xinyin025/hello-algo
1
0
Fork 0
mirror of https://github.com/krahets/hello-algo.git synced 2026-07-14 08:06:06 +00:00
Code Issues Packages Projects Releases Wiki Activity

deploy

Browse Source
This commit is contained in:
krahets
2023-08-21 03:56:52 +08:00
parent 47b7d6fd44
commit c0f960b443
105 changed files with 506 additions and 502 deletions
Download Patch File Download Diff File Expand all files Collapse all files
chapter_computational_complexity/index.html
+9 -9
View File
@@ -26,7 +26,7 @@
<title>第 2 章   复杂度 - Hello 算法</title>
<title>第 2 章   时空复杂度 - Hello 算法</title>
@@ -117,7 +117,7 @@
<div class="md-header__topic" data-md-component="header-topic">
<span class="md-ellipsis">
第 2 章 &nbsp; 复杂度
第 2 章 &nbsp; 时空复杂度
</span>
</div>
@@ -547,7 +547,7 @@
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
<span class="md-ellipsis">
第 2 章 &nbsp; 复杂度
第 2 章 &nbsp; 时空复杂度
</span>
@@ -562,7 +562,7 @@
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="true">
<label class="md-nav__title" for="__nav_3">
<span class="md-nav__icon md-icon"></span>
第 2 章 &nbsp; 复杂度
第 2 章 &nbsp; 时空复杂度
</label>
<ul class="md-nav__list" data-md-scrollfix>
@@ -1157,7 +1157,7 @@
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
<span class="md-ellipsis">
第 6 章 &nbsp; 散列表
第 6 章 &nbsp; 哈希表
</span>
@@ -1172,7 +1172,7 @@
<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 6 章 &nbsp; 散列表
第 6 章 &nbsp; 哈希表
</label>
<ul class="md-nav__list" data-md-scrollfix>
@@ -3350,13 +3350,13 @@
<h1 id="2">第 2 章 &nbsp; 复杂度<a class="headerlink" href="#2" title="Permanent link">&para;</a></h1>
<h1 id="2">第 2 章 &nbsp; 时空复杂度<a class="headerlink" href="#2" title="Permanent link">&para;</a></h1>
<div class="center-table">
<p><img alt="复杂度" src="../assets/covers/chapter_complexity_analysis.jpg" width="600" /></p>
<p><img alt="时空复杂度" src="../assets/covers/chapter_complexity_analysis.jpg" width="600" /></p>
</div>
<div class="admonition abstract">
<p class="admonition-title">Abstract</p>
<p>复杂度犹如浩瀚的算法宇宙中的时空向导。</p>
<p>复杂度分析犹如浩瀚的算法宇宙中的时空向导。</p>
<p>它带领我们在时间与空间这两个维度上深入探索，寻找更优雅的解决方案。</p>
</div>
<h2 id="_1">本章内容<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
chapter_computational_complexity/performance_evaluation/index.html
+6 -6
View File
@@ -547,7 +547,7 @@
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
<span class="md-ellipsis">
第 2 章 &nbsp; 复杂度
第 2 章 &nbsp; 时空复杂度
</span>
@@ -562,7 +562,7 @@
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="true">
<label class="md-nav__title" for="__nav_3">
<span class="md-nav__icon md-icon"></span>
第 2 章 &nbsp; 复杂度
第 2 章 &nbsp; 时空复杂度
</label>
<ul class="md-nav__list" data-md-scrollfix>
@@ -1218,7 +1218,7 @@
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
<span class="md-ellipsis">
第 6 章 &nbsp; 散列表
第 6 章 &nbsp; 哈希表
</span>
@@ -1233,7 +1233,7 @@
<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 6 章 &nbsp; 散列表
第 6 章 &nbsp; 哈希表
</label>
<ul class="md-nav__list" data-md-scrollfix>
@@ -3534,7 +3534,7 @@
<nav class="md-footer__inner md-grid" aria-label="页脚" >
<a href="../" class="md-footer__link md-footer__link--prev" aria-label="上一页: 第 2 章 &amp;nbsp; 复杂度" rel="prev">
<a href="../" class="md-footer__link md-footer__link--prev" aria-label="上一页: 第 2 章 &amp;nbsp; 时空复杂度" 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>
@@ -3544,7 +3544,7 @@
上一页
</span>
<div class="md-ellipsis">
第 2 章 &nbsp; 复杂度
第 2 章 &nbsp; 时空复杂度
</div>
</div>
</a>
chapter_computational_complexity/space_complexity/index.html
+39 -40
View File
@@ -547,7 +547,7 @@
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
<span class="md-ellipsis">
第 2 章 &nbsp; 复杂度
第 2 章 &nbsp; 时空复杂度
</span>
@@ -562,7 +562,7 @@
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="true">
<label class="md-nav__title" for="__nav_3">
<span class="md-nav__icon md-icon"></span>
第 2 章 &nbsp; 复杂度
第 2 章 &nbsp; 时空复杂度
</label>
<ul class="md-nav__list" data-md-scrollfix>
@@ -1266,7 +1266,7 @@
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
<span class="md-ellipsis">
第 6 章 &nbsp; 散列表
第 6 章 &nbsp; 哈希表
</span>
@@ -1281,7 +1281,7 @@
<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 6 章 &nbsp; 散列表
第 6 章 &nbsp; 哈希表
</label>
<ul class="md-nav__list" data-md-scrollfix>
@@ -3553,7 +3553,7 @@
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="cm">/* 函数 */</span>
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a><span class="kt">int</span><span class="w"> </span><span class="nf">function</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a><span class="w"> </span><span class="c1">// do something...</span>
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a><span class="w"> </span><span class="c1">// 执行某些操作...</span>
<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a><span class="p">}</span>
<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>
@@ -3576,7 +3576,7 @@
<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a>
<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="cm">/* 函数 */</span>
<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="kt">int</span><span class="w"> </span><span class="nf">func</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w"> </span><span class="c1">// do something...</span>
<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w"> </span><span class="c1">// 执行某些操作...</span>
<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="p">}</span>
<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a>
@@ -3598,7 +3598,7 @@
<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a>
