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<title data-react-helmet="true">平衡二叉树 | HZFE - 剑指前端 Offer</title><meta data-react-helmet="true" name="twitter:card" content="summary_large_image"><meta data-react-helmet="true" property="og:url" content="https://hzfe.github.io/awesome-interview/book1/algorithm-balanced-binary-trees"><meta data-react-helmet="true" name="docusaurus_locale" content="en"><meta data-react-helmet="true" name="docusaurus_version" content="current"><meta data-react-helmet="true" name="docusaurus_tag" content="docs-default-current"><meta data-react-helmet="true" property="og:title" content="平衡二叉树 | HZFE - 剑指前端 Offer"><meta data-react-helmet="true" name="description" content="题目描述"><meta data-react-helmet="true" property="og:description" content="题目描述"><link data-react-helmet="true" rel="shortcut icon" href="/awesome-interview/img/favicon.ico"><link data-react-helmet="true" rel="canonical" href="https://hzfe.github.io/awesome-interview/book1/algorithm-balanced-binary-trees"><link data-react-helmet="true" rel="alternate" href="https://hzfe.github.io/awesome-interview/book1/algorithm-balanced-binary-trees" hreflang="en"><link data-react-helmet="true" rel="alternate" href="https://hzfe.github.io/awesome-interview/book1/algorithm-balanced-binary-trees" hreflang="x-default"><link rel="stylesheet" href="/awesome-interview/assets/css/styles.36d1aa8c.css">
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<div><a href="#" class="skipToContent_1oUP">Skip to main content</a></div><nav class="navbar navbar--fixed-top"><div class="navbar__inner"><div class="navbar__items"><button aria-label="Navigation bar toggle" class="navbar__toggle clean-btn" type="button" tabindex="0"><svg width="30" height="30" viewBox="0 0 30 30" aria-hidden="true"><path stroke="currentColor" stroke-linecap="round" stroke-miterlimit="10" stroke-width="2" d="M4 7h22M4 15h22M4 23h22"></path></svg></button><a class="navbar__brand" href="/awesome-interview/"><img src="/awesome-interview/img/badge.svg" alt="HZFE" class="themedImage_1VuW themedImage--light_3UqQ navbar__logo"><img src="/awesome-interview/img/badge.svg" alt="HZFE" class="themedImage_1VuW themedImage--dark_hz6m navbar__logo"><b class="navbar__title">剑指前端 Offer</b></a></div><div class="navbar__items navbar__items--right"><a href="https://github.com/hzfe/awesome-interview" target="_blank" rel="noopener noreferrer" class="navbar__item navbar__link"><span>GitHub<svg width="13.5" height="13.5" aria-hidden="true" viewBox="0 0 24 24" class="iconExternalLink_3J9K"><path fill="currentColor" d="M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z"></path></svg></span></a></div></div><div role="presentation" class="navbar-sidebar__backdrop"></div></nav><div class="main-wrapper docs-wrapper docs-doc-page"><div class="docPage_31aa"><button class="clean-btn backToTopButton_35hR" type="button"><svg viewBox="0 0 24 24" width="28"><path d="M7.41 15.41L12 10.83l4.59 4.58L18 14l-6-6-6 6z" fill="currentColor"></path></svg></button><aside class="docSidebarContainer_3Kbt"><div class="sidebar_15mo"><nav class="menu thin-scrollbar menu_Bmed menuWithAnnouncementBar_2WvA"><ul class="menu__list"><li class="menu__list-item"><a class="menu__link" href="/awesome-interview/">前言</a></li><li class="menu__list-item"><a class="menu__link menu__link--sublist menu__link--active" href="#">模拟题一</a><ul style="display:block;overflow:visible;height:auto" class="menu__list"><li class="menu__list-item"><a class="menu__link" tabindex="0" href="/awesome-interview/book1/browser-cross-origin">浏览器：浏览器跨域</a></li><li class="menu__list-item"><a class="menu__link" tabindex="0" href="/awesome-interview/book1/browser-repain-reflow">浏览器：浏览器的重排重绘</a></li><li class="menu__list-item"><a class="menu__link" tabindex="0" href="/awesome-interview/book1/engineer-webpack-workflow">工程化：Webpack 工作流程</a></li><li class="menu__list-item"><a class="menu__link" tabindex="0" href="/awesome-interview/book1/frame-vue-data-binding">框架：Vue 的数据绑定机制</a></li><li class="menu__list-item"><a class="menu__link" tabindex="0" href="/awesome-interview/book1/frame-vue-computed-watch">框架：Vue 的 computed 和 watch 的区别</a></li><li class="menu__list-item"><a class="menu__link" tabindex="0" href="/awesome-interview/book1/js-closures">基础：闭包的作用和原理</a></li><li class="menu__list-item"><a class="menu__link" tabindex="0" href="/awesome-interview/book1/js-module-specs">基础：前端模块化规范</a></li><li class="menu__list-item"><a class="menu__link" tabindex="0" href="/awesome-interview/book1/css-bfc">样式：BFC 的形成和作用</a></li><li class="menu__list-item"><a class="menu__link" tabindex="0" href="/awesome-interview/book1/network-security">网络：前端安全</a></li><li class="menu__list-item"><a class="menu__link" tabindex="0" href="/awesome-interview/book1/coding-promise">编码：实现一个 Promises/A+</a></li><li class="menu__list-item"><a class="menu__link menu__link--active" aria-current="page" tabindex="0" href="/awesome-interview/book1/algorithm-balanced-binary-trees">算法：平衡二叉树</a></li><li class="menu__list-item"><a class="menu__link" tabindex="0" href="/awesome-interview/book1/topic-enter-url-display-xx">综合：浏览器从输入网址到页面展现的过程</a></li></ul></li><li class="menu__list-item menu__list-item--collapsed"><a class="menu__link menu
