| /* | |
|  * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. | |
|  * Copyright 2009 Google Inc.  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 | |
|  * or visit www.oracle.com if you need additional information or have any | |
|  * questions. | |
| */ | |
| package java.util; | |
| /** | |
|  * A stable, adaptive, iterative mergesort that requires far fewer than | |
|  * n lg(n) comparisons when running on partially sorted arrays, while | |
|  * offering performance comparable to a traditional mergesort when run | |
|  * on random arrays.  Like all proper mergesorts, this sort is stable and | |
|  * runs O(n log n) time (worst case).  In the worst case, this sort requires | |
|  * temporary storage space for n/2 object references; in the best case, | |
|  * it requires only a small constant amount of space. | |
|  * | |
|  * This implementation was adapted from Tim Peters's list sort for | |
|  * Python, which is described in detail here: | |
|  * | |
|  *   http://svn.python.org/projects/python/trunk/Objects/listsort.txt | |
|  * | |
|  * Tim's C code may be found here: | |
|  * | |
|  *   http://svn.python.org/projects/python/trunk/Objects/listobject.c | |
|  * | |
|  * The underlying techniques are described in this paper (and may have | |
|  * even earlier origins): | |
|  * | |
|  *  "Optimistic Sorting and Information Theoretic Complexity" | |
|  *  Peter McIlroy | |
|  *  SODA (Fourth Annual ACM-SIAM Symposium on Discrete Algorithms), | |
|  *  pp 467-474, Austin, Texas, 25-27 January 1993. | |
|  * | |
|  * While the API to this class consists solely of static methods, it is | |
|  * (privately) instantiable; a TimSort instance holds the state of an ongoing | |
|  * sort, assuming the input array is large enough to warrant the full-blown | |
|  * TimSort. Small arrays are sorted in place, using a binary insertion sort. | |
|  * | |
|  * @author Josh Bloch | |
| */ | |
| class TimSort<T> { | |
|     /** | |
|      * This is the minimum sized sequence that will be merged.  Shorter | |
|      * sequences will be lengthened by calling binarySort.  If the entire | |
|      * array is less than this length, no merges will be performed. | |
|      * | |
|      * This constant should be a power of two.  It was 64 in Tim Peter's C | |
|      * implementation, but 32 was empirically determined to work better in | |
|      * this implementation.  In the unlikely event that you set this constant | |
|      * to be a number that's not a power of two, you'll need to change the | |
|      * {@link #minRunLength} computation. | |
|      * | |
|      * If you decrease this constant, you must change the stackLen | |
|      * computation in the TimSort constructor, or you risk an | |
|      * ArrayOutOfBounds exception.  See listsort.txt for a discussion | |
|      * of the minimum stack length required as a function of the length | |
|      * of the array being sorted and the minimum merge sequence length. | |
| */ | |
| private static final int MIN_MERGE = 32; | |
|     /** | |
|      * The array being sorted. | |
| */ | |
| private final T[] a; | |
|     /** | |
|      * The comparator for this sort. | |
| */ | |
| private final Comparator<? super T> c; | |
|     /** | |
|      * When we get into galloping mode, we stay there until both runs win less | |
|      * often than MIN_GALLOP consecutive times. | |
| */ | |
| private static final int MIN_GALLOP = 7; | |
|     /** | |
|      * This controls when we get *into* galloping mode.  It is initialized | |
|      * to MIN_GALLOP.  The mergeLo and mergeHi methods nudge it higher for | |
|      * random data, and lower for highly structured data. | |
| */ | |
| private int minGallop = MIN_GALLOP; | |
|     /** | |
|      * Maximum initial size of tmp array, which is used for merging.  The array | |
|      * can grow to accommodate demand. | |
|      * | |
|      * Unlike Tim's original C version, we do not allocate this much storage | |
|      * when sorting smaller arrays.  This change was required for performance. | |
| */ | |
| private static final int INITIAL_TMP_STORAGE_LENGTH = 256; | |
|     /** | |
|      * Temp storage for merges. A workspace array may optionally be | |
|      * provided in constructor, and if so will be used as long as it | |
|      * is big enough. | |
| */ | |
| private T[] tmp; | |
|     private int tmpBase; // base of tmp array slice | |
|     private int tmpLen;  // length of tmp array slice | |