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="k">def</span> <span class="nf">function</span><span class="p">()</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;函数&quot;&quot;&quot;</span>
<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a> <span class="c1"># do something...</span>
<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a> <span class="c1"># 执行某些操作...</span>
<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a> <span class="k">return</span> <span class="mi">0</span>
<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a>
<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="k">def</span> <span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span> <span class="c1"># 输入数据</span>
@@ -3623,7 +3623,7 @@
<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a>
<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="cm">/* 函数 */</span>
<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="kd">func</span><span class="w"> </span><span class="nx">function</span><span class="p">()</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w"> </span><span class="c1">// do something...</span>
<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w"> </span><span class="c1">// 执行某些操作...</span>
<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="p">}</span>
<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a>
@@ -3649,7 +3649,7 @@
<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a>
<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="cm">/* 函数 */</span>
<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="kd">function</span><span class="w"> </span><span class="nx">constFunc</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w"> </span><span class="c1">// do something</span>
<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w"> </span><span class="c1">// 执行某些操作</span>
<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="p">}</span>
<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a>
@@ -3675,7 +3675,7 @@
<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a>
<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="cm">/* 函数 */</span>
<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="kd">function</span><span class="w"> </span><span class="nx">constFunc</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w"> </span><span class="c1">// do something</span>
<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w"> </span><span class="c1">// 执行某些操作</span>
<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="p">}</span>
<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a>
@@ -3691,7 +3691,7 @@
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 函数 */</span>
<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">func</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w"> </span><span class="c1">// do something...</span>
<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w"> </span><span class="c1">// 执行某些操作...</span>
<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="p">}</span>
<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a>
@@ -3713,7 +3713,7 @@
<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a>
<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="cm">/* 函数 */</span>
<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="kt">int</span><span class="w"> </span><span class="nf">function</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w"> </span><span class="c1">// do something...</span>
<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w"> </span><span class="c1">// 执行某些操作...</span>
<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="p">}</span>
<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a>
@@ -3739,7 +3739,7 @@
<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a>
<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="cm">/* 函数 */</span>
<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="kd">func</span> <span class="nf">function</span><span class="p">()</span> <span class="p">-&gt;</span> <span class="nb">Int</span> <span class="p">{</span>
<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a> <span class="c1">// do something...</span>
<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a> <span class="c1">// 执行某些操作...</span>
<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a> <span class="k">return</span> <span class="mi">0</span>
<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="p">}</span>
<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a>
@@ -3766,7 +3766,7 @@
<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a>
<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="cm">/* 函数 */</span>
<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="kt">int</span><span class="w"> </span><span class="n">function</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w"> </span><span class="c1">// do something...</span>
<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w"> </span><span class="c1">// 执行某些操作...</span>
<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="p">}</span>
<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a>
@@ -3911,7 +3911,7 @@
<div class="tabbed-content">
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="kt">int</span><span class="w"> </span><span class="nf">function</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="w"> </span><span class="c1">// do something</span>
<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="w"> </span><span class="c1">// 执行某些操作</span>
