Java内部排序（四）-（交换排序法之快速排序+源码）

快速排序是一个非常快的交换排序算法，他的基本思路很简单：从带排序的数据序列中任取一个数据（如第一个数据）作为分界值，所有比他小的元素放在左边，所有比他大的元素放在右边，经这样一趟下来，该序列形成左、右两个子序列，左边序列中的数据元素的值都比分界值小，右边序列中的数据元素的值都比分界值大。

接下来对左、右两个子序列进行递归，对两个子序列重新选择中心元素并依此规则调整，直到每个子序列的元素只剩一个，排序完成。

实现快速排序的关键在于第一趟要做的事，如下所示：

①选出指定的分界值 --  这个容易(如第一个值)。

②将所有比分界值小的数据元素放在左边。

③将所有比分界值大的数据元素放在右边。

现在的问题是怎样实现上面的第二和第三部，这是就要用到交换了，思路入下：

①定义一个 i 变量， i 变量从左边第一个索引开始，找大于分界值的数据元素的索引，并用 i 来记录它。

②定义一个 j 变量， j 变量从右边第一个索引开始，找小于分界值的数据元素的索引，并用 j 来记录它。

③如果 i < j ，则交换 i、j 两个索引处的元素。

重复执行上面1~3步，直到 i >= j ，可以判断 j 左边的数据元素都小于分界值，j 右边的数据元素都大于分界值，最后将分界值和 j 索引处的元素交换即可。

快速排序的一趟操作如下图：

接下来实现快速排序，

模拟数据如下：9，-16，21，23，-30，-49，21，30,13

public class QuickSort {private static void wrap(DataWrap[] data, int i, int j){DataWrap dw = data[i];data[i] = data[j];data[j] = dw;}private static void quickSort(DataWrap[] data){subSort(data,0,data.length - 1);}/** *  * @param data ：要进行快速排序的数组序列 * @param start ： 开始的索引 * @param end ： 结束的索引 */private static void subSort(DataWrap[] data, int start, int end) {//需要排序if(start < end){//以第一个元素作为分界元素DataWrap base = data[start];//从左边开始搜索，搜索大于分界值的数据元素int i = start;//从右边开始搜索，搜索小于分界值的数据元素int j = end + 1; //因为是索引，所以加一while(true){while(i < end && data[++i].compareTo(base) <= 0);while(j > start && data[--j].compareTo(base) >= 0);if(i < j){wrap(data, i, j);}else{break;}}wrap(data, start, j);subSort(data, start, j - 1);subSort(data, j + 1, end);}}public static void main(String[] args){DataWrap[] data = {new DataWrap(9,""),new DataWrap(-16,""),new DataWrap(21,"*"),new DataWrap(23,""),new DataWrap(-30,""),new DataWrap(-49,""),new DataWrap(21,""),new DataWrap(30,""),new DataWrap(13,""),};System.out.println("-排序前-"+java.util.Arrays.toString(data));quickSort(data);System.out.println( "-排序后-"+java.util.Arrays.toString(data));}}

