--- old/src/share/classes/java/util/DualPivotQuicksort.java Tue Dec 1 15:04:11 2009
+++ new/src/share/classes/java/util/DualPivotQuicksort.java Tue Dec 1 15:04:10 2009
@@ -36,12 +36,12 @@
* @author Jon Bentley
* @author Josh Bloch
*
- * @version 2009.11.16 m765.827.v12a
+ * @version 2009.11.29 m765.827.12i
*/
final class DualPivotQuicksort {
/**
- * Suppresses default constructor.
+ * Prevents instantiation.
*/
private DualPivotQuicksort() {}
@@ -84,7 +84,7 @@
* Sorts the specified range of the array into ascending order. The range
* to be sorted extends from the index {@code fromIndex}, inclusive, to
* the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},
- * the range to be sorted is empty.
+ * the range to be sorted is empty (and the call is a no-op).
*
* @param a the array to be sorted
* @param fromIndex the index of the first element, inclusive, to be sorted
@@ -101,8 +101,8 @@
/**
* Sorts the specified range of the array into ascending order. This
* method differs from the public {@code sort} method in that the
- * {@code right} index is inclusive, and it does no range checking on
- * {@code left} or {@code right}.
+ * {@code right} index is inclusive, and it does no range checking
+ * on {@code left} or {@code right}.
*
* @param a the array to be sorted
* @param left the index of the first element, inclusive, to be sorted
@@ -111,13 +111,13 @@
private static void doSort(int[] a, int left, int right) {
// Use insertion sort on tiny arrays
if (right - left + 1 < INSERTION_SORT_THRESHOLD) {
- for (int k = left + 1; k <= right; k++) {
- int ak = a[k];
+ for (int i = left + 1; i <= right; i++) {
+ int ai = a[i];
int j;
- for (j = k - 1; j >= left && ak < a[j]; j--) {
+ for (j = i - 1; j >= left && ai < a[j]; j--) {
a[j + 1] = a[j];
}
- a[j + 1] = ak;
+ a[j + 1] = ai;
}
} else { // Use Dual-Pivot Quicksort on large arrays
dualPivotQuicksort(a, left, right);
@@ -162,7 +162,7 @@
* second terciles of the array. Note that pivot1 <= pivot2.
*
* The pivots are stored in local variables, and the first and
- * the last of the sorted elements are moved to the locations
+ * the last of the 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.
@@ -170,27 +170,26 @@
int pivot1 = ae2; a[e2] = a[left];
int pivot2 = ae4; a[e4] = a[right];
- /*
- * Partitioning
- *
- * left part center part right part
- * ------------------------------------------------------------
- * [ < pivot1 | pivot1 <= && <= pivot2 | ? | > pivot2 ]
- * ------------------------------------------------------------
- * ^ ^ ^
- * | | |
- * less k great
- */
-
// Pointers
int less = left + 1; // The index of first element of center part
int great = right - 1; // The index before first element of right part
- boolean pivotsDiffer = pivot1 != pivot2;
+ boolean pivotsDiffer = (pivot1 != pivot2);
if (pivotsDiffer) {
/*
+ * 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
@@ -200,37 +199,37 @@
outer:
for (int k = less; k <= great; k++) {
int ak = a[k];
- if (ak < pivot1) {
- if (k > less) {
+ if (ak < pivot1) { // Move a[k] to left part
+ if (k != less) {
a[k] = a[less];
a[less] = ak;
}
less++;
- } else if (ak > pivot2) {
+ } else if (ak > pivot2) { // Move a[k] to right part
while (a[great] > pivot2) {
- if (k == great--) {
+ if (great-- == k) {
break outer;
}
}
- a[k] = a[great];
- a[great--] = ak;
-
- if ((ak = a[k]) < pivot1) {
+ if (a[great] < pivot1) {
a[k] = a[less];
- a[less++] = ak;
+ a[less++] = a[great];
+ a[great--] = ak;
+ } else { // pivot1 <= a[great] <= pivot2
+ a[k] = a[great];
+ a[great--] = ak;
}
}
}
} else { // Pivots are equal
/*
- * Partition degenerates to the traditional 3-way
- * (or "Dutch National Flag") partition:
+ * Partition degenerates to the traditional 3-way,
+ * or "Dutch National Flag", partition:
*
* left part center part right part
- * -------------------------------------------------
- * [ < pivot | == pivot | ? | > pivot ]
- * -------------------------------------------------
- *
+ * +----------------------------------------------+
+ * | < pivot | == pivot | ? | > pivot |
+ * +----------------------------------------------+
* ^ ^ ^
* | | |
* less k great
@@ -243,30 +242,34 @@
*
* Pointer k is the first index of ?-part
*/
- outer:
for (int k = less; k <= great; k++) {
int ak = a[k];
if (ak == pivot1) {
continue;
}
- if (ak < pivot1) {
- if (k > less) {
+ if (ak < pivot1) { // Move a[k] to left part
+ if (k != less) {
a[k] = a[less];
a[less] = ak;
}
less++;
- } else { // a[k] > pivot
+ } else { // (a[k] > pivot1) - Move a[k] to right part
+ /*
+ * We know that pivot1 == a[e3] == pivot2. Thus, we know
+ * that great will still be >= k when the following loop
+ * terminates, even though we don't test for it explicitly.
+ * In other words, a[e3] acts as a sentinel for great.