<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="p">}</span>
<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="cm">/* 循环 O(1) */</span>
@@ -3929,7 +3929,7 @@
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="kt">int</span><span class="w"> </span><span class="nf">func</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="w"> </span><span class="c1">// do something</span>
<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="w"> </span><span class="c1">// 执行某些操作</span>
<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="p">}</span>
<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="cm">/* 循环 O(1) */</span>
@@ -3947,7 +3947,7 @@
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="k">def</span> <span class="nf">function</span><span class="p">()</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a> <span class="c1"># do something</span>
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a> <span class="c1"># 执行某些操作</span>
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a> <span class="k">return</span> <span class="mi">0</span>
<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a>
<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="k">def</span> <span class="nf">loop</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
@@ -3963,7 +3963,7 @@
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="kd">func</span><span class="w"> </span><span class="nx">function</span><span class="p">()</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="w"> </span><span class="c1">// do something</span>
<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="w"> </span><span class="c1">// 执行某些操作</span>
<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="p">}</span>
<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a>
@@ -3985,7 +3985,7 @@
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="kd">function</span><span class="w"> </span><span class="nx">constFunc</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="w"> </span><span class="c1">// do something</span>
<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="w"> </span><span class="c1">// 执行某些操作</span>
<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="p">}</span>
<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a><span class="cm">/* 循环 O(1) */</span>
@@ -4003,7 +4003,7 @@
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="kd">function</span><span class="w"> </span><span class="nx">constFunc</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="w"> </span><span class="c1">// do something</span>
<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="w"> </span><span class="c1">// 执行某些操作</span>
<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="p">}</span>
<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="cm">/* 循环 O(1) */</span>
@@ -4021,7 +4021,7 @@
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="kt">int</span><span class="w"> </span><span class="nf">func</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="w"> </span><span class="c1">// do something</span>
<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="w"> </span><span class="c1">// 执行某些操作</span>
<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="p">}</span>
<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="cm">/* 循环 O(1) */</span>
@@ -4039,7 +4039,7 @@
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="kt">int</span><span class="w"> </span><span class="nf">function</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="w"> </span><span class="c1">// do something</span>
<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="w"> </span><span class="c1">// 执行某些操作</span>
<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
<a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="p">}</span>
<a id="__codelineno-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="cm">/* 循环 O(1) */</span>
@@ -4058,7 +4058,7 @@
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="p">@</span><span class="n">discardableResult</span>
<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="kd">func</span> <span class="nf">function</span><span class="p">()</span> <span class="p">-&gt;</span> <span class="nb">Int</span> <span class="p">{</span>
<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a> <span class="c1">// do something</span>
<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a> <span class="c1">// 执行某些操作</span>
<a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a> <span class="k">return</span> <span class="mi">0</span>
<a id="__codelineno-32-5" name="__codelineno-32-5" href="#__codelineno-32-5"></a><span class="p">}</span>
<a id="__codelineno-32-6" name="__codelineno-32-6" href="#__codelineno-32-6"></a>
@@ -4084,7 +4084,7 @@
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="kt">int</span><span class="w"> </span><span class="n">function</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a><span class="w"> </span><span class="c1">// do something</span>
<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a><span class="w"> </span><span class="c1">// 执行某些操作</span>
<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
<a id="__codelineno-34-4" name="__codelineno-34-4" href="#__codelineno-34-4"></a><span class="p">}</span>
<a id="__codelineno-34-5" name="__codelineno-34-5" href="#__codelineno-34-5"></a><span class="cm">/* 循环 O(1) */</span>
@@ -4129,7 +4129,7 @@ O(1) &lt; O(\log n) &lt; O(n) &lt; O(n^2) &lt; O(2^n) \newline
<div class="tabbed-block">
