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< title > 3.4 字符编码 * - Hello 算法< / title >
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Hello 算法
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3.4 字符编码 *
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第 0 章 前言
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第 0 章 前言
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0.1 关于本书
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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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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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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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第 3 章 数据结构
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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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3.3 数字编码 *
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3.4 字符编码 *
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3.4 字符编码 *
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3.4.1 ASCII 字符集
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3.4.2 GBK 字符集
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3.4.3 Unicode 字符集
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3.4.4 UTF-8 编码
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3.4.5 编程语言的字符编码
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3.5 小结
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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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4.4 小结
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第 5 章 栈与队列
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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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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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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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第 8 章 堆
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8.1 堆
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8.2 建堆操作
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8.3 Top-K 问题
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8.4 小结
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< div class = "md-nav__link md-nav__container" >
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< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z" / > < / svg >
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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" >
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< a href = "../../chapter_graph/graph/" class = "md-nav__link" >
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9.1 图
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< li class = "md-nav__item" >
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< a href = "../../chapter_graph/graph_operations/" class = "md-nav__link" >
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9.2 图基础操作
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< li class = "md-nav__item" >
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< a href = "../../chapter_graph/graph_traversal/" class = "md-nav__link" >
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9.3 图的遍历
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9.4 小结
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< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_searching/" class = "md-nav__link " >
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第 10 章 搜索
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第 10 章 搜索
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< / label >
< ul class = "md-nav__list" data-md-scrollfix >
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< li class = "md-nav__item" >
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< a href = "../../chapter_searching/binary_search/" class = "md-nav__link" >
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10.1 二分查找
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< li class = "md-nav__item" >
