CS_learn/hello-algo
1
0
Fork 0
mirror of https://github.com/krahets/hello-algo.git synced 2026-04-02 02:02:57 +08:00
Code Issues Packages Projects Releases Wiki Activity

deploy

Browse Source
This commit is contained in:
krahets
2023-04-17 18:24:27 +08:00
parent f76b7ed47c
commit ca2ccfea0b
70 changed files with 12269 additions and 13539 deletions
Download Patch File Download Diff File Expand all files Collapse all files

549
chapter_graph/graph_operations/index.html
View File

@@ -25,7 +25,7 @@
<title>9.2.   图基础操作 - Hello 算法</title>
<title>10.2.   图基础操作 - Hello 算法</title>
@@ -79,7 +79,7 @@
<div data-md-component="skip">
<a href="#92" class="md-skip">
<a href="#102" class="md-skip">
跳转至
</a>
@@ -113,7 +113,7 @@
<div class="md-header__topic" data-md-component="header-topic">
<span class="md-ellipsis">
9.2. &nbsp; 图基础操作
10.2. &nbsp; 图基础操作
</span>
</div>
@@ -441,8 +441,6 @@
<label class="md-nav__link" for="__nav_3" id="__nav_3_label" tabindex="0">
@@ -504,23 +502,9 @@
<li class="md-nav__item">
<a href="../../chapter_computational_complexity/space_time_tradeoff/" class="md-nav__link">
2.4. &nbsp; 权衡时间与空间
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
2.5. &nbsp; 小结
2.4. &nbsp; 小结
</a>
</li>
@@ -847,21 +831,17 @@
<label class="md-nav__link" for="__nav_7" id="__nav_7_label" tabindex="0">
6. &nbsp; &nbsp; 散列表
6. &nbsp; &nbsp; 二分查找
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_7">
<span class="md-nav__icon md-icon"></span>
6. &nbsp; &nbsp; 散列表
6. &nbsp; &nbsp; 二分查找
</label>
<ul class="md-nav__list" data-md-scrollfix>
@@ -871,36 +851,8 @@
<li class="md-nav__item">
<a href="../../chapter_hashing/hash_map/" class="md-nav__link">
6.1. &nbsp; 哈希表
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
6.2. &nbsp; 哈希冲突处理
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_hashing/summary/" class="md-nav__link">
6.3. &nbsp; 小结
<a href="../../chapter_binary_search/binary_search/" class="md-nav__link">
6.1. &nbsp; 二分查找
</a>
</li>
@@ -938,21 +890,17 @@
<label class="md-nav__link" for="__nav_8" id="__nav_8_label" tabindex="0">
7. &nbsp; &nbsp; 树
7. &nbsp; &nbsp; 散列表
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_8">
<span class="md-nav__icon md-icon"></span>
7. &nbsp; &nbsp; 树
7. &nbsp; &nbsp; 散列表
</label>
<ul class="md-nav__list" data-md-scrollfix>
@@ -962,8 +910,8 @@
<li class="md-nav__item">
<a href="../../chapter_tree/binary_tree/" class="md-nav__link">
7.1. &nbsp; 二叉树
<a href="../../chapter_hashing/hash_map/" class="md-nav__link">
7.1. &nbsp; 哈希表
</a>
</li>
@@ -976,8 +924,8 @@
<li class="md-nav__item">
<a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
7.2. &nbsp; 二叉树遍历
<a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
7.2. &nbsp; 哈希冲突处理
</a>
</li>
@@ -990,36 +938,8 @@
<li class="md-nav__item">
<a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
7.3. &nbsp; 二叉搜索树
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_tree/avl_tree/" class="md-nav__link">
7.4. &nbsp; AVL 树 *
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_tree/summary/" class="md-nav__link">
7.5. &nbsp; 小结
<a href="../../chapter_hashing/summary/" class="md-nav__link">
7.3. &nbsp; 小结
</a>
</li>
@@ -1057,17 +977,136 @@
<label class="md-nav__link" for="__nav_9" id="__nav_9_label" tabindex="0">
8. &nbsp; &nbsp; 堆
8. &nbsp; &nbsp; 树
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_9">
