j] = T;

    }
}

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