mirror of
https://github.com/krahets/hello-algo.git
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Sort the coding languages by applications. (#721)
This commit is contained in:
Yudong Jin
@ -36,10 +36,10 @@
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=== "Java"
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=== "Python"
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```java title="bubble_sort.java"
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[class]{bubble_sort}-[func]{bubbleSort}
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```python title="bubble_sort.py"
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[class]{}-[func]{bubble_sort}
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```
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=== "C++"
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@ -48,10 +48,16 @@
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[class]{}-[func]{bubbleSort}
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```
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=== "Python"
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=== "Java"
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```python title="bubble_sort.py"
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[class]{}-[func]{bubble_sort}
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```java title="bubble_sort.java"
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[class]{bubble_sort}-[func]{bubbleSort}
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```
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=== "C#"
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```csharp title="bubble_sort.cs"
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[class]{bubble_sort}-[func]{bubbleSort}
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```
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=== "Go"
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@ -60,6 +66,12 @@
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[class]{}-[func]{bubbleSort}
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```
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=== "Swift"
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```swift title="bubble_sort.swift"
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[class]{}-[func]{bubbleSort}
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```
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=== "JS"
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```javascript title="bubble_sort.js"
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@ -72,30 +84,6 @@
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[class]{}-[func]{bubbleSort}
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```
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=== "C"
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```c title="bubble_sort.c"
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[class]{}-[func]{bubbleSort}
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```
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=== "C#"
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```csharp title="bubble_sort.cs"
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[class]{bubble_sort}-[func]{bubbleSort}
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```
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=== "Swift"
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```swift title="bubble_sort.swift"
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[class]{}-[func]{bubbleSort}
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```
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=== "Zig"
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```zig title="bubble_sort.zig"
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[class]{}-[func]{bubbleSort}
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```
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=== "Dart"
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```dart title="bubble_sort.dart"
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@ -108,16 +96,28 @@
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[class]{}-[func]{bubble_sort}
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```
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=== "C"
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```c title="bubble_sort.c"
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[class]{}-[func]{bubbleSort}
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```
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=== "Zig"
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```zig title="bubble_sort.zig"
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[class]{}-[func]{bubbleSort}
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```
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## 效率优化
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我们发现，如果某轮“冒泡”中没有执行任何交换操作，说明数组已经完成排序，可直接返回结果。因此，可以增加一个标志位 `flag` 来监测这种情况，一旦出现就立即返回。
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经过优化，冒泡排序的最差和平均时间复杂度仍为 $O(n^2)$ ；但当输入数组完全有序时，可达到最佳时间复杂度 $O(n)$ 。
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=== "Java"
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=== "Python"
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```java title="bubble_sort.java"
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[class]{bubble_sort}-[func]{bubbleSortWithFlag}
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```python title="bubble_sort.py"
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[class]{}-[func]{bubble_sort_with_flag}
