CS_learn/hello-algo
1
0
Fork 0
mirror of https://github.com/krahets/hello-algo.git synced 2026-04-05 03:30:30 +08:00
Code Issues Packages Projects Releases Wiki Activity

deploy

Browse Source
This commit is contained in:
krahets
2024-04-03 04:41:32 +08:00
parent f95548a8c4
commit f680a185b5
168 changed files with 18077 additions and 8236 deletions
Download Patch File Download Diff File Expand all files Collapse all files

239
chapter_tree/binary_tree/index.html
View File

@@ -334,6 +334,63 @@
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_1" >
<div class="md-nav__link md-nav__container">
<a href="../../chapter_hello_algo/" class="md-nav__link ">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m13.13 22.19-1.63-3.83c1.57-.58 3.04-1.36 4.4-2.27l-2.77 6.1M5.64 12.5l-3.83-1.63 6.1-2.77C7 9.46 6.22 10.93 5.64 12.5M19.22 4c.28 0 .53 0 .74.05.17 1.39-.02 4.25-3.3 7.53-1.7 1.71-3.73 3.02-6.01 3.89l-2.15-2.1c.92-2.31 2.23-4.34 3.92-6.03C15.18 4.58 17.64 4 19.22 4m0-2c-1.98 0-4.98.69-8.22 3.93-2.19 2.19-3.5 4.6-4.35 6.71-.28.75-.09 1.57.46 2.13l2.13 2.12c.38.38.89.61 1.42.61.23 0 .47-.06.7-.15A19.1 19.1 0 0 0 18.07 13c5.66-5.66 3.54-10.61 3.54-10.61S20.7 2 19.22 2m-4.68 7.46c-.78-.78-.78-2.05 0-2.83s2.05-.78 2.83 0c.77.78.78 2.05 0 2.83-.78.78-2.05.78-2.83 0m-5.66 7.07-1.41-1.41 1.41 1.41M6.24 22l3.64-3.64c-.34-.09-.67-.24-.97-.45L4.83 22h1.41M2 22h1.41l4.77-4.76-1.42-1.41L2 20.59V22m0-2.83 4.09-4.08c-.21-.3-.36-.62-.45-.97L2 17.76v1.41Z"/></svg>
<span class="md-ellipsis">
序
</span>
</a>
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_1_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_1">
<span class="md-nav__icon md-icon"></span>
序
</label>
<ul class="md-nav__list" data-md-scrollfix>
</ul>
</nav>
</li>
@@ -349,7 +406,7 @@
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_1" >
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_2" >
@@ -367,14 +424,14 @@
</a>
<label class="md-nav__link " for="__nav_1" id="__nav_1_label" tabindex="0">
<label class="md-nav__link " for="__nav_2" id="__nav_2_label" tabindex="0">
<span class="md-nav__icon md-icon"></span>
</label>
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_1_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_1">
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_2_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_2">
<span class="md-nav__icon md-icon"></span>
第 0 章 &nbsp; 前言
</label>
@@ -480,7 +537,7 @@
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_2" >
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
@@ -498,14 +555,14 @@
</a>
<label class="md-nav__link " for="__nav_2" id="__nav_2_label" tabindex="0">
<label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
<span class="md-nav__icon md-icon"></span>
</label>
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_2_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_2">
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_3">
<span class="md-nav__icon md-icon"></span>
第 1 章 &nbsp; 初识算法
</label>
@@ -615,7 +672,7 @@
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
@@ -633,14 +690,14 @@
</a>
<label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
<label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
<span class="md-nav__icon md-icon"></span>
</label>
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_3">
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_4">
<span class="md-nav__icon md-icon"></span>
第 2 章 &nbsp; 复杂度分析
</label>
@@ -792,7 +849,7 @@
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
@@ -810,14 +867,14 @@
</a>
<label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
<label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
<span class="md-nav__icon md-icon"></span>
</label>
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_4">
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_5">
<span class="md-nav__icon md-icon"></span>
第 3 章 &nbsp; 数据结构
</label>
@@ -969,7 +1026,7 @@
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
@@ -987,14 +1044,14 @@
</a>
<label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
<label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
<span class="md-nav__icon md-icon"></span>
</label>
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_5">
