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chapter_computational_complexity/space_complexity/index.html
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@ -5498,7 +5498,7 @@ O(1) < O(\log n) < O(n) < O(n^2) < O(2^n) \newline
<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> <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。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处划分为两半，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>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处划分为两半，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> <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">\(\lfloor \log_{10} n \rfloor + 1\)</span> ，即对应字符串长度为 <span class="arithmatex">\(\lfloor \log_{10} n \rfloor + 1\)</span> ，因此空间复杂度为 <span class="arithmatex">\(O(\log_{10} n + 1) = O(\log n)\)</span> 。</p>
<h2 id="244">2.4.4 &nbsp; 权衡时间与空间<a class="headerlink" href="#244" title="Permanent link">&para;</a></h2> <h2 id="244">2.4.4 &nbsp; 权衡时间与空间<a class="headerlink" href="#244" 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非常困难。</p> <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非常困难。</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> <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>

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chapter_data_structure/character_encoding/index.html
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@ -3624,7 +3624,7 @@
<li>JavaScript 和 TypeScript 的字符串使用 UTF-16 编码的原因与 Java 类似。当 1995 年 Netscape 公司首次推出 JavaScript 语言时，Unicode 还处于发展早期，那时候使用 16 位的编码就足以表示所有的 Unicode 字符了。</li> <li>JavaScript 和 TypeScript 的字符串使用 UTF-16 编码的原因与 Java 类似。当 1995 年 Netscape 公司首次推出 JavaScript 语言时，Unicode 还处于发展早期，那时候使用 16 位的编码就足以表示所有的 Unicode 字符了。</li>
<li>C# 使用 UTF-16 编码，主要是因为 .NET 平台是由 Microsoft 设计的，而 Microsoft 的很多技术（包括 Windows 操作系统）都广泛使用 UTF-16 编码。</li> <li>C# 使用 UTF-16 编码，主要是因为 .NET 平台是由 Microsoft 设计的，而 Microsoft 的很多技术（包括 Windows 操作系统）都广泛使用 UTF-16 编码。</li>
</ul> </ul>
<p>由于以上编程语言对字符数量的低估，它们不得不采取“代理对”的方式来表示超过 16 位长度的 Unicode 字符。这是一个不得已为之的无奈之举。一方面，包含代理对的字符串中，一个字符可能占用 2 字节或 4 字节，从而丧失了等长编码的优势。另一方面，处理代理对需要增加额外代码，这提高了编程的复杂性和调试难度。</p> <p>由于以上编程语言对字符数量的低估，它们不得不采取“代理对”的方式来表示超过 16 位长度的 Unicode 字符。这是一个不得已为之的无奈之举。一方面，包含代理对的字符串中，一个字符可能占用 2 字节或 4 字节，从而丧失了等长编码的优势。另一方面，处理代理对需要额外增加代码，这提高了编程的复杂性和调试难度。</p>
<p>出于以上原因，部分编程语言提出了一些不同的编码方案。</p> <p>出于以上原因，部分编程语言提出了一些不同的编码方案。</p>
<ul> <ul>
<li>Python 中的 <code>str</code> 使用 Unicode 编码，并采用一种灵活的字符串表示，存储的字符长度取决于字符串中最大的 Unicode 码点。若字符串中全部是 ASCII 字符，则每个字符占用 1 字节；如果有字符超出了 ASCII 范围，但全部在基本多语言平面（BMP）内，则每个字符占用 2 字节；如果有超出 BMP 的字符，则每个字符占用 4 字节。</li> <li>Python 中的 <code>str</code> 使用 Unicode 编码，并采用一种灵活的字符串表示，存储的字符长度取决于字符串中最大的 Unicode 码点。若字符串中全部是 ASCII 字符，则每个字符占用 1 字节；如果有字符超出了 ASCII 范围，但全部在基本多语言平面（BMP）内，则每个字符占用 2 字节；如果有超出 BMP 的字符，则每个字符占用 4 字节。</li>

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chapter_data_structure/classification_of_data_structure/index.html
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@ -3520,18 +3520,17 @@
<p><strong>逻辑结构揭示了数据元素之间的逻辑关系</strong>。在数组和链表中，数据按照一定顺序排列，体现了数据之间的线性关系；而在树中，数据从顶部向下按层次排列，表现出“祖先”与“后代”之间的派生关系；图则由节点和边构成，反映了复杂的网络关系。</p> <p><strong>逻辑结构揭示了数据元素之间的逻辑关系</strong>。在数组和链表中，数据按照一定顺序排列，体现了数据之间的线性关系；而在树中，数据从顶部向下按层次排列，表现出“祖先”与“后代”之间的派生关系；图则由节点和边构成，反映了复杂的网络关系。</p>
<p>如图 3-1 所示，逻辑结构可分为“线性”和“非线性”两大类。线性结构比较直观，指数据在逻辑关系上呈线性排列；非线性结构则相反，呈非线性排列。</p> <p>如图 3-1 所示，逻辑结构可分为“线性”和“非线性”两大类。线性结构比较直观，指数据在逻辑关系上呈线性排列；非线性结构则相反，呈非线性排列。</p>
<ul> <ul>
<li><strong>线性数据结构</strong>：数组、链表、栈、队列、哈希表。</li> <li><strong>线性数据结构</strong>：数组、链表、栈、队列、哈希表，元素之间是一对一的顺序关系。</li>
<li><strong>非线性数据结构</strong>：树、堆、图、哈希表。</li> <li><strong>非线性数据结构</strong>：树、堆、图、哈希表。</li>