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```
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=== "C++"
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@ -126,10 +126,16 @@
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[class]{}-[func]{bubbleSortWithFlag}
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```
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=== "Python"
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=== "Java"
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```python title="bubble_sort.py"
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[class]{}-[func]{bubble_sort_with_flag}
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```java title="bubble_sort.java"
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[class]{bubble_sort}-[func]{bubbleSortWithFlag}
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```
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=== "C#"
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```csharp title="bubble_sort.cs"
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[class]{bubble_sort}-[func]{bubbleSortWithFlag}
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```
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=== "Go"
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@ -138,6 +144,12 @@
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[class]{}-[func]{bubbleSortWithFlag}
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```
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=== "Swift"
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```swift title="bubble_sort.swift"
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[class]{}-[func]{bubbleSortWithFlag}
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```
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=== "JS"
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```javascript title="bubble_sort.js"
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@ -150,30 +162,6 @@
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[class]{}-[func]{bubbleSortWithFlag}
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```
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=== "C"
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```c title="bubble_sort.c"
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[class]{}-[func]{bubbleSortWithFlag}
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```
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=== "C#"
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```csharp title="bubble_sort.cs"
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[class]{bubble_sort}-[func]{bubbleSortWithFlag}
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```
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=== "Swift"
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```swift title="bubble_sort.swift"
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[class]{}-[func]{bubbleSortWithFlag}
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```
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=== "Zig"
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```zig title="bubble_sort.zig"
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[class]{}-[func]{bubbleSortWithFlag}
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```
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=== "Dart"
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```dart title="bubble_sort.dart"
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@ -186,6 +174,18 @@
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[class]{}-[func]{bubble_sort_with_flag}
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```
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=== "C"
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```c title="bubble_sort.c"
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[class]{}-[func]{bubbleSortWithFlag}
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```
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=== "Zig"
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```zig title="bubble_sort.zig"
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[class]{}-[func]{bubbleSortWithFlag}
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```
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## 算法特性
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- **时间复杂度为 $O(n^2)$、自适应排序**：各轮“冒泡”遍历的数组长度依次为 $n - 1$、$n - 2$、$\dots$、$2$、$1$ ，总和为 $(n - 1) n / 2$ 。在引入 `flag` 优化后，最佳时间复杂度可达到 $O(n)$ 。
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@ -14,10 +14,10 @@
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=== "Java"
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=== "Python"
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```java title="bucket_sort.java"
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[class]{bucket_sort}-[func]{bucketSort}
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```python title="bucket_sort.py"
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[class]{}-[func]{bucket_sort}
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```
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=== "C++"
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@ -26,10 +26,16 @@
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[class]{}-[func]{bucketSort}
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```
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=== "Python"
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=== "Java"
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```python title="bucket_sort.py"
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[class]{}-[func]{bucket_sort}
