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<title>4.1. 数组Array - Hello 算法</title>
<title>4.1.   数组Array - Hello 算法</title>
@@ -111,7 +111,7 @@
<div class="md-header__topic" data-md-component="header-topic">
<span class="md-ellipsis">
4.1. 数组Array
4.1. &nbsp; 数组Array
</span>
</div>
@@ -268,14 +268,14 @@
<label class="md-nav__link" for="__nav_1" id="__nav_1_label" tabindex="0">
0. 写在前面
0. &nbsp; &nbsp; 写在前面
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_1_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_1">
<span class="md-nav__icon md-icon"></span>
0. 写在前面
0. &nbsp; &nbsp; 写在前面
</label>
<ul class="md-nav__list" data-md-scrollfix>
@@ -286,7 +286,7 @@
<li class="md-nav__item">
<a href="../../chapter_preface/about_the_book/" class="md-nav__link">
0.1. 关于本书
0.1. &nbsp; 关于本书
</a>
</li>
@@ -300,7 +300,7 @@
<li class="md-nav__item">
<a href="../../chapter_preface/suggestions/" class="md-nav__link">
0.2. 如何使用本书
0.2. &nbsp; 如何使用本书
</a>
</li>
@@ -314,7 +314,7 @@
<li class="md-nav__item">
<a href="../../chapter_preface/installation/" class="md-nav__link">
0.3. 编程环境安装
0.3. &nbsp; 编程环境安装
</a>
</li>
@@ -328,7 +328,7 @@
<li class="md-nav__item">
<a href="../../chapter_preface/contribution/" class="md-nav__link">
0.4. 一起参与创作
0.4. &nbsp; 一起参与创作
</a>
</li>
@@ -367,14 +367,14 @@
<label class="md-nav__link" for="__nav_2" id="__nav_2_label" tabindex="0">
1. 引言
1. &nbsp; &nbsp; 引言
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_2_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_2">
<span class="md-nav__icon md-icon"></span>
1. 引言
1. &nbsp; &nbsp; 引言
</label>
<ul class="md-nav__list" data-md-scrollfix>
@@ -385,7 +385,7 @@
<li class="md-nav__item">
<a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
1.1. 算法无处不在
1.1. &nbsp; 算法无处不在
</a>
</li>
@@ -399,7 +399,7 @@
<li class="md-nav__item">
<a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
1.2. 算法是什么
1.2. &nbsp; 算法是什么
</a>
</li>
@@ -444,14 +444,14 @@
<label class="md-nav__link" for="__nav_3" id="__nav_3_label" tabindex="0">
2. 计算复杂度
2. &nbsp; &nbsp; 计算复杂度
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_3">
<span class="md-nav__icon md-icon"></span>
2. 计算复杂度
2. &nbsp; &nbsp; 计算复杂度
</label>
<ul class="md-nav__list" data-md-scrollfix>
@@ -462,7 +462,7 @@
<li class="md-nav__item">
<a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
2.1. 算法效率评估
2.1. &nbsp; 算法效率评估
</a>
</li>
@@ -476,7 +476,7 @@
<li class="md-nav__item">
<a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
2.2. 时间复杂度
2.2. &nbsp; 时间复杂度
</a>
</li>
@@ -490,7 +490,7 @@
<li class="md-nav__item">
<a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
2.3. 空间复杂度
2.3. &nbsp; 空间复杂度
</a>
</li>
@@ -504,7 +504,7 @@
<li class="md-nav__item">
<a href="../../chapter_computational_complexity/space_time_tradeoff/" class="md-nav__link">