</ul> </ul>
<p>非线性数据结构可以进一步划分为树形结构和网状结构。</p>
<ul>
<li><strong>树形结构</strong>：树、堆、哈希表，元素之间是一对多的关系。</li>
<li><strong>网状结构</strong>：图，元素之间是多对多的关系。</li>
</ul>
<p><a class="glightbox" href="../classification_of_data_structure.assets/classification_logic_structure.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="线性数据结构与非线性数据结构" class="animation-figure" src="../classification_of_data_structure.assets/classification_logic_structure.png" /></a></p> <p><a class="glightbox" href="../classification_of_data_structure.assets/classification_logic_structure.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="线性数据结构与非线性数据结构" class="animation-figure" src="../classification_of_data_structure.assets/classification_logic_structure.png" /></a></p>
<p align="center"> 图 3-1 &nbsp; 线性数据结构与非线性数据结构 </p> <p align="center"> 图 3-1 &nbsp; 线性数据结构与非线性数据结构 </p>
<p>非线性数据结构可以进一步划分为树形结构和网状结构。</p>
<ul>
<li><strong>线性结构</strong>：数组、链表、队列、栈、哈希表，元素之间是一对一的顺序关系。</li>
<li><strong>树形结构</strong>：树、堆、哈希表，元素之间是一对多的关系。</li>
<li><strong>网状结构</strong>：图，元素之间是多对多的关系。</li>
</ul>
<h2 id="312">3.1.2 &nbsp; 物理结构：连续与分散<a class="headerlink" href="#312" title="Permanent link">&para;</a></h2> <h2 id="312">3.1.2 &nbsp; 物理结构：连续与分散<a class="headerlink" href="#312" title="Permanent link">&para;</a></h2>
<p><strong>当算法程序运行时，正在处理的数据主要存储在内存中</strong>。图 3-2 展示了一个计算机内存条，其中每个黑色方块都包含一块内存空间。我们可以将内存想象成一个巨大的 Excel 表格，其中每个单元格都可以存储一定大小的数据。</p> <p><strong>当算法程序运行时，正在处理的数据主要存储在内存中</strong>。图 3-2 展示了一个计算机内存条，其中每个黑色方块都包含一块内存空间。我们可以将内存想象成一个巨大的 Excel 表格，其中每个单元格都可以存储一定大小的数据。</p>
<p><strong>系统通过内存地址来访问目标位置的数据</strong>。如图 3-2 所示，计算机根据特定规则为表格中的每个单元格分配编号，确保每个内存空间都有唯一的内存地址。有了这些地址，程序便可以访问内存中的数据。</p> <p><strong>系统通过内存地址来访问目标位置的数据</strong>。如图 3-2 所示，计算机根据特定规则为表格中的每个单元格分配编号，确保每个内存空间都有唯一的内存地址。有了这些地址，程序便可以访问内存中的数据。</p>

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chapter_stack_and_queue/queue/index.html
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@ -4604,7 +4604,7 @@
<a id="__codelineno-22-16" name="__codelineno-22-16" href="#__codelineno-22-16"></a><span class="cm">/* 析构函数 */</span> <a id="__codelineno-22-16" name="__codelineno-22-16" href="#__codelineno-22-16"></a><span class="cm">/* 析构函数 */</span>
<a id="__codelineno-22-17" name="__codelineno-22-17" href="#__codelineno-22-17"></a><span class="kt">void</span><span class="w"> </span><span class="nf">delLinkedListQueue</span><span class="p">(</span><span class="n">LinkedListQueue</span><span class="w"> </span><span class="o">*</span><span class="n">queue</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> <a id="__codelineno-22-17" name="__codelineno-22-17" href="#__codelineno-22-17"></a><span class="kt">void</span><span class="w"> </span><span class="nf">delLinkedListQueue</span><span class="p">(</span><span class="n">LinkedListQueue</span><span class="w"> </span><span class="o">*</span><span class="n">queue</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-22-18" name="__codelineno-22-18" href="#__codelineno-22-18"></a><span class="w"> </span><span class="c1">// 释放所有节点</span> <a id="__codelineno-22-18" name="__codelineno-22-18" href="#__codelineno-22-18"></a><span class="w"> </span><span class="c1">// 释放所有节点</span>
<a id="__codelineno-22-19" name="__codelineno-22-19" href="#__codelineno-22-19"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">front</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> <a id="__codelineno-22-19" name="__codelineno-22-19" href="#__codelineno-22-19"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">front</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-22-20" name="__codelineno-22-20" href="#__codelineno-22-20"></a><span class="w"> </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">front</span><span class="p">;</span> <a id="__codelineno-22-20" name="__codelineno-22-20" href="#__codelineno-22-20"></a><span class="w"> </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">front</span><span class="p">;</span>
