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11.8. 基数排序（ ）
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0. 写在前面
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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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2.2. 时间复杂度
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2.3. 空间复杂度
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2.5. 小结
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< label class = "md-nav__link" for = "__nav_4" id = "__nav_4_label" tabindex = "0" >
3. 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
< / label >
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< li class = "md-nav__item" >
< a href = "../../chapter_data_structure/data_and_memory/" class = "md-nav__link" >
3.1. 数据与内存
< / a >
< / li >
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< a href = "../../chapter_data_structure/classification_of_data_structure/" class = "md-nav__link" >
3.2. 数据结构分类
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_data_structure/summary/" class = "md-nav__link" >
3.3. 小结
< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_5" >
< label class = "md-nav__link" for = "__nav_5" id = "__nav_5_label" tabindex = "0" >
4. 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 = "false" >
< label class = "md-nav__title" for = "__nav_5" >
< span class = "md-nav__icon md-icon" > < / span >
4. 数组与链表
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/array/" class = "md-nav__link" >
4.1. 数组
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/linked_list/" class = "md-nav__link" >
4.2. 链表
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/list/" class = "md-nav__link" >
4.3. 列表
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/summary/" class = "md-nav__link" >
4.4. 小结
< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_6" >
< label class = "md-nav__link" for = "__nav_6" id = "__nav_6_label" tabindex = "0" >
5. 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
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/stack/" class = "md-nav__link" >
5.1. 栈
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/queue/" class = "md-nav__link" >
5.2. 队列
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/deque/" class = "md-nav__link" >
5.3. 双向队列
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/summary/" class = "md-nav__link" >
5.4. 小结
< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_7" >
< label class = "md-nav__link" for = "__nav_7" id = "__nav_7_label" tabindex = "0" >
6. 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
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_hashing/hash_map/" class = "md-nav__link" >
6.1. 哈希表
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_hashing/hash_collision/" class = "md-nav__link" >
6.2. 哈希冲突处理
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_hashing/summary/" class = "md-nav__link" >
6.3. 小结
< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_8" >
< label class = "md-nav__link" for = "__nav_8" id = "__nav_8_label" tabindex = "0" >
7. 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. 树
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_tree/binary_tree/" class = "md-nav__link" >
7.1. 二叉树
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_tree/binary_tree_traversal/" class = "md-nav__link" >
7.2. 二叉树遍历
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_tree/binary_search_tree/" class = "md-nav__link" >
7.3. 二叉搜索树
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_tree/avl_tree/" class = "md-nav__link" >
7.4. AVL 树 *
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_tree/summary/" class = "md-nav__link" >
7.5. 小结
< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_9" >
< label class = "md-nav__link" for = "__nav_9" id = "__nav_9_label" tabindex = "0" >
8. 堆
< 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
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_heap/heap/" class = "md-nav__link" >
8.1. 堆
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_heap/build_heap/" class = "md-nav__link" >
8.2. 建堆操作 *
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_heap/summary/" class = "md-nav__link" >
8.3. 小结
< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_10" >
< label class = "md-nav__link" for = "__nav_10" id = "__nav_10_label" tabindex = "0" >
9. 图
< 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
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_graph/graph/" class = "md-nav__link" >
9.1. 图
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_graph/graph_operations/" class = "md-nav__link" >
9.2. 图基础操作
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_graph/graph_traversal/" class = "md-nav__link" >
9.3. 图的遍历（ ）
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_graph/summary/" class = "md-nav__link" >
9.4. 小结
< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_11" >
< label class = "md-nav__link" for = "__nav_11" id = "__nav_11_label" tabindex = "0" >
10. 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
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_searching/linear_search/" class = "md-nav__link" >
10.1. 线性查找
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_searching/binary_search/" class = "md-nav__link" >
10.2. 二分查找
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_searching/hashing_search/" class = "md-nav__link" >
10.3. 哈希查找
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_searching/summary/" class = "md-nav__link" >
10.4. 小结
< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--active md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_12" checked >
< label class = "md-nav__link" for = "__nav_12" id = "__nav_12_label" tabindex = "0" >
11. 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 = "true" >
< label class = "md-nav__title" for = "__nav_12" >
< span class = "md-nav__icon md-icon" > < / span >
11. 排序算法
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../intro_to_sort/" class = "md-nav__link" >
11.1. 排序简介
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../bubble_sort/" class = "md-nav__link" >
11.2. 冒泡排序
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../insertion_sort/" class = "md-nav__link" >
11.3. 插入排序
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../quick_sort/" class = "md-nav__link" >
11.4. 快速排序
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../merge_sort/" class = "md-nav__link" >
11.5. 归并排序
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../bucket_sort/" class = "md-nav__link" >
11.6. 桶排序（ ）
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../counting_sort/" class = "md-nav__link" >
11.7. 计数排序（ ）
< / a >
< / li >
< li class = "md-nav__item md-nav__item--active" >
< input class = "md-nav__toggle md-toggle" type = "checkbox" id = "__toc" >
< label class = "md-nav__link md-nav__link--active" for = "__toc" >
11.8. 基数排序（ ）
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< a href = "./" class = "md-nav__link md-nav__link--active" >
11.8. 基数排序（ ）
< / a >
< nav class = "md-nav md-nav--secondary" aria-label = "目录" >
< label class = "md-nav__title" for = "__toc" >
< span class = "md-nav__icon md-icon" > < / span >
目录
< / label >
< ul class = "md-nav__list" data-md-component = "toc" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "#1181" class = "md-nav__link" >
11.8.1. 算法流程
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#1182" class = "md-nav__link" >
11.8.2. 算法特性
< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item" >
< a href = "../summary/" class = "md-nav__link" >
11.9. 小结
< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_13" >
< label class = "md-nav__link" for = "__nav_13" id = "__nav_13_label" tabindex = "0" >
12. 附录
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_13_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_13" >
< span class = "md-nav__icon md-icon" > < / span >
12. 附录
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_appendix/installation/" class = "md-nav__link" >
12.1. 编程环境安装
< / a >
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< a href = "../../chapter_appendix/contribution/" class = "md-nav__link" >