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</span></span><span class="token-line" style="color:#393A34"><span class="token plain"> 3</span></span><span class="token-line" style="color:#393A34"><span class="token plain"> / \</span></span><span class="token-line" style="color:#393A34"><span class="token plain"> 9 20</span></span><span class="token-line" style="color:#393A34"><span class="token plain"> / \</span></span><span class="token-line" style="color:#393A34"><span class="token plain"> 15 7</span></span><span class="token-line" style="color:#393A34"><span class="token plain">返回 true。</span></span></code></pre><button type="button" aria-label="Copy code to clipboard" class="copyButton_Ue-o clean-btn">Copy</button></div></div><p>示例 2:</p><div class="codeBlockContainer_K1bP"><div class="codeBlockContent_hGly"><pre tabindex="0" class="prism-code language-undefined codeBlock_23N8 thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_39YC"><span class="token-line" style="color:#393A34"><span class="token plain">给定二叉树 [1,2,2,3,3,null,null,4,4]</span></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block">
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</span></span><span class="token-line" style="color:#393A34"><span class="token plain"> 1</span></span><span class="token-line" style="color:#393A34"><span class="token plain"> / \</span></span><span class="token-line" style="color:#393A34"><span class="token plain"> 2 2</span></span><span class="token-line" style="color:#393A34"><span class="token plain"> / \</span></span><span class="token-line" style="color:#393A34"><span class="token plain"> 3 3</span></span><span class="token-line" style="color:#393A34"><span class="token plain"> / \</span></span><span class="token-line" style="color:#393A34"><span class="token plain"> 4 4</span></span><span class="token-line" style="color:#393A34"><span class="token plain">返回 false。</span></span></code></pre><button type="button" aria-label="Copy code to clipboard" class="copyButton_Ue-o clean-btn">Copy</button></div></div><p>限制：0 <= 树的结点个数 <= 10000</p><h2><a aria-hidden="true" tabindex="-1" class="anchor anchor__h2 anchorWithStickyNavbar_31ik" id="基本知识点"></a>基本知识点<a class="hash-link" href="#基本知识点" title="Direct link to heading">#</a></h2><p>二叉树的每个节点最多有两个子节点，平衡二叉树中任意一个节点的左右子树高度相差不能大于 1，满二叉树和完全二叉树都是平衡二叉树，普通二叉树有可能是平衡二叉树。</p><h2><a aria-hidden="true" tabindex="-1" class="anchor anchor__h2 anchorWithStickyNavbar_31ik" id="题解"></a>题解<a class="hash-link" href="#题解" title="Direct link to heading">#</a></h2><h3><a aria-hidden="true" tabindex="-1" class="anchor anchor__h3 anchorWithStickyNavbar_31ik" id="解法一"></a>解法一<a class="hash-link" href="#解法一" title="Direct link to heading">#</a></h3><h4><a aria-hidden="true" tabindex="-1" class="anchor anchor__h4 anchorWithStickyNavbar_31ik" id="思路"></a>思路<a class="hash-link" href="#思路" title="Direct link to heading">#</a></h4><p>若想判断二叉树是不是平衡二叉树，只需要判断左右子树的高度差是不是不超过 1 即可。同时，要满足一个树是平衡二叉树，它的子树也必须是平衡二叉树。我们可以从根结点开始，通过递归来求得子树的高度，以及子树是否是平衡二叉树，以此来结合判断二叉树是否是平衡二叉树。</p><h4><a aria-hidden="true" tabindex="-1" class="anchor anchor__h4 anchorWithStickyNavbar_31ik" id="代码"></a>代码<a class="hash-link" href="#代码" title="Direct link to heading">#</a></h4><div class="codeBlockContainer_K1bP"><div class="codeBlockContent_hGly javascript"><pre tabindex="0" class="prism-code language-javascript codeBlock_23N8 thin-scrollbar" style="color:#393A34;background-color:#f6f8fa"><code class="codeBlockLines_39YC"><span class="token-line" style="color:#393A34"><span class="token comment" style="color:#999988;font-style:italic">/**</span></span><span class="token-line" style="color:#393A34"><span class="token comment" style="color:#999988;font-style:italic"> * Definition for a binary tree node.</span></span><span class="token-line" style="color:#393A34"><span class="token comment" style="color:#999988;font-style:italic"> * function TreeNode(val, left, right) {</span></span><span class="token-line" style="color:#393A34"><span class="token comment" style="color:#999988;font-style:italic"> * this.val = (val === undefined ? 0 : val)</span></span><span class="token-line" style="color:#393A34"><span class="token comment" style="color:#999988;font-style:italic"> * this.left = (left === undefined ? null : left)</span></span><span class="token-line" style="color:#393A34"><span class="token comment" style="color:#999988;font-style:italic"> * this.right = (right === undefined ? null : right)</span></span><span class="token-line" style="color:#393A34"><span class="token comment" style="color:#999988;font-style:italic"> * }</span></span><span class="token-line" style="color:#393A34"><span class="token comment" style="color:#999988;font-style:italic"> */