2.4. 权衡时间与空间
2.4. &nbsp; 权衡时间与空间
</a>
</li>
@@ -518,7 +518,7 @@
<li class="md-nav__item">
<a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
2.5. 小结
2.5. &nbsp; 小结
</a>
</li>
@@ -559,14 +559,14 @@
<label class="md-nav__link" for="__nav_4" id="__nav_4_label" tabindex="0">
3. 数据结构简介
3. &nbsp; &nbsp; 数据结构简介
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_4">
<span class="md-nav__icon md-icon"></span>
3. 数据结构简介
3. &nbsp; &nbsp; 数据结构简介
</label>
<ul class="md-nav__list" data-md-scrollfix>
@@ -577,7 +577,7 @@
<li class="md-nav__item">
<a href="../../chapter_data_structure/data_and_memory/" class="md-nav__link">
3.1. 数据与内存
3.1. &nbsp; 数据与内存
</a>
</li>
@@ -591,7 +591,7 @@
<li class="md-nav__item">
<a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
3.2. 数据结构分类
3.2. &nbsp; 数据结构分类
</a>
</li>
@@ -605,7 +605,7 @@
<li class="md-nav__item">
<a href="../../chapter_data_structure/summary/" class="md-nav__link">
3.3. 小结
3.3. &nbsp; 小结
</a>
</li>
@@ -650,14 +650,14 @@
<label class="md-nav__link" for="__nav_5" id="__nav_5_label" tabindex="0">
4. 数组与链表
4. &nbsp; &nbsp; 数组与链表
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="true">
<label class="md-nav__title" for="__nav_5">
<span class="md-nav__icon md-icon"></span>
4. 数组与链表
4. &nbsp; &nbsp; 数组与链表
</label>
<ul class="md-nav__list" data-md-scrollfix>
@@ -677,12 +677,12 @@
<label class="md-nav__link md-nav__link--active" for="__toc">
4.1. 数组Array
4.1. &nbsp; 数组Array
<span class="md-nav__icon md-icon"></span>
</label>
<a href="./" class="md-nav__link md-nav__link--active">
4.1. 数组Array
4.1. &nbsp; 数组Array
</a>
@@ -702,28 +702,28 @@
<li class="md-nav__item">
<a href="#411" class="md-nav__link">
4.1.1. 数组优点
4.1.1. &nbsp; 数组优点
</a>
</li>
<li class="md-nav__item">
<a href="#412" class="md-nav__link">
4.1.2. 数组缺点
4.1.2. &nbsp; 数组缺点
</a>
</li>
<li class="md-nav__item">
<a href="#413" class="md-nav__link">
4.1.3. 数组常用操作
4.1.3. &nbsp; 数组常用操作
</a>
</li>
<li class="md-nav__item">
<a href="#414" class="md-nav__link">
4.1.4. 数组典型应用
4.1.4. &nbsp; 数组典型应用
</a>
</li>
@@ -744,7 +744,7 @@
<li class="md-nav__item">
<a href="../linked_list/" class="md-nav__link">
4.2. 链表LinkedList
4.2. &nbsp; 链表LinkedList
</a>
</li>
@@ -758,7 +758,7 @@
<li class="md-nav__item">
<a href="../list/" class="md-nav__link">
4.3. 列表List
4.3. &nbsp; 列表List
</a>
</li>
@@ -772,7 +772,7 @@
<li class="md-nav__item">
<a href="../summary/" class="md-nav__link">
4.4. 小结
4.4. &nbsp; 小结
</a>
</li>
@@ -815,14 +815,14 @@
<label class="md-nav__link" for="__nav_6" id="__nav_6_label" tabindex="0">
5. 栈与队列
5. &nbsp; &nbsp; 栈与队列
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_6">
<span class="md-nav__icon md-icon"></span>
5. 栈与队列
5. &nbsp; &nbsp; 栈与队列
</label>
<ul class="md-nav__list" data-md-scrollfix>
@@ -833,7 +833,7 @@
