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hello-algo/docs/chapter_sorting/selection_sort.md

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Add the section of selection sort. (#513)
2023-05-24 00:35:46 +08:00
# 选择排序
feat: Revised the book (#978) * Sync recent changes to the revised Word. * Revised the preface chapter * Revised the introduction chapter * Revised the computation complexity chapter * Revised the chapter data structure * Revised the chapter array and linked list * Revised the chapter stack and queue * Revised the chapter hashing * Revised the chapter tree * Revised the chapter heap * Revised the chapter graph * Revised the chapter searching * Reivised the sorting chapter * Revised the divide and conquer chapter * Revised the chapter backtacking * Revised the DP chapter * Revised the greedy chapter * Revised the appendix chapter * Revised the preface chapter doubly * Revised the figures
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「选择排序 selection sort」的工作原理非常简单：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。
Polish some contents.
2023-05-24 11:45:52 +08:00
Mention figures and tables in normal texts. Fix some figures. Finetune texts.
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设数组的长度为 $n$ ，选择排序的算法流程如下图所示。
Add the section of selection sort. (#513)
2023-05-24 00:35:46 +08:00
1. 初始状态下，所有元素未排序，即未排序（索引）区间为 $[0, n-1]$ 。
feat: Revised the book (#978) * Sync recent changes to the revised Word. * Revised the preface chapter * Revised the introduction chapter * Revised the computation complexity chapter * Revised the chapter data structure * Revised the chapter array and linked list * Revised the chapter stack and queue * Revised the chapter hashing * Revised the chapter tree * Revised the chapter heap * Revised the chapter graph * Revised the chapter searching * Reivised the sorting chapter * Revised the divide and conquer chapter * Revised the chapter backtacking * Revised the DP chapter * Revised the greedy chapter * Revised the appendix chapter * Revised the preface chapter doubly * Revised the figures
2023-12-02 06:21:34 +08:00
2. 选取区间 $[0, n-1]$ 中的最小元素，将其与索引 $0$ 处的元素交换。完成后，数组前 1 个元素已排序。
3. 选取区间 $[1, n-1]$ 中的最小元素，将其与索引 $1$ 处的元素交换。完成后，数组前 2 个元素已排序。
Add the section of selection sort. (#513)
2023-05-24 00:35:46 +08:00
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。
Polish the chapter introduction, computational complexity.
2023-08-20 14:51:39 +08:00
5. 仅剩的一个元素必定是最大元素，无须排序，因此数组排序完成。
Add the section of selection sort. (#513)
2023-05-24 00:35:46 +08:00
=== "<1>"
![选择排序步骤](selection_sort.assets/selection_sort_step1.png)
=== "<2>"
![selection_sort_step2](selection_sort.assets/selection_sort_step2.png)
=== "<3>"
![selection_sort_step3](selection_sort.assets/selection_sort_step3.png)
=== "<4>"
![selection_sort_step4](selection_sort.assets/selection_sort_step4.png)
=== "<5>"
![selection_sort_step5](selection_sort.assets/selection_sort_step5.png)
=== "<6>"
![selection_sort_step6](selection_sort.assets/selection_sort_step6.png)
=== "<7>"
![selection_sort_step7](selection_sort.assets/selection_sort_step7.png)
=== "<8>"
![selection_sort_step8](selection_sort.assets/selection_sort_step8.png)
=== "<9>"
![selection_sort_step9](selection_sort.assets/selection_sort_step9.png)
=== "<10>"
![selection_sort_step10](selection_sort.assets/selection_sort_step10.png)
=== "<11>"
![selection_sort_step11](selection_sort.assets/selection_sort_step11.png)
feat: Revised the book (#978) * Sync recent changes to the revised Word. * Revised the preface chapter * Revised the introduction chapter * Revised the computation complexity chapter * Revised the chapter data structure * Revised the chapter array and linked list * Revised the chapter stack and queue * Revised the chapter hashing * Revised the chapter tree * Revised the chapter heap * Revised the chapter graph * Revised the chapter searching * Reivised the sorting chapter * Revised the divide and conquer chapter * Revised the chapter backtacking * Revised the DP chapter * Revised the greedy chapter * Revised the appendix chapter * Revised the preface chapter doubly * Revised the figures
2023-12-02 06:21:34 +08:00
在代码中，我们用 $k$ 来记录未排序区间内的最小元素：
Add the section of selection sort. (#513)
2023-05-24 00:35:46 +08:00
Squash the language code blocks and fix list.md (#865)
2023-10-17 01:06:00 +08:00
```src
[file]{selection_sort}-[class]{}-[func]{selection_sort}
```
Add the section of selection sort. (#513)
2023-05-24 00:35:46 +08:00
## 算法特性
Update punctuation
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- **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 $\frac{(n - 1)(n + 2)}{2}$ 。
- **空间复杂度 $O(1)$、原地排序**：指针 $i$ 和 $j$ 使用常数大小的额外空间。
feat: Revised the book (#978) * Sync recent changes to the revised Word. * Revised the preface chapter * Revised the introduction chapter * Revised the computation complexity chapter * Revised the chapter data structure * Revised the chapter array and linked list * Revised the chapter stack and queue * Revised the chapter hashing * Revised the chapter tree * Revised the chapter heap * Revised the chapter graph * Revised the chapter searching * Reivised the sorting chapter * Revised the divide and conquer chapter * Revised the chapter backtacking * Revised the DP chapter * Revised the greedy chapter * Revised the appendix chapter * Revised the preface chapter doubly * Revised the figures
2023-12-02 06:21:34 +08:00
- **非稳定排序**：如下图所示，元素 `nums[i]` 有可能被交换至与其相等的元素的右边，导致两者的相对顺序发生改变。
Add the section of selection sort. (#513)
2023-05-24 00:35:46 +08:00
Fix the figures of selection sort.
2023-05-24 00:44:55 +08:00
![选择排序非稳定示例](selection_sort.assets/selection_sort_instability.png)
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