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```java title="bucket_sort.java"
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[class]{bucket_sort}-[func]{bucketSort}
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```
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=== "C#"
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```csharp title="bucket_sort.cs"
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[class]{bucket_sort}-[func]{bucketSort}
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```
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=== "Go"
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@ -38,6 +44,12 @@
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[class]{}-[func]{bucketSort}
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```
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=== "Swift"
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```swift title="bucket_sort.swift"
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[class]{}-[func]{bucketSort}
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```
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=== "JS"
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```javascript title="bucket_sort.js"
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@ -50,30 +62,6 @@
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[class]{}-[func]{bucketSort}
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```
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=== "C"
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```c title="bucket_sort.c"
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[class]{}-[func]{bucketSort}
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```
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=== "C#"
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```csharp title="bucket_sort.cs"
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[class]{bucket_sort}-[func]{bucketSort}
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```
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=== "Swift"
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```swift title="bucket_sort.swift"
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[class]{}-[func]{bucketSort}
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```
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=== "Zig"
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```zig title="bucket_sort.zig"
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[class]{}-[func]{bucketSort}
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```
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=== "Dart"
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```dart title="bucket_sort.dart"
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@ -86,6 +74,18 @@
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[class]{}-[func]{bucket_sort}
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```
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=== "C"
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```c title="bucket_sort.c"
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[class]{}-[func]{bucketSort}
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```
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=== "Zig"
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```zig title="bucket_sort.zig"
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[class]{}-[func]{bucketSort}
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```
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## 算法特性
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桶排序适用于处理体量很大的数据。例如，输入数据包含 100 万个元素，由于空间限制，系统内存无法一次性加载所有数据。此时，可以将数据分成 1000 个桶，然后分别对每个桶进行排序，最后将结果合并。
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@ -12,10 +12,10 @@
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=== "Java"
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=== "Python"
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```java title="counting_sort.java"
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[class]{counting_sort}-[func]{countingSortNaive}
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```python title="counting_sort.py"
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[class]{}-[func]{counting_sort_naive}
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```
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=== "C++"
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@ -24,10 +24,16 @@
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[class]{}-[func]{countingSortNaive}
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```
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=== "Python"
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=== "Java"
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```python title="counting_sort.py"
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[class]{}-[func]{counting_sort_naive}
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```java title="counting_sort.java"
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[class]{counting_sort}-[func]{countingSortNaive}
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```
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=== "C#"
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```csharp title="counting_sort.cs"
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[class]{counting_sort}-[func]{countingSortNaive}
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```
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=== "Go"
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@ -36,6 +42,12 @@