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</span></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">const</span><span class="token plain"> </span><span class="token function-variable function" style="color:#d73a49">height</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">function</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token parameter">root</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword control-flow" style="color:#00009f">if</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">root </span><span class="token operator" style="color:#393A34">===</span><span class="token plain"> </span><span class="token keyword null nil" style="color:#00009f">null</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword control-flow" style="color:#00009f">return</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">}</span><span class="token plain"> </span><span class="token keyword control-flow" style="color:#00009f">else</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword control-flow" style="color:#00009f">return</span><span class="token plain"> </span><span class="token known-class-name class-name">Math</span><span class="token punctuation" style="color:#393A34">.</span><span class="token method function property-access" style="color:#d73a49">max</span><span class="token punctuation" style="color:#393A34">(</span><span class="token function" style="color:#d73a49">height</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">root</span><span class="token punctuation" style="color:#393A34">.</span><span class="token property-access">left</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">height</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">root</span><span class="token punctuation" style="color:#393A34">.</span><span class="token property-access">right</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">+</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">}</span><span class="token plain"></span></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><spa
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</span></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token keyword" style="color:#00009f">var</span><span class="token plain"> </span><span class="token function-variable function" style="color:#d73a49">height</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token keyword" style="color:#00009f">function</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token parameter">root</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword control-flow" style="color:#00009f">if</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">root </span><span class="token operator" style="color:#393A34">==</span><span class="token plain"> </span><span class="token keyword null nil" style="color:#00009f">null</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword control-flow" style="color:#00009f">return</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">0</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">}</span><span class="token plain"></span></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block">
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</span></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword" style="color:#00009f">const</span><span class="token plain"> left </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">height</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">root</span><span class="token punctuation" style="color:#393A34">.</span><span class="token property-access">left</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword" style="color:#00009f">const</span><span class="token plain"> right </span><span class="token operator" style="color:#393A34">=</span><span class="token plain"> </span><span class="token function" style="color:#d73a49">height</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">root</span><span class="token punctuation" style="color:#393A34">.</span><span class="token property-access">right</span><span class="token punctuation" style="color:#393A34">)</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block">