12.2. 一起参与创作
< / a >
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< / li >
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< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_14" >
< div class = "md-nav__link md-nav__link--index " >
< a href = "../../chapter_reference/" > 参考文献< / a >
< / div >
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< label class = "md-nav__title" for = "__nav_14" >
< span class = "md-nav__icon md-icon" > < / span >
参考文献
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< / ul >
< / nav >
< / li >
< / ul >
< / nav >
< / div >
< / div >
< / div >
< div class = "md-sidebar md-sidebar--secondary" data-md-component = "sidebar" data-md-type = "toc" >
< div class = "md-sidebar__scrollwrap" >
< div class = "md-sidebar__inner" >
< nav class = "md-nav md-nav--secondary" aria-label = "目录" >
< label class = "md-nav__title" for = "__toc" >
< span class = "md-nav__icon md-icon" > < / span >
目录
< / label >
< ul class = "md-nav__list" data-md-component = "toc" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "#1181" class = "md-nav__link" >
11.8.1. 算法流程
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#1182" class = "md-nav__link" >
11.8.2. 算法特性
< / a >
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< / ul >
< / nav >
< / div >
< / div >
< / div >
< div class = "md-content" data-md-component = "content" >
< article class = "md-content__inner md-typeset" >
< a href = "https://github.com/krahets/hello-algo/tree/main/docs/chapter_sorting/radix_sort.md" title = "编辑此页" class = "md-content__button md-icon" >
< 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 >
< h1 id = "118" > 11.8. 基数排序< a class = "headerlink" href = "#118" title = "Permanent link" > ¶ < / a > < / h1 >
< p > 上一节我们介绍了计数排序，它适用于数据量 < span class = "arithmatex" > \(n\)< / span > 较大但数据范围 < span class = "arithmatex" > \(m\)< / span > 较小的情况。假设我们需要对 < span class = "arithmatex" > \(n = 10^6\)< / span > 个学号进行排序，而学号是一个 < span class = "arithmatex" > \(8\)< / span > 位数字，这意味着数据范围 < span class = "arithmatex" > \(m = 10^8\)< / span > 非常大，使用计数排序需要分配大量内存空间，而基数排序可以避免这种情况。< / p >
< p > 「基数排序 Radix Sort」的核心思想与计数排序一致， ， ， ， < / p >
< h2 id = "1181" > 11.8.1. 算法流程< a class = "headerlink" href = "#1181" title = "Permanent link" > ¶ < / a > < / h2 >
< p > 以学号数据为例，假设数字的最低位是第 < span class = "arithmatex" > \(1\)< / span > 位，最高位是第 < span class = "arithmatex" > \(8\)< / span > 位，基数排序的步骤如下：< / p >
< ol >
< li > 初始化位数 < span class = "arithmatex" > \(k = 1\)< / span > ； < / li >
< li > 对学号的第 < span class = "arithmatex" > \(k\)< / span > 位执行「计数排序」。完成后，数据会根据第 < span class = "arithmatex" > \(k\)< / span > 位从小到大排序；< / li >
< li > 将 < span class = "arithmatex" > \(k\)< / span > 增加 < span class = "arithmatex" > \(1\)< / span > ，然后返回步骤 < code > 2.< / code > 继续迭代，直到所有位都排序完成后结束；< / li >
< / ol >
< p > < img alt = "基数排序算法流程" src = "../radix_sort.assets/radix_sort_overview.png" / > < / p >
< p align = "center" > Fig. 基数排序算法流程 < / p >
< p > 下面来剖析代码实现。对于一个 < span class = "arithmatex" > \(d\)< / span > 进制的数字 < span class = "arithmatex" > \(x\)< / span > ，要获取其第 < span class = "arithmatex" > \(k\)< / span > 位 < span class = "arithmatex" > \(x_k\)< / span > ，可以使用以下计算公式：< / p >
< div class = "arithmatex" > \[
x_k = \lfloor\frac{x}{d^{k-1}}\rfloor \mod d
\]< / div >
< p > 其中 < span class = "arithmatex" > \(\lfloor a \rfloor\)< / span > 表示对浮点数 < span class = "arithmatex" > \(a\)< / span > 向下取整，而 < span class = "arithmatex" > \(\mod d\)< / span > 表示对 < span class = "arithmatex" > \(d\)< / span > 取余。对于学号数据，< span class = "arithmatex" > \(d = 10\)< / span > 且 < span class = "arithmatex" > \(k \in [1, 8]\)< / span > 。< / p >
< p > 此外，我们需要小幅改动计数排序代码，使之可以根据数字的第 < span class = "arithmatex" > \(k\)< / span > 位进行排序。< / p >
< div class = "tabbed-set tabbed-alternate" data-tabs = "1:10" > < input checked = "checked" id = "__tabbed_1_1" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_2" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_3" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_4" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_5" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_6" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_7" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_8" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_9" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_10" name = "__tabbed_1" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_1_1" > Java< / label > < label for = "__tabbed_1_2" > C++< / label > < label for = "__tabbed_1_3" > Python< / label > < label for = "__tabbed_1_4" > Go< / label > < label for = "__tabbed_1_5" > JavaScript< / label > < label for = "__tabbed_1_6" > TypeScript< / label > < label for = "__tabbed_1_7" > C< / label > < label for = "__tabbed_1_8" > C#< / label > < label for = "__tabbed_1_9" > Swift< / label > < label for = "__tabbed_1_10" > Zig< / label > < / div >
< div class = "tabbed-content" >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > radix_sort.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-0-1" name = "__codelineno-0-1" href = "#__codelineno-0-1" > < / a > < span class = "cm" > /* 获取元素 num 的第 k 位，其中 exp = 10^(k-1) */< / span >
< a id = "__codelineno-0-2" name = "__codelineno-0-2" href = "#__codelineno-0-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > digit< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > num< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > exp< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-0-3" name = "__codelineno-0-3" href = "#__codelineno-0-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 传入 exp 而非 k 可以避免在此重复执行昂贵的次方计算< / span >
< a id = "__codelineno-0-4" name = "__codelineno-0-4" href = "#__codelineno-0-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > num< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "n" > exp< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > %< / span > < span class = "w" > < / span > < span class = "mi" > 10< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-0-5" name = "__codelineno-0-5" href = "#__codelineno-0-5" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-0-6" name = "__codelineno-0-6" href = "#__codelineno-0-6" > < / a >
< a id = "__codelineno-0-7" name = "__codelineno-0-7" href = "#__codelineno-0-7" > < / a > < span class = "cm" > /* 计数排序（根据 nums 第 k 位排序） */< / span >
< a id = "__codelineno-0-8" name = "__codelineno-0-8" href = "#__codelineno-0-8" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > countingSortDigit< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "o" > []< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > exp< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-0-9" name = "__codelineno-0-9" href = "#__codelineno-0-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 十进制的位范围为 0~9 ，因此需要长度为 10 的桶< / span >
< a id = "__codelineno-0-10" name = "__codelineno-0-10" href = "#__codelineno-0-10" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "o" > []< / span > < span class = "w" > < / span > < span class = "n" > counter< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "o" > [< / span > < span class = "mi" > 10< / span > < span class = "o" > ]< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-0-11" name = "__codelineno-0-11" href = "#__codelineno-0-11" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > .< / span > < span class = "na" > length< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-0-12" name = "__codelineno-0-12" href = "#__codelineno-0-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 统计 0~9 各数字的出现次数< / span >
< a id = "__codelineno-0-13" name = "__codelineno-0-13" href = "#__codelineno-0-13" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-0-14" name = "__codelineno-0-14" href = "#__codelineno-0-14" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > d< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > digit< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "o" > [< / span > < span class = "n" > i< / span > < span class = "o" > ]< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > exp< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 获取 nums[i] 第 k 位，记为 d< / span >