<div class="highlight"><span class="filename">space_complexity.java</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="cm">/* 函数 */</span>
<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">function</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="w"> </span><span class="c1">// do something</span>
<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="w"> </span><span class="c1">// 执行某些操作</span>
<a id="__codelineno-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-36-5" name="__codelineno-36-5" href="#__codelineno-36-5"></a><span class="p">}</span>
<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></a>
@@ -4154,7 +4154,7 @@ O(1) &lt; O(\log n) &lt; O(n) &lt; O(n^2) &lt; O(2^n) \newline
<div class="tabbed-block">
<div class="highlight"><span class="filename">space_complexity.cpp</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="cm">/* 函数 */</span>
<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">func</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="w"> </span><span class="c1">// do something</span>
<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="w"> </span><span class="c1">// 执行某些操作</span>
<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="p">}</span>
<a id="__codelineno-37-6" name="__codelineno-37-6" href="#__codelineno-37-6"></a>
@@ -4179,7 +4179,7 @@ O(1) &lt; O(\log n) &lt; O(n) &lt; O(n^2) &lt; O(2^n) \newline
<div class="tabbed-block">
<div class="highlight"><span class="filename">space_complexity.py</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="k">def</span> <span class="nf">function</span><span class="p">()</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;函数&quot;&quot;&quot;</span>
<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a> <span class="c1"># do something</span>
<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a> <span class="c1"># 执行某些操作</span>
<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a> <span class="k">return</span> <span class="mi">0</span>
<a id="__codelineno-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></a>
<a id="__codelineno-38-6" name="__codelineno-38-6" href="#__codelineno-38-6"></a><span class="k">def</span> <span class="nf">constant</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
@@ -4199,7 +4199,7 @@ O(1) &lt; O(\log n) &lt; O(n) &lt; O(n^2) &lt; O(2^n) \newline
<div class="tabbed-block">
<div class="highlight"><span class="filename">space_complexity.go</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="cm">/* 函数 */</span>
<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">function</span><span class="p">()</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a><span class="w"> </span><span class="c1">// do something...</span>
<a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a><span class="w"> </span><span class="c1">// 执行某些操作...</span>
<a id="__codelineno-39-4" name="__codelineno-39-4" href="#__codelineno-39-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-39-5" name="__codelineno-39-5" href="#__codelineno-39-5"></a><span class="p">}</span>
<a id="__codelineno-39-6" name="__codelineno-39-6" href="#__codelineno-39-6"></a>
@@ -4226,7 +4226,7 @@ O(1) &lt; O(\log n) &lt; O(n) &lt; O(n^2) &lt; O(2^n) \newline
<div class="tabbed-block">
<div class="highlight"><span class="filename">space_complexity.js</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="cm">/* 函数 */</span>
<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">constFunc</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="w"> </span><span class="c1">// do something</span>
<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="w"> </span><span class="c1">// 执行某些操作</span>
<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a><span class="p">}</span>
<a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a>
@@ -4251,7 +4251,7 @@ O(1) &lt; O(\log n) &lt; O(n) &lt; O(n^2) &lt; O(2^n) \newline
<div class="tabbed-block">
<div class="highlight"><span class="filename">space_complexity.ts</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="cm">/* 函数 */</span>
<a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">constFunc</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></a><span class="w"> </span><span class="c1">// do something</span>
<a id="__codelineno-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></a><span class="w"> </span><span class="c1">// 执行某些操作</span>
<a id="__codelineno-41-4" name="__codelineno-41-4" href="#__codelineno-41-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
<a id="__codelineno-41-5" name="__codelineno-41-5" href="#__codelineno-41-5"></a><span class="p">}</span>
<a id="__codelineno-41-6" name="__codelineno-41-6" href="#__codelineno-41-6"></a>
@@ -4276,7 +4276,7 @@ O(1) &lt; O(\log n) &lt; O(n) &lt; O(n^2) &lt; O(2^n) \newline
<div class="tabbed-block">
<div class="highlight"><span class="filename">space_complexity.c</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="cm">/* 函数 */</span>
<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">func</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a><span class="w"> </span><span class="c1">// do something</span>
<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a><span class="w"> </span><span class="c1">// 执行某些操作</span>
<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a><span class="p">}</span>
<a id="__codelineno-42-6" name="__codelineno-42-6" href="#__codelineno-42-6"></a>
@@ -4302,7 +4302,7 @@ O(1) &lt; O(\log n) &lt; O(n) &lt; O(n^2) &lt; O(2^n) \newline
