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krahets
2023-02-08 16:47:52 +08:00
parent 139e34bdb1
commit 7156a5f832
15 changed files with 367 additions and 208 deletions
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chapter_sorting/quick_sort.md
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@@ -139,7 +139,7 @@ comments: true
=== "JavaScript"
``` js title="quick_sort.js"
```javascript title="quick_sort.js"
/* 元素交换 */
function swap(nums, i, j) {
let tmp = nums[i];
@@ -349,14 +349,14 @@ comments: true
```javascript title="quick_sort.js"
/* 快速排序 */
function quickSort(nums, left, right) {
quickSort(nums, left, right) {
// 子数组长度为 1 时终止递归
if (left >= right) return;
// 哨兵划分
const pivot = partition(nums, left, right);
const pivot = this.partition(nums, left, right);
// 递归左子数组、右子数组
quickSort(nums, left, pivot - 1);
quickSort(nums, pivot + 1, right);
this.quickSort(nums, left, pivot - 1);
this.quickSort(nums, pivot + 1, right);
}
```
@@ -364,16 +364,16 @@ comments: true
```typescript title="quick_sort.ts"
/* 快速排序 */
function quickSort(nums: number[], left: number, right: number): void {
quickSort(nums: number[], left: number, right: number): void {
// 子数组长度为 1 时终止递归
if (left >= right) {
return;
}
// 哨兵划分
const pivot = partition(nums, left, right);
const pivot = this.partition(nums, left, right);
// 递归左子数组、右子数组
quickSort(nums, left, pivot - 1);
quickSort(nums, pivot + 1, right);
this.quickSort(nums, left, pivot - 1);
this.quickSort(nums, pivot + 1, right);
}
```
@@ -585,25 +585,29 @@ comments: true
```javascript title="quick_sort.js"
/* 选取三个元素的中位数 */
function medianThree(nums, left, mid, right) {
medianThree(nums, left, mid, right) {
// 使用了异或操作来简化代码
// 异或规则为 0 ^ 0 = 1 ^ 1 = 0, 0 ^ 1 = 1 ^ 0 = 1
if ((nums[left] < nums[mid]) ^ (nums[left] < nums[right]))
return left;
else if ((nums[mid] < nums[left]) ^ (nums[mid] < nums[right]))
return mid;
else
return right;
if ((nums[left] < nums[mid]) ^ (nums[left] < nums[right])) return left;
else if ((nums[mid] < nums[left]) ^ (nums[mid] < nums[right])) return mid;
else return right;
}
/* 哨兵划分（三数取中值） */
function partition(nums, left, right) {
partition(nums, left, right) {
// 选取三个候选元素的中位数
let med = medianThree(nums, left, Math.floor((left + right) / 2), right);
let med = this.medianThree(nums, left, Math.floor((left + right) / 2), right);
// 将中位数交换至数组最左端
swap(nums, left, med);
this.swap(nums, left, med);
// 以 nums[left] 作为基准数
// 下同省略...
let i = left, j = right;
while (i < j) {
while (i < j && nums[j] >= nums[left]) j--; // 从右向左找首个小于基准数的元素
while (i < j && nums[i] <= nums[left]) i++; // 从左向右找首个大于基准数的元素
this.swap(nums, i, j); // 交换这两个元素
}
this.swap(nums, i, left); // 将基准数交换至两子数组的分界线
return i; // 返回基准数的索引
}
```
@@ -611,7 +615,7 @@ comments: true
```typescript title="quick_sort.ts"
/* 选取三个元素的中位数 */
function medianThree(nums: number[], left: number, mid: number, right: number): number {
medianThree(nums: number[], left: number, mid: number, right: number): number {
// 使用了异或操作来简化代码
// 异或规则为 0 ^ 0 = 1 ^ 1 = 0, 0 ^ 1 = 1 ^ 0 = 1
if (Number(nums[left] < nums[mid]) ^ Number(nums[left] < nums[right])) {
@@ -624,13 +628,25 @@ comments: true
}
/* 哨兵划分（三数取中值） */
function partition(nums: number[], left: number, right: number): number {
partition(nums: number[], left: number, right: number): number {
// 选取三个候选元素的中位数
let med = medianThree(nums, left, Math.floor((left + right) / 2), right);
let med = this.medianThree(nums, left, Math.floor((left + right) / 2), right);
// 将中位数交换至数组最左端
swap(nums, left, med);
this.swap(nums, left, med);
// 以 nums[left] 作为基准数
// 下同省略...
let i = left, j = right;
while (i < j) {
while (i < j && nums[j] >= nums[left]) {
j--; // 从右向左找首个小于基准数的元素
}
while (i < j && nums[i] <= nums[left]) {
i++; // 从左向右找首个大于基准数的元素
}
this.swap(nums, i, j); // 交换这两个元素
}
this.swap(nums, i, left); // 将基准数交换至两子数组的分界线
return i; // 返回基准数的索引
}
```
=== "C"
@@ -789,17 +805,17 @@ comments: true
```javascript title="quick_sort.js"
/* 快速排序（尾递归优化） */
function quickSort(nums, left, right) {
quickSort(nums, left, right) {
// 子数组长度为 1 时终止
while (left < right) {
// 哨兵划分操作
let pivot = partition(nums, left, right);
let pivot = this.partition(nums, left, right);
// 对两个子数组中较短的那个执行快排
if (pivot - left < right - pivot) {
quickSort(nums, left, pivot - 1); // 递归排序左子数组
left = pivot + 1; // 剩余待排序区间为 [pivot + 1, right]
this.quickSort(nums, left, pivot - 1); // 递归排序左子数组
left = pivot + 1; // 剩余待排序区间为 [pivot + 1, right]
} else {
quickSort(nums, pivot + 1, right); // 递归排序右子数组
this.quickSort(nums, pivot + 1, right); // 递归排序右子数组
right = pivot - 1; // 剩余待排序区间为 [left, pivot - 1]
}
}
@@ -810,17 +826,17 @@ comments: true
```typescript title="quick_sort.ts"
/* 快速排序（尾递归优化） */
function quickSort(nums: number[], left: number, right: number): void {
quickSort(nums: number[], left: number, right: number): void {
// 子数组长度为 1 时终止
while (left < right) {
// 哨兵划分操作
let pivot = partition(nums, left, right);
let pivot = this.partition(nums, left, right);
// 对两个子数组中较短的那个执行快排
if (pivot - left < right - pivot) {
quickSort(nums, left, pivot - 1); // 递归排序左子数组
this.quickSort(nums, left, pivot - 1); // 递归排序左子数组
left = pivot + 1; // 剩余待排序区间为 [pivot + 1, right]
} else {
quickSort(nums, pivot + 1, right); // 递归排序右子数组
this.quickSort(nums, pivot + 1, right); // 递归排序右子数组
right = pivot - 1; // 剩余待排序区间为 [left, pivot - 1]
}
}