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0.2   如何使用本书
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0.3   小结
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第 1 章   初识算法
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1.1   算法无处不在
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1.2   算法是什么
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1.3   小结
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第 2 章   复杂度分析
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2.1   算法效率评估
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2.2   迭代与递归
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2.3   时间复杂度
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2.4   空间复杂度
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2.5   小结
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2.6   练习
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第 3 章   数据结构
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3.1   数据结构分类
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3.2   基本数据类型
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3.3   数字编码 *
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3.4   字符编码 *
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3.5   小结
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3.6   练习
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3.6   练习
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3.6.1   知识巩固
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1.   生活场景中的数据关系
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2.   逻辑顺序怎样存进内存
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3.   作业记录中的数据类型与结构
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3.6.2   编程练习
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1.   统计二进制表示中的 1
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第 4 章   数组与链表
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第 4 章   数组与链表
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4.1   数组
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4.2   链表
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4.3   列表
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4.4   内存与缓存 *
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4.5   小结
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4.6   练习
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第 5 章   栈与队列
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5.1   栈
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5.2   队列
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5.3   双向队列
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5.4   小结
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5.5   练习
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第 6 章   哈希表
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第 6 章   哈希表
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6.1   哈希表
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6.2   哈希冲突
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6.3   哈希算法
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6.4   小结
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6.5   练习
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第 7 章   树
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第 7 章   树
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7.1   二叉树
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7.2   二叉树遍历
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7.3   二叉树数组表示
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7.4   二叉搜索树
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7.5   AVL 树 *
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7.6   小结
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7.7   练习
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第 8 章   堆
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第 8 章   堆
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<li class="md-nav__item">
<a class="md-nav__link" href="../../chapter_heap/heap/">
<span class="md-ellipsis">
8.1   堆
</span>
</a>
</li>
<li class="md-nav__item">
<a class="md-nav__link" href="../../chapter_heap/build_heap/">
<span class="md-ellipsis">
8.2   建堆操作
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</a>
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<li class="md-nav__item">
<a class="md-nav__link" href="../../chapter_heap/top_k/">