<div class="tabbed-block">
<div class="highlight"><span class="filename">space_complexity.cs</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="cm">/* 函数 */</span>
<a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">function</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></a><span class="w"> </span><span class="c1">// do something</span>
<a id="__codelineno-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></a><span class="w"> </span><span class="c1">// 执行某些操作</span>
<a id="__codelineno-43-4" name="__codelineno-43-4" href="#__codelineno-43-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
<a id="__codelineno-43-5" name="__codelineno-43-5" href="#__codelineno-43-5"></a><span class="p">}</span>
<a id="__codelineno-43-6" name="__codelineno-43-6" href="#__codelineno-43-6"></a>
@@ -4328,7 +4328,7 @@ O(1) &lt; O(\log n) &lt; O(n) &lt; O(n^2) &lt; O(2^n) \newline
<div class="highlight"><span class="filename">space_complexity.swift</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="cm">/* 函数 */</span>
<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a><span class="p">@</span><span class="n">discardableResult</span>
<a id="__codelineno-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></a><span class="kd">func</span> <span class="nf">function</span><span class="p">()</span> <span class="p">-&gt;</span> <span class="nb">Int</span> <span class="p">{</span>
<a id="__codelineno-44-4" name="__codelineno-44-4" href="#__codelineno-44-4"></a> <span class="c1">// do something</span>
<a id="__codelineno-44-4" name="__codelineno-44-4" href="#__codelineno-44-4"></a> <span class="c1">// 执行某些操作</span>
<a id="__codelineno-44-5" name="__codelineno-44-5" href="#__codelineno-44-5"></a> <span class="k">return</span> <span class="mi">0</span>
<a id="__codelineno-44-6" name="__codelineno-44-6" href="#__codelineno-44-6"></a><span class="p">}</span>
<a id="__codelineno-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></a>
@@ -4381,7 +4381,7 @@ O(1) &lt; O(\log n) &lt; O(n) &lt; O(n^2) &lt; O(2^n) \newline
<div class="tabbed-block">
<div class="highlight"><span class="filename">space_complexity.dart</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="cm">/* 函数 */</span>
<a id="__codelineno-46-2" name="__codelineno-46-2" href="#__codelineno-46-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">function</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-46-3" name="__codelineno-46-3" href="#__codelineno-46-3"></a><span class="w"> </span><span class="c1">// do something</span>
<a id="__codelineno-46-3" name="__codelineno-46-3" href="#__codelineno-46-3"></a><span class="w"> </span><span class="c1">// 执行某些操作</span>
<a id="__codelineno-46-4" name="__codelineno-46-4" href="#__codelineno-46-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
<a id="__codelineno-46-5" name="__codelineno-46-5" href="#__codelineno-46-5"></a><span class="p">}</span>
<a id="__codelineno-46-6" name="__codelineno-46-6" href="#__codelineno-46-6"></a>
@@ -4406,7 +4406,7 @@ O(1) &lt; O(\log n) &lt; O(n) &lt; O(n^2) &lt; O(2^n) \newline
<div class="tabbed-block">
<div class="highlight"><span class="filename">space_complexity.rs</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="cm">/* 函数 */</span>
<a id="__codelineno-47-2" name="__codelineno-47-2" href="#__codelineno-47-2"></a><span class="k">fn</span> <span class="nf">function</span><span class="p">()</span><span class="w"> </span>-&gt;<span class="kt">i32</span> <span class="p">{</span>
<a id="__codelineno-47-3" name="__codelineno-47-3" href="#__codelineno-47-3"></a><span class="w"> </span><span class="c1">// do something</span>
<a id="__codelineno-47-3" name="__codelineno-47-3" href="#__codelineno-47-3"></a><span class="w"> </span><span class="c1">// 执行某些操作</span>
<a id="__codelineno-47-4" name="__codelineno-47-4" href="#__codelineno-47-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-47-5" name="__codelineno-47-5" href="#__codelineno-47-5"></a><span class="p">}</span>
<a id="__codelineno-47-6" name="__codelineno-47-6" href="#__codelineno-47-6"></a>
@@ -4675,7 +4675,7 @@ O(1) &lt; O(\log n) &lt; O(n) &lt; O(n^2) &lt; O(2^n) \newline
</div>
</div>
</div>
<p>以下递归函数会同时存在 <span class="arithmatex">\(n\)</span> 个未返回的 <code>algorithm()</code> 函数，使用 <span class="arithmatex">\(O(n)\)</span> 大小的栈帧空间：</p>
<p>以下函数的递归深度为 <span class="arithmatex">\(n\)</span> ，即同时存在 <span class="arithmatex">\(n\)</span> 个未返回的 <code>linear_recur()</code> 函数，使用 <span class="arithmatex">\(O(n)\)</span> 大小的栈帧空间：</p>
<div class="tabbed-set tabbed-alternate" data-tabs="6:12"><input checked="checked" id="__tabbed_6_1" name="__tabbed_6" type="radio" /><input id="__tabbed_6_2" name="__tabbed_6" type="radio" /><input id="__tabbed_6_3" name="__tabbed_6" type="radio" /><input id="__tabbed_6_4" name="__tabbed_6" type="radio" /><input id="__tabbed_6_5" name="__tabbed_6" type="radio" /><input id="__tabbed_6_6" name="__tabbed_6" type="radio" /><input id="__tabbed_6_7" name="__tabbed_6" type="radio" /><input id="__tabbed_6_8" name="__tabbed_6" type="radio" /><input id="__tabbed_6_9" name="__tabbed_6" type="radio" /><input id="__tabbed_6_10" name="__tabbed_6" type="radio" /><input id="__tabbed_6_11" name="__tabbed_6" type="radio" /><input id="__tabbed_6_12" name="__tabbed_6" type="radio" /><div class="tabbed-labels"><label for="__tabbed_6_1">Java</label><label for="__tabbed_6_2">C++</label><label for="__tabbed_6_3">Python</label><label for="__tabbed_6_4">Go</label><label for="__tabbed_6_5">JS</label><label for="__tabbed_6_6">TS</label><label for="__tabbed_6_7">C</label><label for="__tabbed_6_8">C#</label><label for="__tabbed_6_9">Swift</label><label for="__tabbed_6_10">Zig</label><label for="__tabbed_6_11">Dart</label><label for="__tabbed_6_12">Rust</label></div>