<span class="md-nav__icon md-icon"></span>
8. &nbsp; &nbsp; 堆
8. &nbsp; &nbsp; 树
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../../chapter_tree/binary_tree/" class="md-nav__link">
8.1. &nbsp; 二叉树
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
8.2. &nbsp; 二叉树遍历
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
8.3. &nbsp; 二叉搜索树
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_tree/avl_tree/" class="md-nav__link">
8.4. &nbsp; AVL 树 *
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_tree/summary/" class="md-nav__link">
8.5. &nbsp; 小结
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--section md-nav__item--nested">
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
<label class="md-nav__link" for="__nav_10" id="__nav_10_label" tabindex="0">
9. &nbsp; &nbsp; 堆
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_10">
<span class="md-nav__icon md-icon"></span>
9. &nbsp; &nbsp; 堆
</label>
<ul class="md-nav__list" data-md-scrollfix>
@@ -1078,7 +1117,7 @@
<li class="md-nav__item">
<a href="../../chapter_heap/heap/" class="md-nav__link">
8.1. &nbsp; 堆
9.1. &nbsp; 堆
</a>
</li>
@@ -1092,7 +1131,7 @@
<li class="md-nav__item">
<a href="../../chapter_heap/build_heap/" class="md-nav__link">
8.2. &nbsp; 建堆操作 *
9.2. &nbsp; 建堆操作 *
</a>
</li>
@@ -1106,7 +1145,7 @@
<li class="md-nav__item">
<a href="../../chapter_heap/summary/" class="md-nav__link">
8.3. &nbsp; 小结
9.3. &nbsp; 小结
</a>
</li>
@@ -1136,7 +1175,7 @@
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" checked>
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" checked>
@@ -1150,15 +1189,15 @@
<label class="md-nav__link" for="__nav_10" id="__nav_10_label" tabindex="0">
9. &nbsp; &nbsp; 图
<label class="md-nav__link" for="__nav_11" id="__nav_11_label" tabindex="0">
10. &nbsp; &nbsp; 图
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="true">
<label class="md-nav__title" for="__nav_10">
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="true">
<label class="md-nav__title" for="__nav_11">
<span class="md-nav__icon md-icon"></span>
9. &nbsp; &nbsp; 图
10. &nbsp; &nbsp; 图
</label>
<ul class="md-nav__list" data-md-scrollfix>
@@ -1169,7 +1208,7 @@
<li class="md-nav__item">
<a href="../graph/" class="md-nav__link">
9.1. &nbsp; 图
10.1. &nbsp; 图
</a>
</li>
@@ -1192,12 +1231,12 @@
<label class="md-nav__link md-nav__link--active" for="__toc">
9.2. &nbsp; 图基础操作
10.2. &nbsp; 图基础操作
<span class="md-nav__icon md-icon"></span>
</label>
<a href="./" class="md-nav__link md-nav__link--active">
9.2. &nbsp; 图基础操作
10.2. &nbsp; 图基础操作
</a>
@@ -1216,22 +1255,22 @@
<ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
<li class="md-nav__item">
<a href="#921" class="md-nav__link">
9.2.1. &nbsp; 基于邻接矩阵的实现
<a href="#1021" class="md-nav__link">
10.2.1. &nbsp; 基于邻接矩阵的实现
</a>
</li>
<li class="md-nav__item">
<a href="#922" class="md-nav__link">
9.2.2. &nbsp; 基于邻接表的实现
<a href="#1022" class="md-nav__link">
10.2.2. &nbsp; 基于邻接表的实现
</a>
</li>
<li class="md-nav__item">
<a href="#923" class="md-nav__link">
9.2.3. &nbsp; 效率对比
<a href="#1023" class="md-nav__link">
10.2.3. &nbsp; 效率对比
</a>
</li>
@@ -1252,7 +1291,7 @@
<li class="md-nav__item">
<a href="../graph_traversal/" class="md-nav__link">
9.3. &nbsp; 图的遍历
10.3. &nbsp; 图的遍历
</a>
</li>
@@ -1266,109 +1305,6 @@
<li class="md-nav__item">
<a href="../summary/" class="md-nav__link">
9.4. &nbsp; 小结