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</span></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword control-flow" style="color:#00009f">if</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">left </span><span class="token operator" style="color:#393A34">===</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">-</span><span class="token number" style="color:#36acaa">1</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">||</span><span class="token plain"> right </span><span class="token operator" style="color:#393A34">===</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">-</span><span class="token number" style="color:#36acaa">1</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">||</span><span class="token plain"> </span><span class="token known-class-name class-name">Math</span><span class="token punctuation" style="color:#393A34">.</span><span class="token method function property-access" style="color:#d73a49">abs</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">left </span><span class="token operator" style="color:#393A34">-</span><span class="token plain"> right</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">></span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">{</span><span class="token plain"></span></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword control-flow" style="color:#00009f">return</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">-</span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token punctuation" style="color:#393A34">}</span><span class="token plain"></span></span><span class="token-line" style="color:#393A34"><span class="token plain" style="display:inline-block">
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</span></span><span class="token-line" style="color:#393A34"><span class="token plain"> </span><span class="token keyword control-flow" style="color:#00009f">return</span><span class="token plain"> </span><span class="token known-class-name class-name">Math</span><span class="token punctuation" style="color:#393A34">.</span><span class="token method function property-access" style="color:#d73a49">max</span><span class="token punctuation" style="color:#393A34">(</span><span class="token plain">left</span><span class="token punctuation" style="color:#393A34">,</span><span class="token plain"> right</span><span class="token punctuation" style="color:#393A34">)</span><span class="token plain"> </span><span class="token operator" style="color:#393A34">+</span><span class="token plain"> </span><span class="token number" style="color:#36acaa">1</span><span class="token punctuation" style="color:#393A34">;</span><span class="token plain"></span></span><span class="token-line" style="color:#393A34"><span class="token plain"></span><span class="token punctuation" style="color:#393A34">}</span><span class="token punctuation" style="color:#393A34">;</span></span></code></pre><button type="button" aria-label="Copy code to clipboard" class="copyButton_Ue-o clean-btn">Copy</button></div></div><h4><a aria-hidden="true" tabindex="-1" class="anchor anchor__h4 anchorWithStickyNavbar_31ik" id="时间复杂度分析-1"></a>时间复杂度分析<a class="hash-link" href="#时间复杂度分析-1" title="Direct link to heading">#</a></h4><p>由于是后序遍历，每个节点只会被调用 1 次，所以，该方法的时间复杂度是 O(n)。</p><h4><a aria-hidden="true" tabindex="-1" class="anchor anchor__h4 anchorWithStickyNavbar_31ik" id="空间复杂度分析-1"></a>空间复杂度分析<a class="hash-link" href="#空间复杂度分析-1" title="Direct link to heading">#</a></h4><p>该方法由于使用了递归，并且每次递归都调用了两次自身，导致会函数栈会按照等差数列开辟，所以该方法的空间复杂度应为 O(n^2)。</p></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="Docs pages navigation"><div class="pagination-nav__item"><a class="pagination-nav__link" href="/awesome-interview/book1/coding-promise"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">« 编码：实现一个 Promises/A+</div></a></div><div class="pagination-nav__item pagination-nav__item--next"><a class="pagination-nav__link" href="/awesome-interview/book1/topic-enter-url-display-xx"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">综合：浏览器从输入网址到页面展现的过程 »</div></a></div></nav></div></div><div class="col col--3"><div class="tableOfContents_35-E thin-scrollbar"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#题目描述" class="table-of-contents__link">题目描述</a></li><li><a href="#基本知识点" class="table-of-contents__link">基本知识点</a></li><li><a href="#题解" class="table-of-contents__link">题解</a><ul><li><a href="#解法一" class="table-of-contents__link">解法一</a></li><li><a href="#解法二" class="table-of-contents__link">解法二</a></li></ul></li></ul></div></div></div><div class="row"><div class="col"><div class="react-utterences"><div>Loading script...</div></div></div><div class="col col--3"></div></div></div></main></div></div></div>
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