1683 lines
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数组（Array）
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链表（LinkedList）
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</li>
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列表（List）
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小结
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栈与队列
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栈与队列
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双向队列（Deque）
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散列表
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散列表
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<a href="../../chapter_hashing/hash_map/" class="md-nav__link">
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哈希表（HashMap）
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<li class="md-nav__item">
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<label class="md-nav__link" for="__nav_8">
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二叉树
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<nav class="md-nav" aria-label="二叉树" data-md-level="1">
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二叉树
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</label>
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二叉树（Binary Tree）
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<li class="md-nav__item">
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<a href="../../chapter_tree/binary_tree_types/" class="md-nav__link">
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<a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
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二叉搜索树
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<li class="md-nav__item">
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<a href="../../chapter_tree/avl_tree/" class="md-nav__link">
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AVL 树 *
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_tree/summary/" class="md-nav__link">
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小结
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</ul>
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</nav>
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<li class="md-nav__item md-nav__item--section md-nav__item--nested">
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基本数据类型
|
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</a>
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</li>
|
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|
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<li class="md-nav__item">
|
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<a href="#_3" class="md-nav__link">
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计算机内存
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<a href="https://github.com/krahets/hello-algo/tree/master/docs/chapter_data_structure/data_and_memory.md" title="编辑此页" class="md-content__button md-icon">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M20.71 7.04c.39-.39.39-1.04 0-1.41l-2.34-2.34c-.37-.39-1.02-.39-1.41 0l-1.84 1.83 3.75 3.75M3 17.25V21h3.75L17.81 9.93l-3.75-3.75L3 17.25Z"/></svg>
|
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</a>
|
||
|
||
|
||
<h1 id="_1">数据与内存<a class="headerlink" href="#_1" title="Permanent link">¶</a></h1>
|
||
<h2 id="_2">基本数据类型<a class="headerlink" href="#_2" title="Permanent link">¶</a></h2>
|
||
<p>谈到计算机中的数据，我们能够想到文本、图片、视频、语音、3D 模型等等，这些数据虽然组织形式不同，但是有一个共同点，即都是由各种基本数据类型构成的。</p>
|
||
<p><strong>「基本数据类型」是 CPU 可以直接进行运算的类型，在算法中直接被使用。</strong></p>
|
||
<ul>
|
||
<li>「整数」根据不同的长度分为 byte, short, int, long ，根据算法需求选用，即在满足取值范围的情况下尽量减小内存空间占用。</li>
|
||
<li>「浮点数」代表小数，根据长度分为 float, double ，同样根据算法的实际需求选用。</li>
|
||
<li>「字符」在计算机中是以字符集的形式保存的，char 的值实际上是数字，代表字符集中的编号，计算机通过字符集查表来完成编号到字符的转换。</li>
|
||
<li>「布尔」代表逻辑中的 ”是“ 与 ”否“ ，其占用空间需要具体根据编程语言确定，通常为 1 byte 或 1 bit 。</li>
|
||
</ul>
|
||
<div class="admonition note">
|
||
<p class="admonition-title">字节与比特</p>
|
||
<p>1 字节 (byte) = 8 比特 (bit) ， 1 比特即最基本的 1 个二进制位</p>
|
||
</div>
|
||
<p align="center"> Table. Java 的基本数据类型 </p>
|
||
|
||
<div class="center-table">
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>类别</th>
|
||
<th>符号</th>
|
||
<th>占用空间</th>
|
||
<th>取值范围</th>
|
||
<th>默认值</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr>
|
||
<td>整数</td>
|
||
<td>byte</td>
|
||
<td>1 byte</td>
|
||
<td><span class="arithmatex">\(-2^7\)</span> ~ <span class="arithmatex">\(2^7 - 1\)</span> ( <span class="arithmatex">\(-128\)</span> ~ <span class="arithmatex">\(127\)</span> )</td>
|
||
<td><span class="arithmatex">\(0\)</span></td>
|
||
</tr>
|
||
<tr>
|
||
<td></td>
|
||
<td>short</td>
|
||
<td>2 bytes</td>
|
||
<td><span class="arithmatex">\(-2^{15}\)</span> ~ <span class="arithmatex">\(2^{15} - 1\)</span></td>
|
||
<td><span class="arithmatex">\(0\)</span></td>
|
||
</tr>
|