<div class="tabbed-content">
<div class="tabbed-block">
@@ -4992,7 +4992,7 @@ O(1) &lt; O(\log n) &lt; O(n) &lt; O(n^2) &lt; O(2^n) \newline
</div>
</div>
</div>
<p>在以下递归函数中，同时存在 <span class="arithmatex">\(n\)</span> 个未返回的 <code>algorithm()</code> ，并且每个函数中都初始化了一个数组，长度分别为 <span class="arithmatex">\(n, n-1, n-2, ..., 2, 1\)</span> ，平均长度为 <span class="arithmatex">\(\frac{n}{2}\)</span> ，因此总体占用 <span class="arithmatex">\(O(n^2)\)</span> 空间。</p>
<p>以下函数的递归深度为 <span class="arithmatex">\(n\)</span> ，在每个递归函数中都初始化了一个数组，长度分别为 <span class="arithmatex">\(n, n-1, n-2, ..., 2, 1\)</span> ，平均长度为 <span class="arithmatex">\(n / 2\)</span> ，因此总体占用 <span class="arithmatex">\(O(n^2)\)</span> 空间。</p>
<div class="tabbed-set tabbed-alternate" data-tabs="8:12"><input checked="checked" id="__tabbed_8_1" name="__tabbed_8" type="radio" /><input id="__tabbed_8_2" name="__tabbed_8" type="radio" /><input id="__tabbed_8_3" name="__tabbed_8" type="radio" /><input id="__tabbed_8_4" name="__tabbed_8" type="radio" /><input id="__tabbed_8_5" name="__tabbed_8" type="radio" /><input id="__tabbed_8_6" name="__tabbed_8" type="radio" /><input id="__tabbed_8_7" name="__tabbed_8" type="radio" /><input id="__tabbed_8_8" name="__tabbed_8" type="radio" /><input id="__tabbed_8_9" name="__tabbed_8" type="radio" /><input id="__tabbed_8_10" name="__tabbed_8" type="radio" /><input id="__tabbed_8_11" name="__tabbed_8" type="radio" /><input id="__tabbed_8_12" name="__tabbed_8" type="radio" /><div class="tabbed-labels"><label for="__tabbed_8_1">Java</label><label for="__tabbed_8_2">C++</label><label for="__tabbed_8_3">Python</label><label for="__tabbed_8_4">Go</label><label for="__tabbed_8_5">JS</label><label for="__tabbed_8_6">TS</label><label for="__tabbed_8_7">C</label><label for="__tabbed_8_8">C#</label><label for="__tabbed_8_9">Swift</label><label for="__tabbed_8_10">Zig</label><label for="__tabbed_8_11">Dart</label><label for="__tabbed_8_12">Rust</label></div>
<div class="tabbed-content">
<div class="tabbed-block">
@@ -5283,9 +5283,8 @@ O(1) &lt; O(\log n) &lt; O(n) &lt; O(n^2) &lt; O(2^n) \newline
<p align="center"> 图：满二叉树产生的指数阶空间复杂度 </p>
<h3 id="5-olog-n">5. &nbsp; 对数阶 <span class="arithmatex">\(O(\log n)\)</span><a class="headerlink" href="#5-olog-n" title="Permanent link">&para;</a></h3>
<p>对数阶常见于分治算法和数据类型转换等。</p>
<p>例如归并排序算法，输入长度为 <span class="arithmatex">\(n\)</span> 的数组，每轮递归将数组从中点划分为两半，形成高度为 <span class="arithmatex">\(\log n\)</span> 的递归树，使用 <span class="arithmatex">\(O(\log n)\)</span> 栈帧空间。</p>
<p>再例如将数字转化为字符串，输入任意正整数 <span class="arithmatex">\(n\)</span> ，它的位数为 <span class="arithmatex">\(\log_{10} n + 1\)</span> ，即对应字符串长度为 <span class="arithmatex">\(\log_{10} n + 1\)</span> ，因此空间复杂度为 <span class="arithmatex">\(O(\log_{10} n + 1) = O(\log n)\)</span> 。</p>
<p>对数阶常见于分治算法。例如归并排序，输入长度为 <span class="arithmatex">\(n\)</span> 的数组，每轮递归将数组从中点划分为两半，形成高度为 <span class="arithmatex">\(\log n\)</span> 的递归树，使用 <span class="arithmatex">\(O(\log n)\)</span> 栈帧空间。</p>
<p>再例如将数字转化为字符串，输入一个正整数 <span class="arithmatex">\(n\)</span> ，它的位数为 <span class="arithmatex">\(\log_{10} n + 1\)</span> ，即对应字符串长度为 <span class="arithmatex">\(\log_{10} n + 1\)</span> ，因此空间复杂度为 <span class="arithmatex">\(O(\log_{10} n + 1) = O(\log n)\)</span> 。</p>
<h2 id="234">2.3.4 &nbsp; 权衡时间与空间<a class="headerlink" href="#234" title="Permanent link">&para;</a></h2>
<p>理想情况下，我们希望算法的时间复杂度和空间复杂度都能达到最优。然而在实际情况中，同时优化时间复杂度和空间复杂度通常是非常困难的。</p>
<p><strong>降低时间复杂度通常需要以提升空间复杂度为代价，反之亦然</strong>。我们将牺牲内存空间来提升算法运行速度的思路称为“以空间换时间”；反之，则称为“以时间换空间”。</p>
chapter_computational_complexity/summary/index.html
+4 -4
View File
@@ -547,7 +547,7 @@
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
<span class="md-ellipsis">
第 2 章 &nbsp; 复杂度
第 2 章 &nbsp; 时空复杂度
</span>
@@ -562,7 +562,7 @@
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="true">
<label class="md-nav__title" for="__nav_3">
<span class="md-nav__icon md-icon"></span>
第 2 章 &nbsp; 复杂度
第 2 章 &nbsp; 时空复杂度
</label>
<ul class="md-nav__list" data-md-scrollfix>
@@ -1204,7 +1204,7 @@
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
<span class="md-ellipsis">
第 6 章 &nbsp; 散列表
第 6 章 &nbsp; 哈希表
</span>
@@ -1219,7 +1219,7 @@
<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 6 章 &nbsp; 散列表
第 6 章 &nbsp; 哈希表
</label>
<ul class="md-nav__list" data-md-scrollfix>
chapter_computational_complexity/time_complexity/index.html
+17 -12
View File
@@ -547,7 +547,7 @@
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
<span class="md-ellipsis">
第 2 章 &nbsp; 复杂度
第 2 章 &nbsp; 时空复杂度
</span>
@@ -562,7 +562,7 @@
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="true">
<label class="md-nav__title" for="__nav_3">
<span class="md-nav__icon md-icon"></span>
第 2 章 &nbsp; 复杂度
第 2 章 &nbsp; 时空复杂度
</label>
<ul class="md-nav__list" data-md-scrollfix>
@@ -1307,7 +1307,7 @@
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
<span class="md-ellipsis">
第 6 章 &nbsp; 散列表
第 6 章 &nbsp; 哈希表
</span>
@@ -1322,7 +1322,7 @@
<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 6 章 &nbsp; 散列表
第 6 章 &nbsp; 哈希表
</label>
<ul class="md-nav__list" data-md-scrollfix>
@@ -5021,10 +5021,7 @@ O(1) &lt; O(\log n) &lt; O(n) &lt; O(n \log n) &lt; O(n^2) &lt; O(2^n) &lt; O(n!