| /** | |
| * A stack of pending runs yet to be merged. Run i starts at | |
| * address base[i] and extends for len[i] elements. It's always | |
| * true (so long as the indices are in bounds) that: | |
| * | |
| * runBase[i] + runLen[i] == runBase[i + 1] | |
| * | |
| * so we could cut the storage for this, but it's a minor amount, | |
| * and keeping all the info explicit simplifies the code. | |
| */ | |
|     private int stackSize = 0;  // Number of pending runs on stack | |
| private final int[] runBase; | |
| private final int[] runLen; | |
|     /** | |
|      * Creates a TimSort instance to maintain the state of an ongoing sort. | |
|      * | |
|      * @param a the array to be sorted | |
|      * @param c the comparator to determine the order of the sort | |
|      * @param work a workspace array (slice) | |
|      * @param workBase origin of usable space in work array | |
|      * @param workLen usable size of work array | |
| */ | |
| private TimSort(T[] a, Comparator<? super T> c, T[] work, int workBase, int workLen) { | |
| this.a = a; | |
| this.c = c; | |
|         // Allocate temp storage (which may be increased later if necessary) | |
| int len = a.length; | |
| int tlen = (len < 2 * INITIAL_TMP_STORAGE_LENGTH) ? | |
| len >>> 1 : INITIAL_TMP_STORAGE_LENGTH; | |
| if (work == null || workLen < tlen || workBase + tlen > work.length) { | |
|             @SuppressWarnings({"unchecked", "UnnecessaryLocalVariable"}) | |
| T[] newArray = (T[])java.lang.reflect.Array.newInstance | |
| (a.getClass().getComponentType(), tlen); | |
| tmp = newArray; | |
| tmpBase = 0; | |
| tmpLen = tlen; | |
| } | |
|         else { | |
| tmp = work; | |
| tmpBase = workBase; | |
| tmpLen = workLen; | |
| } | |
|         /* | |
|          * Allocate runs-to-be-merged stack (which cannot be expanded).  The | |
|          * stack length requirements are described in listsort.txt.  The C | |
|          * version always uses the same stack length (85), but this was | |
|          * measured to be too expensive when sorting "mid-sized" arrays (e.g., | |
|          * 100 elements) in Java.  Therefore, we use smaller (but sufficiently | |
|          * large) stack lengths for smaller arrays.  The "magic numbers" in the | |
|          * computation below must be changed if MIN_MERGE is decreased.  See | |
|          * the MIN_MERGE declaration above for more information. | |
|          * The maximum value of 49 allows for an array up to length | |
|          * Integer.MAX_VALUE-4, if array is filled by the worst case stack size | |
|          * increasing scenario. More explanations are given in section 4 of: | |
|          * http://envisage-project.eu/wp-content/uploads/2015/02/sorting.pdf | |
| */ | |
| int stackLen = (len < 120 ? 5 : | |
| len < 1542 ? 10 : | |
| len < 119151 ? 24 : 49); | |
| runBase = new int[stackLen]; | |
| runLen = new int[stackLen]; | |
| } | |
| /* | |
| * The next method (package private and static) constitutes the | |
| * entire API of this class. | |
| */ | |
|     /** | |
|      * Sorts the given range, using the given workspace array slice | |
|      * for temp storage when possible. This method is designed to be | |
|      * invoked from public methods (in class Arrays) after performing | |
|      * any necessary array bounds checks and expanding parameters into | |
|      * the required forms. | |
|      * | |
|      * @param a the array to be sorted | |
|      * @param lo the index of the first element, inclusive, to be sorted | |
|      * @param hi the index of the last element, exclusive, to be sorted | |
|      * @param c the comparator to use | |
|      * @param work a workspace array (slice) | |
|      * @param workBase origin of usable space in work array | |
|      * @param workLen usable size of work array | |
|      * @since 1.8 | |
| */ | |
| static <T> void sort(T[] a, int lo, int hi, Comparator<? super T> c, | |
|                          T[] work, int workBase, int workLen) { | |
| assert c != null && a != null && lo >= 0 && lo <= hi && hi <= a.length; | |
| int nRemaining = hi - lo; | |
| if (nRemaining < 2) | |
|             return;  // Arrays of size 0 and 1 are always sorted | |
|         // If array is small, do a "mini-TimSort" with no merges | |
| if (nRemaining < MIN_MERGE) { | |
| int initRunLen = countRunAndMakeAscending(a, lo, hi, c); | |
| binarySort(a, lo, hi, lo + initRunLen, c); | |