<li class="md-nav__item">
<a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
5.1. 栈Stack
5.1. &nbsp;Stack
</a>
</li>
@@ -847,7 +847,7 @@
<li class="md-nav__item">
<a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
5.2. 队列Queue
5.2. &nbsp; 队列Queue
</a>
</li>
@@ -861,7 +861,7 @@
<li class="md-nav__item">
<a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
5.3. 双向队列Deque
5.3. &nbsp; 双向队列Deque
</a>
</li>
@@ -875,7 +875,7 @@
<li class="md-nav__item">
<a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
5.4. 小结
5.4. &nbsp; 小结
</a>
</li>
@@ -916,14 +916,14 @@
<label class="md-nav__link" for="__nav_7" id="__nav_7_label" tabindex="0">
6. 散列表
6. &nbsp; &nbsp; 散列表
<span class="md-nav__icon md-icon"></span>
</label>
<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>
6. 散列表
6. &nbsp; &nbsp; 散列表
</label>
<ul class="md-nav__list" data-md-scrollfix>
@@ -934,7 +934,7 @@
<li class="md-nav__item">
<a href="../../chapter_hashing/hash_map/" class="md-nav__link">
6.1. 哈希表HashMap
6.1. &nbsp; 哈希表HashMap
</a>
</li>
@@ -948,7 +948,7 @@
<li class="md-nav__item">
<a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
6.2. 哈希冲突处理
6.2. &nbsp; 哈希冲突处理
</a>
</li>
@@ -962,7 +962,7 @@
<li class="md-nav__item">
<a href="../../chapter_hashing/summary/" class="md-nav__link">
6.3. 小结
6.3. &nbsp; 小结
</a>
</li>
@@ -1007,14 +1007,14 @@
<label class="md-nav__link" for="__nav_8" id="__nav_8_label" tabindex="0">
7. 二叉树
7. &nbsp; &nbsp; 二叉树
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_8">
<span class="md-nav__icon md-icon"></span>
7. 二叉树
7. &nbsp; &nbsp; 二叉树
</label>
<ul class="md-nav__list" data-md-scrollfix>
@@ -1025,7 +1025,7 @@
<li class="md-nav__item">
<a href="../../chapter_tree/binary_tree/" class="md-nav__link">
7.1. 二叉树Binary Tree
7.1. &nbsp; 二叉树Binary Tree
</a>
</li>
@@ -1039,7 +1039,7 @@
<li class="md-nav__item">
<a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
7.2. 二叉树遍历
7.2. &nbsp; 二叉树遍历
</a>
</li>
@@ -1053,7 +1053,7 @@
<li class="md-nav__item">
<a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
7.3. 二叉搜索树
7.3. &nbsp; 二叉搜索树
</a>
</li>
@@ -1067,7 +1067,7 @@
<li class="md-nav__item">
<a href="../../chapter_tree/avl_tree/" class="md-nav__link">
7.4. AVL 树 *
7.4. &nbsp; AVL 树 *
</a>
</li>
@@ -1081,7 +1081,7 @@
<li class="md-nav__item">
<a href="../../chapter_tree/summary/" class="md-nav__link">
7.5. 小结
7.5. &nbsp; 小结
</a>
</li>
@@ -1118,14 +1118,14 @@
<label class="md-nav__link" for="__nav_9" id="__nav_9_label" tabindex="0">
8. 堆
8. &nbsp; &nbsp;
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_9">
<span class="md-nav__icon md-icon"></span>
8. 堆
8. &nbsp; &nbsp;
</label>
<ul class="md-nav__list" data-md-scrollfix>
@@ -1136,7 +1136,7 @@
<li class="md-nav__item">
<a href="../../chapter_heap/heap/" class="md-nav__link">
8.1. 堆Heap
8.1. &nbsp;Heap
