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1import{_ as i,e as a,g as n,o as l}from"./app-bYuqBH2G.js";const h={};function k(t,s){return l(),a("div",null,s[0]||(s[0]=[n(`<h2 id="_69-x-的平方根" tabindex="-1"><a class="header-anchor" href="#_69-x-的平方根"><span><a href="https://leetcode.cn/problems/sqrtx/" target="_blank" rel="noopener noreferrer">69. x 的平方根 </a></span></a></h2><p>给你一个非负整数 <code>x</code> ，计算并返回 <code>x</code> 的 <strong>算术平方根</strong> 。</p><p>由于返回类型是整数，结果只保留 <strong>整数部分</strong> ，小数部分将被 <strong>舍去 。</strong></p><p>**注意：**不允许使用任何内置指数函数和算符，例如 <code>pow(x, 0.5)</code> 或者 <code>x ** 0.5</code> 。</p><p><strong>示例 1：</strong></p><div class="language- line-numbers-mode" data-ext="" data-title=""><button class="copy" title="复制代码" data-copied="已复制"></button><pre class="shiki shiki-themes vitesse-light vitesse-dark vp-code"><code><span class="line"><span>输入：x = 4</span></span>
2<span class="line"><span>输出：2</span></span></code></pre><div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0;"><div class="line-number"></div><div class="line-number"></div></div></div><p><strong>示例 2：</strong></p><div class="language- line-numbers-mode" data-ext="" data-title=""><button class="copy" title="复制代码" data-copied="已复制"></button><pre class="shiki shiki-themes vitesse-light vitesse-dark vp-code"><code><span class="line"><span>输入：x = 8</span></span>
3<span class="line"><span>输出：2</span></span>
4<span class="line"><span>解释：8 的算术平方根是 2.82842..., 由于返回类型是整数，小数部分将被舍去。</span></span></code></pre><div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0;"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><p><strong>提示：</strong></p><ul><li><code>0 &lt;= x &lt;= 2^31 - 1</code></li></ul><h2 id="二分查找平方小于等于-x-的数的右边界" tabindex="-1"><a class="header-anchor" href="#二分查找平方小于等于-x-的数的右边界"><span>二分查找平方小于等于 x 的数的右边界</span></a></h2><p>不需要判空检查，因为一定能找到，只有在可能找不到的时候才需要检查；</p><p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">x</span></span></span></span> 平方根的整数部分 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>a</mi><mi>n</mi><mi>s</mi></mrow><annotation encoding="application/x-tex">ans</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">an</span><span class="mord mathnormal">s</span></span></span></span> 是满足 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>k</mi><mn>2</mn></msup><mo>≤</mo><mi>x</mi></mrow><annotation encoding="application/x-tex">k^2 \\leq x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9501em;vertical-align:-0.136em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">x</span></span></span></span> 的最大 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>k</mi></mrow><annotation encoding="application/x-tex">k</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span></span></span></span> 值。</p><p>以下是三种二分查找的写法。</p><div class="language-java line-numbers-mode" data-ext="java" data-title="java"><button class="copy" title="复制代码" data-copied="已复制"></button><pre class="shiki shiki-themes vitesse-light vitesse-dark vp-code"><code><span class="line"><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">class</span><span style="--shiki-light:#2E8F82;--shiki-dark:#5DA994;"> Solution</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> {</span></span>
5<span class="line"><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">    public</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;"> int</span><span style="--shiki-light:#59873A;--shiki-dark:#80A665;"> mySqrt</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">int</span><span style="--shiki-light:#B07D48;--shiki-dark:#BD976A;"> x</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> {</span></span>
6<span class="line"><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">        int</span><span style="--shiki-light:#B07D48;--shiki-dark:#BD976A;"> l</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> =</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> r </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> x</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> ans </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;"> -</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">;</span></span>
7<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">        </span></span>
8<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">        while</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> (</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">l </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">&lt;=</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">

8 r</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> {</span></span>
9<span class="line"><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">            int</span><span style="--shiki-light:#B07D48;--shiki-dark:#BD976A;"> mid</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> =</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> l </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">+</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> (</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">r </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">-</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> l</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;"> /</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 2</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">;</span></span>
10<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;">            // 必须是&lt;=时更新ans，不能只在=x时更新ans，因为有些数开方后不是整数，例如8.</span></span>
11<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">            if</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> ((</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">long</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> mid </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">*</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> mid </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">&lt;=</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> x</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> {</span></span>
12<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">                ans </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> mid</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">;</span></span>
13<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">                l </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> mid </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">+</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">;</span></span>
14<span class="line"><span style="--shiki-light:#999999;--shiki-dark:#666666;">            }</span><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;"> else</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> {</span></span>
15<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">                r </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> mid </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">-</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">;</span></span>
16<span class="line"><span style="--shiki-light:#999999;--shiki-dark:#666666;">            }</span></span>
17<span class="line"><span style="--shiki-light:#999999;--shiki-dark:#666666;">        }</span></span>
18<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">        </span></span>
19<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">        return</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> ans</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">;</span></span>
