2023-05-24 00:35:46 +08:00
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# 选择排序
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2023-05-24 20:57:08 +08:00
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「选择排序 Selection Sort」的工作原理非常直接:开启一个循环,每轮从未排序区间选择最小的元素,将其放到已排序区间的末尾。
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2023-05-24 11:45:52 +08:00
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2023-05-24 20:57:08 +08:00
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设数组的长度为 $n$ ,选择排序的算法流程如下:
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2023-05-24 00:35:46 +08:00
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1. 初始状态下,所有元素未排序,即未排序(索引)区间为 $[0, n-1]$ 。
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2. 选取区间 $[0, n-1]$ 中的最小元素,将其与索引 $0$ 处元素交换。完成后,数组前 1 个元素已排序。
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3. 选取区间 $[1, n-1]$ 中的最小元素,将其与索引 $1$ 处元素交换。完成后,数组前 2 个元素已排序。
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4. 以此类推。经过 $n - 1$ 轮选择与交换后,数组前 $n - 1$ 个元素已排序。
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5. 仅剩的一个元素必定是最大元素,无需排序,因此数组排序完成。
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=== "<1>"
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![选择排序步骤](selection_sort.assets/selection_sort_step1.png)
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=== "<2>"
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![selection_sort_step2](selection_sort.assets/selection_sort_step2.png)
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=== "<3>"
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![selection_sort_step3](selection_sort.assets/selection_sort_step3.png)
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=== "<4>"
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![selection_sort_step4](selection_sort.assets/selection_sort_step4.png)
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=== "<5>"
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![selection_sort_step5](selection_sort.assets/selection_sort_step5.png)
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=== "<6>"
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![selection_sort_step6](selection_sort.assets/selection_sort_step6.png)
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=== "<7>"
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![selection_sort_step7](selection_sort.assets/selection_sort_step7.png)
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=== "<8>"
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![selection_sort_step8](selection_sort.assets/selection_sort_step8.png)
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=== "<9>"
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![selection_sort_step9](selection_sort.assets/selection_sort_step9.png)
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=== "<10>"
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![selection_sort_step10](selection_sort.assets/selection_sort_step10.png)
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=== "<11>"
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![selection_sort_step11](selection_sort.assets/selection_sort_step11.png)
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在代码中,我们用 $k$ 来记录未排序区间内的最小元素。
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=== "Java"
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```java title="selection_sort.java"
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[class]{selection_sort}-[func]{selectionSort}
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```
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=== "C++"
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```cpp title="selection_sort.cpp"
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[class]{}-[func]{selectionSort}
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```
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=== "Python"
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```python title="selection_sort.py"
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[class]{}-[func]{selection_sort}
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```
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=== "Go"
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```go title="selection_sort.go"
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[class]{}-[func]{selectionSort}
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```
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=== "JavaScript"
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```javascript title="selection_sort.js"
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[class]{}-[func]{selectionSort}
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```
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=== "TypeScript"
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```typescript title="selection_sort.ts"
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[class]{}-[func]{selectionSort}
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```
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=== "C"
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```c title="selection_sort.c"
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[class]{}-[func]{selectionSort}
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```
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=== "C#"
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```csharp title="selection_sort.cs"
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[class]{selection_sort}-[func]{selectionSort}
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```
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=== "Swift"
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```swift title="selection_sort.swift"
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[class]{}-[func]{selectionSort}
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```
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=== "Zig"
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```zig title="selection_sort.zig"
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[class]{}-[func]{selectionSort}
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```
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## 算法特性
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- **时间复杂度为 $O(n^2)$ 、非自适应排序**:共有 $n - 1$ 轮外循环,分别包含 $n$ , $n - 1$ , $\cdots$ , $2$ , $2$ 轮内循环,求和为 $\frac{(n - 1)(n + 2)}{2}$ 。
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- **空间复杂度 $O(1)$ 、原地排序**:指针 $i$ , $j$ 使用常数大小的额外空间。
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- **非稳定排序**:在交换元素时,有可能将 `nums[i]` 交换至其相等元素的右边,导致两者的相对顺序发生改变。
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2023-05-24 00:44:55 +08:00
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![选择排序非稳定示例](selection_sort.assets/selection_sort_instability.png)
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