+ */
while (a[great] > pivot1) {
- if (k == great--) {
- break outer;
- }
+ great--;
}
- a[k] = a[great];
- a[great--] = ak;
-
- if ((ak = a[k]) < pivot1) {
+ if (a[great] < pivot1) {
a[k] = a[less];
- a[less++] = ak;
+ a[less++] = a[great];
+ a[great--] = ak;
+ } else { // a[great] == pivot1
+ a[k] = pivot1;
+ a[great--] = ak;
}
}
}
@@ -289,10 +292,10 @@
}
/*
- * If center part is too large (comprises > 5/6 of
- * the array), swap internal pivot values to ends
+ * If center part is too large (comprises > 2/3 of the array),
+ * swap internal pivot values to ends
*/
- if (less < e1 && e5 < great) {
+ if (less < e1 && great > e5) {
while (a[less] == pivot1) {
less++;
}
@@ -299,16 +302,45 @@
while (a[great] == pivot2) {
great--;
}
- for (int k = less + 1; k <= 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; k <= great; k++) {
int ak = a[k];
- if (ak == pivot1) {
- a[k++] = a[less];
- a[less++] = pivot1;
- } else if (ak == pivot2) {
- a[k] = a[great];
+ if (ak == pivot2) { // Move a[k] to right part
+ while (a[great] == pivot2) {
+ if (great-- == k) {
+ break outer;
+ }
+ }
+ if (a[great] == pivot1) {
+ a[k] = a[less];
+ a[less++] = pivot1;
+ } else { // pivot1 < a[great] < pivot2
+ a[k] = a[great];
+ }
a[great--] = pivot2;
- } else {
- k++;
+ } else if (ak == pivot1) { // Move a[k] to left part
+ a[k] = a[less];
+ a[less++] = pivot1;
}
}
}
@@ -330,7 +362,7 @@
* Sorts the specified range of the array into ascending order. The range
* to be sorted extends from the index {@code fromIndex}, inclusive, to
* the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},
- * the range to be sorted is empty.
+ * the range to be sorted is empty (and the call is a no-op).
*
* @param a the array to be sorted
* @param fromIndex the index of the first element, inclusive, to be sorted
@@ -357,13 +389,13 @@
private static void doSort(long[] a, int left, int right) {
// Use insertion sort on tiny arrays
if (right - left + 1 < INSERTION_SORT_THRESHOLD) {
- for (int k = left + 1; k <= right; k++) {
- long ak = a[k];
+ for (int i = left + 1; i <= right; i++) {
+ long ai = a[i];
int j;
- for (j = k - 1; j >= left && ak < a[j]; j--) {
+ for (j = i - 1; j >= left && ai < a[j]; j--) {
a[j + 1] = a[j];
}
- a[j + 1] = ak;
+ a[j + 1] = ai;
}
} else { // Use Dual-Pivot Quicksort on large arrays
dualPivotQuicksort(a, left, right);
@@ -408,7 +440,7 @@
* second terciles of the array. Note that pivot1 <= pivot2.
*
* The pivots are stored in local variables, and the first and
- * the last of the sorted elements are moved to the locations
+ * the last of the 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.
@@ -416,27 +448,26 @@
long pivot1 = ae2; a[e2] = a[left];
long pivot2 = ae4; a[e4] = a[right];
- /*
- * Partitioning
- *
- * left part center part right part
- * ------------------------------------------------------------
- * [ < pivot1 | pivot1 <= && <= pivot2 | ? | > pivot2 ]
- * ------------------------------------------------------------
- * ^ ^ ^
- * | | |
- * less k great
- */
-
// Pointers
int less = left + 1; // The index of first element of center part
int great = right - 1; // The index before first element of right part
- boolean pivotsDiffer = pivot1 != pivot2;
+ boolean pivotsDiffer = (pivot1 != pivot2);
if (pivotsDiffer) {
/*
+ * 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
@@ -446,37 +477,37 @@
outer:
for (int k = less; k <= great; k++) {
long ak = a[k];
- if (ak < pivot1) {
- if (k > less) {
+ if (ak < pivot1) { // Move a[k] to left part
+ if (k != less) {
a[k] = a[less];
a[less] = ak;
}
less++;
- } else if (ak > pivot2) {
+ } else if (ak > pivot2) { // Move a[k] to right part
while (a[great] > pivot2) {
- if (k == great--) {
+ if (great-- == k) {
break outer;
}
}
- a[k] = a[great];
- a[great--] = ak;
-
- if ((ak = a[k]) < pivot1) {
+ if (a[great] < pivot1) {
a[k] = a[less];
- a[less++] = ak;
+ a[less++] = a[great];
+ a[great--] = ak;
+ } else { // pivot1 <= a[great] <= pivot2
+ a[k] = a[great];
+ a[great--] = ak;
}
}
}
} else { // Pivots are equal
/*
- * Partition degenerates to the traditional 3-way
- * (or "Dutch National Flag") partition:
+ * Partition degenerates to the traditional 3-way,
+ * or "Dutch National Flag", partition:
*
* left part center part right part
- * -------------------------------------------------
- * [ < pivot | == pivot | ? | > pivot ]
- * -------------------------------------------------
- *
+ * +----------------------------------------------+
+ * | < pivot | == pivot | ? | > pivot |
+ * +----------------------------------------------+
* ^ ^ ^
* | | |
* less k great
@@ -489,30 +520,34 @@
*
* Pointer k is the first index of ?-part
*/
- outer:
for (int k = less; k <= great; k++) {
long ak = a[k];
if (ak == pivot1) {
continue;
}
- if (ak < pivot1) {
- if (k > less) {
+ if (ak < pivot1) { // Move a[k] to left part
+ if (k != less) {
a[k] = a[less];
a[less] = ak;
}
less++;
- } else { // a[k] > pivot
+ } else { // (a[k] > pivot1) - Move a[k] to right part
+ /*
+ * We know that pivot1 == a[e3] == pivot2. Thus, we know
+ * that great will still be >= k when the following loop
+ * terminates, even though we don't test for it explicitly.