< a href = "../../chapter_searching/binary_search_insertion/" class = "md-nav__link" >
< span class = "md-ellipsis" >
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10.2 二分查找插入点
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< li class = "md-nav__item" >
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< a href = "../../chapter_searching/binary_search_edge/" class = "md-nav__link" >
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10.3 二分查找边界
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< / span >
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< li class = "md-nav__item" >
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< a href = "../../chapter_searching/replace_linear_by_hashing/" class = "md-nav__link" >
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< span class = "md-ellipsis" >
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10.4 哈希优化策略
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< / span >
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< li class = "md-nav__item" >
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< a href = "../../chapter_searching/searching_algorithm_revisited/" class = "md-nav__link" >
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10.5 重识搜索算法
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< li class = "md-nav__item" >
< a href = "../../chapter_searching/summary/" class = "md-nav__link" >
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10.6 小结
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< / span >
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< li class = "md-nav__item md-nav__item--nested" >
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< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_12" >
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< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_sorting/" class = "md-nav__link " >
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第 11 章 排序
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第 11 章 排序
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< / label >
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11.1 排序算法
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< a href = "../../chapter_sorting/selection_sort/" class = "md-nav__link" >
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11.2 选择排序
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/bubble_sort/" class = "md-nav__link" >
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11.3 冒泡排序
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/insertion_sort/" class = "md-nav__link" >
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11.4 插入排序
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/quick_sort/" class = "md-nav__link" >
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11.5 快速排序
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/merge_sort/" class = "md-nav__link" >
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11.6 归并排序
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/heap_sort/" class = "md-nav__link" >
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11.7 堆排序
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/bucket_sort/" class = "md-nav__link" >
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11.8 桶排序
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/counting_sort/" class = "md-nav__link" >
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11.9 计数排序
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< li class = "md-nav__item" >
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< a href = "../../chapter_sorting/radix_sort/" class = "md-nav__link" >
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11.10 基数排序
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/summary/" class = "md-nav__link" >
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11.11 小结
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< li class = "md-nav__item md-nav__item--nested" >
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< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_13" >
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< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_divide_and_conquer/" class = "md-nav__link " >