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[class]{}-[func]{countingSortNaive}
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```
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=== "Swift"
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```swift title="counting_sort.swift"
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[class]{}-[func]{countingSortNaive}
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```
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=== "JS"
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```javascript title="counting_sort.js"
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@ -48,30 +60,6 @@
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[class]{}-[func]{countingSortNaive}
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```
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=== "C"
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```c title="counting_sort.c"
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[class]{}-[func]{countingSortNaive}
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```
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=== "C#"
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|
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```csharp title="counting_sort.cs"
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[class]{counting_sort}-[func]{countingSortNaive}
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```
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|
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=== "Swift"
|
||||
|
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```swift title="counting_sort.swift"
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[class]{}-[func]{countingSortNaive}
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```
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|
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=== "Zig"
|
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|
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```zig title="counting_sort.zig"
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[class]{}-[func]{countingSortNaive}
|
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```
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|
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=== "Dart"
|
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|
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```dart title="counting_sort.dart"
|
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@ -84,6 +72,18 @@
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[class]{}-[func]{counting_sort_naive}
|
||||
```
|
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|
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=== "C"
|
||||
|
||||
```c title="counting_sort.c"
|
||||
[class]{}-[func]{countingSortNaive}
|
||||
```
|
||||
|
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=== "Zig"
|
||||
|
||||
```zig title="counting_sort.zig"
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[class]{}-[func]{countingSortNaive}
|
||||
```
|
||||
|
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!!! note "计数排序与桶排序的联系"
|
||||
|
||||
从桶排序的角度看，我们可以将计数排序中的计数数组 `counter` 的每个索引视为一个桶，将统计数量的过程看作是将各个元素分配到对应的桶中。本质上，计数排序是桶排序在整型数据下的一个特例。
|
||||
@ -131,10 +131,10 @@ $$
|
||||
|
||||
计数排序的实现代码如下所示。
|
||||
|
||||
=== "Java"
|
||||
=== "Python"
|
||||
|
||||
```java title="counting_sort.java"
|
||||
[class]{counting_sort}-[func]{countingSort}
|
||||
```python title="counting_sort.py"
|
||||
[class]{}-[func]{counting_sort}
|
||||
```
|
||||
|
||||
=== "C++"
|
||||
@ -143,10 +143,16 @@ $$
|
||||
[class]{}-[func]{countingSort}
|
||||
```
|
||||
|
||||
=== "Python"
|
||||
=== "Java"
|
||||
|
||||
```python title="counting_sort.py"
|
||||
[class]{}-[func]{counting_sort}
|
||||
```java title="counting_sort.java"
|
||||
[class]{counting_sort}-[func]{countingSort}
|
||||
```
|
||||
|
||||
=== "C#"
|
||||
|
||||
```csharp title="counting_sort.cs"
|
||||
[class]{counting_sort}-[func]{countingSort}
|
||||
```
|
||||
|
||||
=== "Go"
|
||||
@ -155,6 +161,12 @@ $$
|
||||
[class]{}-[func]{countingSort}
|
||||
```
|
||||
|
||||
=== "Swift"
|
||||
|
||||
```swift title="counting_sort.swift"
|
||||
[class]{}-[func]{countingSort}
|
||||
```
|
||||
|
||||
=== "JS"
|
||||
|
||||
```javascript title="counting_sort.js"
|
||||
@ -167,30 +179,6 @@ $$
|
||||
[class]{}-[func]{countingSort}
|
||||
```
|
||||
|
||||
=== "C"
|
||||
|
||||
```c title="counting_sort.c"
|
||||
[class]{}-[func]{countingSort}
|
||||
```
|
||||
|
||||
=== "C#"
|
||||
|
||||
```csharp title="counting_sort.cs"
|
||||
[class]{counting_sort}-[func]{countingSort}
|
||||
```
|
||||
|
||||
=== "Swift"
|
||||
|
||||
```swift title="counting_sort.swift"
|
||||
[class]{}-[func]{countingSort}
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
||||
```zig title="counting_sort.zig"
|
||||
[class]{}-[func]{countingSort}
|
||||
```
|
||||
|
||||
=== "Dart"
|
||||
|
||||
```dart title="counting_sort.dart"
|
||||
@ -203,6 +191,18 @@ $$
|
||||
[class]{}-[func]{counting_sort}
|
||||
```
|
||||
|
||||
=== "C"
|
||||
|
||||
```c title="counting_sort.c"
|
||||
[class]{}-[func]{countingSort}
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
||||
```zig title="counting_sort.zig"
|
||||
[class]{}-[func]{countingSort}
|
||||
```
|
||||
|
||||
## 算法特性
|
||||
|
||||
- **时间复杂度 $O(n + m)$** ：涉及遍历 `nums` 和遍历 `counter` ，都使用线性时间。一般情况下 $n \gg m$ ，时间复杂度趋于 $O(n)$ 。
|
||||
|
||||
@ -62,12 +62,12 @@
|
||||
|
||||
在代码实现中，我们使用了与堆章节相同的从顶至底堆化 `sift_down()` 函数。值得注意的是，由于堆的长度会随着提取最大元素而减小，因此我们需要给 `sift_down()` 函数添加一个长度参数 $n$ ，用于指定堆的当前有效长度。
|
