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序
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第 0 章 &nbsp; 前言
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第 1 章 &nbsp; 初识算法
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第 2 章 &nbsp; 复杂度分析
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第 3 章 &nbsp; 数据结构
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第 4 章 &nbsp; 数组与链表
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第 5 章 &nbsp; 栈与队列
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第 6 章 &nbsp; 哈希表
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第 8 章 &nbsp; 堆
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第 9 章 &nbsp; 图
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第 11 章 &nbsp; 排序
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第 13 章 &nbsp; 回溯
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第 14 章 &nbsp; 动态规划
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第 15 章 &nbsp; 贪心
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第 16 章 &nbsp; 附录
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纸质书
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<!-- Page content -->
<h1 id="41">4.1 &nbsp; 数组<a class="headerlink" href="#41" title="Permanent link">&para;</a></h1>
<p>「数组 array」是一种线性数据结构，其将相同类型的元素存储在连续的内存空间中。我们将元素在数组中的位置称为该元素的「索引 index」。图 4-1 展示了数组的主要概念和存储方式。</p>
<p><u>数组（array）</u>是一种线性数据结构，其将相同类型的元素存储在连续的内存空间中。我们将元素在数组中的位置称为该元素的<u>索引（index）</u>。图 4-1 展示了数组的主要概念和存储方式。</p>
<p><a class="glightbox" href="../array.assets/array_definition.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="数组定义与存储方式" class="animation-figure" src="../array.assets/array_definition.png" /></a></p>
<p align="center"> 图 4-1 &nbsp; 数组定义与存储方式 </p>
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Copyright &copy; 2022-2024 krahets<br>The website content is licensed under <a href="https://creativecommons.org/licenses/by-nc-sa/4.0/">CC BY-NC-SA 4.0</a>
</div>
chapter_array_and_linkedlist/index.html
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序
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序
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</li>
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第 0 章 &nbsp; 前言
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第 1 章 &nbsp; 初识算法
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第 2 章 &nbsp; 复杂度分析
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第 3 章 &nbsp; 数据结构
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第 4 章 &nbsp; 数组与链表
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第 5 章 &nbsp; 栈与队列
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第 6 章 &nbsp; 哈希表
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第 7 章 &nbsp; 树
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第 8 章 &nbsp; 堆
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第 9 章 &nbsp; 图
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第 10 章 &nbsp; 搜索
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第 11 章 &nbsp; 排序
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第 12 章 &nbsp; 分治
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第 13 章 &nbsp; 回溯
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第 14 章 &nbsp; 动态规划
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第 15 章 &nbsp; 贪心
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第 16 章 &nbsp; 附录