< a id = "__codelineno-0-15" name = "__codelineno-0-15" href = "#__codelineno-0-15" > < / a > < span class = "w" > < / span > < span class = "n" > counter< / span > < span class = "o" > [< / span > < span class = "n" > d< / span > < span class = "o" > ]++< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 统计数字 d 的出现次数< / span >
< a id = "__codelineno-0-16" name = "__codelineno-0-16" href = "#__codelineno-0-16" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-0-17" name = "__codelineno-0-17" href = "#__codelineno-0-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 求前缀和，将“出现个数”转换为“数组索引”< / span >
< a id = "__codelineno-0-18" name = "__codelineno-0-18" href = "#__codelineno-0-18" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "mi" > 10< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-0-19" name = "__codelineno-0-19" href = "#__codelineno-0-19" > < / a > < span class = "w" > < / span > < span class = "n" > counter< / span > < span class = "o" > [< / span > < span class = "n" > i< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > counter< / span > < span class = "o" > [< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "o" > ]< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-0-20" name = "__codelineno-0-20" href = "#__codelineno-0-20" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-0-21" name = "__codelineno-0-21" href = "#__codelineno-0-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 倒序遍历，根据桶内统计结果，将各元素填入 res< / span >
< a id = "__codelineno-0-22" name = "__codelineno-0-22" href = "#__codelineno-0-22" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "o" > []< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "o" > [< / span > < span class = "n" > n< / span > < span class = "o" > ]< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-0-23" name = "__codelineno-0-23" href = "#__codelineno-0-23" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > --< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-0-24" name = "__codelineno-0-24" href = "#__codelineno-0-24" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > d< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > digit< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "o" > [< / span > < span class = "n" > i< / span > < span class = "o" > ]< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > exp< / span > < span class = "p" > );< / span >
< a id = "__codelineno-0-25" name = "__codelineno-0-25" href = "#__codelineno-0-25" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > counter< / span > < span class = "o" > [< / span > < span class = "n" > d< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 获取 d 在数组中的索引 j< / span >
< a id = "__codelineno-0-26" name = "__codelineno-0-26" href = "#__codelineno-0-26" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "o" > [< / span > < span class = "n" > j< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "o" > [< / span > < span class = "n" > i< / span > < span class = "o" > ]< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 将当前元素填入索引 j< / span >
< a id = "__codelineno-0-27" name = "__codelineno-0-27" href = "#__codelineno-0-27" > < / a > < span class = "w" > < / span > < span class = "n" > counter< / span > < span class = "o" > [< / span > < span class = "n" > d< / span > < span class = "o" > ]--< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 将 d 的数量减 1< / span >
< a id = "__codelineno-0-28" name = "__codelineno-0-28" href = "#__codelineno-0-28" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-0-29" name = "__codelineno-0-29" href = "#__codelineno-0-29" > < / a > < span class = "w" > < / span > < span class = "c1" > // 使用结果覆盖原数组 nums< / span >
< a id = "__codelineno-0-30" name = "__codelineno-0-30" href = "#__codelineno-0-30" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span >
< a id = "__codelineno-0-31" name = "__codelineno-0-31" href = "#__codelineno-0-31" > < / a > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "o" > [< / span > < span class = "n" > i< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "o" > [< / span > < span class = "n" > i< / span > < span class = "o" > ]< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-0-32" name = "__codelineno-0-32" href = "#__codelineno-0-32" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-0-33" name = "__codelineno-0-33" href = "#__codelineno-0-33" > < / a >
< a id = "__codelineno-0-34" name = "__codelineno-0-34" href = "#__codelineno-0-34" > < / a > < span class = "cm" > /* 基数排序 */< / span >
< a id = "__codelineno-0-35" name = "__codelineno-0-35" href = "#__codelineno-0-35" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > radixSort< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "o" > []< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-0-36" name = "__codelineno-0-36" href = "#__codelineno-0-36" > < / a > < span class = "w" > < / span > < span class = "c1" > // 获取数组的最大元素，用于判断最大位数< / span >
< a id = "__codelineno-0-37" name = "__codelineno-0-37" href = "#__codelineno-0-37" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > m< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > Integer< / span > < span class = "p" > .< / span > < span class = "na" > MIN_VALUE< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-0-38" name = "__codelineno-0-38" href = "#__codelineno-0-38" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > num< / span > < span class = "w" > < / span > < span class = "p" > :< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > )< / span >
< a id = "__codelineno-0-39" name = "__codelineno-0-39" href = "#__codelineno-0-39" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > num< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > m< / span > < span class = "p" > )< / span >
< a id = "__codelineno-0-40" name = "__codelineno-0-40" href = "#__codelineno-0-40" > < / a > < span class = "w" > < / span > < span class = "n" > m< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > num< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-0-41" name = "__codelineno-0-41" href = "#__codelineno-0-41" > < / a > < span class = "w" > < / span > < span class = "c1" > // 按照从低位到高位的顺序遍历< / span >
< a id = "__codelineno-0-42" name = "__codelineno-0-42" href = "#__codelineno-0-42" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > exp< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > exp< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > m< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > exp< / span > < span class = "w" > < / span > < span class = "o" > *=< / span > < span class = "w" > < / span > < span class = "mi" > 10< / span > < span class = "p" > )< / span >
< a id = "__codelineno-0-43" name = "__codelineno-0-43" href = "#__codelineno-0-43" > < / a > < span class = "w" > < / span > < span class = "c1" > // 对数组元素的第 k 位执行计数排序< / span >
< a id = "__codelineno-0-44" name = "__codelineno-0-44" href = "#__codelineno-0-44" > < / a > < span class = "w" > < / span > < span class = "c1" > // k = 1 -> exp = 1< / span >
< a id = "__codelineno-0-45" name = "__codelineno-0-45" href = "#__codelineno-0-45" > < / a > < span class = "w" > < / span > < span class = "c1" > // k = 2 -> exp = 10< / span >
< a id = "__codelineno-0-46" name = "__codelineno-0-46" href = "#__codelineno-0-46" > < / a > < span class = "w" > < / span > < span class = "c1" > // 即 exp = 10^(k-1)< / span >
< a id = "__codelineno-0-47" name = "__codelineno-0-47" href = "#__codelineno-0-47" > < / a > < span class = "w" > < / span > < span class = "n" > countingSortDigit< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > exp< / span > < span class = "p" > );< / span >
< a id = "__codelineno-0-48" name = "__codelineno-0-48" href = "#__codelineno-0-48" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > radix_sort.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-1-1" name = "__codelineno-1-1" href = "#__codelineno-1-1" > < / a > < span class = "cm" > /* 获取元素 num 的第 k 位，其中 exp = 10^(k-1) */< / span >
