深入JDK源码之Arrays类中的排序查找算法

binarySearch()方法

二分法查找算法，算法思想：当数据量很大适宜采用该方法。采用二分法查找时，数据需是排好序的。 基本思想：假设数据是按升序排序的，对于给定值x，从序列的中间位置开始比较，如果当前位置值等于x，则查找成功；若x小于当前位置值，则在数列的前半段中查找；若x大于当前位置值则在数列的后半段中继续查找，直到找到为止。

    //针对int类型数组的二分法查找，key为要查找数的下标
    private static int binarySearch0(int[] a, int fromIndex, int toIndex, int key) {
        int low = fromIndex;
        int high = toIndex - 1;
        while (low <= high) {
            int mid = (low + high) >>> 1;//无符号左移一位，相当于除以二
            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.
    }

sort()方法

针对引用类型数组采取的算法是归并排序，算法思想：归并（Merge）排序法是将两个（或两个以上）有序表合并成一个新的有序表，即把待排序序列分为若干个子序列，每个子序列是有序的。然后再把有序子序列合并为整体有序序列。

    private static final int INSERTIONSORT_THRESHOLD = 7;//插入排序门槛
    public static void sort(Object[] a) {
        Object[] aux = (Object[])a.clone();
        mergeSort(aux, a, 0, a.length, 0);
    }
    //归并排序
    private static void mergeSort(Object[] src, Object[] dest, int low, int high, int off) {
        int length = high - low;
        if (length < INSERTIONSORT_THRESHOLD) { //若数组长度小于7，则用冒泡排序
            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; //无符号左移一位，
        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++];
        }
    }

sort()方法

采取的是快速排序算法，算法思想：通过一趟排序将要排序的数据分割成独立的两部分，其中一部分的所有数据都比另外一部分的所有数据都要小，然后再按此方法对这两部分数据分别进行快速排序，整个排序过程可以递归进行，以此达到整个数据变成有序序列。

    /**
     * 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;
    }
    public static void sort(int[] a) {
        sort1(a, 0, a.length);
    }

    private static int med3(int x[], int a, int b, int c) {//找出三个中的中间值
        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) {//采用冒泡排序
            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;
        }
        //采用快速排序
        // 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 = len/8;
                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);
    }

sort()方法

针对double，float类型数组排序，采取了先把所有的数组元素值为-0.0d的转换成0.0d，再利用快速排序排好序，最后再还原。

    public static void sort(double[] a) {
        sort2(a, 0, a.length);
    }
    private static void sort2(double a[], int fromIndex, int toIndex) {
        //static long doubleToLongBits(double value) 
        //根据 IEEE 754 浮点双精度格式 ("double format") 位布局，返回指定浮点值的表示形式。
        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]) {  //这段搞不懂，源代码怪怪的，感觉多此一举
                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 = binarySearch0(a, fromIndex, n, 0.0d); // 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;
        }
    }