</a>
</li>
@@ -1177,14 +1177,14 @@
<label class="md-nav__link" for="__nav_10" id="__nav_10_label" tabindex="0">
9. 图
9. &nbsp; &nbsp;
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_10">
<span class="md-nav__icon md-icon"></span>
9. 图
9. &nbsp; &nbsp;
</label>
<ul class="md-nav__list" data-md-scrollfix>
@@ -1195,7 +1195,7 @@
<li class="md-nav__item">
<a href="../../chapter_graph/graph/" class="md-nav__link">
9.1. 图Graph
9.1. &nbsp;Graph
</a>
</li>
@@ -1209,7 +1209,7 @@
<li class="md-nav__item">
<a href="../../chapter_graph/graph_operations/" class="md-nav__link">
9.2. 图基础操作
9.2. &nbsp; 图基础操作
</a>
</li>
@@ -1223,7 +1223,7 @@
<li class="md-nav__item">
<a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
9.3. 图的遍历
9.3. &nbsp; 图的遍历
</a>
</li>
@@ -1266,14 +1266,14 @@
<label class="md-nav__link" for="__nav_11" id="__nav_11_label" tabindex="0">
10. 查找算法
10. &nbsp; &nbsp; 查找算法
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_11">
<span class="md-nav__icon md-icon"></span>
10. 查找算法
10. &nbsp; &nbsp; 查找算法
</label>
<ul class="md-nav__list" data-md-scrollfix>
@@ -1284,7 +1284,7 @@
<li class="md-nav__item">
<a href="../../chapter_searching/linear_search/" class="md-nav__link">
10.1. 线性查找
10.1. &nbsp; 线性查找
</a>
</li>
@@ -1298,7 +1298,7 @@
<li class="md-nav__item">
<a href="../../chapter_searching/binary_search/" class="md-nav__link">
10.2. 二分查找
10.2. &nbsp; 二分查找
</a>
</li>
@@ -1312,7 +1312,7 @@
<li class="md-nav__item">
<a href="../../chapter_searching/hashing_search/" class="md-nav__link">
10.3. 哈希查找
10.3. &nbsp; 哈希查找
</a>
</li>
@@ -1326,7 +1326,7 @@
<li class="md-nav__item">
<a href="../../chapter_searching/summary/" class="md-nav__link">
10.4. 小结
10.4. &nbsp; 小结
</a>
</li>
@@ -1373,14 +1373,14 @@
<label class="md-nav__link" for="__nav_12" id="__nav_12_label" tabindex="0">
11. 排序算法
11. &nbsp; &nbsp; 排序算法
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_12">
<span class="md-nav__icon md-icon"></span>
11. 排序算法
11. &nbsp; &nbsp; 排序算法
</label>
<ul class="md-nav__list" data-md-scrollfix>
@@ -1391,7 +1391,7 @@
<li class="md-nav__item">
<a href="../../chapter_sorting/intro_to_sort/" class="md-nav__link">
11.1. 排序简介
11.1. &nbsp; 排序简介
</a>
</li>
@@ -1405,7 +1405,7 @@
<li class="md-nav__item">
<a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
11.2. 冒泡排序
11.2. &nbsp; 冒泡排序
</a>
</li>
@@ -1419,7 +1419,7 @@
<li class="md-nav__item">
<a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
11.3. 插入排序
11.3. &nbsp; 插入排序
</a>
</li>
@@ -1433,7 +1433,7 @@
<li class="md-nav__item">
<a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
11.4. 快速排序
11.4. &nbsp; 快速排序
</a>
</li>
@@ -1447,7 +1447,7 @@
<li class="md-nav__item">
<a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
11.5. 归并排序
11.5. &nbsp; 归并排序
</a>
</li>
@@ -1461,7 +1461,7 @@