<a id="__codelineno-22-21" name="__codelineno-22-21" href="#__codelineno-22-21"></a><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">front</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span> <a id="__codelineno-22-21" name="__codelineno-22-21" href="#__codelineno-22-21"></a><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">front</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
<a id="__codelineno-22-22" name="__codelineno-22-22" href="#__codelineno-22-22"></a><span class="w"> </span><span class="n">free</span><span class="p">(</span><span class="n">tmp</span><span class="p">);</span> <a id="__codelineno-22-22" name="__codelineno-22-22" href="#__codelineno-22-22"></a><span class="w"> </span><span class="n">free</span><span class="p">(</span><span class="n">tmp</span><span class="p">);</span>

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en/chapter_stack_and_queue/queue/index.html
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@ -2471,7 +2471,7 @@
<a id="__codelineno-22-16" name="__codelineno-22-16" href="#__codelineno-22-16"></a><span class="cm">/* 析构函数 */</span> <a id="__codelineno-22-16" name="__codelineno-22-16" href="#__codelineno-22-16"></a><span class="cm">/* 析构函数 */</span>
<a id="__codelineno-22-17" name="__codelineno-22-17" href="#__codelineno-22-17"></a><span class="kt">void</span><span class="w"> </span><span class="nf">delLinkedListQueue</span><span class="p">(</span><span class="n">LinkedListQueue</span><span class="w"> </span><span class="o">*</span><span class="n">queue</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> <a id="__codelineno-22-17" name="__codelineno-22-17" href="#__codelineno-22-17"></a><span class="kt">void</span><span class="w"> </span><span class="nf">delLinkedListQueue</span><span class="p">(</span><span class="n">LinkedListQueue</span><span class="w"> </span><span class="o">*</span><span class="n">queue</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-22-18" name="__codelineno-22-18" href="#__codelineno-22-18"></a><span class="w"> </span><span class="c1">// 释放所有节点</span> <a id="__codelineno-22-18" name="__codelineno-22-18" href="#__codelineno-22-18"></a><span class="w"> </span><span class="c1">// 释放所有节点</span>
<a id="__codelineno-22-19" name="__codelineno-22-19" href="#__codelineno-22-19"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">front</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> <a id="__codelineno-22-19" name="__codelineno-22-19" href="#__codelineno-22-19"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">front</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-22-20" name="__codelineno-22-20" href="#__codelineno-22-20"></a><span class="w"> </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">front</span><span class="p">;</span> <a id="__codelineno-22-20" name="__codelineno-22-20" href="#__codelineno-22-20"></a><span class="w"> </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">front</span><span class="p">;</span>
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style="height: 9.574%; left: 25.409%; top: 40.747%;"> style="height: 9.574%; left: 25.409%; top: 40.747%;">
<p class="hero-caption" style="left: 28.805%; top: 53.808%;">排序</p> <span class="hero-caption" style="left: 28.805%; top: 53.808%;">排序</span>