<span class="md-ellipsis">
8.3   Top-k 问题
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<li class="md-nav__item">
<a class="md-nav__link" href="../../chapter_heap/summary/">
<span class="md-ellipsis">
8.4   小结
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</a>
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<li class="md-nav__item">
<a class="md-nav__link" href="../../chapter_heap/exercises/">
<span class="md-ellipsis">
8.5   练习
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第 9 章   图
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第 9 章   图
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<li class="md-nav__item">
<a class="md-nav__link" href="../../chapter_graph/graph/">
<span class="md-ellipsis">
9.1   图
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</a>
</li>
<li class="md-nav__item">
<a class="md-nav__link" href="../../chapter_graph/graph_operations/">
<span class="md-ellipsis">
9.2   图基础操作
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</a>
</li>
<li class="md-nav__item">
<a class="md-nav__link" href="../../chapter_graph/graph_traversal/">
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9.3   图的遍历
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<a class="md-nav__link" href="../../chapter_graph/summary/">
<span class="md-ellipsis">
9.4   小结
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</a>
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<li class="md-nav__item">
<a class="md-nav__link" href="../../chapter_graph/exercises/">
<span class="md-ellipsis">
9.5   练习
</span>
</a>
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<a class="md-nav__link" href="../../chapter_searching/">
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第 10 章   搜索
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第 10 章   搜索
</label>
<ul class="md-nav__list" data-md-scrollfix="">
<li class="md-nav__item">
<a class="md-nav__link" href="../../chapter_searching/binary_search/">
<span class="md-ellipsis">
10.1   二分查找
</span>
</a>
</li>
<li class="md-nav__item">
<a class="md-nav__link" href="../../chapter_searching/binary_search_insertion/">
<span class="md-ellipsis">
10.2   二分查找插入点
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</a>
</li>
<li class="md-nav__item">
<a class="md-nav__link" href="../../chapter_searching/binary_search_edge/">
<span class="md-ellipsis">
10.3   二分查找边界
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</li>
<li class="md-nav__item">
<a class="md-nav__link" href="../../chapter_searching/replace_linear_by_hashing/">
<span class="md-ellipsis">
10.4   哈希优化策略
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</a>
</li>
<li class="md-nav__item">
<a class="md-nav__link" href="../../chapter_searching/searching_algorithm_revisited/">
<span class="md-ellipsis">
10.5   重识搜索算法
</span>
</a>
</li>
<li class="md-nav__item">
<a class="md-nav__link" href="../../chapter_searching/summary/">
<span class="md-ellipsis">
10.6   小结
</span>
</a>
</li>
<li class="md-nav__item">
<a class="md-nav__link" href="../../chapter_searching/exercises/">
<span class="md-ellipsis">
10.7   练习
</span>
</a>
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</ul>
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第 11 章   排序
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第 11 章   排序
</label>
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<li class="md-nav__item">
<a class="md-nav__link" href="../../chapter_sorting/sorting_algorithm/">
<span class="md-ellipsis">
11.1   排序算法
</span>
</a>
</li>
<li class="md-nav__item">
<a class="md-nav__link" href="../../chapter_sorting/selection_sort/">
<span class="md-ellipsis">
11.2   选择排序
</span>
</a>
</li>
<li class="md-nav__item">
<a class="md-nav__link" href="../../chapter_sorting/bubble_sort/">
<span class="md-ellipsis">
11.3   冒泡排序
</span>
</a>
</li>
<li class="md-nav__item">
<a class="md-nav__link" href="../../chapter_sorting/insertion_sort/">
<span class="md-ellipsis">
11.4   插入排序
</span>
</a>
</li>
<li class="md-nav__item">
<a class="md-nav__link" href="../../chapter_sorting/quick_sort/">
<span class="md-ellipsis">
11.5   快速排序
</span>
</a>
</li>
<li class="md-nav__item">
<a class="md-nav__link" href="../../chapter_sorting/merge_sort/">
<span class="md-ellipsis">
11.6   归并排序
</span>
</a>
</li>
