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< title > 3.4. 字符编码 * - Hello 算法< / title >
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3.4. 字符编码 *
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0. 写在前面
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0. 写在前面
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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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1. 引言
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1. 引言
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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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2. 复杂度分析
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2. 复杂度分析
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2.1. 算法效率评估
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< a href = "../../chapter_computational_complexity/time_complexity/" class = "md-nav__link" >
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2.2. 时间复杂度
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< a href = "../../chapter_computational_complexity/space_complexity/" class = "md-nav__link" >
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2.3. 空间复杂度
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< a href = "../../chapter_computational_complexity/summary/" class = "md-nav__link" >
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2.4. 小结
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< label class = "md-nav__link" for = "__nav_4" id = "__nav_4_label" tabindex = "0" >
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3. 数据结构与数据
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3. 数据结构与数据
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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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< input class = "md-nav__toggle md-toggle" type = "checkbox" id = "__toc" >
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< label class = "md-nav__link md-nav__link--active" for = "__toc" >
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3.4. 字符编码 *
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< a href = "./" class = "md-nav__link md-nav__link--active" >
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3.4. 字符编码 *
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< nav class = "md-nav md-nav--secondary" aria-label = "目录" >
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目录
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< li class = "md-nav__item" >
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3.4.1. ASCII 字符集
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< a href = "#342-gbk" class = "md-nav__link" >
3.4.2. GBK 字符集
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< a href = "#343-unicode" class = "md-nav__link" >
3.4.3. Unicode 字符集
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< a href = "#344-utf-8" class = "md-nav__link" >
3.4.4. UTF-8 编码
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< a href = "../summary/" class = "md-nav__link" >
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3.5. 小结
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< label class = "md-nav__link" for = "__nav_5" id = "__nav_5_label" tabindex = "0" >
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4. 数组与链表
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< label class = "md-nav__title" for = "__nav_5" >
< span class = "md-nav__icon md-icon" > < / span >
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4. 数组与链表
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< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/array/" class = "md-nav__link" >
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4.1. 数组
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< a href = "../../chapter_array_and_linkedlist/linked_list/" class = "md-nav__link" >
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4.2. 链表
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< a href = "../../chapter_array_and_linkedlist/list/" class = "md-nav__link" >
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4.3. 列表
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< a href = "../../chapter_array_and_linkedlist/summary/" class = "md-nav__link" >
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4.4. 小结
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5. 栈与队列
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5. 栈与队列
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< a href = "../../chapter_stack_and_queue/stack/" class = "md-nav__link" >
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5.1. 栈
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< a href = "../../chapter_stack_and_queue/queue/" class = "md-nav__link" >
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5.2. 队列
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< a href = "../../chapter_stack_and_queue/deque/" class = "md-nav__link" >
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5.3. 双向队列
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5.4. 小结
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< label class = "md-nav__link" for = "__nav_7" id = "__nav_7_label" tabindex = "0" >
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6. 二分查找
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< label class = "md-nav__title" for = "__nav_7" >
< span class = "md-nav__icon md-icon" > < / span >
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6. 二分查找
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< a href = "../../chapter_binary_search/binary_search/" class = "md-nav__link" >
6.1. 二分查找
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< label class = "md-nav__link" for = "__nav_8" id = "__nav_8_label" tabindex = "0" >
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7. 散列表
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< span class = "md-nav__icon md-icon" > < / span >
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7. 散列表
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< li class = "md-nav__item" >
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7.1. 哈希表
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< a href = "../../chapter_hashing/hash_collision/" class = "md-nav__link" >
7.2. 哈希冲突处理
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< a href = "../../chapter_hashing/summary/" class = "md-nav__link" >
7.3. 小结
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< label class = "md-nav__link" for = "__nav_9" id = "__nav_9_label" tabindex = "0" >
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8. 树
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< label class = "md-nav__title" for = "__nav_9" >