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<p class="hero-caption" style="left: 4.742%; top: 50.113%;">回溯</p> <span class="hero-caption" style="left: 4.742%; top: 50.113%;">回溯</span>
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<p class="hero-caption" style="left: 8.561%; top: 75.351%;">动态规划</p> <span class="hero-caption" style="left: 8.561%; top: 75.351%;">动态规划</span>
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<p class="hero-caption" style="left: 21.619%; top: 86.85%;">贪心</p> <span class="hero-caption" style="left: 21.619%; top: 86.85%;">贪心</span>
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动画图解、一键运行的数据结构与算法教程 动画图解、一键运行的数据结构与算法教程
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<p>代码仓库</p> <span>代码仓库</span>
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@ -381,7 +381,7 @@
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<p style="margin-top: 2em;">提供网页版和 PDF 版，兼容 PC、平板和手机，随时随地阅读</p> <p style="margin: 2em auto;">提供网页版和 PDF 版，兼容 PC、平板和手机，随时随地阅读</p>
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<h3 style="text-align: center; margin: 1em auto;">推荐语</h3> <h3 style="text-align: center; margin: 1em auto;">推荐语</h3>
<div class="intro-container" style="margin-bottom: 1em;"> <div class="intro-container" style="margin: 0 auto;">
<div class="intro-text endor-text"> <div class="intro-text endor-text">
<p style="margin-bottom: 0;">“一本通俗易懂的数据结构与算法入门书，引导读者手脑并用地学习，强烈推荐算法初学者阅读。”</p> <p style="margin-bottom: 0;">“一本通俗易懂的数据结构与算法入门书，引导读者手脑并用地学习，强烈推荐算法初学者阅读。”</p>
<p style="font-weight: bold;">—— 邓俊辉，清华大学计算机系教授</p> <p style="font-weight: bold;">—— 邓俊辉，清华大学计算机系教授</p>

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stylesheets/extra.css
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@ -204,7 +204,7 @@ body {
background-color: var(--md-default-bg-color); background-color: var(--md-default-bg-color);
color: var(--md-default-fg-color); color: var(--md-default-fg-color);
font-size: 0.9rem; font-size: 0.9rem;
padding: 2em; padding: 3em 2em;
text-align: center; text-align: center;
} }
@ -221,7 +221,7 @@ body {
justify-content: center; justify-content: center;
border-radius: 10em; border-radius: 10em;
margin: 0 0.1em; margin: 0 0.1em;
padding: 0.5em 1.3em; padding: 0.6em 1.3em;
border: none; border: none;
background-color: var(--md-typeset-btn-color); background-color: var(--md-typeset-btn-color);
color: var(--md-primary-fg-color) !important; color: var(--md-primary-fg-color) !important;
@ -234,9 +234,10 @@ body {
background-color: var(--md-typeset-btn-hover-color); background-color: var(--md-typeset-btn-hover-color);
} }
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margin-bottom: 0.1em; margin-bottom: 0.07em;
white-space: nowrap;
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@ -257,18 +258,22 @@ body {
} }
.text-button { .text-button {
width: 100%;
display: flex; display: flex;
flex-direction: row; flex-direction: row;
align-items: center; align-items: center;
color: var(--md-typeset-btn-color); color: var(--md-typeset-btn-color);
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margin: 0 1em;
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display: inline-block; display: inline-block;
fill: var(--md-typeset-btn-color); fill: var(--md-typeset-btn-color);
@ -288,7 +293,7 @@ body {
padding: 0; padding: 0;
position: relative; position: relative;
color: white; color: white;
font-size: min(2vh, 2.5vw); font-size: min(1.8vh, 2.5vw);
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@ -1 +0,0 @@
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