20<span class="line"><span style="--shiki-light:#999999;--shiki-dark:#666666;">    }</span></span>
21<span class="line"><span style="--shiki-light:#999999;--shiki-dark:#666666;">}</span></span></code></pre><div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0;"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><div class="language-java line-numbers-mode" data-ext="java" data-title="java"><button class="copy" title="复制代码" data-copied="已复制"></button><pre class="shiki shiki-themes vitesse-light vitesse-dark vp-code"><code><span class="line"><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">class</span><span style="--shiki-light:#2E8F82;--shiki-dark:#5DA994;"> Solution</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> {</span></span>
22<span class="line"><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">    public</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;"> int</span><span style="--shiki-light:#59873A;--shiki-dark:#80A665;"> mySqrt</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">int</span><span style="--shiki-light:#B07D48;--shiki-dark:#BD976A;"> x</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> {</span></span>
23<span class="line"><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">        int</span><span style="--shiki-light:#B07D48;--shiki-dark:#BD976A;"> l</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> =</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> r </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> x</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">;</span></span>
24<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">        </span></span>
25<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">        while</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> (</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">l </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">&lt;=</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">

25 r</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> {</span></span>
26<span class="line"><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">            int</span><span style="--shiki-light:#B07D48;--shiki-dark:#BD976A;"> mid</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> =</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> l </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">+</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> (</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">r </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">-</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> l</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;"> /</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 2</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">;</span></span>
27<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">            if</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> ((</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">long</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> mid </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">*</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> mid </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">&lt;=</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> x</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> {</span></span>
28<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">                l </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> mid </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">+</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">;</span></span>
29<span class="line"><span style="--shiki-light:#999999;--shiki-dark:#666666;">            }</span><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;"> else</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> {</span></span>
30<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">                r </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> mid </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">-</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">;</span></span>
31<span class="line"><span style="--shiki-light:#999999;--shiki-dark:#666666;">            }</span></span>
32<span class="line"><span style="--shiki-light:#999999;--shiki-dark:#666666;">        }</span></span>
33<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;">        // 注意，每轮循环后，[0,l-1]里全是小于等于x的数，[r+1, length-1]里全是&gt;=x的数，[l,r]里是未确定的数</span></span>
34<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">        return</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> l</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">-</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">;</span></span>
35<span class="line"><span style="--shiki-light:#999999;--shiki-dark:#666666;">    }</span></span>
36<span class="line"><span style="--shiki-light:#999999;--shiki-dark:#666666;">}</span></span></code></pre><div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0;"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><div class="language-java line-numbers-mode" data-ext="java" data-title="java"><button class="copy" title="复制代码" data-copied="已复制"></button><pre class="shiki shiki-themes vitesse-light vitesse-dark vp-code"><code><span class="line"><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">class</span><span style="--shiki-light:#2E8F82;--shiki-dark:#5DA994;"> Solution</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> {</span></span>
37<span class="line"><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">    public</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;"> int</span><span style="--shiki-light:#59873A;--shiki-dark:#80A665;"> mySqrt</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">int</span><span style="--shiki-light:#B07D48;--shiki-dark:#BD976A;"> x</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> {</span></span>
38<span class="line"><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">        int</span><span style="--shiki-light:#B07D48;--shiki-dark:#BD976A;"> l</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> =</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> r </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> x</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> ans </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;"> -</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">;</span></span>
39<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">        </span></span>
40<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">        while</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> (</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">l </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">&lt;=</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">

40 r</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> {</span></span>
41<span class="line"><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">            int</span><span style="--shiki-light:#B07D48;--shiki-dark:#BD976A;"> mid</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> =</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> l </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">+</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> (</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">r </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">-</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> l</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;"> /</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 2</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">;</span></span>