+ * In other words, a[e3] acts as a sentinel for great.
+ */
while (a[great] > pivot1) {
- if (k == great--) {
- break outer;
- }
+ great--;
}
- a[k] = a[great];
- a[great--] = ak;
-
- if ((ak = a[k]) < pivot1) {
+ if (a[great] < pivot1) {
a[k] = a[less];
- a[less++] = ak;
+ a[less++] = a[great];
+ a[great--] = ak;
+ } else { // a[great] == pivot1
+ a[k] = pivot1;
+ a[great--] = ak;
}
}
}
@@ -535,10 +570,10 @@
}
/*
- * If center part is too large (comprises > 5/6 of
- * the array), swap internal pivot values to ends
+ * If center part is too large (comprises > 2/3 of the array),
+ * swap internal pivot values to ends
*/
- if (less < e1 && e5 < great) {
+ if (less < e1 && great > e5) {
while (a[less] == pivot1) {
less++;
}
@@ -545,16 +580,45 @@
while (a[great] == pivot2) {
great--;
}
- for (int k = less + 1; k <= 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; k <= great; k++) {
long ak = a[k];
- if (ak == pivot1) {
- a[k++] = a[less];
- a[less++] = pivot1;
- } else if (ak == pivot2) {
- a[k] = a[great];
+ if (ak == pivot2) { // Move a[k] to right part
+ while (a[great] == pivot2) {
+ if (great-- == k) {
+ break outer;
+ }
+ }
+ if (a[great] == pivot1) {
+ a[k] = a[less];
+ a[less++] = pivot1;
+ } else { // pivot1 < a[great] < pivot2
+ a[k] = a[great];
+ }
a[great--] = pivot2;
- } else {
- k++;
+ } else if (ak == pivot1) { // Move a[k] to left part
+ a[k] = a[less];
+ a[less++] = pivot1;
}
}
}
@@ -576,7 +640,7 @@
* Sorts the specified range of the array into ascending order. The range
* to be sorted extends from the index {@code fromIndex}, inclusive, to
* the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},
- * the range to be sorted is empty.
+ * the range to be sorted is empty (and the call is a no-op).
*
* @param a the array to be sorted
* @param fromIndex the index of the first element, inclusive, to be sorted
@@ -606,13 +670,13 @@
private static void doSort(short[] a, int left, int right) {
// Use insertion sort on tiny arrays
if (right - left + 1 < INSERTION_SORT_THRESHOLD) {
- for (int k = left + 1; k <= right; k++) {
- short ak = a[k];
+ for (int i = left + 1; i <= right; i++) {
+ short ai = a[i];
int j;
- for (j = k - 1; j >= left && ak < a[j]; j--) {
+ for (j = i - 1; j >= left && ai < a[j]; j--) {
a[j + 1] = a[j];
}
- a[j + 1] = ak;
+ a[j + 1] = ai;
}
} else if (right-left+1 > COUNTING_SORT_THRESHOLD_FOR_SHORT_OR_CHAR) {
// Use counting sort on huge arrays
@@ -671,7 +735,7 @@
* second terciles of the array. Note that pivot1 <= pivot2.
*
* The pivots are stored in local variables, and the first and
- * the last of the sorted elements are moved to the locations
+ * the last of the 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.
@@ -679,27 +743,26 @@
short pivot1 = ae2; a[e2] = a[left];
short pivot2 = ae4; a[e4] = a[right];
- /*
- * Partitioning
- *
- * left part center part right part
- * ------------------------------------------------------------
- * [ < pivot1 | pivot1 <= && <= pivot2 | ? | > pivot2 ]
- * ------------------------------------------------------------
- * ^ ^ ^
- * | | |
- * less k great
- */
-
// Pointers
int less = left + 1; // The index of first element of center part
int great = right - 1; // The index before first element of right part
- boolean pivotsDiffer = pivot1 != pivot2;
+ boolean pivotsDiffer = (pivot1 != pivot2);
if (pivotsDiffer) {
/*
+ * 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
@@ -709,37 +772,37 @@
outer:
for (int k = less; k <= great; k++) {
short ak = a[k];
- if (ak < pivot1) {
- if (k > less) {
+ if (ak < pivot1) { // Move a[k] to left part
+ if (k != less) {
a[k] = a[less];
a[less] = ak;
}
less++;
- } else if (ak > pivot2) {
+ } else if (ak > pivot2) { // Move a[k] to right part
while (a[great] > pivot2) {
- if (k == great--) {
+ if (great-- == k) {
break outer;
}
}
- a[k] = a[great];
- a[great--] = ak;
-
- if ((ak = a[k]) < pivot1) {
+ if (a[great] < pivot1) {
a[k] = a[less];
- a[less++] = ak;
+ a[less++] = a[great];
+ a[great--] = ak;
+ } else { // pivot1 <= a[great] <= pivot2
+ a[k] = a[great];
+ a[great--] = ak;
}
}
}
} else { // Pivots are equal
/*
- * Partition degenerates to the traditional 3-way
- * (or "Dutch National Flag") partition:
+ * Partition degenerates to the traditional 3-way,
+ * or "Dutch National Flag", partition:
*
* left part center part right part
- * -------------------------------------------------
- * [ < pivot | == pivot | ? | > pivot ]
- * -------------------------------------------------
- *
+ * +----------------------------------------------+
+ * | < pivot | == pivot | ? | > pivot |
+ * +----------------------------------------------+
* ^ ^ ^
* | | |
* less k great
@@ -752,30 +815,34 @@
*
* Pointer k is the first index of ?-part
*/
- outer:
for (int k = less; k <= great; k++) {
short ak = a[k];
if (ak == pivot1) {
continue;
}
- if (ak < pivot1) {
- if (k > less) {
+ if (ak < pivot1) { // Move a[k] to left part
+ if (k != less) {
a[k] = a[less];
a[less] = ak;
}
less++;
- } else { // a[k] > pivot
+ } else { // (a[k] > pivot1) - Move a[k] to right part
+ /*
+ * We know that pivot1 == a[e3] == pivot2. Thus, we know
+ * that great will still be >= k when the following loop
+ * terminates, even though we don't test for it explicitly.