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参考文献
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纸质书
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纸质书
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Copyright &copy; 2022-2024 krahets</br>The website content is licensed under <a href="https://creativecommons.org/licenses/by-nc-sa/4.0/">CC BY-NC-SA 4.0</a>
Copyright &copy; 2022-2024 krahets<br>The website content is licensed under <a href="https://creativecommons.org/licenses/by-nc-sa/4.0/">CC BY-NC-SA 4.0</a>
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chapter_array_and_linkedlist/linked_list/index.html
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序
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序
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第 0 章 &nbsp; 前言
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第 1 章 &nbsp; 初识算法
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第 2 章 &nbsp; 复杂度分析
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第 3 章 &nbsp; 数据结构
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第 4 章 &nbsp; 数组与链表
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第 5 章 &nbsp; 栈与队列
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第 6 章 &nbsp; 哈希表
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第 7 章 &nbsp; 树
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第 8 章 &nbsp; 堆
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第 9 章 &nbsp; 图
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第 10 章 &nbsp; 搜索
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第 11 章 &nbsp; 排序
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第 12 章 &nbsp; 分治
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第 13 章 &nbsp; 回溯
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第 14 章 &nbsp; 动态规划
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第 15 章 &nbsp; 贪心
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第 16 章 &nbsp; 附录
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参考文献
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<a href="../../chapter_paperbook/" class="md-nav__link ">
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纸质书
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<!-- Page content -->
<h1 id="42">4.2 &nbsp; 链表<a class="headerlink" href="#42" title="Permanent link">&para;</a></h1>
<p>内存空间是所有程序的公共资源，在一个复杂的系统运行环境下，空闲的内存空间可能散落在内存各处。我们知道，存储数组的内存空间必须是连续的，而当数组非常大时，内存可能无法提供如此大的连续空间。此时链表的灵活性优势就体现出来了。</p>
<p>「链表 linked list」是一种线性数据结构，其中的每个元素都是一个节点对象，各个节点通过“引用”相连接。引用记录了下一个节点的内存地址，通过它可以从当前节点访问到下一个节点。</p>
<p><u>链表（linked list）</u>是一种线性数据结构，其中的每个元素都是一个节点对象，各个节点通过“引用”相连接。引用记录了下一个节点的内存地址，通过它可以从当前节点访问到下一个节点。</p>
<p>链表的设计使得各个节点可以分散存储在内存各处，它们的内存地址无须连续。</p>
<p><a class="glightbox" href="../linked_list.assets/linkedlist_definition.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="链表定义与存储方式" class="animation-figure" src="../linked_list.assets/linkedlist_definition.png" /></a></p>
<p align="center"> 图 4-5 &nbsp; 链表定义与存储方式 </p>
<p>观察图 4-5 ，链表的组成单位是「节点 node」对象。每个节点都包含两项数据：节点的“值”和指向下一节点的“引用”。</p>
<p>观察图 4-5 ，链表的组成单位是<u>节点（node）</u>对象。每个节点都包含两项数据：节点的“值”和指向下一节点的“引用”。</p>
<ul>
<li>链表的首个节点被称为“头节点”，最后一个节点被称为“尾节点”。</li>
<li>尾节点指向的是“空”，它在 Java、C++ 和 Python 中分别被记为 <code>null</code>、<code>nullptr</code> 和 <code>None</code> 。</li>
