xinyin025/hello-algo
1
0
Fork 0
mirror of https://github.com/krahets/hello-algo.git synced 2026-07-24 03:56:28 +00:00
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
chapter_heap/build_heap/index.html
+258 -235
View File
@@ -25,7 +25,7 @@
<title>8.2.   建堆操作 * - Hello 算法</title>
<title>9.2.   建堆操作 * - Hello 算法</title>
@@ -79,7 +79,7 @@
<div data-md-component="skip">
<a href="#82" class="md-skip">
<a href="#92" 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">
8.2. &nbsp; 建堆操作 *
9.2. &nbsp; 建堆操作 *
</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 +890,108 @@
<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>
<li class="md-nav__item">
<a href="../../chapter_hashing/hash_map/" class="md-nav__link">
7.1. &nbsp; 哈希表
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
7.2. &nbsp; 哈希冲突处理
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_hashing/summary/" class="md-nav__link">
7.3. &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_9" >
<label class="md-nav__link" for="__nav_9" id="__nav_9_label" tabindex="0">
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; 树
</label>
<ul class="md-nav__list" data-md-scrollfix>
@@ -963,7 +1002,7 @@
<li class="md-nav__item">
<a href="../../chapter_tree/binary_tree/" class="md-nav__link">
7.1. &nbsp; 二叉树
8.1. &nbsp; 二叉树
</a>
</li>
@@ -977,7 +1016,7 @@
<li class="md-nav__item">
<a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
7.2. &nbsp; 二叉树遍历
8.2. &nbsp; 二叉树遍历
</a>
</li>
@@ -991,7 +1030,7 @@
<li class="md-nav__item">
<a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
7.3. &nbsp; 二叉搜索树
8.3. &nbsp; 二叉搜索树
</a>
</li>
@@ -1005,7 +1044,7 @@
<li class="md-nav__item">
<a href="../../chapter_tree/avl_tree/" class="md-nav__link">
7.4. &nbsp; AVL 树 *
8.4. &nbsp; AVL 树 *
</a>
</li>
@@ -1019,7 +1058,7 @@
<li class="md-nav__item">
<a href="../../chapter_tree/summary/" class="md-nav__link">
7.5. &nbsp; 小结
8.5. &nbsp; 小结
</a>
</li>
@@ -1049,7 +1088,7 @@
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" checked>
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" checked>
@@ -1061,15 +1100,15 @@
<label class="md-nav__link" for="__nav_9" id="__nav_9_label" tabindex="0">
8. &nbsp; &nbsp; 堆
<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_9_label" aria-expanded="true">
<label class="md-nav__title" for="__nav_9">
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="true">
<label class="md-nav__title" for="__nav_10">
<span class="md-nav__icon md-icon"></span>
8. &nbsp; &nbsp; 堆
9. &nbsp; &nbsp; 堆
</label>
<ul class="md-nav__list" data-md-scrollfix>
@@ -1080,7 +1119,7 @@
<li class="md-nav__item">
<a href="../heap/" class="md-nav__link">
8.1. &nbsp; 堆
9.1. &nbsp; 堆
</a>
</li>
@@ -1103,12 +1142,12 @@
<label class="md-nav__link md-nav__link--active" for="__toc">
8.2. &nbsp; 建堆操作 *
9.2. &nbsp; 建堆操作 *
<span class="md-nav__icon md-icon"></span>
</label>
<a href="./" class="md-nav__link md-nav__link--active">
8.2. &nbsp; 建堆操作 *
9.2. &nbsp; 建堆操作 *
</a>
@@ -1127,11 +1166,11 @@
<ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
<li class="md-nav__item">
<a href="#821" class="md-nav__link">
8.2.1. &nbsp; 两种建堆方法
<a href="#921" class="md-nav__link">
9.2.1. &nbsp; 两种建堆方法
</a>
<nav class="md-nav" aria-label="8.2.1. &nbsp; 两种建堆方法">
<nav class="md-nav" aria-label="9.2.1. &nbsp; 两种建堆方法">
<ul class="md-nav__list">
<li class="md-nav__item">
@@ -1154,8 +1193,8 @@
</li>
<li class="md-nav__item">
<a href="#822" class="md-nav__link">
8.2.2. &nbsp; 复杂度分析
<a href="#922" class="md-nav__link">
9.2.2. &nbsp; 复杂度分析
</a>
</li>
@@ -1176,110 +1215,7 @@
<li class="md-nav__item">
<a href="../summary/" class="md-nav__link">
8.3. &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; 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="false">
<label class="md-nav__title" for="__nav_10">
<span class="md-nav__icon md-icon"></span>
9. &nbsp; &nbsp; 图
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../../chapter_graph/graph/" class="md-nav__link">
9.1. &nbsp; 图
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_graph/graph_operations/" class="md-nav__link">
9.2. &nbsp; 图基础操作
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
9.3. &nbsp; 图的遍历
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter_graph/summary/" class="md-nav__link">
9.4. &nbsp; 小结
9.3. &nbsp; 小结
</a>
</li>
@@ -1322,14 +1258,14 @@
<label class="md-nav__link" for="__nav_11" id="__nav_11_label" tabindex="0">
10. &nbsp; &nbsp; 查找算法
10. &nbsp; &nbsp; 图
<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
10. &nbsp; &nbsp; 图
</label>
<ul class="md-nav__list" data-md-scrollfix>
@@ -1339,8 +1275,8 @@