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8. 树
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< li class = "md-nav__item" >
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< a href = "../../chapter_tree/binary_tree/" class = "md-nav__link" >
8.1. 二叉树
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< li class = "md-nav__item" >
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< a href = "../../chapter_tree/binary_tree_traversal/" class = "md-nav__link" >
8.2. 二叉树遍历
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< a href = "../../chapter_tree/array_representation_of_tree/" class = "md-nav__link" >
8.3. 二叉树数组表示
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< li class = "md-nav__item" >
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< a href = "../../chapter_tree/binary_search_tree/" class = "md-nav__link" >
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8.4. 二叉搜索树
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< a href = "../../chapter_tree/avl_tree/" class = "md-nav__link" >
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8.5. AVL 树 *
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< a href = "../../chapter_tree/summary/" class = "md-nav__link" >
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8.6. 小结
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< label class = "md-nav__link" for = "__nav_10" id = "__nav_10_label" tabindex = "0" >
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9. 堆
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< label class = "md-nav__title" for = "__nav_10" >
< span class = "md-nav__icon md-icon" > < / span >
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9. 堆
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< li class = "md-nav__item" >
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< a href = "../../chapter_heap/heap/" class = "md-nav__link" >
9.1. 堆
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< li class = "md-nav__item" >
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< a href = "../../chapter_heap/build_heap/" class = "md-nav__link" >
9.2. 建堆操作 *
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< li class = "md-nav__item" >
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< a href = "../../chapter_heap/summary/" class = "md-nav__link" >
9.3. 小结
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< label class = "md-nav__link" for = "__nav_11" id = "__nav_11_label" tabindex = "0" >
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10. 图
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< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_11_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_11" >
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10. 图
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< li class = "md-nav__item" >
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< a href = "../../chapter_graph/graph/" class = "md-nav__link" >
10.1. 图
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< li class = "md-nav__item" >
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< a href = "../../chapter_graph/graph_operations/" class = "md-nav__link" >
10.2. 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" >
10.3. 图的遍历
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< li class = "md-nav__item" >
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< a href = "../../chapter_graph/summary/" class = "md-nav__link" >
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10.4. 小结
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< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_12" >
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< label class = "md-nav__link" for = "__nav_12" id = "__nav_12_label" tabindex = "0" >
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11. 排序算法
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< label class = "md-nav__title" for = "__nav_12" >
< span class = "md-nav__icon md-icon" > < / span >
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11. 排序算法
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< li class = "md-nav__item" >
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< a href = "../../chapter_sorting/sorting_algorithm/" class = "md-nav__link" >
11.1. 排序算法
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/bubble_sort/" class = "md-nav__link" >
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11.2. 冒泡排序
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< / a >
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/insertion_sort/" class = "md-nav__link" >
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11.3. 插入排序
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11.4. 快速排序
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< / a >
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< a href = "../../chapter_sorting/merge_sort/" class = "md-nav__link" >
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11.5. 归并排序
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< / a >
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/bucket_sort/" class = "md-nav__link" >
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11.6. 桶排序
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< / a >
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11.7. 计数排序
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< / a >
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< a href = "../../chapter_sorting/radix_sort/" class = "md-nav__link" >
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11.8. 基数排序
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< / a >
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11.9. 小结
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12. 搜索算法
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12. 搜索算法
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12.1. 搜索算法( New)
< / a >
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12.2. 哈希优化策略
< / a >
< / li >
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12.3. 小结
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13. 回溯算法
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13. 回溯算法
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13.1. 回溯算法( New)
< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_backtracking/permutations_problem/" class = "md-nav__link" >
13.2. 全排列问题( New)
< / a >
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< a href = "../../chapter_backtracking/n_queens_problem/" class = "md-nav__link" >
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13.3. N 皇后问题( New)
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< / a >
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14. 附录
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14. 附录
