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hello-algo/docs/chapter_graph/graph_traversal.md

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Remove the heading numbers in all the source docs.
2023-02-16 03:39:01 +08:00
# 图的遍历
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
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
树代表的是“一对多”的关系，而图则具有更高的自由度，可以表示任意的“多对多”关系。因此，我们可以把树看作图的一种特例。显然，**树的遍历操作也是图的遍历操作的一种特例**。
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
Use underline format for the technical terms (#1213) * Use underline format for the technical terms * Bug fixes
2024-04-03 03:52:17 +08:00
图和树都需要应用搜索算法来实现遍历操作。图的遍历方式也可分为两种：<u>广度优先遍历</u>和<u>深度优先遍历</u>。
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
Remove the heading numbers in all the source docs.
2023-02-16 03:39:01 +08:00
## 广度优先遍历
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
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
**广度优先遍历是一种由近及远的遍历方式，从某个节点出发，始终优先访问距离最近的顶点，并一层层向外扩张**。如下图所示，从左上角顶点出发，首先遍历该顶点的所有邻接顶点，然后遍历下一个顶点的所有邻接顶点，以此类推，直至所有顶点访问完毕。
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
Update the captions of all the figures.
2023-02-26 18:18:34 +08:00
![图的广度优先遍历](graph_traversal.assets/graph_bfs.png)
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
### 算法实现
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
BFS 通常借助队列来实现，代码如下所示。队列具有“先入先出”的性质，这与 BFS 的“由近及远”的思想异曲同工。
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
Unify punctuation.
2023-07-26 08:59:36 +08:00
1. 将遍历起始顶点 `startVet` 加入队列，并开启循环。
2. 在循环的每轮迭代中，弹出队首顶点并记录访问，然后将该顶点的所有邻接顶点加入到队列尾部。
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
3. 循环步骤 `2.` ，直到所有顶点被访问完毕后结束。
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
feat: Add glossary and description for "哈希集合" (#1310)
2024-04-28 22:00:25 +08:00
为了防止重复遍历顶点，我们需要借助一个哈希集合 `visited` 来记录哪些节点已被访问。
!!! tip
哈希集合可以看作一个只存储 `key` 而不存储 `value` 的哈希表，它可以在 $O(1)$ 时间复杂度下进行 `key` 的增删查改操作。根据 `key` 的唯一性，哈希集合通常用于数据去重等场景。
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
Squash the language code blocks and fix list.md (#865)
2023-10-17 01:06:00 +08:00
```src
[file]{graph_bfs}-[class]{}-[func]{graph_bfs}
```
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
Mention figures and tables in normal texts. Fix some figures. Finetune texts.
2023-08-21 19:33:45 +08:00
代码相对抽象，建议对照下图来加深理解。
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
Update the symbols of the animations.
2023-02-22 00:57:43 +08:00
=== "<1>"
Add captions for all the animations.
2023-02-26 19:22:46 +08:00
![图的广度优先遍历步骤](graph_traversal.assets/graph_bfs_step1.png)
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
Update the symbols of the animations.
2023-02-22 00:57:43 +08:00
=== "<2>"
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
![graph_bfs_step2](graph_traversal.assets/graph_bfs_step2.png)
Update the symbols of the animations.
2023-02-22 00:57:43 +08:00
=== "<3>"
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
![graph_bfs_step3](graph_traversal.assets/graph_bfs_step3.png)
Update the symbols of the animations.
2023-02-22 00:57:43 +08:00
=== "<4>"
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
![graph_bfs_step4](graph_traversal.assets/graph_bfs_step4.png)
Update the symbols of the animations.
2023-02-22 00:57:43 +08:00
=== "<5>"
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
![graph_bfs_step5](graph_traversal.assets/graph_bfs_step5.png)
Update the symbols of the animations.
2023-02-22 00:57:43 +08:00
=== "<6>"
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
![graph_bfs_step6](graph_traversal.assets/graph_bfs_step6.png)
Update the symbols of the animations.
2023-02-22 00:57:43 +08:00
=== "<7>"
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
![graph_bfs_step7](graph_traversal.assets/graph_bfs_step7.png)
Update the symbols of the animations.
2023-02-22 00:57:43 +08:00
=== "<8>"
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
![graph_bfs_step8](graph_traversal.assets/graph_bfs_step8.png)
Update the symbols of the animations.
2023-02-22 00:57:43 +08:00
=== "<9>"
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
![graph_bfs_step9](graph_traversal.assets/graph_bfs_step9.png)
Update the symbols of the animations.
2023-02-22 00:57:43 +08:00
=== "<10>"
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
![graph_bfs_step10](graph_traversal.assets/graph_bfs_step10.png)
Update the symbols of the animations.
2023-02-22 00:57:43 +08:00
=== "<11>"
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
![graph_bfs_step11](graph_traversal.assets/graph_bfs_step11.png)
!!! question "广度优先遍历的序列是否唯一？"
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
不唯一。广度优先遍历只要求按“由近及远”的顺序遍历，**而多个相同距离的顶点的遍历顺序允许被任意打乱**。以上图为例，顶点 $1$、$3$ 的访问顺序可以交换，顶点 $2$、$4$、$6$ 的访问顺序也可以任意交换。
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
### 复杂度分析
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
**时间复杂度**：所有顶点都会入队并出队一次，使用 $O(|V|)$ 时间；在遍历邻接顶点的过程中，由于是无向图，因此所有边都会被访问 $2$ 次，使用 $O(2|E|)$ 时间；总体使用 $O(|V| + |E|)$ 时间。
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
feat: Add glossary and description for "哈希集合" (#1310)
2024-04-28 22:00:25 +08:00
**空间复杂度**：列表 `res` ，哈希集合 `visited` ，队列 `que` 中的顶点数量最多为 $|V|$ ，使用 $O(|V|)$ 空间。
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
Remove the heading numbers in all the source docs.