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_6">
<span class="md-nav__icon md-icon"></span>
第 4 章 &nbsp; 数组与链表
</label>
@@ -1152,7 +1209,7 @@
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
@@ -1170,14 +1227,14 @@
</a>
<label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
<label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
<span class="md-nav__icon md-icon"></span>
</label>
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_6">
<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>
第 5 章 &nbsp; 栈与队列
</label>
@@ -1306,7 +1363,7 @@
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
@@ -1324,14 +1381,14 @@
</a>
<label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
<label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
<span class="md-nav__icon md-icon"></span>
</label>
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_7">
<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>
第 6 章 &nbsp; 哈希表
</label>
@@ -1466,7 +1523,7 @@
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" checked>
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" checked>
@@ -1484,14 +1541,14 @@
</a>
<label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
<label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
<span class="md-nav__icon md-icon"></span>
</label>
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="true">
<label class="md-nav__title" for="__nav_8">
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="true">
<label class="md-nav__title" for="__nav_9">
<span class="md-nav__icon md-icon"></span>
第 7 章 &nbsp; 树
</label>
@@ -1804,7 +1861,7 @@
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
@@ -1822,14 +1879,14 @@
</a>
<label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
<label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
<span class="md-nav__icon md-icon"></span>
</label>
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_9">
<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>
第 8 章 &nbsp; 堆
</label>
@@ -1958,7 +2015,7 @@
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
@@ -1976,14 +2033,14 @@
</a>
<label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
<label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
<span class="md-nav__icon md-icon"></span>
</label>
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_10">
<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>
第 9 章 &nbsp; 图
</label>
@@ -2116,7 +2173,7 @@
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
@@ -2134,14 +2191,14 @@
</a>
<label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
<label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
<span class="md-nav__icon md-icon"></span>
</label>
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_11">
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_12">
<span class="md-nav__icon md-icon"></span>
第 10 章 &nbsp; 搜索
</label>
@@ -2326,7 +2383,7 @@
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
@@ -2344,14 +2401,14 @@
</a>
<label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
<label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
<span class="md-nav__icon md-icon"></span>
</label>
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_12">
<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>
第 11 章 &nbsp; 排序
</label>
@@ -2629,7 +2686,7 @@
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
@@ -2647,14 +2704,14 @@
</a>
<label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
<label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
<span class="md-nav__icon md-icon"></span>
</label>
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_13">
<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>
第 12 章 &nbsp; 分治
</label>
@@ -2806,7 +2863,7 @@
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
@@ -2824,14 +2881,14 @@
</a>
<label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
<label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
<span class="md-nav__icon md-icon"></span>
</label>
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_14">
<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>
第 13 章 &nbsp; 回溯
</label>
@@ -2987,7 +3044,7 @@
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
@@ -3005,14 +3062,14 @@
</a>
<label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