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< / label >
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< a href = "../../chapter_appendix/installation/" class = "md-nav__link" >
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14.1. 编程环境安装
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< / a >
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< a href = "../../chapter_appendix/contribution/" class = "md-nav__link" >
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14.2. 一起参与创作
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< a href = "../../chapter_reference/" > 参考文献< / a >
< / div >
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< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_16_label" aria-expanded = "false" >
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< span class = "md-nav__icon md-icon" > < / span >
参考文献
< / label >
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< / ul >
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< / div >
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< nav class = "md-nav md-nav--secondary" aria-label = "目录" >
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< span class = "md-nav__icon md-icon" > < / span >
目录
< / label >
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< li class = "md-nav__item" >
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< a href = "#341-ascii" class = "md-nav__link" >
3.4.1. ASCII 字符集
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "#342-gbk" class = "md-nav__link" >
3.4.2. GBK 字符集
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "#343-unicode" class = "md-nav__link" >
3.4.3. Unicode 字符集
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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 = "#344-utf-8" class = "md-nav__link" >
3.4.4. UTF-8 编码
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< a href = "https://github.com/krahets/hello-algo/tree/main/docs/chapter_data_structure/character_encoding.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 = "M10 20H6V4h7v5h5v3.1l2-2V8l-6-6H6c-1.1 0-2 .9-2 2v16c0 1.1.9 2 2 2h4v-2m10.2-7c.1 0 .3.1.4.2l1.3 1.3c.2.2.2.6 0 .8l-1 1-2.1-2.1 1-1c.1-.1.2-.2.4-.2m0 3.9L14.1 23H12v-2.1l6.1-6.1 2.1 2.1Z" / > < / svg >
< / a >
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< h1 id = "34" > 3.4. 字符集与编码< a class = "headerlink" href = "#34" title = "Permanent link" > ¶ < / a > < / h1 >
< 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 >
< h2 id = "341-ascii" > 3.4.1. ASCII 字符集< a class = "headerlink" href = "#341-ascii" title = "Permanent link" > ¶ < / a > < / h2 >
< 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(即一个字节的前 7 位)表示一个字符,最多能够表示 128 个不同的字符。这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 >
< p > < img alt = "ASCII 码" src = "../character_encoding.assets/ascii_table.png" / > < / p >
< p align = "center" > Fig. ASCII 码 < / p >
< p > 然而, ASCII 码仅局限于表示英文。随着计算机的全球化, 一种能够表示更多语言的字符集「EASCII」应运而生。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。世界陆续诞生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 个字符定义了不同语言的字符。< / p >
< h2 id = "342-gbk" > 3.4.2. GBK 字符集< a class = "headerlink" href = "#342-gbk" title = "Permanent link" > ¶ < / a > < / h2 >
< p > EASCII 码仍然无法满足许多语言的字符数量要求。例如,汉字大约有近十万个,光日常使用的就有几千个。为此,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。之后在 GB2312 的基础上, 扩展得到了「GBK」字符集, 它共收录了 21886 个汉字。在 GBK 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 >
< h2 id = "343-unicode" > 3.4.3. Unicode 字符集< a class = "headerlink" href = "#343-unicode" title = "Permanent link" > ¶ < / a > < / h2 >
< p > 随着计算机的蓬勃发展,在世界范围内诞生了许多字符集与编码标准,而这带来了许多问题。一方面,这些字符集一般只定义了某种特定语言的字符,无法实现跨语言解析;另一方面,同一种语言也存在多种字符集,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 > 那个时代的人们会想: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纳入其中,不就可以解决跨语言环境和乱码问题了吗?在这种思考下,一个庞大的字符集 Unicode 应运而生。< / p >
< 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 >
< 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 >
< p > < strong > 最直接的解决方案是将所有字符存储为等长的编码< / strong > 。如下图所示, “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 >
< p > < img alt = "Unicode 编码示例" src = "../character_encoding.assets/unicode_hello_algo.png" / > < / p >
< p align = "center" > Fig. Unicode 编码示例 < / p >
< 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 2 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 >
< h2 id = "344-utf-8" > 3.4.4. UTF-8 编码< a class = "headerlink" href = "#344-utf-8" title = "Permanent link" > ¶ < / a > < / h2 >
< p > 随着互联网的发展, UTF-8 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。UTF-8 的编码规则是:< / p >
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< ul >
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< li > 对于长度为 1 字节的字符,将最高位设置为 0 、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 >
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< / ul >
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< p > 下图展示了“Hello算法”对应的 UTF-8 编码。将最高 < span class = "arithmatex" > \(n\)< / span > 位设置为 < span class = "arithmatex" > \(1\)< / span > 比较容易理解,可以向系统指出字符的长度为 < span class = "arithmatex" > \(n\)< / span > 。那么,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,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 > 。这是因为长度为 1 字节的字符的最高一位是 < span class = "arithmatex" > \(0\)< / span > 。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 > < img alt = "UTF-8 编码示例" src = "../character_encoding.assets/utf-8_hello_algo.png" / > < / p >
< p align = "center" > Fig. UTF-8 编码示例 < / p >
< p > 除了 UTF-8 之外,常见的编码方式还包括 UTF-16 和 UTF-32 。它们为 Unicode 字符集提供了不同的编码方法。< / 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 字符和很多常用的中文字符,都用 2 个字节表示。少数字符需要用到 4 个字节表示。< / 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,特别是对于主要使用 ASCII 字符的文本。< / 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。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 >
< p > 如下表所示,为各个编程语言的字符串默认编码方式。由于 UTF-16 和 UTF-32 属于等长的编码方法,因此编程语言可以直接计算字符串的长度,也可以快速地访问字符串中的任意字符。而如果使用 UTF-8 这种变长的编码方法,编程语言往往需要额外维护一个字符数组,才能实现高效的随机访问。< / p >
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< div class = "center-table" >
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< table >
< thead >
< tr >
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< th > 编码< / th >
< th > 编程语言< / th >
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< / tr >
< / thead >
< tbody >
< tr >
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< td > UTF-8< / td >
< td > Python, Go, Rust, Swift< / td >
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< / tr >
< tr >
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< td > UTF-16< / td >
< td > Java, C#, JavaScript, TypeScript< / td >
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