||||
|
||||
=== "Java"
|
||||
=== "Python"
|
||||
|
||||
```java title="heap_sort.java"
|
||||
[class]{heap_sort}-[func]{siftDown}
|
||||
```python title="heap_sort.py"
|
||||
[class]{}-[func]{sift_down}
|
||||
|
||||
[class]{heap_sort}-[func]{heapSort}
|
||||
[class]{}-[func]{heap_sort}
|
||||
```
|
||||
|
||||
=== "C++"
|
||||
@ -78,12 +78,20 @@
|
||||
[class]{}-[func]{heapSort}
|
||||
```
|
||||
|
||||
=== "Python"
|
||||
=== "Java"
|
||||
|
||||
```python title="heap_sort.py"
|
||||
[class]{}-[func]{sift_down}
|
||||
```java title="heap_sort.java"
|
||||
[class]{heap_sort}-[func]{siftDown}
|
||||
|
||||
[class]{}-[func]{heap_sort}
|
||||
[class]{heap_sort}-[func]{heapSort}
|
||||
```
|
||||
|
||||
=== "C#"
|
||||
|
||||
```csharp title="heap_sort.cs"
|
||||
[class]{heap_sort}-[func]{siftDown}
|
||||
|
||||
[class]{heap_sort}-[func]{heapSort}
|
||||
```
|
||||
|
||||
=== "Go"
|
||||
@ -94,6 +102,14 @@
|
||||
[class]{}-[func]{heapSort}
|
||||
```
|
||||
|
||||
=== "Swift"
|
||||
|
||||
```swift title="heap_sort.swift"
|
||||
[class]{}-[func]{siftDown}
|
||||
|
||||
[class]{}-[func]{heapSort}
|
||||
```
|
||||
|
||||
=== "JS"
|
||||
|
||||
```javascript title="heap_sort.js"
|
||||
@ -110,38 +126,6 @@
|
||||
[class]{}-[func]{heapSort}
|
||||
```
|
||||
|
||||
=== "C"
|
||||
|
||||
```c title="heap_sort.c"
|
||||
[class]{}-[func]{siftDown}
|
||||
|
||||
[class]{}-[func]{heapSort}
|
||||
```
|
||||
|
||||
=== "C#"
|
||||
|
||||
```csharp title="heap_sort.cs"
|
||||
[class]{heap_sort}-[func]{siftDown}
|
||||
|
||||
[class]{heap_sort}-[func]{heapSort}
|
||||
```
|
||||
|
||||
=== "Swift"
|
||||
|
||||
```swift title="heap_sort.swift"
|
||||
[class]{}-[func]{siftDown}
|
||||
|
||||
[class]{}-[func]{heapSort}
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
||||
```zig title="heap_sort.zig"
|
||||
[class]{}-[func]{siftDown}
|
||||
|
||||
[class]{}-[func]{heapSort}
|
||||
```
|
||||
|
||||
=== "Dart"
|
||||
|
||||
```dart title="heap_sort.dart"
|
||||
@ -158,6 +142,22 @@
|
||||
[class]{}-[func]{heap_sort}
|
||||
```
|
||||
|
||||
=== "C"
|
||||
|
||||
```c title="heap_sort.c"
|
||||
[class]{}-[func]{siftDown}
|
||||
|
||||
[class]{}-[func]{heapSort}
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
||||
```zig title="heap_sort.zig"
|
||||
[class]{}-[func]{siftDown}
|
||||
|
||||
[class]{}-[func]{heapSort}
|
||||
```
|
||||
|
||||
## 算法特性
|
||||
|
||||
- **时间复杂度 $O(n \log n)$、非自适应排序**：建堆操作使用 $O(n)$ 时间。从堆中提取最大元素的时间复杂度为 $O(\log n)$ ，共循环 $n - 1$ 轮。
|
||||
|
||||
@ -19,10 +19,10 @@
|
||||
|
||||
|
||||
|
||||
=== "Java"
|
||||
=== "Python"
|
||||
|
||||
```java title="insertion_sort.java"
|
||||
[class]{insertion_sort}-[func]{insertionSort}
|
||||
```python title="insertion_sort.py"
|
||||
[class]{}-[func]{insertion_sort}
|
||||
```
|
||||
|
||||
=== "C++"
|
||||
@ -31,10 +31,16 @@
|
||||
[class]{}-[func]{insertionSort}
|
||||
```
|
||||
|
||||
=== "Python"
|
||||
=== "Java"
|
||||
|
||||
```python title="insertion_sort.py"
|
||||
[class]{}-[func]{insertion_sort}
|
||||
```java title="insertion_sort.java"
|
||||
[class]{insertion_sort}-[func]{insertionSort}
|
||||
```
|
||||
|
||||
=== "C#"
|
||||
|
||||
```csharp title="insertion_sort.cs"
|
||||
[class]{insertion_sort}-[func]{insertionSort}
|
||||
```
|
||||
|
||||
=== "Go"
|
||||
@ -43,6 +49,12 @@
|
||||
[class]{}-[func]{insertionSort}
|
||||
```
|
||||
|
||||
=== "Swift"
|
||||
|
||||
```swift title="insertion_sort.swift"
|
||||
[class]{}-[func]{insertionSort}
|
||||
```
|
||||
|
||||
=== "JS"
|
||||
|
||||
```javascript title="insertion_sort.js"
|
||||
@ -55,30 +67,6 @@
|
||||
[class]{}-[func]{insertionSort}
|
||||
```
|
||||
|
||||
=== "C"
|
||||
|
||||
```c title="insertion_sort.c"
|
||||
[class]{}-[func]{insertionSort}
|
||||
```
|
||||
|
||||
=== "C#"
|
||||
|
||||
```csharp title="insertion_sort.cs"
|
||||
[class]{insertion_sort}-[func]{insertionSort}
|
||||
```
|
||||
|
||||
=== "Swift"
|
||||
|
||||
```swift title="insertion_sort.swift"
|
||||
[class]{}-[func]{insertionSort}
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
||||
```zig title="insertion_sort.zig"
|
||||
[class]{}-[func]{insertionSort}
|
||||
```
|
||||
|
||||
=== "Dart"
|
||||
|
||||
```dart title="insertion_sort.dart"
|
||||
@ -91,6 +79,18 @@
|
||||
[class]{}-[func]{insertion_sort}
|
||||
```
|
||||
|
||||
=== "C"
|
||||
|
||||
```c title="insertion_sort.c"
|
||||
[class]{}-[func]{insertionSort}
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
||||
```zig title="insertion_sort.zig"
|
||||
[class]{}-[func]{insertionSort}
|
||||
```
|
||||
|
||||
## 算法特性
|
||||
|
||||
- **时间复杂度 $O(n^2)$、自适应排序**：最差情况下，每次插入操作分别需要循环 $n - 1$、$n-2$、$\dots$、$2$、$1$ 次，求和得到 $(n - 1) n / 2$ ，因此时间复杂度为 $O(n^2)$ 。在遇到有序数据时，插入操作会提前终止。当输入数组完全有序时，插入排序达到最佳时间复杂度 $O(n)$ 。
|
||||
|
||||
@ -51,12 +51,12 @@
|
||||
- **后序遍历**：先递归左子树，再递归右子树，最后处理根节点。
|
||||
- **归并排序**：先递归左子数组，再递归右子数组，最后处理合并。
|
||||
|
||||
=== "Java"
|
||||
=== "Python"
|
||||
|
||||
```java title="merge_sort.java"
|
||||
[class]{merge_sort}-[func]{merge}
|
||||
```python title="merge_sort.py"
|
||||
[class]{}-[func]{merge}
|
||||
|
||||
[class]{merge_sort}-[func]{mergeSort}
|
||||
[class]{}-[func]{merge_sort}
|
||||
```
|
||||
|
||||
=== "C++"
|
||||
@ -67,12 +67,20 @@
|
||||
[class]{}-[func]{mergeSort}
|
||||
```
|
||||
|
||||
=== "Python"
|
||||
=== "Java"
|
||||
|
||||
```python title="merge_sort.py"
|
||||
[class]{}-[func]{merge}
|
||||
```java title="merge_sort.java"
|
||||
[class]{merge_sort}-[func]{merge}
|
||||
|
||||
[class]{}-[func]{merge_sort}
|
||||
[class]{merge_sort}-[func]{mergeSort}
|
||||
```
|
||||
|
||||
=== "C#"
|
||||
|
||||
```csharp title="merge_sort.cs"
|
||||
[class]{merge_sort}-[func]{merge}
|