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< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z" / > < / svg >
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第 12 章 分治
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第 12 章 分治
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< / label >
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12.1 分治算法
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< li class = "md-nav__item" >
< a href = "../../chapter_divide_and_conquer/binary_search_recur/" class = "md-nav__link" >
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12.2 分治搜索策略
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< li class = "md-nav__item" >
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12.3 构建树问题
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< li class = "md-nav__item" >
< a href = "../../chapter_divide_and_conquer/hanota_problem/" class = "md-nav__link" >
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12.4 汉诺塔问题
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< a href = "../../chapter_divide_and_conquer/summary/" class = "md-nav__link" >
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12.5 小结
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第 13 章 回溯
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13.1 回溯算法
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13.2 全排列问题
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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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14.2 DP 问题特性
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14.3 DP 解题思路
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14.4 0-1 背包问题
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14.7 小结
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第 15 章 贪心
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15.1 贪心算法
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15.5 小结
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第 16 章 附录
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16.1 编程环境安装
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16.2 一起参与创作
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3.4.1 ASCII 字符集
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3.4.2 GBK 字符集
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3.4.3 Unicode 字符集
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3.4.4 UTF-8 编码
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3.4.5 编程语言的字符编码
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< h1 id = "34" > 3.4 字符编码 *< a class = "headerlink" href = "#34" title = "Permanent link" > ¶ < / a > < / h1 >
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< p > 在计算机中,所有数据都是以二进制数的形式存储的,字符 < code > char< / code > 也不例外。为了表示字符,我们需要建立一套“字符集”,规定每个字符和二进制数之间的一一对应关系。有了字符集之后,计算机就可以通过查表完成二进制数到字符的转换。< / p >
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< h2 id = "341-ascii" > 3.4.1 ASCII 字符集< a class = "headerlink" href = "#341-ascii" title = "Permanent link" > ¶ < / a > < / h2 >
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< p > 「ASCII 码」是最早出现的字符集,全称为“美国标准信息交换代码”。它使用 7 位二进制数(即一个字节的低 7 位)表示一个字符,最多能够表示 128 个不同的字符。如图 3-6 所示, ASCII 码包括英文字母的大小写、数字 0 ~ 9、一些标点符号, 以及一些控制字符( 如换行符和制表符) 。< / p >
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< p > < a class = "glightbox" href = "../character_encoding.assets/ascii_table.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "ASCII 码" src = "../character_encoding.assets/ascii_table.png" / > < / a > < / p >
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< p align = "center" > 图 3-6 ASCII 码 < / p >
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< p > 然而,< strong > ASCII 码仅能够表示英文< / strong > 。随着计算机的全球化, 诞生了一种能够表示更多语言的字符集「EASCII」。它在 ASCII 的 7 位基础上扩展到 8 位,能够表示 256 个不同的字符。< / p >
< p > 在世界范围内,陆续出现了一批适用于不同地区的 EASCII 字符集。这些字符集的前 128 个字符统一为 ASCII 码,后 128 个字符定义不同,以适应不同语言的需求。< / p >
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< h2 id = "342-gbk" > 3.4.2 GBK 字符集< a class = "headerlink" href = "#342-gbk" title = "Permanent link" > ¶ < / a > < / h2 >