< a id = "__codelineno-1-2" name = "__codelineno-1-2" href = "#__codelineno-1-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > digit< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > num< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > exp< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-3" name = "__codelineno-1-3" href = "#__codelineno-1-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 传入 exp 而非 k 可以避免在此重复执行昂贵的次方计算< / span >
< a id = "__codelineno-1-4" name = "__codelineno-1-4" href = "#__codelineno-1-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > num< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "n" > exp< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > %< / span > < span class = "w" > < / span > < span class = "mi" > 10< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-5" name = "__codelineno-1-5" href = "#__codelineno-1-5" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-1-6" name = "__codelineno-1-6" href = "#__codelineno-1-6" > < / a >
< a id = "__codelineno-1-7" name = "__codelineno-1-7" href = "#__codelineno-1-7" > < / a > < span class = "cm" > /* 计数排序（根据 nums 第 k 位排序） */< / span >
< a id = "__codelineno-1-8" name = "__codelineno-1-8" href = "#__codelineno-1-8" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > countingSortDigit< / span > < span class = "p" > (< / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > exp< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-9" name = "__codelineno-1-9" href = "#__codelineno-1-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 十进制的位范围为 0~9 ，因此需要长度为 10 的桶< / span >
< a id = "__codelineno-1-10" name = "__codelineno-1-10" href = "#__codelineno-1-10" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > counter< / span > < span class = "p" > (< / span > < span class = "mi" > 10< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > );< / span >
< a id = "__codelineno-1-11" name = "__codelineno-1-11" href = "#__codelineno-1-11" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > .< / span > < span class = "n" > size< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-1-12" name = "__codelineno-1-12" href = "#__codelineno-1-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 统计 0~9 各数字的出现次数< / span >
< a id = "__codelineno-1-13" name = "__codelineno-1-13" href = "#__codelineno-1-13" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-14" name = "__codelineno-1-14" href = "#__codelineno-1-14" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > d< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > digit< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "n" > exp< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 获取 nums[i] 第 k 位，记为 d< / span >
< a id = "__codelineno-1-15" name = "__codelineno-1-15" href = "#__codelineno-1-15" > < / a > < span class = "w" > < / span > < span class = "n" > counter< / span > < span class = "p" > [< / span > < span class = "n" > d< / span > < span class = "p" > ]< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 统计数字 d 的出现次数< / span >
< a id = "__codelineno-1-16" name = "__codelineno-1-16" href = "#__codelineno-1-16" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-1-17" name = "__codelineno-1-17" href = "#__codelineno-1-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 求前缀和，将“出现个数”转换为“数组索引”< / span >
< a id = "__codelineno-1-18" name = "__codelineno-1-18" href = "#__codelineno-1-18" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "mi" > 10< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-19" name = "__codelineno-1-19" href = "#__codelineno-1-19" > < / a > < span class = "w" > < / span > < span class = "n" > counter< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > counter< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-1-20" name = "__codelineno-1-20" href = "#__codelineno-1-20" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-1-21" name = "__codelineno-1-21" href = "#__codelineno-1-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 倒序遍历，根据桶内统计结果，将各元素填入 res< / span >
< a id = "__codelineno-1-22" name = "__codelineno-1-22" href = "#__codelineno-1-22" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > );< / span >
< a id = "__codelineno-1-23" name = "__codelineno-1-23" href = "#__codelineno-1-23" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > --< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-24" name = "__codelineno-1-24" href = "#__codelineno-1-24" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > d< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > digit< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "n" > exp< / span > < span class = "p" > );< / span >
< a id = "__codelineno-1-25" name = "__codelineno-1-25" href = "#__codelineno-1-25" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > counter< / span > < span class = "p" > [< / span > < span class = "n" > d< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 获取 d 在数组中的索引 j< / span >
< a id = "__codelineno-1-26" name = "__codelineno-1-26" href = "#__codelineno-1-26" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ];< / span > < span class = "w" > < / span > < span class = "c1" > // 将当前元素填入索引 j< / span >
< a id = "__codelineno-1-27" name = "__codelineno-1-27" href = "#__codelineno-1-27" > < / a > < span class = "w" > < / span > < span class = "n" > counter< / span > < span class = "p" > [< / span > < span class = "n" > d< / span > < span class = "p" > ]< / span > < span class = "o" > --< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 将 d 的数量减 1< / span >
< a id = "__codelineno-1-28" name = "__codelineno-1-28" href = "#__codelineno-1-28" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-1-29" name = "__codelineno-1-29" href = "#__codelineno-1-29" > < / a > < span class = "w" > < / span > < span class = "c1" > // 使用结果覆盖原数组 nums< / span >
< a id = "__codelineno-1-30" name = "__codelineno-1-30" href = "#__codelineno-1-30" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span >
< a id = "__codelineno-1-31" name = "__codelineno-1-31" href = "#__codelineno-1-31" > < / a > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-1-32" name = "__codelineno-1-32" href = "#__codelineno-1-32" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-1-33" name = "__codelineno-1-33" href = "#__codelineno-1-33" > < / a >
< a id = "__codelineno-1-34" name = "__codelineno-1-34" href = "#__codelineno-1-34" > < / a > < span class = "cm" > /* 基数排序 */< / span >
< a id = "__codelineno-1-35" name = "__codelineno-1-35" href = "#__codelineno-1-35" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > radixSort< / span > < span class = "p" > (< / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > nums< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-36" name = "__codelineno-1-36" href = "#__codelineno-1-36" > < / a > < span class = "w" > < / span > < span class = "c1" > // 获取数组的最大元素，用于判断最大位数< / span >
< a id = "__codelineno-1-37" name = "__codelineno-1-37" href = "#__codelineno-1-37" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > m< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > max_element< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > .< / span > < span class = "n" > begin< / span > < span class = "p" > (),< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > .< / span > < span class = "n" > end< / span > < span class = "p" > ());< / span >
< a id = "__codelineno-1-38" name = "__codelineno-1-38" href = "#__codelineno-1-38" > < / a > < span class = "w" > < / span > < span class = "c1" > // 按照从低位到高位的顺序遍历< / span >
< a id = "__codelineno-1-39" name = "__codelineno-1-39" href = "#__codelineno-1-39" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > exp< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > exp< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > m< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > exp< / span > < span class = "w" > < / span > < span class = "o" > *=< / span > < span class = "w" > < / span > < span class = "mi" > 10< / span > < span class = "p" > )< / span >