运行结果：

快速排序算法的时间效率很好，因为它每趟能确定的元素成指数增长。

快速排序算法需要使用递归，而递归使用栈，因此它的使用空间效率为 O(log2N)。

快速排序算法包含跳跃式交换，因此它是不稳定的排序算法。

最后贴上jdk7的快速排序源码：膜拜吧：

/**     * Sorts the specified range of the array by Dual-Pivot Quicksort.     *     * @param a the array to be sorted     * @param left the index of the first element, inclusive, to be sorted     * @param right the index of the last element, inclusive, to be sorted     * @param leftmost indicates if this part is the leftmost in the range     */    private static void sort(char[] a, int left, int right, boolean leftmost) {        int length = right - left + 1;        // Use insertion sort on tiny arrays        if (length < INSERTION_SORT_THRESHOLD) {            if (leftmost) {                /*                 * Traditional (without sentinel) insertion sort,                 * optimized for server VM, is used in case of                 * the leftmost part.                 */                for (int i = left, j = i; i < right; j = ++i) {                    char ai = a[i + 1];                    while (ai < a[j]) {                        a[j + 1] = a[j];                        if (j-- == left) {                            break;                        }                    }                    a[j + 1] = ai;                }            } else {                /*                 * Skip the longest ascending sequence.                 */                do {                    if (left >= right) {                        return;                    }                } while (a[++left] >= a[left - 1]);                /*                 * Every element from adjoining part plays the role                 * of sentinel, therefore this allows us to avoid the                 * left range check on each iteration. Moreover, we use                 * the more optimized algorithm, so called pair insertion                 * sort, which is faster (in the context of Quicksort)                 * than traditional implementation of insertion sort.                 */                for (int k = left; ++left <= right; k = ++left) {                    char a1 = a[k], a2 = a[left];                    if (a1 < a2) {                        a2 = a1; a1 = a[left];                    }                    while (a1 < a[--k]) {                        a[k + 2] = a[k];                    }                    a[++k + 1] = a1;                    while (a2 < a[--k]) {                        a[k + 1] = a[k];                    }                    a[k + 1] = a2;                }                char last = a[right];                while (last < a[--right]) {                    a[right + 1] = a[right];                }                a[right + 1] = last;            }            return;        }        // Inexpensive approximation of length / 7        int seventh = (length >> 3) + (length >> 6) + 1;        /*         * Sort five evenly spaced elements around (and including) the         * center element in the range. These elements will be used for         * pivot selection as described below. The choice for spacing         * these elements was empirically determined to work well on         * a wide variety of inputs.         */        int e3 = (left + right) >>> 1; // The midpoint        int e2 = e3 - seventh;        int e1 = e2 - seventh;        int e4 = e3 + seventh;        int e5 = e4 + seventh;        // Sort these elements using insertion sort        if (a[e2] < a[e1]) { char t = a[e2]; a[e2] = a[e1]; a[e1] = t; }        if (a[e3] < a[e2]) { char t = a[e3]; a[e3] = a[e2]; a[e2] = t;            if (t < a[e1]) { a[e2] = a[e1]; a[e1] = t; }        }        if (a[e4] < a[e3]) { char t = a[e4]; a[e4] = a[e3]; a[e3] = t;            if (t < a[e2]) { a[e3] = a[e2]; a[e2] = t;                if (t < a[e1]) { a[e2] = a[e1]; a[e1] = t; }            }        }        if (a[e5] < a[e4]) { char t = a[e5]; a[e5] = a[e4]; a[e4] = t;            if (t < a[e3]) { a[e4] = a[e3]; a[e3] = t;                if (t < a[e2]) { a[e3] = a[e2]; a[e2] = t;                    if (t < a[e1]) { a[e2] = a[e1]; a[e1] = t; }                }            }        }        // Pointers        int less  = left;  // The index of the first element of center part        int great = right; // The index before the first element of right part        if (a[e1] != a[e2] && a[e2] != a[e3] && a[e3] != a[e4] && a[e4] != a[e5]) {            /*             * Use the second and fourth of the five sorted elements as pivots.             * These values are inexpensive approximations of the first and             * second terciles of the array. Note that pivot1 <= pivot2.             */            char pivot1 = a[e2];            char pivot2 = a[e4];            /*             * The first and the last elements to be sorted are moved to the             * locations formerly occupied by the pivots. When partitioning             * is complete, the pivots are swapped back into their final             * positions, and excluded from subsequent sorting.             */            a[e2] = a[left];            a[e4] = a[right];            /*             * Skip elements, which are less or greater than pivot values.             */            while (a[++less] < pivot1);            while (a[--great] > pivot2);            /*             * Partitioning:             *             *   left part           center part                   right part             * +--------------------------------------------------------------+             * |  < pivot1  |  pivot1 <= && <= pivot2  |    ?    |  > pivot2  |             * +--------------------------------------------------------------+             *               ^                          ^       ^             *               |                          |       |             *              less                        k     great             *             * Invariants:             *             *              all in (left, less)   < pivot1             *    pivot1 <= all in [less, k)     <= pivot2             *              all in (great, right) > pivot2             *             * Pointer k is the first index of ?-part.             */            outer:            for (int k = less - 1; ++k <= great; ) {                char ak = a[k];                if (ak < pivot1) { // Move a[k] to left part                    a[k] = a[less];                    /*                     * Here and below we use "a[i] = b; i++;" instead                     * of "a[i++] = b;" due to performance issue.                     */                    a[less] = ak;                    ++less;                } else if (ak > pivot2) { // Move a[k] to right part                    while (a[great] > pivot2) {                        if (great-- == k) {                            break outer;                        }                    }                    if (a[great] < pivot1) { // a[great] <= pivot2                        a[k] = a[less];                        a[less] = a[great];                        ++less;                    } else { // pivot1 <= a[great] <= pivot2                        a[k] = a[great];                    }                    /*                     * Here and below we use "a[i] = b; i--;" instead                     * of "a[i--] = b;" due to performance issue.                     */                    a[great] = ak;                    --great;                }            }            // Swap pivots into their final positions            a[left]  = a[less  - 1]; a[less  - 1] = pivot1;            a[right] = a[great + 1]; a[great + 1] = pivot2;            // Sort left and right parts recursively, excluding known pivots            sort(a, left, less - 2, leftmost);            sort(a, great + 2, right, false);            /*             * If center part is too large (comprises > 4/7 of the array),             * swap internal pivot values to ends.             */            if (less < e1 && e5 < great) {                /*                 * Skip elements, which are equal to pivot values.                 */                while (a[less] == pivot1) {                    ++less;                }                while (a[great] == pivot2) {                    --great;                }                /*                 * Partitioning:                 *                 *   left part         center part                  right part                 * +----------------------------------------------------------+                 * | == pivot1 |  pivot1 < && < pivot2  |    ?    | == pivot2 |                 * +----------------------------------------------------------+                 *              ^                        ^       ^                 *              |                        |       |                 *             less                      k     great                 *                 * Invariants:                 *                 *              all in (*,  less) == pivot1                 *     pivot1 < all in [less,  k)  < pivot2                 *              all in (great, *) == pivot2                 *                 * Pointer k is the first index of ?-part.                 */                outer:                for (int k = less - 1; ++k <= great; ) {                    char ak = a[k];                    if (ak == pivot1) { // Move a[k] to left part                        a[k] = a[less];                        a[less] = ak;                        ++less;                    } else if (ak == pivot2) { // Move a[k] to right part                        while (a[great] == pivot2) {                            if (great-- == k) {                                break outer;                            }                        }                        if (a[great] == pivot1) { // a[great] < pivot2                            a[k] = a[less];                            /*                             * Even though a[great] equals to pivot1, the                             * assignment a[less] = pivot1 may be incorrect,                             * if a[great] and pivot1 are floating-point zeros                             * of different signs. Therefore in float and                             * double sorting methods we have to use more                             * accurate assignment a[less] = a[great].                             */                            a[less] = pivot1;                            ++less;                        } else { // pivot1 < a[great] < pivot2                            a[k] = a[great];                        }                        a[great] = ak;                        --great;                    }                }            }            // Sort center part recursively            sort(a, less, great, false);        } else { // Partitioning with one pivot            /*             * Use the third of the five sorted elements as pivot.             * This value is inexpensive approximation of the median.             */            char pivot = a[e3];            /*             * Partitioning degenerates to the traditional 3-way             * (or "Dutch National Flag") schema:             *             *   left part    center part              right part             * +-------------------------------------------------+             * |  < pivot  |   == pivot   |     ?    |  > pivot  |             * +-------------------------------------------------+             *              ^              ^        ^             *              |              |        |             *             less            k      great             *             * Invariants:             *             *   all in (left, less)   < pivot             *   all in [less, k)     == pivot             *   all in (great, right) > pivot             *             * Pointer k is the first index of ?-part.             */            for (int k = less; k <= great; ++k) {                if (a[k] == pivot) {                    continue;                }                char ak = a[k];                if (ak < pivot) { // Move a[k] to left part                    a[k] = a[less];                    a[less] = ak;                    ++less;                } else { // a[k] > pivot - Move a[k] to right part                    while (a[great] > pivot) {                        --great;                    }                    if (a[great] < pivot) { // a[great] <= pivot                        a[k] = a[less];                        a[less] = a[great];                        ++less;                    } else { // a[great] == pivot                        /*                         * Even though a[great] equals to pivot, the                         * assignment a[k] = pivot may be incorrect,                         * if a[great] and pivot are floating-point                         * zeros of different signs. Therefore in float                         * and double sorting methods we have to use                         * more accurate assignment a[k] = a[great].                         */                        a[k] = pivot;                    }                    a[great] = ak;                    --great;                }            }            /*             * Sort left and right parts recursively.             * All elements from center part are equal             * and, therefore, already sorted.             */            sort(a, left, less - 1, leftmost);            sort(a, great + 1, right, false);        }    }