<li class="md-nav__item">
<a class="md-nav__link" href="../../chapter_sorting/heap_sort/">
<span class="md-ellipsis">
11.7   堆排序
</span>
</a>
</li>
<li class="md-nav__item">
<a class="md-nav__link" href="../../chapter_sorting/bucket_sort/">
<span class="md-ellipsis">
11.8   桶排序
</span>
</a>
</li>
<li class="md-nav__item">
<a class="md-nav__link" href="../../chapter_sorting/counting_sort/">
<span class="md-ellipsis">
11.9   计数排序
</span>
</a>
</li>
<li class="md-nav__item">
<a class="md-nav__link" href="../../chapter_sorting/radix_sort/">
<span class="md-ellipsis">
11.10   基数排序
</span>
</a>
</li>
<li class="md-nav__item">
<a class="md-nav__link" href="../../chapter_sorting/summary/">
<span class="md-ellipsis">
11.11   小结
</span>
</a>
</li>
<li class="md-nav__item">
<a class="md-nav__link" href="../../chapter_sorting/exercises/">
<span class="md-ellipsis">
11.12   练习
</span>
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第 12 章   分治
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第 12 章   分治
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<a class="md-nav__link" href="../../chapter_divide_and_conquer/divide_and_conquer/">
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12.1   分治算法
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</li>
<li class="md-nav__item">
<a class="md-nav__link" href="../../chapter_divide_and_conquer/binary_search_recur/">
<span class="md-ellipsis">
12.2   分治搜索策略
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</a>
</li>
<li class="md-nav__item">
<a class="md-nav__link" href="../../chapter_divide_and_conquer/build_binary_tree_problem/">
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12.3   构建树问题
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</li>
<li class="md-nav__item">
<a class="md-nav__link" href="../../chapter_divide_and_conquer/hanota_problem/">
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12.4   汉诺塔问题
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</a>
</li>
<li class="md-nav__item">
<a class="md-nav__link" href="../../chapter_divide_and_conquer/summary/">
<span class="md-ellipsis">
12.5   小结
</span>
</a>
</li>
<li class="md-nav__item">
<a class="md-nav__link" href="../../chapter_divide_and_conquer/exercises/">
<span class="md-ellipsis">
12.6   练习
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第 13 章   回溯
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第 13 章   回溯
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<a class="md-nav__link" href="../../chapter_backtracking/backtracking_algorithm/">
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13.1   回溯算法
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<li class="md-nav__item">
<a class="md-nav__link" href="../../chapter_backtracking/permutations_problem/">
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13.2   全排列问题
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<a class="md-nav__link" href="../../chapter_backtracking/subset_sum_problem/">
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13.3   子集和问题
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13.4   N 皇后问题
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13.5   小结
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<a class="md-nav__link" href="../../chapter_backtracking/exercises/">
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13.6   练习
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第 14 章   动态规划
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第 14 章   动态规划
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<a class="md-nav__link" href="../../chapter_dynamic_programming/intro_to_dynamic_programming/">
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14.1   初探动态规划
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</a>
</li>
<li class="md-nav__item">
<a class="md-nav__link" href="../../chapter_dynamic_programming/dp_problem_features/">
<span class="md-ellipsis">
14.2   DP 问题特性
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<a class="md-nav__link" href="../../chapter_dynamic_programming/dp_solution_pipeline/">
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14.3   DP 解题思路
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</li>
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<a class="md-nav__link" href="../../chapter_dynamic_programming/knapsack_problem/">