< a id = "__codelineno-1-40" name = "__codelineno-1-40" href = "#__codelineno-1-40" > < / a > < span class = "w" > < / span > < span class = "c1" > // 对数组元素的第 k 位执行计数排序< / span >
< a id = "__codelineno-1-41" name = "__codelineno-1-41" href = "#__codelineno-1-41" > < / a > < span class = "w" > < / span > < span class = "c1" > // k = 1 -> exp = 1< / span >
< a id = "__codelineno-1-42" name = "__codelineno-1-42" href = "#__codelineno-1-42" > < / a > < span class = "w" > < / span > < span class = "c1" > // k = 2 -> exp = 10< / span >
< a id = "__codelineno-1-43" name = "__codelineno-1-43" href = "#__codelineno-1-43" > < / a > < span class = "w" > < / span > < span class = "c1" > // 即 exp = 10^(k-1)< / span >
< a id = "__codelineno-1-44" name = "__codelineno-1-44" href = "#__codelineno-1-44" > < / a > < span class = "w" > < / span > < span class = "n" > countingSortDigit< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > exp< / span > < span class = "p" > );< / span >
< a id = "__codelineno-1-45" name = "__codelineno-1-45" href = "#__codelineno-1-45" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > radix_sort.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-2-1" name = "__codelineno-2-1" href = "#__codelineno-2-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > digit< / span > < span class = "p" > (< / span > < span class = "n" > num< / span > < span class = "p" > :< / span > < span class = "nb" > int< / span > < span class = "p" > ,< / span > < span class = "n" > exp< / span > < span class = "p" > :< / span > < span class = "nb" > int< / span > < span class = "p" > )< / span > < span class = "o" > -> < / span > < span class = "nb" > int< / span > < span class = "p" > :< / span >
< a id = "__codelineno-2-2" name = "__codelineno-2-2" href = "#__codelineno-2-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 获取元素 num 的第 k 位，其中 exp = 10^(k-1)" " " < / span >
< a id = "__codelineno-2-3" name = "__codelineno-2-3" href = "#__codelineno-2-3" > < / a > < span class = "c1" > # 传入 exp 而非 k 可以避免在此重复执行昂贵的次方计算< / span >
< a id = "__codelineno-2-4" name = "__codelineno-2-4" href = "#__codelineno-2-4" > < / a > < span class = "k" > return< / span > < span class = "p" > (< / span > < span class = "n" > num< / span > < span class = "o" > //< / span > < span class = "n" > exp< / span > < span class = "p" > )< / span > < span class = "o" > %< / span > < span class = "mi" > 10< / span >
< a id = "__codelineno-2-5" name = "__codelineno-2-5" href = "#__codelineno-2-5" > < / a >
< a id = "__codelineno-2-6" name = "__codelineno-2-6" href = "#__codelineno-2-6" > < / a > < span class = "k" > def< / span > < span class = "nf" > counting_sort_digit< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > int< / span > < span class = "p" > ],< / span > < span class = "n" > exp< / span > < span class = "p" > :< / span > < span class = "nb" > int< / span > < span class = "p" > )< / span > < span class = "o" > -> < / span > < span class = "kc" > None< / span > < span class = "p" > :< / span >
< a id = "__codelineno-2-7" name = "__codelineno-2-7" href = "#__codelineno-2-7" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 计数排序（根据 nums 第 k 位排序）" " " < / span >
< a id = "__codelineno-2-8" name = "__codelineno-2-8" href = "#__codelineno-2-8" > < / a > < span class = "c1" > # 十进制的位范围为 0~9 ，因此需要长度为 10 的桶< / span >
< a id = "__codelineno-2-9" name = "__codelineno-2-9" href = "#__codelineno-2-9" > < / a > < span class = "n" > counter< / span > < span class = "o" > =< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ]< / span > < span class = "o" > *< / span > < span class = "mi" > 10< / span >
< a id = "__codelineno-2-10" name = "__codelineno-2-10" href = "#__codelineno-2-10" > < / a > < span class = "n" > n< / span > < span class = "o" > =< / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > )< / span >
< a id = "__codelineno-2-11" name = "__codelineno-2-11" href = "#__codelineno-2-11" > < / a > < span class = "c1" > # 统计 0~9 各数字的出现次数< / span >
< a id = "__codelineno-2-12" name = "__codelineno-2-12" href = "#__codelineno-2-12" > < / a > < span class = "k" > for< / span > < span class = "n" > i< / span > < span class = "ow" > in< / span > < span class = "nb" > range< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-2-13" name = "__codelineno-2-13" href = "#__codelineno-2-13" > < / a > < span class = "n" > d< / span > < span class = "o" > =< / span > < span class = "n" > digit< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ],< / span > < span class = "n" > exp< / span > < span class = "p" > )< / span > < span class = "c1" > # 获取 nums[i] 第 k 位，记为 d< / span >
< a id = "__codelineno-2-14" name = "__codelineno-2-14" href = "#__codelineno-2-14" > < / a > < span class = "n" > counter< / span > < span class = "p" > [< / span > < span class = "n" > d< / span > < span class = "p" > ]< / span > < span class = "o" > +=< / span > < span class = "mi" > 1< / span > < span class = "c1" > # 统计数字 d 的出现次数< / span >
< a id = "__codelineno-2-15" name = "__codelineno-2-15" href = "#__codelineno-2-15" > < / a > < span class = "c1" > # 求前缀和，将“出现个数”转换为“数组索引”< / span >
< a id = "__codelineno-2-16" name = "__codelineno-2-16" href = "#__codelineno-2-16" > < / a > < span class = "k" > for< / span > < span class = "n" > i< / span > < span class = "ow" > in< / span > < span class = "nb" > range< / span > < span class = "p" > (< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "mi" > 10< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-2-17" name = "__codelineno-2-17" href = "#__codelineno-2-17" > < / a > < span class = "n" > counter< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "o" > +=< / span > < span class = "n" > counter< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-2-18" name = "__codelineno-2-18" href = "#__codelineno-2-18" > < / a > < span class = "c1" > # 倒序遍历，根据桶内统计结果，将各元素填入 res< / span >
< a id = "__codelineno-2-19" name = "__codelineno-2-19" href = "#__codelineno-2-19" > < / a > < span class = "n" > res< / span > < span class = "o" > =< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ]< / span > < span class = "o" > *< / span > < span class = "n" > n< / span >
< a id = "__codelineno-2-20" name = "__codelineno-2-20" href = "#__codelineno-2-20" > < / a > < span class = "k" > for< / span > < span class = "n" > i< / span > < span class = "ow" > in< / span > < span class = "nb" > range< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-2-21" name = "__codelineno-2-21" href = "#__codelineno-2-21" > < / a > < span class = "n" > d< / span > < span class = "o" > =< / span > < span class = "n" > digit< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ],< / span > < span class = "n" > exp< / span > < span class = "p" > )< / span >
< a id = "__codelineno-2-22" name = "__codelineno-2-22" href = "#__codelineno-2-22" > < / a > < span class = "n" > j< / span > < span class = "o" > =< / span > < span class = "n" > counter< / span > < span class = "p" > [< / span > < span class = "n" > d< / span > < span class = "p" > ]< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "c1" > # 获取 d 在数组中的索引 j< / span >
< a id = "__codelineno-2-23" name = "__codelineno-2-23" href = "#__codelineno-2-23" > < / a > < span class = "n" > res< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "n" > nums< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "c1" > # 将当前元素填入索引 j< / span >
< a id = "__codelineno-2-24" name = "__codelineno-2-24" href = "#__codelineno-2-24" > < / a > < span class = "n" > counter< / span > < span class = "p" > [< / span > < span class = "n" > d< / span > < span class = "p" > ]< / span > < span class = "o" > -=< / span > < span class = "mi" > 1< / span > < span class = "c1" > # 将 d 的数量减 1< / span >
< a id = "__codelineno-2-25" name = "__codelineno-2-25" href = "#__codelineno-2-25" > < / a > < span class = "c1" > # 使用结果覆盖原数组 nums< / span >
