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<!-- Page content -->
<h1 id="22">2.2 &nbsp; 迭代与递归<a class="headerlink" href="#22" title="Permanent link">&para;</a></h1>
<p>在数据结构与算法中，重复执行某个任务是很常见的，其与算法的复杂度密切相关。而要重复执行某个任务，我们通常会选用两种基本的程序结构：迭代和递归。</p>
<p>在算法中，重复执行某个任务是很常见的，其与复杂度分析息息相关。因此，在展开介绍时间复杂度和空间复杂度之前，我们先来了解如何在程序中实现重复执行任务，即两种基本的程序控制结构：迭代、递归。</p>
<h2 id="221">2.2.1 &nbsp; 迭代<a class="headerlink" href="#221" title="Permanent link">&para;</a></h2>
<p>「迭代 iteration」是一种重复执行某个任务的控制结构。在迭代中，程序会在满足一定的条件下重复执行某段代码，直到这个条件不再满足。</p>
<h3 id="1-for">1. &nbsp; for 循环<a class="headerlink" href="#1-for" title="Permanent link">&para;</a></h3>

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<li>整数类型 <code>byte</code> 占用 <span class="arithmatex">\(1\)</span> byte = <span class="arithmatex">\(8\)</span> bits ，可以表示 <span class="arithmatex">\(2^{8}\)</span> 个数字。</li>
<li>整数类型 <code>int</code> 占用 <span class="arithmatex">\(4\)</span> bytes = <span class="arithmatex">\(32\)</span> bits ，可以表示 <span class="arithmatex">\(2^{32}\)</span> 个数字。</li>
</ul>
<p>表 3-1 列举了各种基本数据类型的占用空间、取值范围和默认值。此表格无须硬背，大致理解即可，需要时可以通过查表来回忆。</p>
<p>表 3-1 列举了 Java 中各种基本数据类型的占用空间、取值范围和默认值。此表格无须硬背，大致理解即可，需要时可以通过查表来回忆。</p>
<p align="center"> 表 3-1 &nbsp; 基本数据类型的占用空间和取值范围 </p>
<div class="center-table">
@ -3354,7 +3354,7 @@
<td>4 bytes</td>
<td><span class="arithmatex">\(1.175 \times 10^{-38}\)</span></td>
<td><span class="arithmatex">\(3.403 \times 10^{38}\)</span></td>
<td><span class="arithmatex">\(0.0 f\)</span></td>
<td><span class="arithmatex">\(0.0f\)</span></td>
</tr>
<tr>
<td></td>
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<tr>
<td>字符</td>
<td><code>char</code></td>
<td>2 bytes / 1 byte</td>
<td>2 bytes</td>
<td><span class="arithmatex">\(0\)</span></td>
<td><span class="arithmatex">\(2^{16} - 1\)</span></td>
<td><span class="arithmatex">\(0\)</span></td>
@ -3383,8 +3383,9 @@
</tbody>
</table>
</div>
<p>对于表 3-1 ，需要注意以下几点。</p>
<p>请注意，表 3-1 针对的是 Java 的基本数据类型的情况。每种编程语言有各自的数据类型定义，它们的占用空间、取值范围和默认值可能会有所不同。</p>
<ul>
<li>在 Python 中，整数类型 <code>int</code> 可以是任意大小，只受限于可用内存；浮点数 <code>float</code> 是双精度 64 位；没有 <code>char</code> 类型，单个字符实际上是长度为 1 的字符串 <code>str</code> 。</li>
<li>C 和 C++ 未明确规定基本数据类型大小，而因实现和平台各异。表 3-1 遵循 LP64 <a href="https://en.cppreference.com/w/cpp/language/types#Properties">数据模型</a>，其用于包括 Linux 和 macOS 在内的 Unix 64 位操作系统。</li>
<li>字符 <code>char</code> 的大小在 C 和 C++ 中为 1 字节，在大多数编程语言中取决于特定的字符编码方法，详见“字符编码”章节。</li>
<li>即使表示布尔量仅需 1 位（<span class="arithmatex">\(0\)</span> 或 <span class="arithmatex">\(1\)</span>），它在内存中通常被存储为 1 字节。这是因为现代计算机 CPU 通常将 1 字节作为最小寻址内存单元。</li>

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<p align="center"> 图 1-4 &nbsp; 数据结构与算法的关系 </p>
<p>数据结构与算法犹如图 1-5 所示的拼装积木。一套积木，除了包含许多零件之外，还附有详细的组装说明书。我们按照说明书一步步操作，就能组装出精美的积木模型。</p>
<p><a class="glightbox" href="../what_is_dsa.assets/assembling_blocks.jpg" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="拼装积木" src="../what_is_dsa.assets/assembling_blocks.jpg" /></a></p>
<p><a class="glightbox" href="../what_is_dsa.assets/assembling_blocks.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="拼装积木" src="../what_is_dsa.assets/assembling_blocks.png" /></a></p>
<p align="center"> 图 1-5 &nbsp; 拼装积木 </p>
<p>两者的详细对应关系如表 1-1 所示。</p>

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<a href=".." title="Hello 算法" class="md-nav__button md-logo" aria-label="Hello 算法" data-md-component="logo">
<img src="../assets/images/logo.png" alt="logo">
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<img src="../../assets/images/logo.svg" alt="logo">
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<a href="../.." title="Hello 算法" class="md-nav__button md-logo" aria-label="Hello 算法" data-md-component="logo">
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<a href="../.." title="Hello 算法" class="md-nav__button md-logo" aria-label="Hello 算法" data-md-component="logo">
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Hello 算法

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<img src="../../assets/images/logo.png" alt="logo">
<img src="../../assets/images/logo.svg" alt="logo">
</a>
Hello 算法

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