<label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
<span class="md-nav__icon md-icon"></span>
</label>
</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>
第 14 章 &nbsp; 动态规划
</label>
@@ -3206,7 +3263,7 @@
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
@@ -3224,14 +3281,14 @@
</a>
<label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
<label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
<span class="md-nav__icon md-icon"></span>
</label>
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_16">
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_17">
<span class="md-nav__icon md-icon"></span>
第 15 章 &nbsp; 贪心
</label>
@@ -3379,7 +3436,7 @@
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
@@ -3397,14 +3454,14 @@
</a>
<label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
<label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
<span class="md-nav__icon md-icon"></span>
</label>
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_17">
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_18">
<span class="md-nav__icon md-icon"></span>
第 16 章 &nbsp; 附录
</label>
@@ -3504,7 +3561,7 @@
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_19" >
@@ -3523,8 +3580,8 @@
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_18">
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_19">
<span class="md-nav__icon md-icon"></span>
参考文献
</label>
@@ -3561,7 +3618,7 @@
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_19" >
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_20" >
@@ -3569,7 +3626,7 @@
<a href="../../chapter_paperbook/" class="md-nav__link ">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M96 0C43 0 0 43 0 96v320c0 53 43 96 96 96h320c17.7 0 32-14.3 32-32s-14.3-32-32-32v-64c17.7 0 32-14.3 32-32V32c0-17.7-14.3-32-32-32H96zm0 384h256v64H96c-17.7 0-32-14.3-32-32s14.3-32 32-32zm32-240c0-8.8 7.2-16 16-16h192c8.8 0 16 7.2 16 16s-7.2 16-16 16H144c-8.8 0-16-7.2-16-16zm16 48h192c8.8 0 16 7.2 16 16s-7.2 16-16 16H144c-8.8 0-16-7.2-16-16s7.2-16 16-16z"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19 2-5 4.5v11l5-4.5V2M6.5 5C4.55 5 2.45 5.4 1 6.5v14.66c0 .25.25.5.5.5.1 0 .15-.07.25-.07 1.35-.65 3.3-1.09 4.75-1.09 1.95 0 4.05.4 5.5 1.5 1.35-.85 3.8-1.5 5.5-1.5 1.65 0 3.35.31 4.75 1.06.1.05.15.03.25.03.25 0 .5-.25.5-.5V6.5c-.6-.45-1.25-.75-2-1V19c-1.1-.35-2.3-.5-3.5-.5-1.7 0-4.15.65-5.5 1.5V6.5C10.55 5.4 8.45 5 6.5 5Z"/></svg>
<span class="md-ellipsis">
纸质书
@@ -3588,8 +3645,8 @@
</div>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_19">
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_20_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_20">
<span class="md-nav__icon md-icon"></span>
纸质书
</label>
@@ -3769,7 +3826,7 @@
<!-- Page content -->
<h1 id="71">7.1 &nbsp; 二叉树<a class="headerlink" href="#71" title="Permanent link">&para;</a></h1>
<p>「二叉树 binary tree」是一种非线性数据结构，代表“祖先”与“后代”之间的派生关系，体现了“一分为二”的分治逻辑。与链表类似，二叉树的基本单元是节点，每个节点包含值、左子节点引用和右子节点引用。</p>
<p><u>二叉树（binary tree）</u>是一种非线性数据结构，代表“祖先”与“后代”之间的派生关系，体现了“一分为二”的分治逻辑。与链表类似，二叉树的基本单元是节点，每个节点包含值、左子节点引用和右子节点引用。</p>
<div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
<div class="tabbed-content">
<div class="tabbed-block">
@@ -3942,7 +3999,7 @@
</div>
</div>
</div>
<p>每个节点都有两个引用（指针），分别指向「左子节点 left-child node」和「右子节点 right-child node」，该节点被称为这两个子节点的「父节点 parent node」。当给定一个二叉树的节点时，我们将该节点的左子节点及其以下节点形成的树称为该节点的「左子树 left subtree」，同理可得「右子树 right subtree」。</p>
<p>每个节点都有两个引用（指针），分别指向<u>左子节点（left-child node）</u>和<u>右子节点（right-child node）</u>，该节点被称为这两个子节点的<u>父节点（parent node）</u>。当给定一个二叉树的节点时，我们将该节点的左子节点及其以下节点形成的树称为该节点的<u>左子树（left subtree）</u>，同理可得<u>右子树（right subtree）</u>。</p>
<p><strong>在二叉树中，除叶节点外，其他所有节点都包含子节点和非空子树</strong>。如图 7-1 所示，如果将“节点 2”视为父节点，则其左子节点和右子节点分别是“节点 4”和“节点 5”，左子树是“节点 4 及其以下节点形成的树”，右子树是“节点 5 及其以下节点形成的树”。</p>
<p><a class="glightbox" href="../binary_tree.assets/binary_tree_definition.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="父节点、子节点、子树" class="animation-figure" src="../binary_tree.assets/binary_tree_definition.png" /></a></p>
<p align="center"> 图 7-1 &nbsp; 父节点、子节点、子树 </p>
@@ -3950,14 +4007,14 @@
<h2 id="711">7.1.1 &nbsp; 二叉树常见术语<a class="headerlink" href="#711" title="Permanent link">&para;</a></h2>
<p>二叉树的常用术语如图 7-2 所示。</p>
<ul>