< a id = "__codelineno-2-26" name = "__codelineno-2-26" href = "#__codelineno-2-26" > < / a > < span class = "k" > for< / span > < span class = "n" > i< / span > < span class = "ow" > in< / span > < span class = "nb" > range< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-2-27" name = "__codelineno-2-27" href = "#__codelineno-2-27" > < / a > < span class = "n" > nums< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "n" > res< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-2-28" name = "__codelineno-2-28" href = "#__codelineno-2-28" > < / a >
< a id = "__codelineno-2-29" name = "__codelineno-2-29" href = "#__codelineno-2-29" > < / a > < span class = "k" > def< / span > < span class = "nf" > radix_sort< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > int< / span > < span class = "p" > ])< / span > < span class = "o" > -> < / span > < span class = "kc" > None< / span > < span class = "p" > :< / span >
< a id = "__codelineno-2-30" name = "__codelineno-2-30" href = "#__codelineno-2-30" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 基数排序" " " < / span >
< a id = "__codelineno-2-31" name = "__codelineno-2-31" href = "#__codelineno-2-31" > < / a > < span class = "c1" > # 获取数组的最大元素，用于判断最大位数< / span >
< a id = "__codelineno-2-32" name = "__codelineno-2-32" href = "#__codelineno-2-32" > < / a > < span class = "n" > m< / span > < span class = "o" > =< / span > < span class = "nb" > max< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > )< / span >
< a id = "__codelineno-2-33" name = "__codelineno-2-33" href = "#__codelineno-2-33" > < / a > < span class = "c1" > # 按照从低位到高位的顺序遍历< / span >
< a id = "__codelineno-2-34" name = "__codelineno-2-34" href = "#__codelineno-2-34" > < / a > < span class = "n" > exp< / span > < span class = "o" > =< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-2-35" name = "__codelineno-2-35" href = "#__codelineno-2-35" > < / a > < span class = "k" > while< / span > < span class = "n" > exp< / span > < span class = "o" > < =< / span > < span class = "n" > m< / span > < span class = "p" > :< / span >
< a id = "__codelineno-2-36" name = "__codelineno-2-36" href = "#__codelineno-2-36" > < / a > < span class = "c1" > # 对数组元素的第 k 位执行计数排序< / span >
< a id = "__codelineno-2-37" name = "__codelineno-2-37" href = "#__codelineno-2-37" > < / a > < span class = "c1" > # k = 1 -> exp = 1< / span >
< a id = "__codelineno-2-38" name = "__codelineno-2-38" href = "#__codelineno-2-38" > < / a > < span class = "c1" > # k = 2 -> exp = 10< / span >
< a id = "__codelineno-2-39" name = "__codelineno-2-39" href = "#__codelineno-2-39" > < / a > < span class = "c1" > # 即 exp = 10^(k-1)< / span >
< a id = "__codelineno-2-40" name = "__codelineno-2-40" href = "#__codelineno-2-40" > < / a > < span class = "n" > counting_sort_digit< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "n" > exp< / span > < span class = "p" > )< / span >
< a id = "__codelineno-2-41" name = "__codelineno-2-41" href = "#__codelineno-2-41" > < / a > < span class = "n" > exp< / span > < span class = "o" > *=< / span > < span class = "mi" > 10< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > radix_sort.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-3-1" name = "__codelineno-3-1" href = "#__codelineno-3-1" > < / a > < span class = "cm" > /* 获取元素 num 的第 k 位，其中 exp = 10^(k-1) */< / span >
< a id = "__codelineno-3-2" name = "__codelineno-3-2" href = "#__codelineno-3-2" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > digit< / span > < span class = "p" > (< / span > < span class = "nx" > num< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > exp< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-3" name = "__codelineno-3-3" href = "#__codelineno-3-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 传入 exp 而非 k 可以避免在此重复执行昂贵的次方计算< / span >
< a id = "__codelineno-3-4" name = "__codelineno-3-4" href = "#__codelineno-3-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > num< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "nx" > exp< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > %< / span > < span class = "w" > < / span > < span class = "mi" > 10< / span >
< a id = "__codelineno-3-5" name = "__codelineno-3-5" href = "#__codelineno-3-5" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-3-6" name = "__codelineno-3-6" href = "#__codelineno-3-6" > < / a >
< a id = "__codelineno-3-7" name = "__codelineno-3-7" href = "#__codelineno-3-7" > < / a > < span class = "cm" > /* 计数排序（根据 nums 第 k 位排序） */< / span >
< a id = "__codelineno-3-8" name = "__codelineno-3-8" href = "#__codelineno-3-8" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > countingSortDigit< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "w" > < / span > < span class = "p" > []< / span > < span class = "kt" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > exp< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-9" name = "__codelineno-3-9" href = "#__codelineno-3-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 十进制的位范围为 0~9 ，因此需要长度为 10 的桶< / span >
< a id = "__codelineno-3-10" name = "__codelineno-3-10" href = "#__codelineno-3-10" > < / a > < span class = "w" > < / span > < span class = "nx" > counter< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nb" > make< / span > < span class = "p" > ([]< / span > < span class = "kt" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 10< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-11" name = "__codelineno-3-11" href = "#__codelineno-3-11" > < / a > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-12" name = "__codelineno-3-12" href = "#__codelineno-3-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 统计 0~9 各数字的出现次数< / span >
< a id = "__codelineno-3-13" name = "__codelineno-3-13" href = "#__codelineno-3-13" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "p" > < < / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-14" name = "__codelineno-3-14" href = "#__codelineno-3-14" > < / a > < span class = "w" > < / span > < span class = "nx" > d< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > digit< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "nx" > exp< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "c1" > // 获取 nums[i] 第 k 位，记为 d< / span >
< a id = "__codelineno-3-15" name = "__codelineno-3-15" href = "#__codelineno-3-15" > < / a > < span class = "w" > < / span > < span class = "nx" > counter< / span > < span class = "p" > [< / span > < span class = "nx" > d< / span > < span class = "p" > ]< / span > < span class = "o" > ++< / span > < span class = "w" > < / span > < span class = "c1" > // 统计数字 d 的出现次数< / span >
< a id = "__codelineno-3-16" name = "__codelineno-3-16" href = "#__codelineno-3-16" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-17" name = "__codelineno-3-17" href = "#__codelineno-3-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 求前缀和，将“出现个数”转换为“数组索引”< / span >
< a id = "__codelineno-3-18" name = "__codelineno-3-18" href = "#__codelineno-3-18" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "p" > < < / span > < span class = "w" > < / span > < span class = "mi" > 10< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-19" name = "__codelineno-3-19" href = "#__codelineno-3-19" > < / a > < span class = "w" > < / span > < span class = "nx" > counter< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "nx" > counter< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-3-20" name = "__codelineno-3-20" href = "#__codelineno-3-20" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-21" name = "__codelineno-3-21" href = "#__codelineno-3-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 倒序遍历，根据桶内统计结果，将各元素填入 res< / span >
< a id = "__codelineno-3-22" name = "__codelineno-3-22" href = "#__codelineno-3-22" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nb" > make< / span > < span class = "p" > ([]< / span > < span class = "kt" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-23" name = "__codelineno-3-23" href = "#__codelineno-3-23" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > --< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-24" name = "__codelineno-3-24" href = "#__codelineno-3-24" > < / a > < span class = "w" > < / span > < span class = "nx" > d< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > digit< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "nx" > exp< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-25" name = "__codelineno-3-25" href = "#__codelineno-3-25" > < / a > < span class = "w" > < / span > < span class = "nx" > j< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > counter< / span > < span class = "p" > [< / span > < span class = "nx" > d< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "w" > < / span > < span class = "c1" > // 获取 d 在数组中的索引 j< / span >