+ * In other words, a[e3] acts as a sentinel for great.
+ */
while (a[great] > pivot1) {
- if (k == great--) {
- break outer;
- }
+ great--;
}
- a[k] = a[great];
- a[great--] = ak;
-
- if ((ak = a[k]) < pivot1) {
+ if (a[great] < pivot1) {
a[k] = a[less];
- a[less++] = ak;
+ a[less++] = a[great];
+ a[great--] = ak;
+ } else { // a[great] == pivot1
+ a[k] = pivot1;
+ a[great--] = ak;
}
}
}
@@ -798,10 +865,10 @@
}
/*
- * If center part is too large (comprises > 5/6 of
- * the array), swap internal pivot values to ends
+ * If center part is too large (comprises > 2/3 of the array),
+ * swap internal pivot values to ends
*/
- if (less < e1 && e5 < great) {
+ if (less < e1 && great > e5) {
while (a[less] == pivot1) {
less++;
}
@@ -808,16 +875,45 @@
while (a[great] == pivot2) {
great--;
}
- for (int k = less + 1; k <= 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; k <= great; k++) {
short ak = a[k];
- if (ak == pivot1) {
- a[k++] = a[less];
- a[less++] = pivot1;
- } else if (ak == pivot2) {
- a[k] = a[great];
+ if (ak == pivot2) { // Move a[k] to right part
+ while (a[great] == pivot2) {
+ if (great-- == k) {
+ break outer;
+ }
+ }
+ if (a[great] == pivot1) {
+ a[k] = a[less];
+ a[less++] = pivot1;
+ } else { // pivot1 < a[great] < pivot2
+ a[k] = a[great];
+ }
a[great--] = pivot2;
- } else {
- k++;
+ } else if (ak == pivot1) { // Move a[k] to left part
+ a[k] = a[less];
+ a[less++] = pivot1;
}
}
}
@@ -839,7 +935,7 @@
* Sorts the specified range of the array into ascending order. The range
* to be sorted extends from the index {@code fromIndex}, inclusive, to
* the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},
- * the range to be sorted is empty.
+ * the range to be sorted is empty (and the call is a no-op).
*
* @param a the array to be sorted
* @param fromIndex the index of the first element, inclusive, to be sorted
@@ -869,13 +965,13 @@
private static void doSort(char[] a, int left, int right) {
// Use insertion sort on tiny arrays
if (right - left + 1 < INSERTION_SORT_THRESHOLD) {
- for (int k = left + 1; k <= right; k++) {
- char ak = a[k];
+ for (int i = left + 1; i <= right; i++) {
+ char ai = a[i];
int j;
- for (j = k - 1; j >= left && ak < a[j]; j--) {
+ for (j = i - 1; j >= left && ai < a[j]; j--) {
a[j + 1] = a[j];
}
- a[j + 1] = ak;
+ a[j + 1] = ai;
}
} else if (right-left+1 > COUNTING_SORT_THRESHOLD_FOR_SHORT_OR_CHAR) {
// Use counting sort on huge arrays
@@ -932,7 +1028,7 @@
* second terciles of the array. Note that pivot1 <= pivot2.
*
* The pivots are stored in local variables, and the first and
- * the last of the sorted elements are moved to the locations
+ * the last of the 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.
