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 * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved.

 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.

 *

 * This code is free software; you can redistribute it and/or modify it

 * under the terms of the GNU General Public License version 2 only, as

 * published by the Free Software Foundation.  Oracle designates this

 * particular file as subject to the "Classpath" exception as provided

 * by Oracle in the LICENSE file that accompanied this code.

 *

 * This code is distributed in the hope that it will be useful, but WITHOUT

 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or

 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License

 * version 2 for more details (a copy is included in the LICENSE file that

 * accompanied this code).

 *

 * You should have received a copy of the GNU General Public License version

 * 2 along with this work; if not, write to the Free Software Foundation,

 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.

 *

 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA

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 */

package java.util;

/**

 * This class implements the Dual-Pivot Quicksort algorithm by

 * Vladimir Yaroslavskiy, Jon Bentley, and Josh Bloch. The algorithm

 * offers O(n log(n)) performance on many data sets that cause other

 * quicksorts to degrade to quadratic performance, and is typically

 * faster than traditional (one-pivot) Quicksort implementations.

 *

 * All exposed methods are package-private, designed to be invoked

 * from public methods (in class Arrays) after performing any

 * necessary array bounds checks and expanding parameters into the

 * required forms.

 *

 * @author Vladimir Yaroslavskiy

 * @author Jon Bentley

 * @author Josh Bloch

 *

 * @version 2011.02.11 m765.827.12i:5\7pm

 * @since 1.7

 */

final class DualPivotQuicksort {

    /**

     * Prevents instantiation.

     */

    private DualPivotQuicksort() {}

    /*

     * Tuning parameters.

     */

    /**

     * The maximum number of runs in merge sort.

     */

    private static final int MAX_RUN_COUNT = 67;

    /**

     * The maximum length of run in merge sort.

     */

    private static final int MAX_RUN_LENGTH = 33;

    /**

     * If the length of an array to be sorted is less than this

     * constant, Quicksort is used in preference to merge sort.

     */

    private static final int QUICKSORT_THRESHOLD = 286;

    /**

     * If the length of an array to be sorted is less than this

     * constant, insertion sort is used in preference to Quicksort.

     */

    private static final int INSERTION_SORT_THRESHOLD = 47;

    /**

     * If the length of a byte array to be sorted is greater than this

     * constant, counting sort is used in preference to insertion sort.

     */

    private static final int COUNTING_SORT_THRESHOLD_FOR_BYTE = 29;

    /**

     * If the length of a short or char array to be sorted is greater

     * than this constant, counting sort is used in preference to Quicksort.

     */

    private static final int COUNTING_SORT_THRESHOLD_FOR_SHORT_OR_CHAR = 3200;

    /*

     * Sorting methods for seven primitive types.

     */

    /**

     * Sorts the specified range of the array using the given

     * workspace array slice if possible for merging

     *

     * @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 work a workspace array (slice)

     * @param workBase origin of usable space in work array

     * @param workLen usable size of work array

     */

    static void sort(int[] a, int left, int right,

                     int[] work, int workBase, int workLen) {

        // Use Quicksort on small arrays

        if (right - left < QUICKSORT_THRESHOLD) {

            sort(a, left, right, true);

            return;

        }

        /*

         * Index run[i] is the start of i-th run

         * (ascending or descending sequence).

         */

        int[] run = new int[MAX_RUN_COUNT + 1];

        int count = 0; run[0] = left;

        // Check if the array is nearly sorted

        for (int k = left; k < right; run[count] = k) {

            if (a[k] < a[k + 1]) { // ascending

                while (++k <= right && a[k - 1] <= a[k]);

            } else if (a[k] > a[k + 1]) { // descending

                while (++k <= right && a[k - 1] >= a[k]);

                for (int lo = run[count] - 1, hi = k; ++lo < --hi; ) {

                    int t = a[lo]; a[lo] = a[hi]; a[hi] = t;

                }

            } else { // equal

                for (int m = MAX_RUN_LENGTH; ++k <= right && a[k - 1] == a[k]; ) {

                    if (--m == 0) {

                        sort(a, left, right, true);

                        return;

                    }

                }

            }

            /*

             * The array is not highly structured,

             * use Quicksort instead of merge sort.

             */

            if (++count == MAX_RUN_COUNT) {

                sort(a, left, right, true);

                return;

            }

        }

        // Check special cases

        // Implementation note: variable "right" is increased by 1.

        if (run[count] == right++) { // The last run contains one element

            run[++count] = right;

        } else if (count == 1) { // The array is already sorted

            return;

        }

        // Determine alternation base for merge

        byte odd = 0;

        for (int n = 1; (n <<= 1) < count; odd ^= 1);

        // Use or create temporary array b for merging

        int[] b;                 // temp array; alternates with a

        int ao, bo;              // array offsets from 'left'

        int blen = right - left; // space needed for b

        if (work == null || workLen < blen || workBase + blen > work.length) {

            work = new int[blen];

            workBase = 0;

        }

        if (odd == 0) {

            System.arraycopy(a, left, work, workBase, blen);

            b = a;

            bo = 0;

            a = work;

            ao = workBase - left;

        } else {

            b = work;

            ao = 0;

            bo = workBase - left;

        }

        // Merging

        for (int last; count > 1; count = last) {

            for (int k = (last = 0) + 2; k <= count; k += 2) {

                int hi = run[k], mi = run[k - 1];

                for (int i = run[k - 2], p = i, q = mi; i < hi; ++i) {

                    if (q >= hi || p < mi && a[p + ao] <= a[q + ao]) {

                        b[i + bo] = a[p++ + ao];

                    } else {

                        b[i + bo] = a[q++ + ao];

                    }

                }

                run[++last] = hi;

            }

            if ((count & 1) != 0) {

                for (int i = right, lo = run[count - 1]; --i >= lo;

                    b[i + bo] = a[i + ao]

                );

                run[++last] = right;

            }

            int[] t = a; a = b; b = t;

            int o = ao; ao = bo; bo = o;

        }

    }

    /**

     * 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(int[] 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) {

                    int 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) {

                    int 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;

                }

                int 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]) { int t = a[e2]; a[e2] = a[e1]; a[e1] = t; }

        if (a[e3] < a[e2]) { int 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]) { int 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]) { int 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.

             */

            int pivot1 = a[e2];

            int 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; ) {

                int 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; ) {

                    int 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.

             */

            int 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