| return; | |
| } | |
|         /** | |
|          * March over the array once, left to right, finding natural runs, | |
|          * extending short natural runs to minRun elements, and merging runs | |
|          * to maintain stack invariant. | |
| */ | |
| TimSort<T> ts = new TimSort<>(a, c, work, workBase, workLen); | |
| int minRun = minRunLength(nRemaining); | |
|         do { | |
|             // Identify next run | |
| int runLen = countRunAndMakeAscending(a, lo, hi, c); | |
|             // If run is short, extend to min(minRun, nRemaining) | |
| if (runLen < minRun) { | |
| int force = nRemaining <= minRun ? nRemaining : minRun; | |
| binarySort(a, lo, lo + force, lo + runLen, c); | |
| runLen = force; | |
| } | |
|             // Push run onto pending-run stack, and maybe merge | |
| ts.pushRun(lo, runLen); | |
| ts.mergeCollapse(); | |
|             // Advance to find next run | |
| lo += runLen; | |
| nRemaining -= runLen; | |
| } while (nRemaining != 0); | |
|         // Merge all remaining runs to complete sort | |
| assert lo == hi; | |
| ts.mergeForceCollapse(); | |
| assert ts.stackSize == 1; | |
| } | |
|     /** | |
|      * Sorts the specified portion of the specified array using a binary | |
|      * insertion sort.  This is the best method for sorting small numbers | |
|      * of elements.  It requires O(n log n) compares, but O(n^2) data | |
|      * movement (worst case). | |
|      * | |
|      * If the initial part of the specified range is already sorted, | |
|      * this method can take advantage of it: the method assumes that the | |
|      * elements from index {@code lo}, inclusive, to {@code start}, | |
|      * exclusive are already sorted. | |
|      * | |
|      * @param a the array in which a range is to be sorted | |
|      * @param lo the index of the first element in the range to be sorted | |
|      * @param hi the index after the last element in the range to be sorted | |
|      * @param start the index of the first element in the range that is | |
|      *        not already known to be sorted ({@code lo <= start <= hi}) | |
|      * @param c comparator to used for the sort | |
| */ | |
|     @SuppressWarnings("fallthrough") | |
| private static <T> void binarySort(T[] a, int lo, int hi, int start, | |
| Comparator<? super T> c) { | |
| assert lo <= start && start <= hi; | |
| if (start == lo) | |
| start++; | |
| for ( ; start < hi; start++) { | |
| T pivot = a[start]; | |
|             // Set left (and right) to the index where a[start] (pivot) belongs | |
| int left = lo; | |
| int right = start; | |
| assert left <= right; | |
|             /* | |
|              * Invariants: | |
|              *   pivot >= all in [lo, left). | |
|              *   pivot <  all in [right, start). | |
| */ | |
| while (left < right) { | |
| int mid = (left + right) >>> 1; | |
| if (c.compare(pivot, a[mid]) < 0) | |
| right = mid; | |
| else | |
| left = mid + 1; | |
| } | |
| assert left == right; | |
| /* | |
| * The invariants still hold: pivot >= all in [lo, left) and | |
| * pivot < all in [left, start), so pivot belongs at left. Note | |
| * that if there are elements equal to pivot, left points to the | |
| * first slot after them -- that's why this sort is stable. | |
| * Slide elements over to make room for pivot. | |
| */ | |
| int n = start - left; // The number of elements to move | |
|             // Switch is just an optimization for arraycopy in default case | |
| switch (n) { | |
| case 2: a[left + 2] = a[left + 1]; | |
| case 1: a[left + 1] = a[left]; | |
| break; | |
| default: System.arraycopy(a, left, a, left + 1, n); | |
| } | |
| a[left] = pivot; | |
| } | |
| } | |
|     /** | |
|      * Returns the length of the run beginning at the specified position in | |
|      * the specified array and reverses the run if it is descending (ensuring | |
|      * that the run will always be ascending when the method returns). | |
|      * | |
|      * A run is the longest ascending sequence with: | |
|      * | |
|      *    a[lo] <= a[lo + 1] <= a[lo + 2] <= ... | |
|      * | |
|      * or the longest descending sequence with: | |
|      * | |
|      *    a[lo] >  a[lo + 1] >  a[lo + 2] >  ... | |
|      * | |
|      * For its intended use in a stable mergesort, the strictness of the | |
|      * definition of "descending" is needed so that the call can safely | |
|      * reverse a descending sequence without violating stability. | |