@@ -940,27 +1036,26 @@
char pivot1 = ae2; a[e2] = a[left];
char pivot2 = ae4; a[e4] = a[right];
- /*
- * Partitioning
- *
- * left part center part right part
- * ------------------------------------------------------------
- * [ < pivot1 | pivot1 <= && <= pivot2 | ? | > pivot2 ]
- * ------------------------------------------------------------
- * ^ ^ ^
- * | | |
- * less k great
- */
-
// Pointers
int less = left + 1; // The index of first element of center part
int great = right - 1; // The index before first element of right part
- boolean pivotsDiffer = pivot1 != pivot2;
+ boolean pivotsDiffer = (pivot1 != pivot2);
if (pivotsDiffer) {
/*
+ * 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
@@ -970,37 +1065,37 @@
outer:
for (int k = less; k <= great; k++) {
char ak = a[k];
- if (ak < pivot1) {
- if (k > less) {
+ if (ak < pivot1) { // Move a[k] to left part
+ if (k != less) {
a[k] = a[less];
a[less] = ak;
}
less++;
- } else if (ak > pivot2) {
+ } else if (ak > pivot2) { // Move a[k] to right part
while (a[great] > pivot2) {
- if (k == great--) {
+ if (great-- == k) {
break outer;
}
}
- a[k] = a[great];
- a[great--] = ak;
-
- if ((ak = a[k]) < pivot1) {
+ if (a[great] < pivot1) {
a[k] = a[less];
- a[less++] = ak;
+ a[less++] = a[great];
+ a[great--] = ak;
+ } else { // pivot1 <= a[great] <= pivot2
+ a[k] = a[great];
+ a[great--] = ak;
}
}
}
} else { // Pivots are equal
/*
- * Partition degenerates to the traditional 3-way
- * (or "Dutch National Flag") partition:
+ * Partition degenerates to the traditional 3-way,
+ * or "Dutch National Flag", partition:
*
* left part center part right part
- * -------------------------------------------------
- * [ < pivot | == pivot | ? | > pivot ]
- * -------------------------------------------------
- *
+ * +----------------------------------------------+
+ * | < pivot | == pivot | ? | > pivot |
+ * +----------------------------------------------+
* ^ ^ ^
* | | |
* less k great
@@ -1013,30 +1108,34 @@
*
* Pointer k is the first index of ?-part
*/
- outer:
for (int k = less; k <= great; k++) {
char ak = a[k];
if (ak == pivot1) {
continue;
}
- if (ak < pivot1) {
- if (k > less) {
+ if (ak < pivot1) { // Move a[k] to left part
+ if (k != less) {
a[k] = a[less];
a[less] = ak;
}
less++;
- } else { // a[k] > pivot
+ } else { // (a[k] > pivot1) - Move a[k] to right part
+ /*
+ * We know that pivot1 == a[e3] == pivot2. Thus, we know
+ * that great will still be >= k when the following loop
+ * terminates, even though we don't test for it explicitly.
+ * In other words, a[e3] acts as a sentinel for great.
+ */
while (a[great] > pivot1) {
- if (k == great--) {
- break outer;
- }
+ great--;
}
- a[k] = a[great];
- a[great--] = ak;
-
- if ((ak = a[k]) < pivot1) {
+ if (a[great] < pivot1) {
a[k] = a[less];
- a[less++] = ak;
+ a[less++] = a[great];
+ a[great--] = ak;
+ } else { // a[great] == pivot1
+ a[k] = pivot1;
+ a[great--] = ak;
}
}
}
@@ -1059,10 +1158,10 @@
}
/*
- * If center part is too large (comprises > 5/6 of
- * the array), swap internal pivot values to ends
+ * If center part is too large (comprises > 2/3 of the array),
+ * swap internal pivot values to ends
*/
- if (less < e1 && e5 < great) {
+ if (less < e1 && great > e5) {
while (a[less] == pivot1) {
less++;
}
@@ -1069,16 +1168,45 @@
while (a[great] == pivot2) {
great--;
}
- for (int k = less + 1; k <= 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; k <= great; k++) {
char ak = a[k];
- if (ak == pivot1) {
- a[k++] = a[less];
- a[less++] = pivot1;
- } else if (ak == pivot2) {
- a[k] = a[great];
+ if (ak == pivot2) { // Move a[k] to right part
+ while (a[great] == pivot2) {
+ if (great-- == k) {
+ break outer;
+ }
+ }
+ if (a[great] == pivot1) {
+ a[k] = a[less];
+ a[less++] = pivot1;
+ } else { // pivot1 < a[great] < pivot2
+ a[k] = a[great];
+ }
a[great--] = pivot2;
- } else {
- k++;
+ } else if (ak == pivot1) { // Move a[k] to left part
+ a[k] = a[less];
+ a[less++] = pivot1;
}
}
}
@@ -1100,7 +1228,7 @@
* Sorts the specified range of the array into ascending order. The range
* to be sorted extends from the index {@code fromIndex}, inclusive, to
* the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},
- * the range to be sorted is empty.
+ * the range to be sorted is empty (and the call is a no-op).
*
* @param a the array to be sorted
* @param fromIndex the index of the first element, inclusive, to be sorted
@@ -1130,13 +1258,13 @@
private static void doSort(byte[] a, int left, int right) {
// Use insertion sort on tiny arrays
if (right - left + 1 < INSERTION_SORT_THRESHOLD) {
- for (int k = left + 1; k <= right; k++) {
- byte ak = a[k];
+ for (int i = left + 1; i <= right; i++) {
+ byte ai = a[i];
int j;
- for (j = k - 1; j >= left && ak < a[j]; j--) {
+ for (j = i - 1; j >= left && ai < a[j]; j--) {
a[j + 1] = a[j];
}
- a[j + 1] = ak;
+ a[j + 1] = ai;
}
} else if (right - left + 1 > COUNTING_SORT_THRESHOLD_FOR_BYTE) {
// Use counting sort on huge arrays
@@ -1195,7 +1323,7 @@
* second terciles of the array. Note that pivot1 <= pivot2.
*
* The pivots are stored in local variables, and the first and
- * the last of the sorted elements are moved to the locations
+ * the last of the 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.