<li class="md-nav__item">
<a href="../../chapter_searching/linear_search/" class="md-nav__link">
10.1. &nbsp; 线性查找
<a href="../../chapter_graph/graph/" class="md-nav__link">
10.1. &nbsp; 图
</a>
</li>
@@ -1353,8 +1289,8 @@
<li class="md-nav__item">
<a href="../../chapter_searching/binary_search/" class="md-nav__link">
10.2. &nbsp; 二分查找
<a href="../../chapter_graph/graph_operations/" class="md-nav__link">
10.2. &nbsp; 图基础操作
</a>
</li>
@@ -1367,8 +1303,8 @@
<li class="md-nav__item">
<a href="../../chapter_searching/hashing_search/" class="md-nav__link">
10.3. &nbsp; 哈希查找
<a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
10.3. &nbsp; 图的遍历
</a>
</li>
@@ -1381,7 +1317,7 @@
<li class="md-nav__item">
<a href="../../chapter_searching/summary/" class="md-nav__link">
<a href="../../chapter_graph/summary/" class="md-nav__link">
10.4. &nbsp; 小结
</a>
</li>
@@ -1523,7 +1459,7 @@
<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>
@@ -1537,7 +1473,7 @@
<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>
@@ -1551,7 +1487,7 @@
<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>
@@ -1599,17 +1535,21 @@
<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>
@@ -1619,8 +1559,36 @@
<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>
@@ -1654,19 +1622,17 @@
<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>
@@ -1676,22 +1642,8 @@
<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>
@@ -1724,6 +1676,77 @@
<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" >
@@ -1736,8 +1759,8 @@
</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>
@@ -1778,11 +1801,11 @@
<ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
<li class="md-nav__item">
<a href="#821" class="md-nav__link">
8.2.1. &nbsp; 两种建堆方法
<a href="#921" class="md-nav__link">
9.2.1. &nbsp; 两种建堆方法
</a>
<nav class="md-nav" aria-label="8.2.1. &nbsp; 两种建堆方法">
<nav class="md-nav" aria-label="9.2.1. &nbsp; 两种建堆方法">
<ul class="md-nav__list">
<li class="md-nav__item">
@@ -1805,8 +1828,8 @@
</li>
<li class="md-nav__item">
<a href="#822" class="md-nav__link">
8.2.2. &nbsp; 复杂度分析
<a href="#922" class="md-nav__link">
9.2.2. &nbsp; 复杂度分析
</a>
</li>
@@ -1834,9 +1857,9 @@
<h1 id="82">8.2. &nbsp; 建堆操作 *<a class="headerlink" href="#82" title="Permanent link">&para;</a></h1>
<h1 id="92">9.2. &nbsp; 建堆操作 *<a class="headerlink" href="#92" title="Permanent link">&para;</a></h1>
<p>如果我们想要根据输入列表生成一个堆，这个过程被称为「建堆」。</p>
<h2 id="821">8.2.1. &nbsp; 两种建堆方法<a class="headerlink" href="#821" title="Permanent link">&para;</a></h2>
<h2 id="921">9.2.1. &nbsp; 两种建堆方法<a class="headerlink" href="#921" title="Permanent link">&para;</a></h2>
<h3 id="_1">借助入堆方法实现<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h3>
<p>最直接的方法是借助“元素入堆操作”实现，首先创建一个空堆，然后将列表元素依次添加到堆中。</p>
<p>设元素数量为 <span class="arithmatex">\(n\)</span> ，则最后一个元素入堆的时间复杂度为 <span class="arithmatex">\(O(\log n)\)</span> 。在依次添加元素时，堆的平均长度为 <span class="arithmatex">\(\frac{n}{2}\)</span> ，因此该方法的总体时间复杂度为 <span class="arithmatex">\(O(n \log n)\)</span> 。</p>
@@ -1963,7 +1986,7 @@
</div>
</div>
</div>
<h2 id="822">8.2.2. &nbsp; 复杂度分析<a class="headerlink" href="#822" title="Permanent link">&para;</a></h2>
<h2 id="922">9.2.2. &nbsp; 复杂度分析<a class="headerlink" href="#922" title="Permanent link">&para;</a></h2>
<p>为什么第二种建堆方法的时间复杂度是 <span class="arithmatex">\(O(n)\)</span> ？我们来展开推算一下。</p>
<ul>
<li>完全二叉树中，设节点总数为 <span class="arithmatex">\(n\)</span> ，则叶节点数量为 <span class="arithmatex">\((n + 1) / 2\)</span> ，其中 <span class="arithmatex">\(/\)</span> 为向下整除。因此，在排除叶节点后，需要堆化的节点数量为 <span class="arithmatex">\((n - 1)/2\)</span> ，复杂度为 <span class="arithmatex">\(O(n)\)</span> ；</li>
@@ -2075,7 +2098,7 @@ T(h) &amp; = 2 \frac{1 - 2^h}{1 - 2} - h \newline
<nav class="md-footer__inner md-grid" aria-label="页脚" >
<a href="../heap/" class="md-footer__link md-footer__link--prev" aria-label="上一页: 8.1. &amp;nbsp; 堆" rel="prev">
<a href="../heap/" class="md-footer__link md-footer__link--prev" aria-label="上一页: 9.1. &amp;nbsp; 堆" 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>
@@ -2084,20 +2107,20 @@ T(h) &amp; = 2 \frac{1 - 2^h}{1 - 2} - h \newline
上一页
</span>
<div class="md-ellipsis">
8.1. &nbsp; 堆
9.1. &nbsp; 堆
</div>
</div>
</a>
<a href="../summary/" class="md-footer__link md-footer__link--next" aria-label="下一页: 8.3. &amp;nbsp; 小结" rel="next">
<a href="../summary/" class="md-footer__link md-footer__link--next" aria-label="下一页: 9.3. &amp;nbsp; 小结" rel="next">
<div class="md-footer__title">
<span class="md-footer__direction">
下一页
</span>
<div class="md-ellipsis">
8.3. &nbsp; 小结
9.3. &nbsp; 小结
</div>
</div>
<div class="md-footer__button md-icon">