|      * | |
|      * @param a the array in which a run is to be counted and possibly reversed | |
|      * @param lo index of the first element in the run | |
|      * @param hi index after the last element that may be contained in the run. | |
|      *        It is required that {@code lo < hi}. | |
|      * @param c the comparator to used for the sort | |
|      * @return  the length of the run beginning at the specified position in | |
|      *          the specified array | |
| */ | |
| private static <T> int countRunAndMakeAscending(T[] a, int lo, int hi, | |
| Comparator<? super T> c) { | |
| assert lo < hi; | |
| int runHi = lo + 1; | |
| if (runHi == hi) | |
| return 1; | |
|         // Find end of run, and reverse range if descending | |
| if (c.compare(a[runHi++], a[lo]) < 0) { // Descending | |
| while (runHi < hi && c.compare(a[runHi], a[runHi - 1]) < 0) | |
| runHi++; | |
| reverseRange(a, lo, runHi); | |
|         } else {                              // Ascending | |
| while (runHi < hi && c.compare(a[runHi], a[runHi - 1]) >= 0) | |
| runHi++; | |
| } | |
| return runHi - lo; | |
| } | |
|     /** | |
|      * Reverse the specified range of the specified array. | |
|      * | |
|      * @param a the array in which a range is to be reversed | |
|      * @param lo the index of the first element in the range to be reversed | |
|      * @param hi the index after the last element in the range to be reversed | |
| */ | |
| private static void reverseRange(Object[] a, int lo, int hi) { | |
| hi--; | |
| while (lo < hi) { | |
| Object t = a[lo]; | |
| a[lo++] = a[hi]; | |
| a[hi--] = t; | |
| } | |
| } | |
|     /** | |
|      * Returns the minimum acceptable run length for an array of the specified | |
|      * length. Natural runs shorter than this will be extended with | |
|      * {@link #binarySort}. | |
|      * | |
|      * Roughly speaking, the computation is: | |
|      * | |
|      *  If n < MIN_MERGE, return n (it's too small to bother with fancy stuff). | |
|      *  Else if n is an exact power of 2, return MIN_MERGE/2. | |
|      *  Else return an int k, MIN_MERGE/2 <= k <= MIN_MERGE, such that n/k | |
|      *   is close to, but strictly less than, an exact power of 2. | |
|      * | |
|      * For the rationale, see listsort.txt. | |
|      * | |
|      * @param n the length of the array to be sorted | |
|      * @return the length of the minimum run to be merged | |
| */ | |
|     private static int minRunLength(int n) { | |
| assert n >= 0; | |
|         int r = 0;      // Becomes 1 if any 1 bits are shifted off | |
| while (n >= MIN_MERGE) { | |
| r |= (n & 1); | |
| n >>= 1; | |
| } | |
| return n + r; | |
| } | |
|     /** | |
|      * Pushes the specified run onto the pending-run stack. | |
|      * | |
|      * @param runBase index of the first element in the run | |
|      * @param runLen  the number of elements in the run | |
| */ | |
|     private void pushRun(int runBase, int runLen) { | |
| this.runBase[stackSize] = runBase; | |
| this.runLen[stackSize] = runLen; | |
| stackSize++; | |
| } | |
|     /** | |
|      * Examines the stack of runs waiting to be merged and merges adjacent runs | |
|      * until the stack invariants are reestablished: | |
|      * | |
|      *     1. runLen[i - 3] > runLen[i - 2] + runLen[i - 1] | |
|      *     2. runLen[i - 2] > runLen[i - 1] | |
|      * | |
|      * This method is called each time a new run is pushed onto the stack, | |
|      * so the invariants are guaranteed to hold for i < stackSize upon | |
|      * entry to the method. | |
|      * | |
|      * Thanks to Stijn de Gouw, Jurriaan Rot, Frank S. de Boer, | |
|      * Richard Bubel and Reiner Hahnle, this is fixed with respect to | |
|      * the analysis in "On the Worst-Case Complexity of TimSort" by | |
|      * Nicolas Auger, Vincent Jug, Cyril Nicaud, and Carine Pivoteau. | |
| */ | |
|     private void mergeCollapse() { | |
| while (stackSize > 1) { | |
| int n = stackSize - 2; | |
| if (n > 0 && runLen[n-1] <= runLen[n] + runLen[n+1] || | |
| n > 1 && runLen[n-2] <= runLen[n] + runLen[n-1]) { | |
| if (runLen[n - 1] < runLen[n + 1]) | |
| n--; | |
| } else if (n < 0 || runLen[n] > runLen[n + 1]) { | |
|                 break; // Invariant is established | |
| } | |
| mergeAt(n); | |
| } | |
| } | |
|     /** | |
|      * Merges all runs on the stack until only one remains.  This method is | |