<li>「根节点 root node」：位于二叉树顶层的节点，没有父节点。</li>
<li>「叶节点 leaf node」：没有子节点的节点，其两个指针均指向 <code>None</code> 。</li>
<li>「边 edge」：连接两个节点的线段，即节点引用（指针）。</li>
<li>节点所在的「层 level」：从顶至底递增，根节点所在层为 1 。</li>
<li>节点的「度 degree」：节点的子节点的数量。在二叉树中，度的取值范围是 0、1、2 。</li>
<li>二叉树的「高度 height」：从根节点到最远叶节点所经过的边的数量。</li>
<li>节点的「深度 depth」：从根节点到该节点所经过的边的数量。</li>
<li>节点的「高度 height」：从距离该节点最远的叶节点到该节点所经过的边的数量。</li>
<li><u>根节点（root node）</u>：位于二叉树顶层的节点，没有父节点。</li>
<li><u>叶节点（leaf node）</u>：没有子节点的节点，其两个指针均指向 <code>None</code> 。</li>
<li><u>边（edge）</u>：连接两个节点的线段，即节点引用（指针）。</li>
<li>节点所在的<u>层（level）</u>：从顶至底递增，根节点所在层为 1 。</li>
<li>节点的<u>度（degree）</u>：节点的子节点的数量。在二叉树中，度的取值范围是 0、1、2 。</li>
<li>二叉树的<u>高度（height）</u>：从根节点到最远叶节点所经过的边的数量。</li>
<li>节点的<u>深度（depth）</u>：从根节点到该节点所经过的边的数量。</li>
<li>节点的<u>高度（height）</u>：从距离该节点最远的叶节点到该节点所经过的边的数量。</li>
</ul>
<p><a class="glightbox" href="../binary_tree.assets/binary_tree_terminology.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="二叉树的常用术语" class="animation-figure" src="../binary_tree.assets/binary_tree_terminology.png" /></a></p>
<p align="center"> 图 7-2 &nbsp; 二叉树的常用术语 </p>
@@ -4306,26 +4363,26 @@
</div>
<h2 id="713">7.1.3 &nbsp; 常见二叉树类型<a class="headerlink" href="#713" title="Permanent link">&para;</a></h2>
<h3 id="1_1">1. &nbsp; 完美二叉树<a class="headerlink" href="#1_1" title="Permanent link">&para;</a></h3>
<p>如图 7-4 所示，「完美二叉树 perfect binary tree」所有层的节点都被完全填满。在完美二叉树中，叶节点的度为 <span class="arithmatex">\(0\)</span> ，其余所有节点的度都为 <span class="arithmatex">\(2\)</span> ；若树的高度为 <span class="arithmatex">\(h\)</span> ，则节点总数为 <span class="arithmatex">\(2^{h+1} - 1\)</span> ，呈现标准的指数级关系，反映了自然界中常见的细胞分裂现象。</p>
<p>如图 7-4 所示，<u>完美二叉树（perfect binary tree）</u>所有层的节点都被完全填满。在完美二叉树中，叶节点的度为 <span class="arithmatex">\(0\)</span> ，其余所有节点的度都为 <span class="arithmatex">\(2\)</span> ；若树的高度为 <span class="arithmatex">\(h\)</span> ，则节点总数为 <span class="arithmatex">\(2^{h+1} - 1\)</span> ，呈现标准的指数级关系，反映了自然界中常见的细胞分裂现象。</p>
<div class="admonition tip">
<p class="admonition-title">Tip</p>
<p>请注意，在中文社区中，完美二叉树常被称为「满二叉树」。</p>
<p>请注意，在中文社区中，完美二叉树常被称为<u>满二叉树</u>。</p>
</div>
<p><a class="glightbox" href="../binary_tree.assets/perfect_binary_tree.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="完美二叉树" class="animation-figure" src="../binary_tree.assets/perfect_binary_tree.png" /></a></p>
<p align="center"> 图 7-4 &nbsp; 完美二叉树 </p>
<h3 id="2_1">2. &nbsp; 完全二叉树<a class="headerlink" href="#2_1" title="Permanent link">&para;</a></h3>
<p>如图 7-5 所示，「完全二叉树 complete binary tree」只有最底层的节点未被填满，且最底层节点尽量靠左填充。</p>
<p>如图 7-5 所示，<u>完全二叉树（complete binary tree）</u>只有最底层的节点未被填满，且最底层节点尽量靠左填充。</p>
<p><a class="glightbox" href="../binary_tree.assets/complete_binary_tree.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="完全二叉树" class="animation-figure" src="../binary_tree.assets/complete_binary_tree.png" /></a></p>
<p align="center"> 图 7-5 &nbsp; 完全二叉树 </p>
<h3 id="3">3. &nbsp; 完满二叉树<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
<p>如图 7-6 所示，「完满二叉树 full binary tree」除了叶节点之外，其余所有节点都有两个子节点。</p>
<p>如图 7-6 所示，<u>完满二叉树（full binary tree）</u>除了叶节点之外，其余所有节点都有两个子节点。</p>
<p><a class="glightbox" href="../binary_tree.assets/full_binary_tree.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="完满二叉树" class="animation-figure" src="../binary_tree.assets/full_binary_tree.png" /></a></p>
<p align="center"> 图 7-6 &nbsp; 完满二叉树 </p>
<h3 id="4">4. &nbsp; 平衡二叉树<a class="headerlink" href="#4" title="Permanent link">&para;</a></h3>
<p>如图 7-7 所示，「平衡二叉树 balanced binary tree」中任意节点的左子树和右子树的高度之差的绝对值不超过 1 。</p>
<p>如图 7-7 所示，<u>平衡二叉树（balanced binary tree）</u>中任意节点的左子树和右子树的高度之差的绝对值不超过 1 。</p>
<p><a class="glightbox" href="../binary_tree.assets/balanced_binary_tree.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="平衡二叉树" class="animation-figure" src="../binary_tree.assets/balanced_binary_tree.png" /></a></p>
<p align="center"> 图 7-7 &nbsp; 平衡二叉树 </p>
@@ -4561,7 +4618,7 @@ aria-label="页脚"
<div class="md-copyright">
<div class="md-copyright__highlight">
Copyright &copy; 2022-2024 krahets</br>The website content is licensed under <a href="https://creativecommons.org/licenses/by-nc-sa/4.0/">CC BY-NC-SA 4.0</a>
Copyright &copy; 2022-2024 krahets<br>The website content is licensed under <a href="https://creativecommons.org/licenses/by-nc-sa/4.0/">CC BY-NC-SA 4.0</a>
</div>