@@ -1203,27 +1331,26 @@
byte pivot1 = ae2; a[e2] = a[left];
byte pivot2 = ae4; a[e4] = a[right];
- /*
- * Partitioning
- *
- * left part center part right part
- * ------------------------------------------------------------
- * [ < pivot1 | pivot1 <= && <= pivot2 | ? | > pivot2 ]
- * ------------------------------------------------------------
- * ^ ^ ^
- * | | |
- * less k great
- */
-
// Pointers
int less = left + 1; // The index of first element of center part
int great = right - 1; // The index before first element of right part
- boolean pivotsDiffer = pivot1 != pivot2;
+ boolean pivotsDiffer = (pivot1 != pivot2);
if (pivotsDiffer) {
/*
+ * 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
@@ -1233,37 +1360,37 @@
outer:
for (int k = less; k <= great; k++) {
byte ak = a[k];
- if (ak < pivot1) {
- if (k > less) {
+ if (ak < pivot1) { // Move a[k] to left part
+ if (k != less) {
a[k] = a[less];
a[less] = ak;
}
less++;
- } else if (ak > pivot2) {
+ } else if (ak > pivot2) { // Move a[k] to right part
while (a[great] > pivot2) {
- if (k == great--) {
+ if (great-- == k) {
break outer;
}
}
- a[k] = a[great];
- a[great--] = ak;
-
- if ((ak = a[k]) < pivot1) {
+ if (a[great] < pivot1) {
a[k] = a[less];
- a[less++] = ak;
+ a[less++] = a[great];
+ a[great--] = ak;
+ } else { // pivot1 <= a[great] <= pivot2
+ a[k] = a[great];
+ a[great--] = ak;
}
}
}
} else { // Pivots are equal
/*
- * Partition degenerates to the traditional 3-way
- * (or "Dutch National Flag") partition:
+ * Partition degenerates to the traditional 3-way,
+ * or "Dutch National Flag", partition:
*
* left part center part right part
- * -------------------------------------------------
- * [ < pivot | == pivot | ? | > pivot ]
- * -------------------------------------------------
- *
+ * +----------------------------------------------+
+ * | < pivot | == pivot | ? | > pivot |
+ * +----------------------------------------------+
* ^ ^ ^
* | | |
* less k great
@@ -1276,30 +1403,34 @@
*
* Pointer k is the first index of ?-part
*/
- outer:
for (int k = less; k <= great; k++) {
byte ak = a[k];
if (ak == pivot1) {
continue;
}
- if (ak < pivot1) {
- if (k > less) {
+ if (ak < pivot1) { // Move a[k] to left part
+ if (k != less) {
a[k] = a[less];
a[less] = ak;
}
less++;
- } else { // a[k] > pivot
+ } else { // (a[k] > pivot1) - Move a[k] to right part
+ /*
+ * We know that pivot1 == a[e3] == pivot2. Thus, we know
+ * that great will still be >= k when the following loop
+ * terminates, even though we don't test for it explicitly.
+ * In other words, a[e3] acts as a sentinel for great.
+ */
while (a[great] > pivot1) {
- if (k == great--) {
- break outer;
- }
+ great--;
}
- a[k] = a[great];
- a[great--] = ak;
-
- if ((ak = a[k]) < pivot1) {
+ if (a[great] < pivot1) {
a[k] = a[less];
- a[less++] = ak;
+ a[less++] = a[great];
+ a[great--] = ak;
+ } else { // a[great] == pivot1
+ a[k] = pivot1;
+ a[great--] = ak;
}
}
}
@@ -1322,10 +1453,10 @@
}
/*
- * If center part is too large (comprises > 5/6 of
- * the array), swap internal pivot values to ends
+ * If center part is too large (comprises > 2/3 of the array),
+ * swap internal pivot values to ends
*/
- if (less < e1 && e5 < great) {
+ if (less < e1 && great > e5) {
while (a[less] == pivot1) {
less++;
}
@@ -1332,16 +1463,45 @@
while (a[great] == pivot2) {
great--;
}
- for (int k = less + 1; k <= 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; k <= great; k++) {
byte ak = a[k];
- if (ak == pivot1) {
- a[k++] = a[less];
- a[less++] = pivot1;
- } else if (ak == pivot2) {
- a[k] = a[great];
+ if (ak == pivot2) { // Move a[k] to right part
+ while (a[great] == pivot2) {
+ if (great-- == k) {
+ break outer;
+ }
+ }
+ if (a[great] == pivot1) {
+ a[k] = a[less];
+ a[less++] = pivot1;
+ } else { // pivot1 < a[great] < pivot2
+ a[k] = a[great];
+ }
a[great--] = pivot2;
- } else {
- k++;
+ } else if (ak == pivot1) { // Move a[k] to left part
+ a[k] = a[less];
+ a[less++] = pivot1;
}
}
}
@@ -1371,7 +1531,7 @@
* Sorts the specified range of the array into ascending order. The range
* to be sorted extends from the index {@code fromIndex}, inclusive, to
* the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},
- * the range to be sorted is empty.
+ * the range to be sorted is empty and the call is a no-op).
*
* The {@code <} relation does not provide a total order on all float
* values: {@code -0.0f == 0.0f} is {@code true} and a {@code Float.NaN}
@@ -1485,13 +1645,13 @@
private static void doSort(float[] a, int left, int right) {
// Use insertion sort on tiny arrays
if (right - left + 1 < INSERTION_SORT_THRESHOLD) {
- for (int k = left + 1; k <= right; k++) {
- float ak = a[k];
+ for (int i = left + 1; i <= right; i++) {
+ float ai = a[i];
int j;
- for (j = k - 1; j >= left && ak < a[j]; j--) {
+ for (j = i - 1; j >= left && ai < a[j]; j--) {
a[j + 1] = a[j];
}
- a[j + 1] = ak;
+ a[j + 1] = ai;
}
} else { // Use Dual-Pivot Quicksort on large arrays
dualPivotQuicksort(a, left, right);
@@ -1536,7 +1696,7 @@
* second terciles of the array. Note that pivot1 <= pivot2.
*
* The pivots are stored in local variables, and the first and
- * the last of the sorted elements are moved to the locations
+ * the last of the 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.