|      * called once, to complete the sort. | |
| */ | |
|     private void mergeForceCollapse() { | |
| while (stackSize > 1) { | |
| int n = stackSize - 2; | |
| if (n > 0 && runLen[n - 1] < runLen[n + 1]) | |
| n--; | |
| mergeAt(n); | |
| } | |
| } | |
|     /** | |
|      * Merges the two runs at stack indices i and i+1.  Run i must be | |
|      * the penultimate or antepenultimate run on the stack.  In other words, | |
|      * i must be equal to stackSize-2 or stackSize-3. | |
|      * | |
|      * @param i stack index of the first of the two runs to merge | |
| */ | |
|     private void mergeAt(int i) { | |
| assert stackSize >= 2; | |
| assert i >= 0; | |
| assert i == stackSize - 2 || i == stackSize - 3; | |
| int base1 = runBase[i]; | |
| int len1 = runLen[i]; | |
| int base2 = runBase[i + 1]; | |
| int len2 = runLen[i + 1]; | |
| assert len1 > 0 && len2 > 0; | |
| assert base1 + len1 == base2; | |
|         /* | |
|          * Record the length of the combined runs; if i is the 3rd-last | |
|          * run now, also slide over the last run (which isn't involved | |
|          * in this merge).  The current run (i+1) goes away in any case. | |
| */ | |
| runLen[i] = len1 + len2; | |
| if (i == stackSize - 3) { | |
| runBase[i + 1] = runBase[i + 2]; | |
| runLen[i + 1] = runLen[i + 2]; | |
| } | |
| stackSize--; | |
|         /* | |
|          * Find where the first element of run2 goes in run1. Prior elements | |
|          * in run1 can be ignored (because they're already in place). | |
| */ | |
| int k = gallopRight(a[base2], a, base1, len1, 0, c); | |
| assert k >= 0; | |
| base1 += k; | |
| len1 -= k; | |
| if (len1 == 0) | |
| return; | |
|         /* | |
|          * Find where the last element of run1 goes in run2. Subsequent elements | |
|          * in run2 can be ignored (because they're already in place). | |
| */ | |
| len2 = gallopLeft(a[base1 + len1 - 1], a, base2, len2, len2 - 1, c); | |
| assert len2 >= 0; | |
| if (len2 == 0) | |
| return; | |
|         // Merge remaining runs, using tmp array with min(len1, len2) elements | |
| if (len1 <= len2) | |
| mergeLo(base1, len1, base2, len2); | |
| else | |
| mergeHi(base1, len1, base2, len2); | |
| } | |
|     /** | |
|      * Locates the position at which to insert the specified key into the | |
|      * specified sorted range; if the range contains an element equal to key, | |
|      * returns the index of the leftmost equal element. | |
|      * | |
|      * @param key the key whose insertion point to search for | |
|      * @param a the array in which to search | |
|      * @param base the index of the first element in the range | |
|      * @param len the length of the range; must be > 0 | |
|      * @param hint the index at which to begin the search, 0 <= hint < n. | |
|      *     The closer hint is to the result, the faster this method will run. | |
|      * @param c the comparator used to order the range, and to search | |
|      * @return the int k,  0 <= k <= n such that a[b + k - 1] < key <= a[b + k], | |
|      *    pretending that a[b - 1] is minus infinity and a[b + n] is infinity. | |
|      *    In other words, key belongs at index b + k; or in other words, | |
|      *    the first k elements of a should precede key, and the last n - k | |
|      *    should follow it. | |
| */ | |
| private static <T> int gallopLeft(T key, T[] a, int base, int len, int hint, | |
| Comparator<? super T> c) { | |
| assert len > 0 && hint >= 0 && hint < len; | |
| int lastOfs = 0; | |
| int ofs = 1; | |
| if (c.compare(key, a[base + hint]) > 0) { | |
|             // Gallop right until a[base+hint+lastOfs] < key <= a[base+hint+ofs] | |
| int maxOfs = len - hint; | |
| while (ofs < maxOfs && c.compare(key, a[base + hint + ofs]) > 0) { | |
| lastOfs = ofs; | |
| ofs = (ofs << 1) + 1; | |
| if (ofs <= 0) // int overflow | |
| ofs = maxOfs; | |
| } | |
| if (ofs > maxOfs) | |
| ofs = maxOfs; | |
|             // Make offsets relative to base | |
| lastOfs += hint; | |
| ofs += hint; | |
|         } else { // key <= a[base + hint] | |
|             // Gallop left until a[base+hint-ofs] < key <= a[base+hint-lastOfs] | |
| final int maxOfs = hint + 1; | |
| while (ofs < maxOfs && c.compare(key, a[base + hint - ofs]) <= 0) { | |
| lastOfs = ofs; | |
| ofs = (ofs << 1) + 1; | |
| if (ofs <= 0) // int overflow | |
| ofs = maxOfs; | |
| } | |
| if (ofs > maxOfs) | |
| ofs = maxOfs; | |