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< p > 后来人们发现,< strong > EASCII 码仍然无法满足许多语言的字符数量要求< / strong > 。比如汉字大约有近十万个,光日常使用的就有几千个。中国国家标准总局于 1980 年发布了「GB2312」字符集, 其收录了 6763 个汉字,基本满足了汉字的计算机处理需要。< / p >
< p > 然而, GB2312 无法处理部分的罕见字和繁体字。「GBK」字符集是在 GB2312 的基础上扩展得到的,它共收录了 21886 个汉字。在 GBK 的编码方案中, ASCII 字符使用一个字节表示,汉字使用两个字节表示。< / p >
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< h2 id = "343-unicode" > 3.4.3 Unicode 字符集< a class = "headerlink" href = "#343-unicode" title = "Permanent link" > ¶ < / a > < / h2 >
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< p > 随着计算机的蓬勃发展,字符集与编码标准百花齐放,而这带来了许多问题。一方面,这些字符集一般只定义了特定语言的字符,无法在多语言环境下正常工作。另一方面,同一种语言也存在多种字符集标准,如果两台电脑安装的是不同的编码标准,则在信息传递时就会出现乱码。< / p >
< p > 那个时代的研究人员就在想:< strong > 如果推出一个足够完整的字符集,将世界范围内的所有语言和符号都收录其中,不就可以解决跨语言环境和乱码问题了吗< / strong > ?在这种想法的驱动下,一个大而全的字符集 Unicode 应运而生。< / p >
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< p > 「Unicode」的全称为“统一字符编码”, 理论上能容纳一百多万个字符。它致力于将全球范围内的字符纳入到统一的字符集之中, 提供一种通用的字符集来处理和显示各种语言文字, 减少因为编码标准不同而产生的乱码问题。< / p >
< p > 自 1991 年发布以来, Unicode 不断扩充新的语言与字符。截止 2022 年 9 月, Unicode 已经包含 149186 个字符,包括各种语言的字符、符号、甚至是表情符号等。在庞大的 Unicode 字符集中,常用的字符占用 2 字节,有些生僻的字符占 3 字节甚至 4 字节。< / p >
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< p > Unicode 是一种字符集标准,本质上是给每个字符分配一个编号(称为“码点”),< strong > 但它并没有规定在计算机中如何存储这些字符码点< / strong > 。我们不禁会问:当多种长度的 Unicode 码点同时出现在同一个文本中时,系统如何解析字符?例如给定一个长度为 2 字节的编码,系统如何确认它是一个 2 字节的字符还是两个 1 字节的字符?< / p >
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< p > 对于以上问题,< strong > 一种直接的解决方案是将所有字符存储为等长的编码< / strong > 。如图 3-7 所示, “Hello”中的每个字符占用 1 字节,“算法”中的每个字符占用 2 字节。我们可以通过高位填 0 , 将“Hello 算法”中的所有字符都编码为 2 字节长度。这样系统就可以每隔 2 字节解析一个字符,恢复出这个短语的内容了。< / p >
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< p > < a class = "glightbox" href = "../character_encoding.assets/unicode_hello_algo.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "Unicode 编码示例" src = "../character_encoding.assets/unicode_hello_algo.png" / > < / a > < / p >
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< p align = "center" > 图 3-7 Unicode 编码示例 < / p >
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< p > 然而 ASCII 码已经向我们证明,编码英文只需要 1 字节。若采用上述方案,英文文本占用空间的大小将会是 ASCII 编码下大小的两倍,非常浪费内存空间。因此,我们需要一种更加高效的 Unicode 编码方法。< / p >
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< h2 id = "344-utf-8" > 3.4.4 UTF-8 编码< a class = "headerlink" href = "#344-utf-8" title = "Permanent link" > ¶ < / a > < / h2 >
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< p > 目前, UTF-8 已成为国际上使用最广泛的 Unicode 编码方法。< strong > 它是一种可变长的编码< / strong > ,使用 1 到 4 个字节来表示一个字符, 根据字符的复杂性而变。ASCII 字符只需要 1 个字节,拉丁字母和希腊字母需要 2 个字节,常用的中文字符需要 3 个字节,其他的一些生僻字符需要 4 个字节。< / p >
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< p > UTF-8 的编码规则并不复杂,分为以下两种情况。< / p >
< ul >
< li > 对于长度为 1 字节的字符,将最高位设置为 < span class = "arithmatex" > \(0\)< / span > 、其余 7 位设置为 Unicode 码点。值得注意的是, ASCII 字符在 Unicode 字符集中占据了前 128 个码点。也就是说,< strong > UTF-8 编码可以向下兼容 ASCII 码< / strong > 。这意味着我们可以使用 UTF-8 来解析年代久远的 ASCII 码文本。< / li >
< li > 对于长度为 < span class = "arithmatex" > \(n\)< / span > 字节的字符(其中 < span class = "arithmatex" > \(n > 1\)< / span > ),将首个字节的高 < span class = "arithmatex" > \(n\)< / span > 位都设置为 < span class = "arithmatex" > \(1\)< / span > 、第 < span class = "arithmatex" > \(n + 1\)< / span > 位设置为 < span class = "arithmatex" > \(0\)< / span > ;从第二个字节开始,将每个字节的高 2 位都设置为 < span class = "arithmatex" > \(10\)< / span > ;其余所有位用于填充字符的 Unicode 码点。< / li >
< / ul >
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< p > 图 3-8 展示了“Hello算法”对应的 UTF-8 编码。观察发现,由于最高 < span class = "arithmatex" > \(n\)< / span > 位都被设置为 < span class = "arithmatex" > \(1\)< / span > ,因此系统可以通过读取最高位 < span class = "arithmatex" > \(1\)< / span > 的个数来解析出字符的长度为 < span class = "arithmatex" > \(n\)< / span > 。< / p >
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< p > 但为什么要将其余所有字节的高 2 位都设置为 < span class = "arithmatex" > \(10\)< / span > 呢?实际上,这个 < span class = "arithmatex" > \(10\)< / span > 能够起到校验符的作用。假设系统从一个错误的字节开始解析文本,字节头部的 < span class = "arithmatex" > \(10\)< / span > 能够帮助系统快速的判断出异常。< / p >
< p > 之所以将 < span class = "arithmatex" > \(10\)< / span > 当作校验符,是因为在 UTF-8 编码规则下,不可能有字符的最高两位是 < span class = "arithmatex" > \(10\)< / span > 。这个结论可以用反证法来证明:假设一个字符的最高两位是 < span class = "arithmatex" > \(10\)< / span > ,说明该字符的长度为 < span class = "arithmatex" > \(1\)< / span > ,对应 ASCII 码。而 ASCII 码的最高位应该是 < span class = "arithmatex" > \(0\)< / span > ,与假设矛盾。< / p >