@@ -1544,27 +1704,26 @@
float pivot1 = ae2; a[e2] = a[left];
float pivot2 = ae4; a[e4] = a[right];
- /*
- * Partitioning
- *
- * left part center part right part
- * ------------------------------------------------------------
- * [ < pivot1 | pivot1 <= && <= pivot2 | ? | > pivot2 ]
- * ------------------------------------------------------------
- * ^ ^ ^
- * | | |
- * less k great
- */
-
// Pointers
int less = left + 1; // The index of first element of center part
int great = right - 1; // The index before first element of right part
- boolean pivotsDiffer = pivot1 != pivot2;
+ boolean pivotsDiffer = (pivot1 != pivot2);
if (pivotsDiffer) {
/*
+ * 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
@@ -1574,37 +1733,37 @@
outer:
for (int k = less; k <= great; k++) {
float ak = a[k];
- if (ak < pivot1) {
- if (k > less) {
+ if (ak < pivot1) { // Move a[k] to left part
+ if (k != less) {
a[k] = a[less];
a[less] = ak;
}
less++;
- } else if (ak > pivot2) {
+ } else if (ak > pivot2) { // Move a[k] to right part
while (a[great] > pivot2) {
- if (k == great--) {
+ if (great-- == k) {
break outer;
}
}
- a[k] = a[great];
- a[great--] = ak;
-
- if ((ak = a[k]) < pivot1) {
+ if (a[great] < pivot1) {
a[k] = a[less];
- a[less++] = ak;
+ a[less++] = a[great];
+ a[great--] = ak;
+ } else { // pivot1 <= a[great] <= pivot2
+ a[k] = a[great];
+ a[great--] = ak;
}
}
}
} else { // Pivots are equal
/*
- * Partition degenerates to the traditional 3-way
- * (or "Dutch National Flag") partition:
+ * Partition degenerates to the traditional 3-way,
+ * or "Dutch National Flag", partition:
*
* left part center part right part
- * -------------------------------------------------
- * [ < pivot | == pivot | ? | > pivot ]
- * -------------------------------------------------
- *
+ * +----------------------------------------------+
+ * | < pivot | == pivot | ? | > pivot |
+ * +----------------------------------------------+
* ^ ^ ^
* | | |
* less k great
@@ -1617,30 +1776,34 @@
*
* Pointer k is the first index of ?-part
*/
- outer:
for (int k = less; k <= great; k++) {
float ak = a[k];
if (ak == pivot1) {
continue;
}
- if (ak < pivot1) {
- if (k > less) {
+ if (ak < pivot1) { // Move a[k] to left part
+ if (k != less) {
a[k] = a[less];
a[less] = ak;
}
less++;
- } else { // a[k] > pivot
+ } else { // (a[k] > pivot1) - Move a[k] to right part
+ /*
+ * We know that pivot1 == a[e3] == pivot2. Thus, we know
+ * that great will still be >= k when the following loop
+ * terminates, even though we don't test for it explicitly.
+ * In other words, a[e3] acts as a sentinel for great.
+ */
while (a[great] > pivot1) {
- if (k == great--) {
- break outer;
- }
+ great--;
}
- a[k] = a[great];
- a[great--] = ak;
-
- if ((ak = a[k]) < pivot1) {
+ if (a[great] < pivot1) {
a[k] = a[less];
- a[less++] = ak;
+ a[less++] = a[great];
+ a[great--] = ak;
+ } else { // a[great] == pivot1
+ a[k] = pivot1;
+ a[great--] = ak;
}
}
}
@@ -1663,10 +1826,10 @@
}
/*
- * If center part is too large (comprises > 5/6 of
- * the array), swap internal pivot values to ends
+ * If center part is too large (comprises > 2/3 of the array),
+ * swap internal pivot values to ends
*/
- if (less < e1 && e5 < great) {
+ if (less < e1 && great > e5) {
while (a[less] == pivot1) {
less++;
}
@@ -1673,16 +1836,45 @@
while (a[great] == pivot2) {
great--;
}
- for (int k = less + 1; k <= 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; k <= great; k++) {
float ak = a[k];
- if (ak == pivot1) {
- a[k++] = a[less];
- a[less++] = pivot1;
- } else if (ak == pivot2) {
- a[k] = a[great];
+ if (ak == pivot2) { // Move a[k] to right part
+ while (a[great] == pivot2) {
+ if (great-- == k) {
+ break outer;
+ }
+ }
+ if (a[great] == pivot1) {
+ a[k] = a[less];
+ a[less++] = pivot1;
+ } else { // pivot1 < a[great] < pivot2
+ a[k] = a[great];
+ }
a[great--] = pivot2;
- } else {
- k++;
+ } else if (ak == pivot1) { // Move a[k] to left part
+ a[k] = a[less];
+ a[less++] = pivot1;
}
}
}
@@ -1712,7 +1904,7 @@
* Sorts the specified range of the array into ascending order. The range
* to be sorted extends from the index {@code fromIndex}, inclusive, to
* the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},
- * the range to be sorted is empty.
+ * the range to be sorted is empty (and the call is a no-op).