|             // Make offsets relative to base | |
| int tmp = lastOfs; | |
| lastOfs = hint - ofs; | |
| ofs = hint - tmp; | |
| } | |
| assert -1 <= lastOfs && lastOfs < ofs && ofs <= len; | |
|         /* | |
|          * Now a[base+lastOfs] < key <= a[base+ofs], so key belongs somewhere | |
|          * to the right of lastOfs but no farther right than ofs.  Do a binary | |
|          * search, with invariant a[base + lastOfs - 1] < key <= a[base + ofs]. | |
| */ | |
| lastOfs++; | |
| while (lastOfs < ofs) { | |
| int m = lastOfs + ((ofs - lastOfs) >>> 1); | |
| if (c.compare(key, a[base + m]) > 0) | |
| lastOfs = m + 1; // a[base + m] < key | |
| else | |
| ofs = m; // key <= a[base + m] | |
| } | |
| assert lastOfs == ofs; // so a[base + ofs - 1] < key <= a[base + ofs] | |
| return ofs; | |
| } | |
|     /** | |
|      * Like gallopLeft, except that if the range contains an element equal to | |
|      * key, gallopRight returns the index after the rightmost equal element. | |
|      * | |
|      * @param key the key whose insertion point to search for | |
|      * @param a the array in which to search | |
|      * @param base the index of the first element in the range | |
|      * @param len the length of the range; must be > 0 | |
|      * @param hint the index at which to begin the search, 0 <= hint < n. | |
|      *     The closer hint is to the result, the faster this method will run. | |
|      * @param c the comparator used to order the range, and to search | |
|      * @return the int k,  0 <= k <= n such that a[b + k - 1] <= key < a[b + k] | |
| */ | |
| private static <T> int gallopRight(T key, T[] a, int base, int len, | |
| int hint, Comparator<? super T> c) { | |
| assert len > 0 && hint >= 0 && hint < len; | |
| int ofs = 1; | |
| int lastOfs = 0; | |
| if (c.compare(key, a[base + hint]) < 0) { | |
|             // Gallop left until a[b+hint - ofs] <= key < a[b+hint - lastOfs] | |
| int maxOfs = hint + 1; | |
| while (ofs < maxOfs && c.compare(key, a[base + hint - ofs]) < 0) { | |
| lastOfs = ofs; | |
| ofs = (ofs << 1) + 1; | |
| if (ofs <= 0) // int overflow | |
| ofs = maxOfs; | |
| } | |
| if (ofs > maxOfs) | |
| ofs = maxOfs; | |
|             // Make offsets relative to b | |
| int tmp = lastOfs; | |
| lastOfs = hint - ofs; | |
| ofs = hint - tmp; | |
|         } else { // a[b + hint] <= key | |
|             // Gallop right until a[b+hint + lastOfs] <= key < a[b+hint + ofs] | |
| int maxOfs = len - hint; | |
| while (ofs < maxOfs && c.compare(key, a[base + hint + ofs]) >= 0) { | |
| lastOfs = ofs; | |
| ofs = (ofs << 1) + 1; | |
| if (ofs <= 0) // int overflow | |
| ofs = maxOfs; | |
| } | |
| if (ofs > maxOfs) | |
| ofs = maxOfs; | |
|             // Make offsets relative to b | |
| lastOfs += hint; | |
| ofs += hint; | |
| } | |
| assert -1 <= lastOfs && lastOfs < ofs && ofs <= len; | |
|         /* | |
|          * Now a[b + lastOfs] <= key < a[b + ofs], so key belongs somewhere to | |
|          * the right of lastOfs but no farther right than ofs.  Do a binary | |
|          * search, with invariant a[b + lastOfs - 1] <= key < a[b + ofs]. | |
| */ | |
| lastOfs++; | |
| while (lastOfs < ofs) { | |
| int m = lastOfs + ((ofs - lastOfs) >>> 1); | |
| if (c.compare(key, a[base + m]) < 0) | |
| ofs = m; // key < a[b + m] | |
| else | |
| lastOfs = m + 1; // a[b + m] <= key | |
| } | |
| assert lastOfs == ofs; // so a[b + ofs - 1] <= key < a[b + ofs] | |
| return ofs; | |
| } | |
|     /** | |
|      * Merges two adjacent runs in place, in a stable fashion.  The first | |
|      * element of the first run must be greater than the first element of the | |
|      * second run (a[base1] > a[base2]), and the last element of the first run | |
|      * (a[base1 + len1-1]) must be greater than all elements of the second run. | |
|      * | |
|      * For performance, this method should be called only when len1 <= len2; | |
|      * its twin, mergeHi should be called if len1 >= len2.  (Either method | |
|      * may be called if len1 == len2.) | |
|      * | |
|      * @param base1 index of first element in first run to be merged | |
|      * @param len1  length of first run to be merged (must be > 0) | |
|      * @param base2 index of first element in second run to be merged | |
|      *        (must be aBase + aLen) | |
|      * @param len2  length of second run to be merged (must be > 0) | |
| */ | |
|     private void mergeLo(int base1, int len1, int base2, int len2) { | |