<p><img alt="常数阶、线性阶和平方阶的时间复杂度" src="../time_complexity.assets/time_complexity_constant_linear_quadratic.png" /></p>
<p align="center"> 图：常数阶、线性阶和平方阶的时间复杂度 </p>
<p>以冒泡排序为例，外层循环执行 <span class="arithmatex">\(n - 1\)</span> 次，内层循环执行 <span class="arithmatex">\(n-1, n-2, \cdots, 2, 1\)</span> 次，平均为 <span class="arithmatex">\(\frac{n}{2}\)</span> 次，因此时间复杂度为 <span class="arithmatex">\(O(n^2)\)</span> ：</p>
<div class="arithmatex">\[
O((n - 1) \frac{n}{2}) = O(n^2)
\]</div>
<p>以冒泡排序为例，外层循环执行 <span class="arithmatex">\(n - 1\)</span> 次，内层循环执行 <span class="arithmatex">\(n-1, n-2, \dots, 2, 1\)</span> 次，平均为 <span class="arithmatex">\(n / 2\)</span> 次，因此时间复杂度为 <span class="arithmatex">\(O((n - 1) n / 2) = O(n^2)\)</span> 。</p>
<div class="tabbed-set tabbed-alternate" data-tabs="9:12"><input checked="checked" id="__tabbed_9_1" name="__tabbed_9" type="radio" /><input id="__tabbed_9_2" name="__tabbed_9" type="radio" /><input id="__tabbed_9_3" name="__tabbed_9" type="radio" /><input id="__tabbed_9_4" name="__tabbed_9" type="radio" /><input id="__tabbed_9_5" name="__tabbed_9" type="radio" /><input id="__tabbed_9_6" name="__tabbed_9" type="radio" /><input id="__tabbed_9_7" name="__tabbed_9" type="radio" /><input id="__tabbed_9_8" name="__tabbed_9" type="radio" /><input id="__tabbed_9_9" name="__tabbed_9" type="radio" /><input id="__tabbed_9_10" name="__tabbed_9" type="radio" /><input id="__tabbed_9_11" name="__tabbed_9" type="radio" /><input id="__tabbed_9_12" name="__tabbed_9" type="radio" /><div class="tabbed-labels"><label for="__tabbed_9_1">Java</label><label for="__tabbed_9_2">C++</label><label for="__tabbed_9_3">Python</label><label for="__tabbed_9_4">Go</label><label for="__tabbed_9_5">JS</label><label for="__tabbed_9_6">TS</label><label for="__tabbed_9_7">C</label><label for="__tabbed_9_8">C#</label><label for="__tabbed_9_9">Swift</label><label for="__tabbed_9_10">Zig</label><label for="__tabbed_9_11">Dart</label><label for="__tabbed_9_12">Rust</label></div>
<div class="tabbed-content">
<div class="tabbed-block">
@@ -5860,7 +5857,15 @@ O((n - 1) \frac{n}{2}) = O(n^2)
</div>
</div>
</div>
<p>对数阶常出现于基于分治策略的算法中，体现了“一分为多”和“化繁为简”的算法思想。它增长缓慢，是理想的时间复杂度，仅次于常数阶。</p>
<p>对数阶常出现于基于分治策略的算法中，体现了“一分为多”和“化繁为简”的算法思想。它增长缓慢，是仅次于常数阶的理想的时间复杂度。</p>
<div class="admonition tip">
<p class="admonition-title">Tip</p>
<p>准确来说，“一分为 <span class="arithmatex">\(m\)</span>”对应的时间复杂度是 <span class="arithmatex">\(O(\log_m n)\)</span> 。而通过对数换底公式，我们可以得到具有不同底数的、相等的时间复杂度：</p>
<div class="arithmatex">\[
O(\log_m n) = O(\log_k n / \log_k m) = O(\log_k n)
\]</div>
<p>因此我们通常会省略底数 <span class="arithmatex">\(m\)</span> ，将对数阶直接记为 <span class="arithmatex">\(O(\log n)\)</span> 。</p>
</div>
<h3 id="6-on-log-n">6. &nbsp; 线性对数阶 <span class="arithmatex">\(O(n \log n)\)</span><a class="headerlink" href="#6-on-log-n" title="Permanent link">&para;</a></h3>
<p>线性对数阶常出现于嵌套循环中，两层循环的时间复杂度分别为 <span class="arithmatex">\(O(\log n)\)</span> 和 <span class="arithmatex">\(O(n)\)</span> 。相关代码如下：</p>
<div class="tabbed-set tabbed-alternate" data-tabs="14:12"><input checked="checked" id="__tabbed_14_1" name="__tabbed_14" type="radio" /><input id="__tabbed_14_2" name="__tabbed_14" type="radio" /><input id="__tabbed_14_3" name="__tabbed_14" type="radio" /><input id="__tabbed_14_4" name="__tabbed_14" type="radio" /><input id="__tabbed_14_5" name="__tabbed_14" type="radio" /><input id="__tabbed_14_6" name="__tabbed_14" type="radio" /><input id="__tabbed_14_7" name="__tabbed_14" type="radio" /><input id="__tabbed_14_8" name="__tabbed_14" type="radio" /><input id="__tabbed_14_9" name="__tabbed_14" type="radio" /><input id="__tabbed_14_10" name="__tabbed_14" type="radio" /><input id="__tabbed_14_11" name="__tabbed_14" type="radio" /><input id="__tabbed_14_12" name="__tabbed_14" type="radio" /><div class="tabbed-labels"><label for="__tabbed_14_1">Java</label><label for="__tabbed_14_2">C++</label><label for="__tabbed_14_3">Python</label><label for="__tabbed_14_4">Go</label><label for="__tabbed_14_5">JS</label><label for="__tabbed_14_6">TS</label><label for="__tabbed_14_7">C</label><label for="__tabbed_14_8">C#</label><label for="__tabbed_14_9">Swift</label><label for="__tabbed_14_10">Zig</label><label for="__tabbed_14_11">Dart</label><label for="__tabbed_14_12">Rust</label></div>