< a id = "__codelineno-3-26" name = "__codelineno-3-26" href = "#__codelineno-3-26" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > [< / span > < span class = "nx" > j< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "c1" > // 将当前元素填入索引 j< / span >
< a id = "__codelineno-3-27" name = "__codelineno-3-27" href = "#__codelineno-3-27" > < / a > < span class = "w" > < / span > < span class = "nx" > counter< / span > < span class = "p" > [< / span > < span class = "nx" > d< / span > < span class = "p" > ]< / span > < span class = "o" > --< / span > < span class = "w" > < / span > < span class = "c1" > // 将 d 的数量减 1< / span >
< a id = "__codelineno-3-28" name = "__codelineno-3-28" href = "#__codelineno-3-28" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-29" name = "__codelineno-3-29" href = "#__codelineno-3-29" > < / a > < span class = "w" > < / span > < span class = "c1" > // 使用结果覆盖原数组 nums< / span >
< a id = "__codelineno-3-30" name = "__codelineno-3-30" href = "#__codelineno-3-30" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "p" > < < / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-31" name = "__codelineno-3-31" href = "#__codelineno-3-31" > < / a > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-3-32" name = "__codelineno-3-32" href = "#__codelineno-3-32" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-33" name = "__codelineno-3-33" href = "#__codelineno-3-33" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-3-34" name = "__codelineno-3-34" href = "#__codelineno-3-34" > < / a >
< a id = "__codelineno-3-35" name = "__codelineno-3-35" href = "#__codelineno-3-35" > < / a > < span class = "cm" > /* 基数排序 */< / span >
< a id = "__codelineno-3-36" name = "__codelineno-3-36" href = "#__codelineno-3-36" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > radixSort< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "w" > < / span > < span class = "p" > []< / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-37" name = "__codelineno-3-37" href = "#__codelineno-3-37" > < / a > < span class = "w" > < / span > < span class = "c1" > // 获取数组的最大元素，用于判断最大位数< / span >
< a id = "__codelineno-3-38" name = "__codelineno-3-38" href = "#__codelineno-3-38" > < / a > < span class = "w" > < / span > < span class = "nx" > max< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > math< / span > < span class = "p" > .< / span > < span class = "nx" > MinInt< / span >
< a id = "__codelineno-3-39" name = "__codelineno-3-39" href = "#__codelineno-3-39" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > _< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > num< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "k" > range< / span > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-40" name = "__codelineno-3-40" href = "#__codelineno-3-40" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > num< / span > < span class = "w" > < / span > < span class = "p" > > < / span > < span class = "w" > < / span > < span class = "nx" > max< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-41" name = "__codelineno-3-41" href = "#__codelineno-3-41" > < / a > < span class = "w" > < / span > < span class = "nx" > max< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > num< / span >
< a id = "__codelineno-3-42" name = "__codelineno-3-42" href = "#__codelineno-3-42" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-43" name = "__codelineno-3-43" href = "#__codelineno-3-43" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-44" name = "__codelineno-3-44" href = "#__codelineno-3-44" > < / a > < span class = "w" > < / span > < span class = "c1" > // 按照从低位到高位的顺序遍历< / span >
< a id = "__codelineno-3-45" name = "__codelineno-3-45" href = "#__codelineno-3-45" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > exp< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > max< / span > < span class = "w" > < / span > < span class = "o" > > =< / span > < span class = "w" > < / span > < span class = "nx" > exp< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > exp< / span > < span class = "w" > < / span > < span class = "o" > *=< / span > < span class = "w" > < / span > < span class = "mi" > 10< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-46" name = "__codelineno-3-46" href = "#__codelineno-3-46" > < / a > < span class = "w" > < / span > < span class = "c1" > // 对数组元素的第 k 位执行计数排序< / span >
< a id = "__codelineno-3-47" name = "__codelineno-3-47" href = "#__codelineno-3-47" > < / a > < span class = "w" > < / span > < span class = "c1" > // k = 1 -> exp = 1< / span >
< a id = "__codelineno-3-48" name = "__codelineno-3-48" href = "#__codelineno-3-48" > < / a > < span class = "w" > < / span > < span class = "c1" > // k = 2 -> exp = 10< / span >
< a id = "__codelineno-3-49" name = "__codelineno-3-49" href = "#__codelineno-3-49" > < / a > < span class = "w" > < / span > < span class = "c1" > // 即 exp = 10^(k-1)< / span >
< a id = "__codelineno-3-50" name = "__codelineno-3-50" href = "#__codelineno-3-50" > < / a > < span class = "w" > < / span > < span class = "nx" > countingSortDigit< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > exp< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-51" name = "__codelineno-3-51" href = "#__codelineno-3-51" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-52" name = "__codelineno-3-52" href = "#__codelineno-3-52" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > radix_sort.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-4-1" name = "__codelineno-4-1" href = "#__codelineno-4-1" > < / a > < span class = "cm" > /* 获取元素 num 的第 k 位，其中 exp = 10^(k-1) */< / span >
< a id = "__codelineno-4-2" name = "__codelineno-4-2" href = "#__codelineno-4-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > digit< / span > < span class = "p" > (< / span > < span class = "nx" > num< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > exp< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-3" name = "__codelineno-4-3" href = "#__codelineno-4-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 传入 exp 而非 k 可以避免在此重复执行昂贵的次方计算< / span >
< a id = "__codelineno-4-4" name = "__codelineno-4-4" href = "#__codelineno-4-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nb" > Math< / span > < span class = "p" > .< / span > < span class = "nx" > floor< / span > < span class = "p" > (< / span > < span class = "nx" > num< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "nx" > exp< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > %< / span > < span class = "w" > < / span > < span class = "mf" > 10< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-4-5" name = "__codelineno-4-5" href = "#__codelineno-4-5" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-4-6" name = "__codelineno-4-6" href = "#__codelineno-4-6" > < / a >
< a id = "__codelineno-4-7" name = "__codelineno-4-7" href = "#__codelineno-4-7" > < / a > < span class = "cm" > /* 计数排序（根据 nums 第 k 位排序） */< / span >
< a id = "__codelineno-4-8" name = "__codelineno-4-8" href = "#__codelineno-4-8" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > countingSortDigit< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > exp< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-9" name = "__codelineno-4-9" href = "#__codelineno-4-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 十进制的位范围为 0~9 ，因此需要长度为 10 的桶< / span >