||
<tr>
|
||
<td></td>
|
||
<td><strong>int</strong></td>
|
||
<td>4 bytes</td>
|
||
<td><span class="arithmatex">\(-2^{31}\)</span> ~ <span class="arithmatex">\(2^{31} - 1\)</span></td>
|
||
<td><span class="arithmatex">\(0\)</span></td>
|
||
</tr>
|
||
<tr>
|
||
<td></td>
|
||
<td>long</td>
|
||
<td>8 bytes</td>
|
||
<td><span class="arithmatex">\(-2^{63}\)</span> ~ <span class="arithmatex">\(2^{63} - 1\)</span></td>
|
||
<td><span class="arithmatex">\(0\)</span></td>
|
||
</tr>
|
||
<tr>
|
||
<td>浮点数</td>
|
||
<td><strong>float</strong></td>
|
||
<td>4 bytes</td>
|
||
<td><span class="arithmatex">\(-3.4 \times 10^{38}\)</span> ~ <span class="arithmatex">\(3.4 \times 10^{38}\)</span></td>
|
||
<td><span class="arithmatex">\(0.0\)</span> f</td>
|
||
</tr>
|
||
<tr>
|
||
<td></td>
|
||
<td>double</td>
|
||
<td>8 bytes</td>
|
||
<td><span class="arithmatex">\(-1.7 \times 10^{308}\)</span> ~ <span class="arithmatex">\(1.7 \times 10^{308}\)</span></td>
|
||
<td><span class="arithmatex">\(0.0\)</span></td>
|
||
</tr>
|
||
<tr>
|
||
<td>字符</td>
|
||
<td><strong>char</strong></td>
|
||
<td>2 bytes</td>
|
||
<td><span class="arithmatex">\(0\)</span> ~ <span class="arithmatex">\(2^{16} - 1\)</span></td>
|
||
<td><span class="arithmatex">\(0\)</span></td>
|
||
</tr>
|
||
<tr>
|
||
<td>布尔</td>
|
||
<td><strong>boolean(bool)</strong></td>
|
||
<td>1 byte / 1 bit</td>
|
||
<td><span class="arithmatex">\(\text{true}\)</span> 或 <span class="arithmatex">\(\text{false}\)</span></td>
|
||
<td><span class="arithmatex">\(\text{false}\)</span></td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
</div>
|
||
<div class="admonition tip">
|
||
<p class="admonition-title">Tip</p>
|
||
<p>以上表格中，加粗项在「算法题」中最为常用。此表格无需硬背，大致理解即可，需要时可以通过查表来回忆。</p>
|
||
</div>
|
||
<p><strong>「基本数据类型」与「数据结构」之间的联系与区别</strong></p>
|
||
<p>我们知道，数据结构是在计算机中 <strong>组织与存储数据的方式</strong> ，它的主语是 “结构” ，而不是 “数据” 。比如，我们想要表示 “一排数字” ，自然应该使用「数组」这个数据结构。数组的存储方式使之可以表示数字的相邻关系、先后关系等一系列我们需要的信息，但至于其中存储的是整数 int ，还是小数 float ，或是字符 char ，<strong>则与所谓的数据的结构无关了</strong>。</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="1:8"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Java</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Python</label><label for="__tabbed_1_4">Go</label><label for="__tabbed_1_5">JavaScript</label><label for="__tabbed_1_6">TypeScript</label><label for="__tabbed_1_7">C</label><label for="__tabbed_1_8">C#</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="cm">/* 使用多种「基本数据类型」来初始化「数组」 */</span><span class="w"></span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">numbers</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="mi">5</span><span class="o">]</span><span class="p">;</span><span class="w"></span>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="kt">float</span><span class="o">[]</span><span class="w"> </span><span class="n">decimals</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">float</span><span class="o">[</span><span class="mi">5</span><span class="o">]</span><span class="p">;</span><span class="w"></span>
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="kt">char</span><span class="o">[]</span><span class="w"> </span><span class="n">characters</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">char</span><span class="o">[</span><span class="mi">5</span><span class="o">]</span><span class="p">;</span><span class="w"></span>
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="kt">boolean</span><span class="o">[]</span><span class="w"> </span><span class="n">booleans</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">boolean</span><span class="o">[</span><span class="mi">5</span><span class="o">]</span><span class="p">;</span><span class="w"></span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a>
|
||
</code></pre></div>
|
||
</div>
|
||
<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>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<h2 id="_3">计算机内存<a class="headerlink" href="#_3" title="Permanent link">¶</a></h2>
|
||
<p>在计算机中，内存和硬盘是两种主要的存储硬件设备。「硬盘」主要用于长期存储数据，容量较大（通常可达到 TB 级别）、速度较慢。「内存」用于运行程序时暂存数据，速度更快，但容量较小（通常为 GB 级别）。</p>
|
||
<p><strong>算法运行中，相关数据都被存储在内存中。</strong> 下图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 1 byte 的数据，在算法运行时，所有数据都被存储在这些单元格中。</p>
|
||
<p><strong>系统通过「内存地址 Memory Location」来访问目标内存位置的数据。</strong> 计算机根据特定规则给表格中每个单元格编号，保证每块内存空间都有独立的内存地址。自此，程序便通过这些地址，访问内存中的数据。</p>
|
||
<p><img alt="computer_memory_location" src="../data_and_memory.assets/computer_memory_location.png" /></p>
|
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<p align="center"> Fig. 内存条、内存空间、内存地址 </p>
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<p><strong>内存资源是设计数据结构与算法的重要考虑因素。</strong> 内存是所有程序的公共资源，当内存被某程序占用时，不能被其它程序同时使用。我们需要根据剩余内存资源的情况来设计算法。例如，若剩余内存空间有限，则要求算法占用的峰值内存不能超过系统剩余内存；若运行的程序很多、缺少大块连续的内存空间，则要求选取的数据结构必须能够存储在离散的内存空间内。</p>
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