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< p > < a class = "glightbox" href = "../character_encoding.assets/utf-8_hello_algo.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "UTF-8 编码示例" src = "../character_encoding.assets/utf-8_hello_algo.png" / > < / a > < / p >
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< p align = "center" > 图 3-8 UTF-8 编码示例 < / p >
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< p > 除了 UTF-8 之外,常见的编码方式还包括以下两种。< / p >
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< ul >
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< li > < strong > UTF-16 编码< / strong > :使用 2 或 4 个字节来表示一个字符。所有的 ASCII 字符和常用的非英文字符,都用 2 个字节表示;少数字符需要用到 4 个字节表示。对于 2 字节的字符, UTF-16 编码与 Unicode 码点相等。< / li >
< li > < strong > UTF-32 编码< / strong > :每个字符都使用 4 个字节。这意味着 UTF-32 会比 UTF-8 和 UTF-16 更占用空间,特别是对于 ASCII 字符占比较高的文本。< / li >
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< / ul >
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< p > 从存储空间的角度看,使用 UTF-8 表示英文字符非常高效,因为它仅需 1 个字节;使用 UTF-16 编码某些非英文字符(例如中文)会更加高效,因为它只需要 2 个字节,而 UTF-8 可能需要 3 个字节。< / p >
< p > 从兼容性的角度看, UTF-8 的通用性最佳,许多工具和库都优先支持 UTF-8 。< / p >
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< h2 id = "345" > 3.4.5 编程语言的字符编码< a class = "headerlink" href = "#345" title = "Permanent link" > ¶ < / a > < / h2 >
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< p > 对于以往的大多数编程语言,程序运行中的字符串都采用 UTF-16 或 UTF-32 这类等长的编码。在等长编码下,我们可以将字符串看作数组来处理,这种做法具有以下优点。< / p >
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< ul >
< li > < strong > 随机访问< / strong > : UTF-16 编码的字符串可以很容易地进行随机访问。UTF-8 是一种变长编码,要找到第 < span class = "arithmatex" > \(i\)< / span > 个字符,我们需要从字符串的开始处遍历到第 < span class = "arithmatex" > \(i\)< / span > 个字符,这需要 < span class = "arithmatex" > \(O(n)\)< / span > 的时间。< / li >
< li > < strong > 字符计数< / strong > : 与随机访问类似,计算 UTF-16 字符串的长度也是 < span class = "arithmatex" > \(O(1)\)< / span > 的操作。但是,计算 UTF-8 编码的字符串的长度需要遍历整个字符串。< / li >
< li > < strong > 字符串操作< / strong > : 在 UTF-16 编码的字符串中,很多字符串操作(如分割、连接、插入、删除等)都更容易进行。在 UTF-8 编码的字符串上进行这些操作通常需要额外的计算,以确保不会产生无效的 UTF-8 编码。< / li >
< / ul >
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< p > 实际上,编程语言的字符编码方案设计是一个很有趣的话题,其涉及到许多因素。< / p >
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< ul >
< li > Java 的 < code > String< / code > 类型使用 UTF-16 编码,每个字符占用 2 字节。这是因为 Java 语言设计之初,人们认为 16 位足以表示所有可能的字符。然而,这是一个不正确的判断。后来 Unicode 规范扩展到了超过 16 位,所以 Java 中的字符现在可能由一对 16 位的值(称为“代理对”)表示。< / li >
< li > JavaScript 和 TypeScript 的字符串使用 UTF-16 编码的原因与 Java 类似。当 JavaScript 语言在 1995 年被 Netscape 公司首次引入时, Unicode 还处于相对早期的阶段,那时候使用 16 位的编码就足够表示所有的 Unicode 字符了。< / li >
< li > C# 使用 UTF-16 编码,主要因为 .NET 平台是由 Microsoft 设计的,而 Microsoft 的很多技术,包括 Windows 操作系统,都广泛地使用 UTF-16 编码。< / li >
< / ul >
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< p > 由于以上编程语言对字符数量的低估,它们不得不采取“代理对”的方式来表示超过 16 位长度的 Unicode 字符。这是一个不得已为之的无奈之举。一方面,包含代理对的字符串中,一个字符可能占用 2 字节或 4 字节,从而丧失了等长编码的优势。另一方面,处理代理对需要增加额外代码,这增加了编程的复杂性和 Debug 难度。< / p >
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< p > 出于以上原因,部分编程语言提出了一些不同的编码方案。< / p >
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< ul >
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< li > Python 中的 < code > str< / code > 使用 Unicode 编码,并采用一种灵活的字符串表示,存储的字符长度取决于字符串中最大的 Unicode 码点。若字符串中全部是 ASCII 字符,则每个字符占用 1 个字节;如果有字符超出了 ASCII 范围, 但全部在基本多语言平面( BMP) 内, 则每个字符占用 2 个字节;如果有超出 BMP 的字符,则每个字符占用 4 个字节。< / li >
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< li > Go 语言的 < code > string< / code > 类型在内部使用 UTF-8 编码。Go 语言还提供了 < code > rune< / code > 类型,它用于表示单个 Unicode 码点。< / li >
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< li > Rust 语言的 str 和 String 类型在内部使用 UTF-8 编码。Rust 也提供了 < code > char< / code > 类型,用于表示单个 Unicode 码点。< / li >
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< / ul >
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< p > 需要注意的是,以上讨论的都是字符串在编程语言中的存储方式,< strong > 这和字符串如何在文件中存储或在网络中传输是两个不同的问题< / strong > 。在文件存储或网络传输中,我们通常会将字符串编码为 UTF-8 格式,以达到最优的兼容性和空间效率。< / p >
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