*
*
The {@code <} relation does not provide a total order on all double
* values: {@code -0.0d == 0.0d} is {@code true} and a {@code Double.NaN}
@@ -1826,13 +2018,13 @@
private static void doSort(double[] a, int left, int right) {
// Use insertion sort on tiny arrays
if (right - left + 1 < INSERTION_SORT_THRESHOLD) {
- for (int k = left + 1; k <= right; k++) {
- double ak = a[k];
+ for (int i = left + 1; i <= right; i++) {
+ double ai = a[i];
int j;
- for (j = k - 1; j >= left && ak < a[j]; j--) {
+ for (j = i - 1; j >= left && ai < a[j]; j--) {
a[j + 1] = a[j];
}
- a[j + 1] = ak;
+ a[j + 1] = ai;
}
} else { // Use Dual-Pivot Quicksort on large arrays
dualPivotQuicksort(a, left, right);
@@ -1877,7 +2069,7 @@
* second terciles of the array. Note that pivot1 <= pivot2.
*
* The pivots are stored in local variables, and the first and
- * the last of the sorted elements are moved to the locations
+ * the last of the 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.
@@ -1885,27 +2077,26 @@
double pivot1 = ae2; a[e2] = a[left];
double pivot2 = ae4; a[e4] = a[right];
- /*
- * Partitioning
- *
- * left part center part right part
- * ------------------------------------------------------------
- * [ < pivot1 | pivot1 <= && <= pivot2 | ? | > pivot2 ]
- * ------------------------------------------------------------
- * ^ ^ ^
- * | | |
- * less k great
- */
-
// Pointers
int less = left + 1; // The index of first element of center part
int great = right - 1; // The index before first element of right part
- boolean pivotsDiffer = pivot1 != pivot2;
+ boolean pivotsDiffer = (pivot1 != pivot2);
if (pivotsDiffer) {
/*
+ * 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
@@ -1915,37 +2106,37 @@
outer:
for (int k = less; k <= great; k++) {
double ak = a[k];
- if (ak < pivot1) {
- if (k > less) {
+ if (ak < pivot1) { // Move a[k] to left part
+ if (k != less) {
a[k] = a[less];
a[less] = ak;
}
less++;
- } else if (ak > pivot2) {
+ } else if (ak > pivot2) { // Move a[k] to right part
while (a[great] > pivot2) {
- if (k == great--) {
+ if (great-- == k) {
break outer;
}
}
- a[k] = a[great];
- a[great--] = ak;
-
- if ((ak = a[k]) < pivot1) {
+ if (a[great] < pivot1) {
a[k] = a[less];
- a[less++] = ak;
+ a[less++] = a[great];
+ a[great--] = ak;
+ } else { // pivot1 <= a[great] <= pivot2
+ a[k] = a[great];
+ a[great--] = ak;
}
}
}
} else { // Pivots are equal
/*
- * Partition degenerates to the traditional 3-way
- * (or "Dutch National Flag") partition:
+ * Partition degenerates to the traditional 3-way,
+ * or "Dutch National Flag", partition:
*
* left part center part right part
- * -------------------------------------------------
- * [ < pivot | == pivot | ? | > pivot ]
- * -------------------------------------------------
- *
+ * +----------------------------------------------+
+ * | < pivot | == pivot | ? | > pivot |
+ * +----------------------------------------------+
* ^ ^ ^
* | | |
* less k great
@@ -1958,30 +2149,34 @@
*
* Pointer k is the first index of ?-part
*/
- outer:
for (int k = less; k <= great; k++) {
double ak = a[k];
if (ak == pivot1) {
continue;
}
- if (ak < pivot1) {
- if (k > less) {
+ if (ak < pivot1) { // Move a[k] to left part
+ if (k != less) {
a[k] = a[less];
a[less] = ak;
}
less++;
- } else { // a[k] > pivot
+ } else { // (a[k] > pivot1) - Move a[k] to right part
+ /*
+ * We know that pivot1 == a[e3] == pivot2. Thus, we know
+ * that great will still be >= k when the following loop
+ * terminates, even though we don't test for it explicitly.
+ * In other words, a[e3] acts as a sentinel for great.
+ */
while (a[great] > pivot1) {
- if (k == great--) {
- break outer;
- }
+ great--;
}
- a[k] = a[great];
- a[great--] = ak;
-
- if ((ak = a[k]) < pivot1) {
+ if (a[great] < pivot1) {
a[k] = a[less];
- a[less++] = ak;
+ a[less++] = a[great];
+ a[great--] = ak;
+ } else { // a[great] == pivot1
+ a[k] = pivot1;
+ a[great--] = ak;
}
}
}
@@ -2004,10 +2199,10 @@
}
/*
- * If center part is too large (comprises > 5/6 of
- * the array), swap internal pivot values to ends
+ * If center part is too large (comprises > 2/3 of the array),
+ * swap internal pivot values to ends
*/
- if (less < e1 && e5 < great) {
+ if (less < e1 && great > e5) {
while (a[less] == pivot1) {
less++;
}
@@ -2014,16 +2209,45 @@
while (a[great] == pivot2) {
great--;
}
- for (int k = less + 1; k <= 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; k <= great; k++) {
double ak = a[k];
- if (ak == pivot1) {
- a[k++] = a[less];
- a[less++] = pivot1;
- } else if (ak == pivot2) {
- a[k] = a[great];
+ if (ak == pivot2) { // Move a[k] to right part
+ while (a[great] == pivot2) {
+ if (great-- == k) {
+ break outer;
+ }
+ }
+ if (a[great] == pivot1) {
+ a[k] = a[less];
+ a[less++] = pivot1;
+ } else { // pivot1 < a[great] < pivot2
+ a[k] = a[great];
+ }
a[great--] = pivot2;
- } else {
- k++;
+ } else if (ak == pivot1) { // Move a[k] to left part
+ a[k] = a[less];
+ a[less++] = pivot1;
}
}
}