||||
|
||||
[class]{merge_sort}-[func]{mergeSort}
|
||||
```
|
||||
|
||||
=== "Go"
|
||||
@ -83,6 +91,14 @@
|
||||
[class]{}-[func]{mergeSort}
|
||||
```
|
||||
|
||||
=== "Swift"
|
||||
|
||||
```swift title="merge_sort.swift"
|
||||
[class]{}-[func]{merge}
|
||||
|
||||
[class]{}-[func]{mergeSort}
|
||||
```
|
||||
|
||||
=== "JS"
|
||||
|
||||
```javascript title="merge_sort.js"
|
||||
@ -99,38 +115,6 @@
|
||||
[class]{}-[func]{mergeSort}
|
||||
```
|
||||
|
||||
=== "C"
|
||||
|
||||
```c title="merge_sort.c"
|
||||
[class]{}-[func]{merge}
|
||||
|
||||
[class]{}-[func]{mergeSort}
|
||||
```
|
||||
|
||||
=== "C#"
|
||||
|
||||
```csharp title="merge_sort.cs"
|
||||
[class]{merge_sort}-[func]{merge}
|
||||
|
||||
[class]{merge_sort}-[func]{mergeSort}
|
||||
```
|
||||
|
||||
=== "Swift"
|
||||
|
||||
```swift title="merge_sort.swift"
|
||||
[class]{}-[func]{merge}
|
||||
|
||||
[class]{}-[func]{mergeSort}
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
||||
```zig title="merge_sort.zig"
|
||||
[class]{}-[func]{merge}
|
||||
|
||||
[class]{}-[func]{mergeSort}
|
||||
```
|
||||
|
||||
=== "Dart"
|
||||
|
||||
```dart title="merge_sort.dart"
|
||||
@ -147,6 +131,22 @@
|
||||
[class]{}-[func]{merge_sort}
|
||||
```
|
||||
|
||||
=== "C"
|
||||
|
||||
```c title="merge_sort.c"
|
||||
[class]{}-[func]{merge}
|
||||
|
||||
[class]{}-[func]{mergeSort}
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
||||
```zig title="merge_sort.zig"
|
||||
[class]{}-[func]{merge}
|
||||
|
||||
[class]{}-[func]{mergeSort}
|
||||
```
|
||||
|
||||
实现合并函数 `merge()` 存在以下难点。
|
||||
|
||||
- **需要特别注意各个变量的含义**。`nums` 的待合并区间为 `[left, right]` ，但由于 `tmp` 仅复制了 `nums` 该区间的元素，因此 `tmp` 对应区间为 `[0, right - left]` 。
|
||||
|
||||
@ -41,11 +41,9 @@
|
||||
|
||||
哨兵划分的实质是将一个较长数组的排序问题简化为两个较短数组的排序问题。
|
||||
|
||||
=== "Java"
|
||||
|
||||
```java title="quick_sort.java"
|
||||
[class]{QuickSort}-[func]{swap}
|
||||
=== "Python"
|
||||
|
||||
```python title="quick_sort.py"
|
||||
[class]{QuickSort}-[func]{partition}
|
||||
```
|
||||
|
||||
@ -57,9 +55,19 @@
|
||||
[class]{QuickSort}-[func]{partition}
|
||||
```
|
||||
|
||||
=== "Python"
|
||||
=== "Java"
|
||||
|
||||
```java title="quick_sort.java"
|
||||
[class]{QuickSort}-[func]{swap}
|
||||
|
||||
[class]{QuickSort}-[func]{partition}
|
||||
```
|
||||
|
||||
=== "C#"
|
||||
|
||||
```csharp title="quick_sort.cs"
|
||||
[class]{QuickSort}-[func]{swap}
|
||||
|
||||
```python title="quick_sort.py"
|
||||
[class]{QuickSort}-[func]{partition}
|
||||
```
|
||||
|
||||
@ -69,6 +77,14 @@
|
||||
[class]{quickSort}-[func]{partition}
|
||||
```
|
||||
|
||||
=== "Swift"
|
||||
|
||||
```swift title="quick_sort.swift"
|
||||
[class]{}-[func]{swap}
|
||||
|
||||
[class]{}-[func]{partition}
|
||||
```
|
||||
|
||||
=== "JS"
|
||||
|
||||
```javascript title="quick_sort.js"
|
||||
@ -85,38 +101,6 @@
|
||||
[class]{QuickSort}-[func]{partition}
|
||||
```
|
||||
|
||||
=== "C"
|
||||
|
||||
```c title="quick_sort.c"
|
||||
[class]{}-[func]{swap}
|
||||
|
||||
[class]{}-[func]{partition}
|
||||
```
|
||||
|
||||
=== "C#"
|
||||
|
||||
```csharp title="quick_sort.cs"
|
||||
[class]{QuickSort}-[func]{swap}
|
||||
|
||||
[class]{QuickSort}-[func]{partition}
|
||||
```
|
||||
|
||||
=== "Swift"
|
||||
|
||||
```swift title="quick_sort.swift"
|
||||
[class]{}-[func]{swap}
|
||||
|
||||
[class]{}-[func]{partition}
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
||||
```zig title="quick_sort.zig"
|
||||
[class]{QuickSort}-[func]{swap}
|
||||
|
||||
[class]{QuickSort}-[func]{partition}
|
||||
```
|
||||
|
||||
=== "Dart"
|
||||
|
||||
```dart title="quick_sort.dart"
|
||||
@ -131,6 +115,22 @@
|
||||
[class]{QuickSort}-[func]{partition}
|
||||
```
|
||||
|
||||
=== "C"
|
||||
|
||||
```c title="quick_sort.c"
|
||||
[class]{}-[func]{swap}
|
||||
|
||||
[class]{}-[func]{partition}
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
||||
```zig title="quick_sort.zig"
|
||||
[class]{QuickSort}-[func]{swap}
|
||||
|
||||
[class]{QuickSort}-[func]{partition}
|
||||
```
|
||||
|
||||
## 算法流程
|
||||
|
||||
快速排序的整体流程如下图所示。
|
||||
@ -141,10 +141,10 @@
|
||||
|
||||
|
||||
|
||||
=== "Java"
|
||||
=== "Python"
|
||||
|
||||
```java title="quick_sort.java"
|
||||
[class]{QuickSort}-[func]{quickSort}
|
||||
```python title="quick_sort.py"
|
||||
[class]{QuickSort}-[func]{quick_sort}
|
||||
```
|
||||
|
||||
=== "C++"
|
||||
@ -153,10 +153,16 @@
|
||||
[class]{QuickSort}-[func]{quickSort}
|
||||
```
|
||||
|
||||
=== "Python"
|
||||
=== "Java"
|
||||
|
||||
```python title="quick_sort.py"
|
||||
[class]{QuickSort}-[func]{quick_sort}
|
||||
```java title="quick_sort.java"
|
||||
[class]{QuickSort}-[func]{quickSort}
|
||||
```
|
||||
|
||||
=== "C#"
|
||||
|
||||
```csharp title="quick_sort.cs"
|
||||
[class]{QuickSort}-[func]{quickSort}
|
||||
```
|
||||
|
||||
=== "Go"
|
||||
@ -165,6 +171,12 @@
|
||||
[class]{quickSort}-[func]{quickSort}
|
||||
```
|
||||
|
||||
=== "Swift"
|
||||
|
||||
```swift title="quick_sort.swift"
|
||||
[class]{}-[func]{quickSort}
|
||||
```
|
||||
|
||||
=== "JS"
|
||||
|
||||
```javascript title="quick_sort.js"
|
||||
@ -177,30 +189,6 @@
|
||||
[class]{QuickSort}-[func]{quickSort}
|
||||
```
|
||||
|
||||
=== "C"
|
||||
|
||||
```c title="quick_sort.c"
|
||||
[class]{}-[func]{quickSort}
|
||||
```
|
||||
|
||||
=== "C#"
|
||||
|
||||
```csharp title="quick_sort.cs"
|
||||
[class]{QuickSort}-[func]{quickSort}
|
||||
```
|
||||
|
||||
=== "Swift"
|
||||
|
||||
```swift title="quick_sort.swift"
|
||||
[class]{}-[func]{quickSort}
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
||||
```zig title="quick_sort.zig"
|
||||
[class]{QuickSort}-[func]{quickSort}