| assert len1 > 0 && len2 > 0 && base1 + len1 == base2; | |
| // Copy first run into temp array | |
|         T[] a = this.a; // For performance | |
| T[] tmp = ensureCapacity(len1); | |
| int cursor1 = tmpBase; // Indexes into tmp array | |
| int cursor2 = base2; // Indexes int a | |
| int dest = base1; // Indexes int a | |
| System.arraycopy(a, base1, tmp, cursor1, len1); | |
|         // Move first element of second run and deal with degenerate cases | |
| a[dest++] = a[cursor2++]; | |
| if (--len2 == 0) { | |
| System.arraycopy(tmp, cursor1, a, dest, len1); | |
| return; | |
| } | |
| if (len1 == 1) { | |
| System.arraycopy(a, cursor2, a, dest, len2); | |
| a[dest + len2] = tmp[cursor1]; // Last elt of run 1 to end of merge | |
| return; | |
| } | |
| Comparator<? super T> c = this.c; // Use local variable for performance | |
|         int minGallop = this.minGallop;    //  "    "       "     "      " | |
| outer: | |
|         while (true) { | |
|             int count1 = 0; // Number of times in a row that first run won | |
|             int count2 = 0; // Number of times in a row that second run won | |
|             /* | |
|              * Do the straightforward thing until (if ever) one run starts | |
|              * winning consistently. | |
| */ | |
|             do { | |
| assert len1 > 1 && len2 > 0; | |
| if (c.compare(a[cursor2], tmp[cursor1]) < 0) { | |
| a[dest++] = a[cursor2++]; | |
| count2++; | |
| count1 = 0; | |
| if (--len2 == 0) | |
| break outer; | |
|                 } else { | |
| a[dest++] = tmp[cursor1++]; | |
| count1++; | |
| count2 = 0; | |
| if (--len1 == 1) | |
| break outer; | |
| } | |
| } while ((count1 | count2) < minGallop); | |
|             /* | |
|              * One run is winning so consistently that galloping may be a | |
|              * huge win. So try that, and continue galloping until (if ever) | |
|              * neither run appears to be winning consistently anymore. | |
| */ | |
|             do { | |
| assert len1 > 1 && len2 > 0; | |
| count1 = gallopRight(a[cursor2], tmp, cursor1, len1, 0, c); | |
| if (count1 != 0) { | |
| System.arraycopy(tmp, cursor1, a, dest, count1); | |
| dest += count1; | |
| cursor1 += count1; | |
| len1 -= count1; | |
| if (len1 <= 1) // len1 == 1 || len1 == 0 | |
| break outer; | |
| } | |
| a[dest++] = a[cursor2++]; | |
| if (--len2 == 0) | |
| break outer; | |
| count2 = gallopLeft(tmp[cursor1], a, cursor2, len2, 0, c); | |
| if (count2 != 0) { | |
| System.arraycopy(a, cursor2, a, dest, count2); | |
| dest += count2; | |
| cursor2 += count2; | |
| len2 -= count2; | |
| if (len2 == 0) | |
| break outer; | |
| } | |
| a[dest++] = tmp[cursor1++]; | |
| if (--len1 == 1) | |
| break outer; | |
| minGallop--; | |
| } while (count1 >= MIN_GALLOP | count2 >= MIN_GALLOP); | |
| if (minGallop < 0) | |
| minGallop = 0; | |
| minGallop += 2; // Penalize for leaving gallop mode | |
| } // End of "outer" loop | |
| this.minGallop = minGallop < 1 ? 1 : minGallop; // Write back to field | |
| if (len1 == 1) { | |
| assert len2 > 0; | |
| System.arraycopy(a, cursor2, a, dest, len2); | |
| a[dest + len2] = tmp[cursor1]; // Last elt of run 1 to end of merge | |
| } else if (len1 == 0) { | |
| throw new IllegalArgumentException( | |
|                 "Comparison method violates its general contract!"); | |
|         } else { | |
| assert len2 == 0; | |
| assert len1 > 1; | |
| System.arraycopy(tmp, cursor1, a, dest, len1); | |
| } | |
| } | |
|     /** | |
|      * Like mergeLo, except that this method should be called only if | |
|      * len1 >= len2; mergeLo should be called if len1 <= len2.  (Either method | |
|      * may be called if len1 == len2.) | |
|      * | |
|      * @param base1 index of first element in first run to be merged | |
|      * @param len1  length of first run to be merged (must be > 0) | |
|      * @param base2 index of first element in second run to be merged | |
|      *        (must be aBase + aLen) | |
|      * @param len2  length of second run to be merged (must be > 0) | |
| */ | |
|     private void mergeHi(int base1, int len1, int base2, int len2) { | |
| assert len1 > 0 && len2 > 0 && base1 + len1 == base2; | |
| // Copy second run into temp array | |
|         T[] a = this.a; // For performance | |
| T[] tmp = ensureCapacity(len2); | |
| int tmpBase = this.tmpBase; | |
| System.arraycopy(a, base2, tmp, tmpBase, len2); | |