42<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">            if</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> ((</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">long</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> mid </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">*</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> mid </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">&lt;</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> x</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> {</span></span>
43<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">                ans </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> mid</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">;</span></span>
44<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">                l </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> mid </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">+</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">;</span></span>
45<span class="line"><span style="--shiki-light:#999999;--shiki-dark:#666666;">            }</span><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;"> else</span><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;"> if</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> ((</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">long</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> mid </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">*</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> mid </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">==</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> x</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> {</span></span>
46<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">                return</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> mid</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">;</span></span>
47<span class="line"><span style="--shiki-light:#999999;--shiki-dark:#666666;">            }</span><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;"> else</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> {</span></span>
48<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">                r </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> mid </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">-</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">;</span></span>
49<span class="line"><span style="--shiki-light:#999999;--shiki-dark:#666666;">            }</span></span>
50<span class="line"><span style="--shiki-light:#999999;--shiki-dark:#666666;">        }</span></span>
51<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">        return</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> ans</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">;</span></span>
52<span class="line"><span style="--shiki-light:#999999;--shiki-dark:#666666;">    }</span></span>
53<span class="line"><span style="--shiki-light:#999999;--shiki-dark:#666666;">}</span></span></code></pre><div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0;"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><ul><li>时间复杂度：O(log x)，即为二分查找需要的次数。</li><li>空间复杂度：O(1)。</li></ul><h2 id="牛顿迭代" tabindex="-1"><a class="header-anchor" href="#牛顿迭代"><span>牛顿迭代</span></a></h2><div class="language-java line-numbers-mode" data-ext="java" data-title="java"><button class="copy" title="复制代码" data-copied="已复制"></button><pre class="shiki shiki-themes vitesse-light vitesse-dark vp-code"><code><span class="line"><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">class</span><span style="--shiki-light:#2E8F82;--shiki-dark:#5DA994;"> Solution</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> {</span></span>
54<span class="line"><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">    public</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;"> int</span><span style="--shiki-light:#59873A;--shiki-dark:#80A665;"> mySqrt</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">int</span><span style="--shiki-light:#B07D48;--shiki-dark:#BD976A;"> x</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> {</span></span>
55<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">        if</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> (</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">x </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">==</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> {</span></span>
56<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">            return</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">;</span></span>
57<span class="line"><span style="--shiki-light:#999999;--shiki-dark:#666666;">        }</span></span>
58<span class="line"></span>
59<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;">        // 计算sqrt{2}(C)，C=x</span></span>
60<span class="line"><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">        double</span><span style="--shiki-light:#B07D48;--shiki-dark:#BD976A;"> C</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> =</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> x</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> x0 </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> x</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">;</span><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;"> // 这里把int类型的x换成了double类型的x</span></span>
61<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">        while</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> (</span><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">true</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> {</span></span>
62<span class="line"><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">            double</span><span style="--shiki-light:#B07D48;--shiki-dark:#BD976A;"> xi</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> =</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0.5</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;"> *</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> (</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">x0 </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">+</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> C </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">/</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> x0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">);</span></span>
63<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;">            // 当相邻两次迭代得到的交点非常接近时。注意这里的x0是上一轮的xi。</span></span>
64<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">            if</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> (</span><span style="--shiki-light:#B07D48;--shiki-dark:#BD976A;">Math</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">.</span><span style="--shiki-light:#59873A;--shiki-dark:#80A665;">abs</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">x0 </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">-</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> xi</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;"> &lt;</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1e-7</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> {</span></span>
65<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">                break</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">;</span></span>