|
||||
```
|
||||
|
||||
=== "Dart"
|
||||
|
||||
```dart title="quick_sort.dart"
|
||||
@ -213,6 +201,18 @@
|
||||
[class]{QuickSort}-[func]{quick_sort}
|
||||
```
|
||||
|
||||
=== "C"
|
||||
|
||||
```c title="quick_sort.c"
|
||||
[class]{}-[func]{quickSort}
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
||||
```zig title="quick_sort.zig"
|
||||
[class]{QuickSort}-[func]{quickSort}
|
||||
```
|
||||
|
||||
## 算法特性
|
||||
|
||||
- **时间复杂度 $O(n \log n)$、自适应排序**：在平均情况下，哨兵划分的递归层数为 $\log n$ ，每层中的总循环数为 $n$ ，总体使用 $O(n \log n)$ 时间。在最差情况下，每轮哨兵划分操作都将长度为 $n$ 的数组划分为长度为 $0$ 和 $n - 1$ 的两个子数组，此时递归层数达到 $n$ 层，每层中的循环数为 $n$ ，总体使用 $O(n^2)$ 时间。
|
||||
@ -237,10 +237,10 @@
|
||||
|
||||
为了进一步改进，我们可以在数组中选取三个候选元素（通常为数组的首、尾、中点元素），**并将这三个候选元素的中位数作为基准数**。这样一来，基准数“既不太小也不太大”的概率将大幅提升。当然，我们还可以选取更多候选元素，以进一步提高算法的稳健性。采用这种方法后，时间复杂度劣化至 $O(n^2)$ 的概率大大降低。
|
||||
|
||||
=== "Java"
|
||||
=== "Python"
|
||||
|
||||
```java title="quick_sort.java"
|
||||
[class]{QuickSortMedian}-[func]{medianThree}
|
||||
```python title="quick_sort.py"
|
||||
[class]{QuickSortMedian}-[func]{median_three}
|
||||
|
||||
[class]{QuickSortMedian}-[func]{partition}
|
||||
```
|
||||
@ -253,10 +253,18 @@
|
||||
[class]{QuickSortMedian}-[func]{partition}
|
||||
```
|
||||
|
||||
=== "Python"
|
||||
=== "Java"
|
||||
|
||||
```python title="quick_sort.py"
|
||||
[class]{QuickSortMedian}-[func]{median_three}
|
||||
```java title="quick_sort.java"
|
||||
[class]{QuickSortMedian}-[func]{medianThree}
|
||||
|
||||
[class]{QuickSortMedian}-[func]{partition}
|
||||
```
|
||||
|
||||
=== "C#"
|
||||
|
||||
```csharp title="quick_sort.cs"
|
||||
[class]{QuickSortMedian}-[func]{medianThree}
|
||||
|
||||
[class]{QuickSortMedian}-[func]{partition}
|
||||
```
|
||||
@ -269,6 +277,14 @@
|
||||
[class]{quickSortMedian}-[func]{partition}
|
||||
```
|
||||
|
||||
=== "Swift"
|
||||
|
||||
```swift title="quick_sort.swift"
|
||||
[class]{}-[func]{medianThree}
|
||||
|
||||
[class]{}-[func]{partitionMedian}
|
||||
```
|
||||
|
||||
=== "JS"
|
||||
|
||||
```javascript title="quick_sort.js"
|
||||
@ -285,38 +301,6 @@
|
||||
[class]{QuickSortMedian}-[func]{partition}
|
||||
```
|
||||
|
||||
=== "C"
|
||||
|
||||
```c title="quick_sort.c"
|
||||
[class]{}-[func]{medianThree}
|
||||
|
||||
[class]{}-[func]{partitionMedian}
|
||||
```
|
||||
|
||||
=== "C#"
|
||||
|
||||
```csharp title="quick_sort.cs"
|
||||
[class]{QuickSortMedian}-[func]{medianThree}
|
||||
|
||||
[class]{QuickSortMedian}-[func]{partition}
|
||||
```
|
||||
|
||||
=== "Swift"
|
||||
|
||||
```swift title="quick_sort.swift"
|
||||
[class]{}-[func]{medianThree}
|
||||
|
||||
[class]{}-[func]{partitionMedian}
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
||||
```zig title="quick_sort.zig"
|
||||
[class]{QuickSortMedian}-[func]{medianThree}
|
||||
|
||||
[class]{QuickSortMedian}-[func]{partition}
|
||||
```
|
||||
|
||||
=== "Dart"
|
||||
|
||||
```dart title="quick_sort.dart"
|
||||
@ -333,16 +317,32 @@
|
||||
[class]{QuickSortMedian}-[func]{partition}
|
||||
```
|
||||
|
||||
=== "C"
|
||||
|
||||
```c title="quick_sort.c"
|
||||
[class]{}-[func]{medianThree}
|
||||
|
||||
[class]{}-[func]{partitionMedian}
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
||||
```zig title="quick_sort.zig"
|
||||
[class]{QuickSortMedian}-[func]{medianThree}
|
||||
|
||||
[class]{QuickSortMedian}-[func]{partition}
|
||||
```
|
||||
|
||||
## 尾递归优化
|
||||
|
||||
**在某些输入下，快速排序可能占用空间较多**。以完全倒序的输入数组为例，由于每轮哨兵划分后右子数组长度为 $0$ ，递归树的高度会达到 $n - 1$ ，此时需要占用 $O(n)$ 大小的栈帧空间。
|
||||
|
||||
为了防止栈帧空间的累积，我们可以在每轮哨兵排序完成后，比较两个子数组的长度，**仅对较短的子数组进行递归**。由于较短子数组的长度不会超过 $n / 2$ ，因此这种方法能确保递归深度不超过 $\log n$ ，从而将最差空间复杂度优化至 $O(\log n)$ 。
|
||||
|
||||
=== "Java"
|
||||
=== "Python"
|
||||
|
||||
```java title="quick_sort.java"
|
||||
[class]{QuickSortTailCall}-[func]{quickSort}
|
||||
```python title="quick_sort.py"
|
||||
[class]{QuickSortTailCall}-[func]{quick_sort}
|
||||
```
|
||||
|
||||
=== "C++"
|
||||
@ -351,10 +351,16 @@
|
||||
[class]{QuickSortTailCall}-[func]{quickSort}
|
||||
```
|
||||
|
||||
=== "Python"
|
||||
=== "Java"
|
||||
|
||||
```python title="quick_sort.py"
|
||||
[class]{QuickSortTailCall}-[func]{quick_sort}
|
||||
```java title="quick_sort.java"
|
||||
[class]{QuickSortTailCall}-[func]{quickSort}
|
||||
```
|
||||
|
||||
=== "C#"
|
||||
|
||||
```csharp title="quick_sort.cs"
|
||||
[class]{QuickSortTailCall}-[func]{quickSort}
|
||||
```
|
||||
|
||||
=== "Go"
|
||||
@ -363,6 +369,12 @@
|
||||
[class]{quickSortTailCall}-[func]{quickSort}
|
||||
```
|
||||
|
||||
=== "Swift"
|
||||
|
||||
```swift title="quick_sort.swift"
|
||||
[class]{}-[func]{quickSortTailCall}
|
||||
```
|
||||
|
||||
=== "JS"
|
||||
|
||||
```javascript title="quick_sort.js"
|
||||
@ -375,30 +387,6 @@
|
||||
[class]{QuickSortTailCall}-[func]{quickSort}
|
||||
```
|
||||
|
||||
=== "C"
|
||||
|
||||
```c title="quick_sort.c"
|
||||
[class]{}-[func]{quickSortTailCall}
|
||||
```
|
||||
|
||||
=== "C#"
|
||||
|
||||
```csharp title="quick_sort.cs"
|
||||
[class]{QuickSortTailCall}-[func]{quickSort}
|
||||
```
|
||||
|
||||
=== "Swift"
|
||||
|
||||
```swift title="quick_sort.swift"
|
||||
[class]{}-[func]{quickSortTailCall}
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
||||
```zig title="quick_sort.zig"
|
||||
[class]{QuickSortTailCall}-[func]{quickSort}
|
||||
```
|
||||
|
||||
=== "Dart"
|
||||
|
||||
```dart title="quick_sort.dart"
|
||||
@ -410,3 +398,15 @@
|
||||
```rust title="quick_sort.rs"
|
||||
[class]{QuickSortTailCall}-[func]{quick_sort}
|
||||
```
|
||||
|
||||
=== "C"
|
||||
|
||||
```c title="quick_sort.c"
|
||||
[class]{}-[func]{quickSortTailCall}
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