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--section md-nav__item--nested">
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
<label class="md-nav__link" for="__nav_11" id="__nav_11_label" tabindex="0">
10. &nbsp; &nbsp; 查找算法
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_11">
<span class="md-nav__icon md-icon"></span>
10. &nbsp; &nbsp; 查找算法
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../../chapter_searching/linear_search/" class="md-nav__link">
10.1. &nbsp; 线性查找
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_searching/binary_search/" class="md-nav__link">
10.2. &nbsp; 二分查找
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_searching/hashing_search/" class="md-nav__link">
10.3. &nbsp; 哈希查找
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_searching/summary/" class="md-nav__link">
10.4. &nbsp; 小结
</a>
</li>
@@ -1510,7 +1446,7 @@
<li class="md-nav__item">
<a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
11.6. &nbsp; 桶排序（New）
11.6. &nbsp; 桶排序
</a>
</li>
@@ -1524,7 +1460,7 @@
<li class="md-nav__item">
<a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
11.7. &nbsp; 计数排序（New）
11.7. &nbsp; 计数排序
</a>
</li>
@@ -1538,7 +1474,7 @@
<li class="md-nav__item">
<a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
11.8. &nbsp; 基数排序（New）
11.8. &nbsp; 基数排序
</a>
</li>
@@ -1586,17 +1522,21 @@
<label class="md-nav__link" for="__nav_13" id="__nav_13_label" tabindex="0">
12. &nbsp; &nbsp; 回溯算法
12. &nbsp; &nbsp; 搜索算法
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_13">
<span class="md-nav__icon md-icon"></span>
12. &nbsp; &nbsp; 回溯算法
12. &nbsp; &nbsp; 搜索算法
</label>
<ul class="md-nav__list" data-md-scrollfix>
@@ -1606,8 +1546,36 @@
<li class="md-nav__item">
<a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
12.1. &nbsp; 回溯算法（New）
<a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
12.1. &nbsp; 搜索算法（New）
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
12.2. &nbsp; 哈希优化策略
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_searching/summary/" class="md-nav__link">
12.3. &nbsp; 小结
</a>
</li>
@@ -1641,19 +1609,17 @@
<label class="md-nav__link" for="__nav_14" id="__nav_14_label" tabindex="0">
13. &nbsp; &nbsp; 附录
13. &nbsp; &nbsp; 回溯算法
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_14">
<span class="md-nav__icon md-icon"></span>
13. &nbsp; &nbsp; 附录
13. &nbsp; &nbsp; 回溯算法
</label>
<ul class="md-nav__list" data-md-scrollfix>
@@ -1663,22 +1629,8 @@
<li class="md-nav__item">
<a href="../../chapter_appendix/installation/" class="md-nav__link">
13.1. &nbsp; 编程环境安装
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_appendix/contribution/" class="md-nav__link">
13.2. &nbsp; 一起参与创作
<a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
13.1. &nbsp; 回溯算法（New）
</a>
</li>
@@ -1711,6 +1663,77 @@
<label class="md-nav__link" for="__nav_15" id="__nav_15_label" tabindex="0">
14. &nbsp; &nbsp; 附录
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_15">
<span class="md-nav__icon md-icon"></span>
14. &nbsp; &nbsp; 附录
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../../chapter_appendix/installation/" class="md-nav__link">
14.1. &nbsp; 编程环境安装
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_appendix/contribution/" class="md-nav__link">
14.2. &nbsp; 一起参与创作
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--section md-nav__item--nested">