66<span class="line"><span style="--shiki-light:#999999;--shiki-dark:#666666;">            }</span></span>
67<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;">            // x0前进到xi处</span></span>
68<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">            x0 </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> xi</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">;</span></span>
69<span class="line"><span style="--shiki-light:#999999;--shiki-dark:#666666;">        }</span></span>
70<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">        return</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> (</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">int</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> x0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">;</span></span>
71<span class="line"><span style="--shiki-light:#999999;--shiki-dark:#666666;">    }</span></span>
72<span class="line"><span style="--shiki-light:#999999;--shiki-dark:#666666;">}</span></span>
73<span class="line"></span>
74<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;">// 返回xi也可以，但是要在break的时候返回，因为xi是局部变量</span></span>
75<span class="line"><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">class</span><span style="--shiki-light:#2E8F82;--shiki-dark:#5DA994;"> Solution</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> {</span></span>
76<span class="line"><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">    public</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;"> int</span><span style="--shiki-light:#59873A;--shiki-dark:#80A665;"> mySqrt</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">int</span><span style="--shiki-light:#B07D48;--shiki-dark:#BD976A;"> x</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> {</span></span>
77<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">        if</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> (</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">x </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">==</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> {</span></span>
78<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">            return</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">;</span></span>
79<span class="line"><span style="--shiki-light:#999999;--shiki-dark:#666666;">        }</span></span>
80<span class="line"></span>
81<span class="line"><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">        double</span><span style="--shiki-light:#B07D48;--shiki-dark:#BD976A;"> C</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> =</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> x</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> x0 </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> x</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">;</span></span>
82<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">        while</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> (</span><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">true</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> {</span></span>
83<span class="line"><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">            double</span><span style="--shiki-light:#B07D48;--shiki-dark:#BD976A;"> xi</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> =</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0.5</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;"> *</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> (</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">x0 </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">+</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> C </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">/</span><span style="--shiki-light:#393A34;--shiki-dark:#DB

83D7CAEE;"> x0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">);</span></span>
84<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">            if</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> (</span><span style="--shiki-light:#B07D48;--shiki-dark:#BD976A;">Math</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">.</span><span style="--shiki-light:#59873A;--shiki-dark:#80A665;">abs</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">x0 </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">-</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> xi</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;"> &lt;</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1e-7</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> {</span></span>
85<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">                return</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> (</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">int</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> xi</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">;</span></span>
86<span class="line"><span style="--shiki-light:#999999;--shiki-dark:#666666;">            }</span></span>
87<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">            x0 </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> xi</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">;</span></span>
88<span class="line"><span style="--shiki-light:#999999;--shiki-dark:#666666;">        }</span></span>
89<span class="line"><span style="--shiki-light:#999999;--shiki-dark:#666666;">    }</span></span>
90<span class="line"><span style="--shiki-light:#999999;--shiki-dark:#666666;">}</span></span></code></pre><div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0;"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><ul><li>时间复杂度：O(log x)，此方法是二次收敛的，相较于二分查找更快。</li><li>空间复杂度：O(1)。</li></ul>`,21)]))}const e=i(h,[["render",k],["__file","index.html.vue"]]),d=JSON.parse('{"path":"/article/bw3yredc/","title":"x 的平方根","lang":"zh-CN","frontmatter":{"title":"x 的平方根","createTime":"2025/02/24 23:06:03","permalink":"/article/bw3yredc/","tags":["二分"],"description":"69. x 的平方根 给你一个非负整数 x ，计算并返回 x 的 算术平方根 。 由于返回类型是整数，结果只保留 整数部分 ，小数部分将被 舍去 。 **注意：**不允许使用任何内置指数函数和算符，例如 pow(x, 0.5) 或者 x ** 0.5 。 示例 1： 示例 2： 提示： 0 <= x <= 2^31 - 1 二分查找平方小于等于 x 的...","head":[["meta",{"property":"og:url","content":"https://jingzhen.vercel.app/article/bw3yredc/"}],["meta",{"property":"og:site_name","content":"景真"}],["meta",{"property":"og:title","content":"x 的平方根"}],["meta",{"property":"og:description","content":"69. x 的平方根 给你一个非负整数 x ，计算并返回 x 的 算术平方根 。 由于返回类型是整数，结果只保留 整数部分 ，小数部分将被 舍去 。 **注意：**不允许使用任何内置指数函数和算符，例如 pow(x, 0.5) 或者 x ** 0.5 。 示例 1： 示例 2： 提示： 0 <= x <= 2^31 - 1 二分查找平方小于等于 x 的..."}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}

90],["meta",{"property":"og:updated_time","content":"2025-03-12T14:22:51.000Z"}],["meta",{"property":"article:tag","content":"二分"}],["meta",{"property":"article:modified_time","content":"2025-03-12T14:22:51.000Z"}],["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"x 的平方根\\",\\"image\\":[\\"\\"],\\"dateModified\\":\\"2025-03-12T14:22:51.000Z\\",\\"author\\":[]}"]]},"headers":[],"readingTime":{"minutes":2.2,"words":660},"git":{"updatedTime":1741789371000,"contributors":[{"name":"Jingzhenzxz","username":"Jingzhenzxz","email":"[email protected]","commits":1,"avatar":"https://gravatar.com/avatar/7ac662851709be161105ced983b0f788aed7cadf1101f03ac144637d73e4ed18?d=retro"}]},"autoDesc":true,"filePathRelative":"algorithm/x 的平方根.md","categoryList":[{"id":"ed4696","sort":10005,"name":"algorithm"}]}');export{e as comp,d as data};

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