||||
```zig title="quick_sort.zig"
|
||||
[class]{QuickSortTailCall}-[func]{quickSort}
|
||||
```
|
||||
|
||||
@ -24,14 +24,14 @@ $$
|
||||
|
||||
此外，我们需要小幅改动计数排序代码，使之可以根据数字的第 $k$ 位进行排序。
|
||||
|
||||
=== "Java"
|
||||
=== "Python"
|
||||
|
||||
```java title="radix_sort.java"
|
||||
[class]{radix_sort}-[func]{digit}
|
||||
```python title="radix_sort.py"
|
||||
[class]{}-[func]{digit}
|
||||
|
||||
[class]{radix_sort}-[func]{countingSortDigit}
|
||||
[class]{}-[func]{counting_sort_digit}
|
||||
|
||||
[class]{radix_sort}-[func]{radixSort}
|
||||
[class]{}-[func]{radix_sort}
|
||||
```
|
||||
|
||||
=== "C++"
|
||||
@ -44,14 +44,24 @@ $$
|
||||
[class]{}-[func]{radixSort}
|
||||
```
|
||||
|
||||
=== "Python"
|
||||
=== "Java"
|
||||
|
||||
```python title="radix_sort.py"
|
||||
[class]{}-[func]{digit}
|
||||
```java title="radix_sort.java"
|
||||
[class]{radix_sort}-[func]{digit}
|
||||
|
||||
[class]{}-[func]{counting_sort_digit}
|
||||
[class]{radix_sort}-[func]{countingSortDigit}
|
||||
|
||||
[class]{}-[func]{radix_sort}
|
||||
[class]{radix_sort}-[func]{radixSort}
|
||||
```
|
||||
|
||||
=== "C#"
|
||||
|
||||
```csharp title="radix_sort.cs"
|
||||
[class]{radix_sort}-[func]{digit}
|
||||
|
||||
[class]{radix_sort}-[func]{countingSortDigit}
|
||||
|
||||
[class]{radix_sort}-[func]{radixSort}
|
||||
```
|
||||
|
||||
=== "Go"
|
||||
@ -64,6 +74,16 @@ $$
|
||||
[class]{}-[func]{radixSort}
|
||||
```
|
||||
|
||||
=== "Swift"
|
||||
|
||||
```swift title="radix_sort.swift"
|
||||
[class]{}-[func]{digit}
|
||||
|
||||
[class]{}-[func]{countingSortDigit}
|
||||
|
||||
[class]{}-[func]{radixSort}
|
||||
```
|
||||
|
||||
=== "JS"
|
||||
|
||||
```javascript title="radix_sort.js"
|
||||
@ -84,46 +104,6 @@ $$
|
||||
[class]{}-[func]{radixSort}
|
||||
```
|
||||
|
||||
=== "C"
|
||||
|
||||
```c title="radix_sort.c"
|
||||
[class]{}-[func]{digit}
|
||||
|
||||
[class]{}-[func]{countingSortDigit}
|
||||
|
||||
[class]{}-[func]{radixSort}
|
||||
```
|
||||
|
||||
=== "C#"
|
||||
|
||||
```csharp title="radix_sort.cs"
|
||||
[class]{radix_sort}-[func]{digit}
|
||||
|
||||
[class]{radix_sort}-[func]{countingSortDigit}
|
||||
|
||||
[class]{radix_sort}-[func]{radixSort}
|
||||
```
|
||||
|
||||
=== "Swift"
|
||||
|
||||
```swift title="radix_sort.swift"
|
||||
[class]{}-[func]{digit}
|
||||
|
||||
[class]{}-[func]{countingSortDigit}
|
||||
|
||||
[class]{}-[func]{radixSort}
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
||||
```zig title="radix_sort.zig"
|
||||
[class]{}-[func]{digit}
|
||||
|
||||
[class]{}-[func]{countingSortDigit}
|
||||
|
||||
[class]{}-[func]{radixSort}
|
||||
```
|
||||
|
||||
=== "Dart"
|
||||
|
||||
```dart title="radix_sort.dart"
|
||||
@ -144,6 +124,26 @@ $$
|
||||
[class]{}-[func]{radix_sort}
|
||||
```
|
||||
|
||||
=== "C"
|
||||
|
||||
```c title="radix_sort.c"
|
||||
[class]{}-[func]{digit}
|
||||
|
||||
[class]{}-[func]{countingSortDigit}
|
||||
|
||||
[class]{}-[func]{radixSort}
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
||||
```zig title="radix_sort.zig"
|
||||
[class]{}-[func]{digit}
|
||||
|
||||
[class]{}-[func]{countingSortDigit}
|
||||
|
||||
[class]{}-[func]{radixSort}
|
||||
```
|
||||
|
||||
!!! question "为什么从最低位开始排序？"
|
||||
|
||||
在连续的排序轮次中，后一轮排序会覆盖前一轮排序的结果。举例来说，如果第一轮排序结果 $a < b$ ，而第二轮排序结果 $a > b$ ，那么第二轮的结果将取代第一轮的结果。由于数字的高位优先级高于低位，我们应该先排序低位再排序高位。
|
||||
|
||||
@ -45,10 +45,10 @@
|
||||
|
||||
在代码中，我们用 $k$ 来记录未排序区间内的最小元素。
|
||||
|
||||
=== "Java"
|
||||
=== "Python"
|
||||
|
||||
```java title="selection_sort.java"
|
||||
[class]{selection_sort}-[func]{selectionSort}
|
||||
```python title="selection_sort.py"
|
||||
[class]{}-[func]{selection_sort}
|
||||
```
|
||||
|
||||
=== "C++"
|
||||
@ -57,10 +57,16 @@
|
||||
[class]{}-[func]{selectionSort}
|
||||
```
|
||||
|
||||
=== "Python"
|
||||
=== "Java"
|
||||
|
||||
```python title="selection_sort.py"
|
||||
[class]{}-[func]{selection_sort}
|
||||
```java title="selection_sort.java"
|
||||
[class]{selection_sort}-[func]{selectionSort}
|
||||
```
|
||||
|
||||
=== "C#"
|
||||
|
||||
```csharp title="selection_sort.cs"
|
||||
[class]{selection_sort}-[func]{selectionSort}
|
||||
```
|
||||
|
||||
=== "Go"
|
||||
@ -69,6 +75,12 @@
|
||||
[class]{}-[func]{selectionSort}
|
||||
```
|
||||
|
||||
=== "Swift"
|
||||
|
||||
```swift title="selection_sort.swift"
|
||||
[class]{}-[func]{selectionSort}
|
||||
```
|
||||
|
||||
=== "JS"
|
||||
|
||||
```javascript title="selection_sort.js"
|
||||
@ -81,30 +93,6 @@
|
||||
[class]{}-[func]{selectionSort}
|
||||
```
|
||||
|
||||
=== "C"
|
||||
|
||||
```c title="selection_sort.c"
|
||||
[class]{}-[func]{selectionSort}
|
||||
```
|
||||
|
||||
=== "C#"
|
||||
|
||||
```csharp title="selection_sort.cs"
|
||||
[class]{selection_sort}-[func]{selectionSort}
|
||||
```
|
||||
|
||||
=== "Swift"
|
||||
|
||||
```swift title="selection_sort.swift"
|
||||
[class]{}-[func]{selectionSort}
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
||||
```zig title="selection_sort.zig"
|
||||
[class]{}-[func]{selectionSort}
|
||||
```
|
||||
|
||||
=== "Dart"
|
||||
|
||||
```dart title="selection_sort.dart"
|
||||
@ -117,6 +105,18 @@
|
||||
[class]{}-[func]{selection_sort}
|
||||
```
|
||||
|
||||
=== "C"
|
||||
|
||||
```c title="selection_sort.c"
|
||||
[class]{}-[func]{selectionSort}
|
||||
```
|
||||
|
||||
=== "Zig"
|
||||
|
||||
```zig title="selection_sort.zig"
|
||||
[class]{}-[func]{selectionSort}
|
||||
```
|
||||
|
||||
## 算法特性
|
||||
|
||||
- **时间复杂度为 $O(n^2)$、非自适应排序**：外循环共 $n - 1$ 轮，第一轮的未排序区间长度为 $n$ ，最后一轮的未排序区间长度为 $2$ ，即各轮外循环分别包含 $n$、$n - 1$、$\dots$、$3$、$2$ 轮内循环，求和为 $\frac{(n - 1)(n + 2)}{2}$ 。
|
||||
|
||||
Reference in New Issue
Block a user