@@ -6032,7 +6037,7 @@ O((n - 1) \frac{n}{2}) = O(n^2)
<h3 id="7-on">7. &nbsp; 阶乘阶 <span class="arithmatex">\(O(n!)\)</span><a class="headerlink" href="#7-on" title="Permanent link">&para;</a></h3>
<p>阶乘阶对应数学上的“全排列”问题。给定 <span class="arithmatex">\(n\)</span> 个互不重复的元素，求其所有可能的排列方案，方案数量为：</p>
<div class="arithmatex">\[
n! = n \times (n - 1) \times (n - 2) \times \cdots \times 2 \times 1
n! = n \times (n - 1) \times (n - 2) \times \dots \times 2 \times 1
\]</div>
<p>阶乘通常使用递归实现。例如在以下代码中，第一层分裂出 <span class="arithmatex">\(n\)</span> 个，第二层分裂出 <span class="arithmatex">\(n - 1\)</span> 个，以此类推，直至第 <span class="arithmatex">\(n\)</span> 层时停止分裂：</p>
<div class="tabbed-set tabbed-alternate" data-tabs="15:12"><input checked="checked" id="__tabbed_15_1" name="__tabbed_15" type="radio" /><input id="__tabbed_15_2" name="__tabbed_15" type="radio" /><input id="__tabbed_15_3" name="__tabbed_15" type="radio" /><input id="__tabbed_15_4" name="__tabbed_15" type="radio" /><input id="__tabbed_15_5" name="__tabbed_15" type="radio" /><input id="__tabbed_15_6" name="__tabbed_15" type="radio" /><input id="__tabbed_15_7" name="__tabbed_15" type="radio" /><input id="__tabbed_15_8" name="__tabbed_15" type="radio" /><input id="__tabbed_15_9" name="__tabbed_15" type="radio" /><input id="__tabbed_15_10" name="__tabbed_15" type="radio" /><input id="__tabbed_15_11" name="__tabbed_15" type="radio" /><input id="__tabbed_15_12" name="__tabbed_15" type="radio" /><div class="tabbed-labels"><label for="__tabbed_15_1">Java</label><label for="__tabbed_15_2">C++</label><label for="__tabbed_15_3">Python</label><label for="__tabbed_15_4">Go</label><label for="__tabbed_15_5">JS</label><label for="__tabbed_15_6">TS</label><label for="__tabbed_15_7">C</label><label for="__tabbed_15_8">C#</label><label for="__tabbed_15_9">Swift</label><label for="__tabbed_15_10">Zig</label><label for="__tabbed_15_11">Dart</label><label for="__tabbed_15_12">Rust</label></div>
@@ -6206,7 +6211,7 @@ n! = n \times (n - 1) \times (n - 2) \times \cdots \times 2 \times 1
<p><img alt="阶乘阶的时间复杂度" src="../time_complexity.assets/time_complexity_factorial.png" /></p>
<p align="center"> 图：阶乘阶的时间复杂度 </p>
<p>请注意，因为 <span class="arithmatex">\(n! &gt; 2^n\)</span> ，所以阶乘阶比指数阶增长得更快，在 <span class="arithmatex">\(n\)</span> 较大时也是不可接受的。</p>
<p>请注意，因为当 <span class="arithmatex">\(n \geq 4\)</span> 时恒有 <span class="arithmatex">\(n! &gt; 2^n\)</span> ，所以阶乘阶比指数阶增长得更快，在 <span class="arithmatex">\(n\)</span> 较大时也是不可接受的。</p>
<h2 id="225">2.2.5 &nbsp; 最差、最佳、平均时间复杂度<a class="headerlink" href="#225" title="Permanent link">&para;</a></h2>
<p><strong>算法的时间效率往往不是固定的，而是与输入数据的分布有关</strong>。假设输入一个长度为 <span class="arithmatex">\(n\)</span> 的数组 <code>nums</code> ，其中 <code>nums</code> 由从 <span class="arithmatex">\(1\)</span> 至 <span class="arithmatex">\(n\)</span> 的数字组成，每个数字只出现一次，但元素顺序是随机打乱的，任务目标是返回元素 <span class="arithmatex">\(1\)</span> 的索引。我们可以得出以下结论。</p>
<ul>
@@ -6546,7 +6551,7 @@ n! = n \times (n - 1) \times (n - 2) \times \cdots \times 2 \times 1
</div>
<p>值得说明的是，我们在实际中很少使用最佳时间复杂度，因为通常只有在很小概率下才能达到，可能会带来一定的误导性。<strong>而最差时间复杂度更为实用，因为它给出了一个效率安全值</strong>，让我们可以放心地使用算法。</p>
<p>从上述示例可以看出，最差或最佳时间复杂度只出现于“特殊的数据分布”，这些情况的出现概率可能很小，并不能真实地反映算法运行效率。相比之下，<strong>平均时间复杂度可以体现算法在随机输入数据下的运行效率</strong>，用 <span class="arithmatex">\(\Theta\)</span> 记号来表示。</p>
<p>对于部分算法，我们可以简单地推算出随机数据分布下的平均情况。比如上述示例，由于输入数组是被打乱的，因此元素 <span class="arithmatex">\(1\)</span> 出现在任意索引的概率都是相等的，那么算法的平均循环次数就是数组长度的一半 <span class="arithmatex">\(\frac{n}{2}\)</span> ，平均时间复杂度为 <span class="arithmatex">\(\Theta(\frac{n}{2}) = \Theta(n)\)</span> 。</p>
<p>对于部分算法，我们可以简单地推算出随机数据分布下的平均情况。比如上述示例，由于输入数组是被打乱的，因此元素 <span class="arithmatex">\(1\)</span> 出现在任意索引的概率都是相等的，那么算法的平均循环次数就是数组长度的一半 <span class="arithmatex">\(n / 2\)</span> ，平均时间复杂度为 <span class="arithmatex">\(\Theta(n / 2) = \Theta(n)\)</span> 。</p>
<p>但对于较为复杂的算法，计算平均时间复杂度往往是比较困难的，因为很难分析出在数据分布下的整体数学期望。在这种情况下，我们通常使用最差时间复杂度作为算法效率的评判标准。</p>
<div class="admonition question">
<p class="admonition-title">为什么很少看到 <span class="arithmatex">\(\Theta\)</span> 符号？</p>