<li class="md-nav__item">
<a href="../../chapter_sorting/summary/" class="md-nav__link">
11.6. 小结
11.6. &nbsp; 小结
</a>
</li>
@@ -1549,28 +1549,28 @@
<li class="md-nav__item">
<a href="#411" class="md-nav__link">
4.1.1. 数组优点
4.1.1. &nbsp; 数组优点
</a>
</li>
<li class="md-nav__item">
<a href="#412" class="md-nav__link">
4.1.2. 数组缺点
4.1.2. &nbsp; 数组缺点
</a>
</li>
<li class="md-nav__item">
<a href="#413" class="md-nav__link">
4.1.3. 数组常用操作
4.1.3. &nbsp; 数组常用操作
</a>
</li>
<li class="md-nav__item">
<a href="#414" class="md-nav__link">
4.1.4. 数组典型应用
4.1.4. &nbsp; 数组典型应用
</a>
</li>
@@ -1599,7 +1599,7 @@
<h1 id="41">4.1. 数组<a class="headerlink" href="#41" title="Permanent link">&para;</a></h1>
<h1 id="41">4.1. &nbsp; 数组<a class="headerlink" href="#41" title="Permanent link">&para;</a></h1>
<p>「数组 Array」是一种将 <strong>相同类型元素</strong> 存储在 <strong>连续内存空间</strong> 的数据结构,将元素在数组中的位置称为元素的「索引 Index」。</p>
<p><img alt="array_definition" src="../array.assets/array_definition.png" /></p>
<p align="center"> Fig. 数组定义与存储方式 </p>
@@ -1679,7 +1679,7 @@
</div>
</div>
</div>
<h2 id="411">4.1.1. 数组优点<a class="headerlink" href="#411" title="Permanent link">&para;</a></h2>
<h2 id="411">4.1.1. &nbsp; 数组优点<a class="headerlink" href="#411" title="Permanent link">&para;</a></h2>
<p><strong>在数组中访问元素非常高效</strong>。这是因为在数组中,计算元素的内存地址非常容易。给定数组首个元素的地址、和一个元素的索引,利用以下公式可以直接计算得到该元素的内存地址,从而直接访问此元素。</p>
<p><img alt="array_memory_location_calculation" src="../array.assets/array_memory_location_calculation.png" /></p>
<p align="center"> Fig. 数组元素的内存地址计算 </p>
@@ -1798,7 +1798,7 @@
</div>
</div>
</div>
<h2 id="412">4.1.2. 数组缺点<a class="headerlink" href="#412" title="Permanent link">&para;</a></h2>
<h2 id="412">4.1.2. &nbsp; 数组缺点<a class="headerlink" href="#412" title="Permanent link">&para;</a></h2>
<p><strong>数组在初始化后长度不可变</strong>。由于系统无法保证数组之后的内存空间是可用的,因此数组长度无法扩展。而若希望扩容数组,则需新建一个数组,然后把原数组元素依次拷贝到新数组,在数组很大的情况下,这是非常耗时的。</p>
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<h2 id="413">4.1.3. 数组常用操作<a class="headerlink" href="#413" title="Permanent link">&para;</a></h2>
<h2 id="413">4.1.3. &nbsp; 数组常用操作<a class="headerlink" href="#413" title="Permanent link">&para;</a></h2>
<p><strong>数组遍历</strong>。以下介绍两种常用的遍历方法。</p>
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<h2 id="414">4.1.4. 数组典型应用<a class="headerlink" href="#414" title="Permanent link">&para;</a></h2>
<h2 id="414">4.1.4. &nbsp; 数组典型应用<a class="headerlink" href="#414" title="Permanent link">&para;</a></h2>
<p><strong>随机访问</strong>。如果我们想要随机抽取一些样本,那么可以用数组存储,并生成一个随机序列,根据索引实现样本的随机抽取。</p>
<p><strong>二分查找</strong>。例如前文查字典的例子,我们可以将字典中的所有字按照拼音顺序存储在数组中,然后使用与日常查纸质字典相同的“翻开中间,排除一半”的方式,来实现一个查电子字典的算法。</p>
<p><strong>深度学习</strong>。神经网络中大量使用了向量、矩阵、张量之间的线性代数运算,这些数据都是以数组的形式构建的。数组是神经网络编程中最常使用的数据结构。</p>
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