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
@@ -1723,8 +1746,8 @@
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_15">
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_16">
<span class="md-nav__icon md-icon"></span>
参考文献
</label>
@@ -1765,22 +1788,22 @@
<ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
<li class="md-nav__item">
<a href="#921" class="md-nav__link">
9.2.1. &nbsp; 基于邻接矩阵的实现
<a href="#1021" class="md-nav__link">
10.2.1. &nbsp; 基于邻接矩阵的实现
</a>
</li>
<li class="md-nav__item">
<a href="#922" class="md-nav__link">
9.2.2. &nbsp; 基于邻接表的实现
<a href="#1022" class="md-nav__link">
10.2.2. &nbsp; 基于邻接表的实现
</a>
</li>
<li class="md-nav__item">
<a href="#923" class="md-nav__link">
9.2.3. &nbsp; 效率对比
<a href="#1023" class="md-nav__link">
10.2.3. &nbsp; 效率对比
</a>
</li>
@@ -1808,9 +1831,9 @@
<h1 id="92">9.2. &nbsp; 图基础操作<a class="headerlink" href="#92" title="Permanent link">&para;</a></h1>
<h1 id="102">10.2. &nbsp; 图基础操作<a class="headerlink" href="#102" title="Permanent link">&para;</a></h1>
<p>图的基础操作可分为对「边」的操作和对「顶点」的操作。在「邻接矩阵」和「邻接表」两种表示方法下，实现方式有所不同。</p>
<h2 id="921">9.2.1. &nbsp; 基于邻接矩阵的实现<a class="headerlink" href="#921" title="Permanent link">&para;</a></h2>
<h2 id="1021">10.2.1. &nbsp; 基于邻接矩阵的实现<a class="headerlink" href="#1021" title="Permanent link">&para;</a></h2>
<p>给定一个顶点数量为 <span class="arithmatex">\(n\)</span> 的无向图，则有：</p>
<ul>
<li><strong>添加或删除边</strong>：直接在邻接矩阵中修改指定的边即可，使用 <span class="arithmatex">\(O(1)\)</span> 时间。而由于是无向图，因此需要同时更新两个方向的边。</li>
@@ -2565,7 +2588,7 @@
</div>
</div>
</div>
<h2 id="922">9.2.2. &nbsp; 基于邻接表的实现<a class="headerlink" href="#922" title="Permanent link">&para;</a></h2>
<h2 id="1022">10.2.2. &nbsp; 基于邻接表的实现<a class="headerlink" href="#1022" title="Permanent link">&para;</a></h2>
<p>设无向图的顶点总数为 <span class="arithmatex">\(n\)</span> 、边总数为 <span class="arithmatex">\(m\)</span> ，则有：</p>
<ul>
<li><strong>添加边</strong>：在顶点对应链表的末尾添加边即可，使用 <span class="arithmatex">\(O(1)\)</span> 时间。因为是无向图，所以需要同时添加两个方向的边。</li>
@@ -3236,7 +3259,7 @@
</div>
</div>
</div>
<h2 id="923">9.2.3. &nbsp; 效率对比<a class="headerlink" href="#923" title="Permanent link">&para;</a></h2>
<h2 id="1023">10.2.3. &nbsp; 效率对比<a class="headerlink" href="#1023" title="Permanent link">&para;</a></h2>
<p>设图中共有 <span class="arithmatex">\(n\)</span> 个顶点和 <span class="arithmatex">\(m\)</span> 条边，下表为邻接矩阵和邻接表的时间和空间效率对比。</p>
<div class="center-table">
<table>
@@ -3366,7 +3389,7 @@
<nav class="md-footer__inner md-grid" aria-label="页脚" >
<a href="../graph/" class="md-footer__link md-footer__link--prev" aria-label="上一页: 9.1. &amp;nbsp; 图" rel="prev">
<a href="../graph/" class="md-footer__link md-footer__link--prev" aria-label="上一页: 10.1. &amp;nbsp; 图" rel="prev">
<div class="md-footer__button md-icon">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11h12Z"/></svg>
</div>
@@ -3375,20 +3398,20 @@
上一页
</span>
<div class="md-ellipsis">
9.1. &nbsp; 图
10.1. &nbsp; 图
</div>
</div>
</a>
<a href="../graph_traversal/" class="md-footer__link md-footer__link--next" aria-label="下一页: 9.3. &amp;nbsp; 图的遍历" rel="next">
<a href="../graph_traversal/" class="md-footer__link md-footer__link--next" aria-label="下一页: 10.3. &amp;nbsp; 图的遍历" rel="next">
<div class="md-footer__title">
<span class="md-footer__direction">
下一页
</span>
<div class="md-ellipsis">
9.3. &nbsp; 图的遍历
10.3. &nbsp; 图的遍历
</div>
</div>
<div class="md-footer__button md-icon">