欢迎点击「算法与编程之美」↑关注我们!
本文首发于微信公众号:"算法与编程之美",欢迎关注,及时了解更多此系列文章。
作者|杨旭
来源|https://blog.csdn.net/Alex_NINE
改进后的快速排序
在分析上述代码时,可以发现程序会在特殊的情况调用sort()方法即改进后得快速排序,接下来就来分析sort()快速排序的代码实现。
/**
* Sorts the specified range of the array by Dual-Pivot Quicksort.
* 通过双轴快速排序对指定范围内的数据进行排序
* @param a the array to be sorted 被排序的数组
* @param left the index of the first element, inclusive, to be sorted 需要排序的第一个元素的位置(包括在内)
* @param right the index of the last element, inclusive, to be sorted 需要排序的最后一个元素的位置(包括在内)
* @param leftmost indicates if this part is the leftmost in the range leftmost表示该部分是否是范围内最左的部分
*/
private static void sort(int[] a, int left, int right, boolean leftmost) {
int length = right - left + 1;
// Use insertion sort on tiny arrays
//当数组的长度很小时就是用插入排序,INSERTION_SORT_THRESHOLD=47
if (length < INSERTION_SORT_THRESHOLD) {
if (leftmost) {
/*
* Traditional (without sentinel) insertion sort, 传统的插入排序,不使用哨兵元素
* optimized for server VM, is used in case of 针对最左边的部分的情况进行了服务器虚拟机的优化
* 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. 跳过最长的升序情况,提高算法效率
*/
do {
if (left >= right) {
return;
}
} while (a[++left] >= a[left - 1]);
/*
* Every element from adjoining part plays the role 在这种排序方法中相邻的每个元素都起到了哨兵的作用
* of sentinel, therefore this allows us to avoid the 这种办法可以避免我们每次迭代时都要进行左范围检查。
* left range check on each iteration. Moreover, we use 而且我们还使用了一个效率更好的算法,我们称之为“双插入排序”,
* the more optimized algorithm, so called pair insertion 在快速排序的上下文中(即满足进入sort()方法的数组)他比传统的
* sort, which is faster (in the context of Quicksort) 插入排序更快
* 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;
}
//从这里开始是对待排序的元素进行分组处理
// Inexpensive approximation of length / 7
// 使用length/7作为近似的加权长度
int seventh = (length >> 3) + (length >> 6) + 1;
/*
* Sort five evenly spaced elements around (and including) the 在范围内的中心元素附近找到5个均匀间隔的元素
* center element in the range. These elements will be used for 这些元素将用于下面代码中的枢轴选择
* pivot selection as described below. The choice for spacing 根据经验,这些元素的间距能够很好的应对和处理各种各样的输入(待排序的数组)
* 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 使用插入排序对这些元素进行排序
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; }
}
}
}//分组完成
// Pointers 指针
int less = left; // The index of the first element of center part 中心部分第一个元素的位置
int great = right; // The index before the first element of right part 右边第一个元素之前的位置
//五个分位点的值各不相同
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. 使用五个分位点中的第二个和第四个作为枢轴
* These values are inexpensive approximations of the first and 因为有上面的排序 所以在这里pivot1 <= pivot2
* 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 将要排序的第一个和最后一个元素换到枢轴的位置
* locations formerly occupied by the pivots. When partitioning 当分区操作完成后,枢轴元素将和这个元素交换回到原来的位置
* is complete, the pivots are swapped back into their final 并排除到后续排序之外
* positions, and excluded from subsequent sorting.
*/
a[e2] = a[left];
a[e4] = a[right];
/*
* Skip elements, which are less or greater than pivot values.
* 筛选那些比枢轴元素更大或者更小的元素 以此来确定less和great的位置
*/
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.
* 以下的forless-1开始向右遍历至great,把小于pivot1的元素移动到less左边,大于pivot2的元素移动到great右边。
*/
//outer标签
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.
* 在这里分开写的原因是因为前者效率更佳
* 想要了解的可以看这里的讨论:https://www.oschina.net/question/3037675_2206753
*/
a[less] = ak;
++less;
} else if (ak > pivot2) { // Move a[k] to right part
while (a[great] > pivot2) {
if (great-- == k) {
break outer;
}
}
//通过上面已知great
最近更新
- 深拷贝和浅拷贝的区别(重点)
- 【Vue】走进Vue框架世界
- 【云服务器】项目部署—搭建网站—vue电商后台管理系统
- 【React介绍】 一文带你深入React
- 【React】React组件实例的三大属性之state,props,refs(你学废了吗)
- 【脚手架VueCLI】从零开始,创建一个VUE项目
- 【React】深入理解React组件生命周期----图文详解(含代码)
- 【React】DOM的Diffing算法是什么?以及DOM中key的作用----经典面试题
- 【React】1_使用React脚手架创建项目步骤--------详解(含项目结构说明)
- 【React】2_如何使用react脚手架写一个简单的页面?


微信扫码登录