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<!-- Page content -->
<h1 id="43">4.3 &nbsp; 列表<a class="headerlink" href="#43" title="Permanent link">&para;</a></h1>
<p>「列表 list」是一个抽象的数据结构概念，它表示元素的有序集合，支持元素访问、修改、添加、删除和遍历等操作，无须使用者考虑容量限制的问题。列表可以基于链表或数组实现。</p>
<p><u>列表（list）</u>是一个抽象的数据结构概念，它表示元素的有序集合，支持元素访问、修改、添加、删除和遍历等操作，无须使用者考虑容量限制的问题。列表可以基于链表或数组实现。</p>
<ul>
<li>链表天然可以看作一个列表，其支持元素增删查改操作，并且可以灵活动态扩容。</li>
<li>数组也支持元素增删查改，但由于其长度不可变，因此只能看作一个具有长度限制的列表。</li>
</ul>
<p>当使用数组实现列表时，<strong>长度不可变的性质会导致列表的实用性降低</strong>。这是因为我们通常无法事先确定需要存储多少数据，从而难以选择合适的列表长度。若长度过小，则很可能无法满足使用需求；若长度过大，则会造成内存空间浪费。</p>
<p>为解决此问题，我们可以使用「动态数组 dynamic array」来实现列表。它继承了数组的各项优点，并且可以在程序运行过程中进行动态扩容。</p>
<p>为解决此问题，我们可以使用<u>动态数组（dynamic array）</u>来实现列表。它继承了数组的各项优点，并且可以在程序运行过程中进行动态扩容。</p>
<p>实际上，<strong>许多编程语言中的标准库提供的列表是基于动态数组实现的</strong>，例如 Python 中的 <code>list</code> 、Java 中的 <code>ArrayList</code> 、C++ 中的 <code>vector</code> 和 C# 中的 <code>List</code> 等。在接下来的讨论中，我们将把“列表”和“动态数组”视为等同的概念。</p>
<h2 id="431">4.3.1 &nbsp; 列表常用操作<a class="headerlink" href="#431" title="Permanent link">&para;</a></h2>
<h3 id="1">1. &nbsp; 初始化列表<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
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<p>在本章的前两节中，我们探讨了数组和链表这两种基础且重要的数据结构，它们分别代表了“连续存储”和“分散存储”两种物理结构。</p>
<p>实际上，<strong>物理结构在很大程度上决定了程序对内存和缓存的使用效率</strong>，进而影响算法程序的整体性能。</p>
<h2 id="441">4.4.1 &nbsp; 计算机存储设备<a class="headerlink" href="#441" title="Permanent link">&para;</a></h2>
<p>计算机中包括三种类型的存储设备：「硬盘 hard disk」、「内存 random-access memory, RAM」、「缓存 cache memory」。表 4-2 展示了它们在计算机系统中的不同角色和性能特点。</p>
<p>计算机中包括三种类型的存储设备：<u>硬盘（hard disk）</u>、<u>内存（random-access memory, RAM）</u>、<u>缓存（cache memory）</u>。表 4-2 展示了它们在计算机系统中的不同角色和性能特点。</p>
<p align="center"> 表 4-2 &nbsp; 计算机的存储设备 </p>
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<p>一方面，<strong>内存是有限的，且同一块内存不能被多个程序共享</strong>，因此我们希望数据结构能够尽可能高效地利用空间。数组的元素紧密排列，不需要额外的空间来存储链表节点间的引用（指针），因此空间效率更高。然而，数组需要一次性分配足够的连续内存空间，这可能导致内存浪费，数组扩容也需要额外的时间和空间成本。相比之下，链表以“节点”为单位进行动态内存分配和回收，提供了更大的灵活性。</p>
<p>另一方面，在程序运行时，<strong>随着反复申请与释放内存，空闲内存的碎片化程度会越来越高</strong>，从而导致内存的利用效率降低。数组由于其连续的存储方式，相对不容易导致内存碎片化。相反，链表的元素是分散存储的，在频繁的插入与删除操作中，更容易导致内存碎片化。</p>
<h2 id="443">4.4.3 &nbsp; 数据结构的缓存效率<a class="headerlink" href="#443" title="Permanent link">&para;</a></h2>
<p>缓存虽然在空间容量上远小于内存，但它比内存快得多，在程序执行速度上起着至关重要的作用。由于缓存的容量有限，只能存储一小部分频繁访问的数据，因此当 CPU 尝试访问的数据不在缓存中时，就会发生「缓存未命中 cache miss」，此时 CPU 不得不从速度较慢的内存中加载所需数据。</p>
<p>显然，<strong>“缓存未命中”越少，CPU 读写数据的效率就越高</strong>，程序性能也就越好。我们将 CPU 从缓存中成功获取数据的比例称为「缓存命中率 cache hit rate」，这个指标通常用来衡量缓存效率。</p>
<p>缓存虽然在空间容量上远小于内存，但它比内存快得多，在程序执行速度上起着至关重要的作用。由于缓存的容量有限，只能存储一小部分频繁访问的数据，因此当 CPU 尝试访问的数据不在缓存中时，就会发生<u>缓存未命中（cache miss）</u>，此时 CPU 不得不从速度较慢的内存中加载所需数据。</p>
<p>显然，<strong>“缓存未命中”越少，CPU 读写数据的效率就越高</strong>，程序性能也就越好。我们将 CPU 从缓存中成功获取数据的比例称为<u>缓存命中率（cache hit rate）</u>，这个指标通常用来衡量缓存效率。</p>
<p>为了尽可能达到更高的效率，缓存会采取以下数据加载机制。</p>
<ul>
<li><strong>缓存行</strong>：缓存不是单个字节地存储与加载数据，而是以缓存行为单位。相比于单个字节的传输，缓存行的传输形式更加高效。</li>
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第 0 章 &nbsp; 前言
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第 1 章 &nbsp; 初识算法
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第 2 章 &nbsp; 复杂度分析
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第 3 章 &nbsp; 数据结构
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第 16 章 &nbsp; 附录
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