2023-02-16 03:39:01 +08:00
## 深度优先遍历
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
Mention figures and tables in normal texts. Fix some figures. Finetune texts.
2023-08-21 19:33:45 +08:00
**深度优先遍历是一种优先走到底、无路可走再回头的遍历方式**。如下图所示，从左上角顶点出发，访问当前顶点的某个邻接顶点，直到走到尽头时返回，再继续走到尽头并返回，以此类推，直至所有顶点遍历完成。
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
Update the captions of all the figures.
2023-02-26 18:18:34 +08:00
![图的深度优先遍历](graph_traversal.assets/graph_dfs.png)
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
### 算法实现
feat: Add glossary and description for "哈希集合" (#1310)
2024-04-28 22:00:25 +08:00
这种“走到尽头再返回”的算法范式通常基于递归来实现。与广度优先遍历类似，在深度优先遍历中，我们也需要借助一个哈希集合 `visited` 来记录已被访问的顶点，以避免重复访问顶点。
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
Squash the language code blocks and fix list.md (#865)
2023-10-17 01:06:00 +08:00
```src
[file]{graph_dfs}-[class]{}-[func]{graph_dfs}
```
Release Rust code to documents. (#656)
2023-07-26 11:00:53 +08:00
Replace "：" with "。"
2023-08-27 22:49:47 +08:00
深度优先遍历的算法流程如下图所示。
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
Unify punctuation.
2023-07-26 08:59:36 +08:00
- **直虚线代表向下递推**，表示开启了一个新的递归方法来访问新顶点。
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
- **曲虚线代表向上回溯**，表示此递归方法已经返回，回溯到了开启此方法的位置。
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
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
为了加深理解，建议将下图与代码结合起来，在脑中模拟（或者用笔画下来）整个 DFS 过程，包括每个递归方法何时开启、何时返回。
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
Update the symbols of the animations.
2023-02-22 00:57:43 +08:00
=== "<1>"
Add captions for all the animations.
2023-02-26 19:22:46 +08:00
![图的深度优先遍历步骤](graph_traversal.assets/graph_dfs_step1.png)
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
Update the symbols of the animations.
2023-02-22 00:57:43 +08:00
=== "<2>"
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
![graph_dfs_step2](graph_traversal.assets/graph_dfs_step2.png)
Update the symbols of the animations.
2023-02-22 00:57:43 +08:00
=== "<3>"
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
![graph_dfs_step3](graph_traversal.assets/graph_dfs_step3.png)
Update the symbols of the animations.
2023-02-22 00:57:43 +08:00
=== "<4>"
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
![graph_dfs_step4](graph_traversal.assets/graph_dfs_step4.png)
Update the symbols of the animations.
2023-02-22 00:57:43 +08:00
=== "<5>"
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
![graph_dfs_step5](graph_traversal.assets/graph_dfs_step5.png)
Update the symbols of the animations.
2023-02-22 00:57:43 +08:00
=== "<6>"
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
![graph_dfs_step6](graph_traversal.assets/graph_dfs_step6.png)
Update the symbols of the animations.
2023-02-22 00:57:43 +08:00
=== "<7>"
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
![graph_dfs_step7](graph_traversal.assets/graph_dfs_step7.png)
Update the symbols of the animations.
2023-02-22 00:57:43 +08:00
=== "<8>"
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
![graph_dfs_step8](graph_traversal.assets/graph_dfs_step8.png)
Update the symbols of the animations.
2023-02-22 00:57:43 +08:00
=== "<9>"
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
![graph_dfs_step9](graph_traversal.assets/graph_dfs_step9.png)
Update the symbols of the animations.
2023-02-22 00:57:43 +08:00
=== "<10>"
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
![graph_dfs_step10](graph_traversal.assets/graph_dfs_step10.png)
Update the symbols of the animations.
2023-02-22 00:57:43 +08:00
=== "<11>"
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
![graph_dfs_step11](graph_traversal.assets/graph_dfs_step11.png)
!!! question "深度优先遍历的序列是否唯一？"
Polish the chapter of graph, hashing, appendix
2023-04-09 03:09:06 +08:00
与广度优先遍历类似，深度优先遍历序列的顺序也不是唯一的。给定某顶点，先往哪个方向探索都可以，即邻接顶点的顺序可以任意打乱，都是深度优先遍历。
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
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
以树的遍历为例，“根 $\rightarrow$ 左 $\rightarrow$ 右”“左 $\rightarrow$ 根 $\rightarrow$ 右”“左 $\rightarrow$ 右 $\rightarrow$ 根”分别对应前序、中序、后序遍历，它们展示了三种遍历优先级，然而这三者都属于深度优先遍历。
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
### 复杂度分析
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
**时间复杂度**：所有顶点都会被访问 $1$ 次，使用 $O(|V|)$ 时间；所有边都会被访问 $2$ 次，使用 $O(2|E|)$ 时间；总体使用 $O(|V| + |E|)$ 时间。
feat: add the section of Graph Traversal (#367) * Graph dev * Add the section of Graph Traversal. * Add missing Vertex.java * Add mkdocs.yml * Update numbering * Fix indentation and update array.md
2023-02-15 03:34:06 +08:00
feat: Add glossary and description for "哈希集合" (#1310)
2024-04-28 22:00:25 +08:00
**空间复杂度**：列表 `res` ，哈希集合 `visited` 顶点数量最多为 $|V|$ ，递归深度最大为 $|V|$ ，因此使用 $O(|V|)$ 空间。
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