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14.4   0-1 背包问题
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<a class="md-nav__link" href="../../chapter_dynamic_programming/unbounded_knapsack_problem/">
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14.5   完全背包问题
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<a class="md-nav__link" href="../../chapter_dynamic_programming/edit_distance_problem/">
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14.6   编辑距离问题
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<a class="md-nav__link" href="../../chapter_dynamic_programming/summary/">
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14.7   小结
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14.8   练习
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<h1 id="36">3.6   练习<a class="headerlink" href="#36" title="Permanent link"></a></h1>
<h2 id="361">3.6.1   知识巩固<a class="headerlink" href="#361" title="Permanent link"></a></h2>
<h3 id="1">1.   生活场景中的数据关系<a class="headerlink" href="#1" title="Permanent link"></a></h3>
<p>请根据数据之间的关系,为下面三个场景选择“线性结构、树形结构、网状结构”中的一种,并说明理由:</p>
<!-- numbered-subquestions -->
<ol>
<li>同学们排成一列,每人只关心自己前面和后面的人;</li>
<li>学校按“学校 → 年级 → 班级”分层管理;</li>
<li>城市道路连接多个路口,一个路口可以通向多个其他路口,也可能形成环路。</li>
</ol>
<details class="success">
<summary>参考答案</summary>
<ol>
<li>
<p>是线性结构。除排在最前和最后的人外,每个人都只与前面和后面各一人相邻,关系沿一条线展开。</p>
</li>
<li>
<p>是树形结构。每个班级属于一个年级,每个年级又属于学校,关系从上到下分层展开。</p>
</li>
<li>
<p>是网状结构。一个路口可以连接多个路口,路线之间还能形成环,不能排成单一顺序或严格层级。</p>
<p>判断结构时应先观察元素之间的关系,而不是先考虑它在内存中占多少空间。</p>
</li>
</ol>
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<h3 id="2">2.   逻辑顺序怎样存进内存<a class="headerlink" href="#2" title="Permanent link"></a></h3>
<p>为了保存逻辑顺序 <code>A → B → C</code>,现有两种简化的内存安排:</p>
<ul>
<li>方案甲:<code>A、B、C</code> 分别放在编号为 <code>20、21、22</code> 的内存格中;</li>
<li>方案乙:<code>A、B、C</code> 分别放在编号为 <code>20、7、31</code> 的内存格中,并由 <code>A</code> 记录 <code>B</code> 的位置、<code>B</code> 记录 <code>C</code> 的位置。</li>
</ul>
<!-- numbered-subquestions -->
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<li>哪个方案属于连续空间存储?哪个属于分散空间存储?</li>
<li>两个方案分别更接近数组还是链表?</li>
<li>方案乙的内存格编号没有按大小排列,为什么仍能表示 <code>A → B → C</code> 的逻辑顺序?</li>
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<summary>参考答案</summary>
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<li>
<p>方案甲使用连续的内存格,属于连续空间存储;方案乙的节点分散在不同位置,属于分散空间存储。</p>
</li>
<li>
<p>方案甲更接近数组,方案乙更接近链表。</p>
</li>
<li>
<p>逻辑顺序由节点之间记录的连接关系决定,而不是由内存格编号的大小决定。
从 <code>A</code> 记录的位置可以找到 <code>B</code>,再从 <code>B</code> 记录的位置找到 <code>C</code>,所以仍能依次访问 <code>A、B、C</code>。</p>
<p>这也说明逻辑结构和物理结构是观察同一组数据的两个不同角度。</p>
</li>
</ol>
</details>
<h3 id="3">3.   作业记录中的数据类型与结构<a class="headerlink" href="#3" title="Permanent link"></a></h3>
<p>某学习小组按座位顺序记录 4 名同学是否交了作业,得到:</p>
<p><code>[true, false, true, true]</code></p>
<!-- numbered-subquestions -->
<ol>
<li>每个元素适合使用哪种基本数据类型?</li>
<li>这 4 个元素按座位顺序排成一列,使用了什么逻辑结构?</li>
<li>如果以后改为记录每人的作业分数 <code>[90, 0, 85, 100]</code>,改变的是数据的“内容类型”还是“组织方式”?说明理由。</li>
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<summary>参考答案</summary>
<ol>
<li>
<p>每个元素只表示“是”或“否”,适合使用布尔类型 <code>bool</code>。</p>
</li>
<li>
<p>这些元素按座位顺序排列,形成线性结构,可以用数组保存。</p>
</li>
<li>
<p>改变的是内容类型:元素由布尔值变成了整数。组织方式没有改变,
这些数据仍然按座位顺序排成一列,仍可使用数组这一线性结构。</p>
<p>基本数据类型描述“存的是什么”,数据结构描述“数据怎样组织”。</p>
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<h2 id="362">3.6.2   编程练习<a class="headerlink" href="#362" title="Permanent link"></a></h2>
<h3 id="1-1">1.   统计二进制表示中的 1<a class="headerlink" href="#1-1" title="Permanent link"></a></h3>
<p>给定非负整数 <code>n</code>,请统计它的二进制表示中共有多少个 1。</p>
<p>要求使用位运算完成,不把二进制表示转换成字符串,也不使用直接统计 1 的内置函数。</p>
<details class="tip">
<summary>解题提示</summary>
<ol>
<li>n &amp; 1 可以取出 n 的最右边一位,用它判断这一位是否为 1</li>
<li>右移一位表示丢掉当前最右边的二进制位;多数语言使用运算符 &gt;&gt;</li>
<li>完成逐位检查并右移的方法后,再观察:n &amp; (n - 1) 会把 n 中最右边的一个 1 变成 0</li>
</ol>
</details>
<p><a class="rounded-button exercise-button" href="https://leetcode.cn/problems/number-of-1-bits/" rel="noopener noreferrer" target="_blank">LeetCode</a> <a class="rounded-button exercise-button" href="https://leetcode.cn/problems/number-of-1-bits/solutions/2361978/191-wei-1-de-ge-shu-wei-yun-suan-qing-xi-40rw/" rel="noopener noreferrer" target="_blank">题目解析</a></p>
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