| int cursor1 = base1 + len1 - 1; // Indexes into a | |
| int cursor2 = tmpBase + len2 - 1; // Indexes into tmp array | |
| int dest = base2 + len2 - 1; // Indexes into a | |
|         // Move last element of first run and deal with degenerate cases | |
| a[dest--] = a[cursor1--]; | |
| if (--len1 == 0) { | |
| System.arraycopy(tmp, tmpBase, a, dest - (len2 - 1), len2); | |
| return; | |
| } | |
| if (len2 == 1) { | |
| dest -= len1; | |
| cursor1 -= len1; | |
| System.arraycopy(a, cursor1 + 1, a, dest + 1, len1); | |
| a[dest] = tmp[cursor2]; | |
| return; | |
| } | |
| Comparator<? super T> c = this.c; // Use local variable for performance | |
|         int minGallop = this.minGallop;    //  "    "       "     "      " | |
| outer: | |
|         while (true) { | |
|             int count1 = 0; // Number of times in a row that first run won | |
|             int count2 = 0; // Number of times in a row that second run won | |
|             /* | |
|              * Do the straightforward thing until (if ever) one run | |
|              * appears to win consistently. | |
| */ | |
|             do { | |
| assert len1 > 0 && len2 > 1; | |
| if (c.compare(tmp[cursor2], a[cursor1]) < 0) { | |
| a[dest--] = a[cursor1--]; | |
| count1++; | |
| count2 = 0; | |
| if (--len1 == 0) | |
| break outer; | |
|                 } else { | |
| a[dest--] = tmp[cursor2--]; | |
| count2++; | |
| count1 = 0; | |
| if (--len2 == 1) | |
| break outer; | |
| } | |
| } while ((count1 | count2) < minGallop); | |
|             /* | |
|              * One run is winning so consistently that galloping may be a | |
|              * huge win. So try that, and continue galloping until (if ever) | |
|              * neither run appears to be winning consistently anymore. | |
| */ | |
|             do { | |
| assert len1 > 0 && len2 > 1; | |
| count1 = len1 - gallopRight(tmp[cursor2], a, base1, len1, len1 - 1, c); | |
| if (count1 != 0) { | |
| dest -= count1; | |
| cursor1 -= count1; | |
| len1 -= count1; | |
| System.arraycopy(a, cursor1 + 1, a, dest + 1, count1); | |
| if (len1 == 0) | |
| break outer; | |
| } | |
| a[dest--] = tmp[cursor2--]; | |
| if (--len2 == 1) | |
| break outer; | |
| count2 = len2 - gallopLeft(a[cursor1], tmp, tmpBase, len2, len2 - 1, c); | |
| if (count2 != 0) { | |
| dest -= count2; | |
| cursor2 -= count2; | |
| len2 -= count2; | |
| System.arraycopy(tmp, cursor2 + 1, a, dest + 1, count2); | |
| if (len2 <= 1) // len2 == 1 || len2 == 0 | |
| break outer; | |
| } | |
| a[dest--] = a[cursor1--]; | |
| if (--len1 == 0) | |
| break outer; | |
| minGallop--; | |
| } while (count1 >= MIN_GALLOP | count2 >= MIN_GALLOP); | |
| if (minGallop < 0) | |
| minGallop = 0; | |
| minGallop += 2; // Penalize for leaving gallop mode | |
| } // End of "outer" loop | |
| this.minGallop = minGallop < 1 ? 1 : minGallop; // Write back to field | |
| if (len2 == 1) { | |
| assert len1 > 0; | |
| dest -= len1; | |
| cursor1 -= len1; | |
| System.arraycopy(a, cursor1 + 1, a, dest + 1, len1); | |
| a[dest] = tmp[cursor2]; // Move first elt of run2 to front of merge | |
| } else if (len2 == 0) { | |
| throw new IllegalArgumentException( | |
|                 "Comparison method violates its general contract!"); | |
|         } else { | |
| assert len1 == 0; | |
| assert len2 > 0; | |
| System.arraycopy(tmp, tmpBase, a, dest - (len2 - 1), len2); | |
| } | |
| } | |
|     /** | |
|      * Ensures that the external array tmp has at least the specified | |
|      * number of elements, increasing its size if necessary.  The size | |
|      * increases exponentially to ensure amortized linear time complexity. | |
|      * | |
|      * @param minCapacity the minimum required capacity of the tmp array | |
|      * @return tmp, whether or not it grew | |
| */ | |
|     private T[] ensureCapacity(int minCapacity) { | |
| if (tmpLen < minCapacity) { | |
|             // Compute smallest power of 2 > minCapacity | |
| int newSize = -1 >>> Integer.numberOfLeadingZeros(minCapacity); | |
| newSize++; | |
| if (newSize < 0) // Not bloody likely! | |
| newSize = minCapacity; | |
| else | |
| newSize = Math.min(newSize, a.length >>> 1); | |
|             @SuppressWarnings({"unchecked", "UnnecessaryLocalVariable"}) | |
| T[] newArray = (T[])java.lang.reflect.Array.newInstance | |
| (a.getClass().getComponentType(), newSize); | |
| tmp = newArray; | |
| tmpLen = newSize; | |
| tmpBase = 0; | |
| } | |
| return tmp; | |
| } | |
| } |