< a id = "__codelineno-4-10" name = "__codelineno-4-10" href = "#__codelineno-4-10" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > counter< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "ow" > new< / span > < span class = "w" > < / span > < span class = "nb" > Array< / span > < span class = "p" > (< / span > < span class = "mf" > 10< / span > < span class = "p" > ).< / span > < span class = "nx" > fill< / span > < span class = "p" > (< / span > < span class = "mf" > 0< / span > < span class = "p" > );< / span >
< a id = "__codelineno-4-11" name = "__codelineno-4-11" href = "#__codelineno-4-11" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "p" > .< / span > < span class = "nx" > length< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-4-12" name = "__codelineno-4-12" href = "#__codelineno-4-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 统计 0~9 各数字的出现次数< / span >
< a id = "__codelineno-4-13" name = "__codelineno-4-13" href = "#__codelineno-4-13" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-14" name = "__codelineno-4-14" href = "#__codelineno-4-14" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > d< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > digit< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "nx" > exp< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 获取 nums[i] 第 k 位，记为 d< / span >
< a id = "__codelineno-4-15" name = "__codelineno-4-15" href = "#__codelineno-4-15" > < / a > < span class = "w" > < / span > < span class = "nx" > counter< / span > < span class = "p" > [< / span > < span class = "nx" > d< / span > < span class = "p" > ]< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 统计数字 d 的出现次数< / span >
< a id = "__codelineno-4-16" name = "__codelineno-4-16" href = "#__codelineno-4-16" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-17" name = "__codelineno-4-17" href = "#__codelineno-4-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 求前缀和，将“出现个数”转换为“数组索引”< / span >
< a id = "__codelineno-4-18" name = "__codelineno-4-18" href = "#__codelineno-4-18" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "mf" > 10< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-19" name = "__codelineno-4-19" href = "#__codelineno-4-19" > < / a > < span class = "w" > < / span > < span class = "nx" > counter< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "nx" > counter< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-4-20" name = "__codelineno-4-20" href = "#__codelineno-4-20" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-21" name = "__codelineno-4-21" href = "#__codelineno-4-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 倒序遍历，根据桶内统计结果，将各元素填入 res< / span >
< a id = "__codelineno-4-22" name = "__codelineno-4-22" href = "#__codelineno-4-22" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "ow" > new< / span > < span class = "w" > < / span > < span class = "nb" > Array< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "p" > ).< / span > < span class = "nx" > fill< / span > < span class = "p" > (< / span > < span class = "mf" > 0< / span > < span class = "p" > );< / span >
< a id = "__codelineno-4-23" name = "__codelineno-4-23" href = "#__codelineno-4-23" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > > =< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > --< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-24" name = "__codelineno-4-24" href = "#__codelineno-4-24" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > d< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > digit< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "nx" > exp< / span > < span class = "p" > );< / span >
< a id = "__codelineno-4-25" name = "__codelineno-4-25" href = "#__codelineno-4-25" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > j< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > counter< / span > < span class = "p" > [< / span > < span class = "nx" > d< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 获取 d 在数组中的索引 j< / span >
< a id = "__codelineno-4-26" name = "__codelineno-4-26" href = "#__codelineno-4-26" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > [< / span > < span class = "nx" > j< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ];< / span > < span class = "w" > < / span > < span class = "c1" > // 将当前元素填入索引 j< / span >
< a id = "__codelineno-4-27" name = "__codelineno-4-27" href = "#__codelineno-4-27" > < / a > < span class = "w" > < / span > < span class = "nx" > counter< / span > < span class = "p" > [< / span > < span class = "nx" > d< / span > < span class = "p" > ]< / span > < span class = "o" > --< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 将 d 的数量减 1< / span >
< a id = "__codelineno-4-28" name = "__codelineno-4-28" href = "#__codelineno-4-28" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-29" name = "__codelineno-4-29" href = "#__codelineno-4-29" > < / a > < span class = "w" > < / span > < span class = "c1" > // 使用结果覆盖原数组 nums< / span >
< a id = "__codelineno-4-30" name = "__codelineno-4-30" href = "#__codelineno-4-30" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-31" name = "__codelineno-4-31" href = "#__codelineno-4-31" > < / a > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-4-32" name = "__codelineno-4-32" href = "#__codelineno-4-32" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-33" name = "__codelineno-4-33" href = "#__codelineno-4-33" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-4-34" name = "__codelineno-4-34" href = "#__codelineno-4-34" > < / a >
< a id = "__codelineno-4-35" name = "__codelineno-4-35" href = "#__codelineno-4-35" > < / a > < span class = "cm" > /* 基数排序 */< / span >
< a id = "__codelineno-4-36" name = "__codelineno-4-36" href = "#__codelineno-4-36" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > radixSort< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-37" name = "__codelineno-4-37" href = "#__codelineno-4-37" > < / a > < span class = "w" > < / span > < span class = "c1" > // 获取数组的最大元素，用于判断最大位数< / span >
< a id = "__codelineno-4-38" name = "__codelineno-4-38" href = "#__codelineno-4-38" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > m< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > Number< / span > < span class = "p" > .< / span > < span class = "nx" > MIN_VALUE< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-4-39" name = "__codelineno-4-39" href = "#__codelineno-4-39" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > num< / span > < span class = "w" > < / span > < span class = "k" > of< / span > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-40" name = "__codelineno-4-40" href = "#__codelineno-4-40" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > num< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "nx" > m< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-41" name = "__codelineno-4-41" href = "#__codelineno-4-41" > < / a > < span class = "w" > < / span > < span class = "nx" > m< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > num< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-4-42" name = "__codelineno-4-42" href = "#__codelineno-4-42" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-43" name = "__codelineno-4-43" href = "#__codelineno-4-43" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-44" name = "__codelineno-4-44" href = "#__codelineno-4-44" > < / a > < span class = "w" > < / span > < span class = "c1" > // 按照从低位到高位的顺序遍历< / span >
< a id = "__codelineno-4-45" name = "__codelineno-4-45" href = "#__codelineno-4-45" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > exp< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > exp< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "nx" > m< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > exp< / span > < span class = "w" > < / span > < span class = "o" > *=< / span > < span class = "w" > < / span > < span class = "mf" > 10< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-46" name = "__codelineno-4-46" href = "#__codelineno-4-46" > < / a > < span class = "w" > < / span > < span class = "c1" > // 对数组元素的第 k 位执行计数排序< / span >
< a id = "__codelineno-4-47" name = "__codelineno-4-47" href = "#__codelineno-4-47" > < / a > < span class = "w" > < / span > < span class = "c1" > // k = 1 -> exp = 1< / span >
< a id = "__codelineno-4-48" name = "__codelineno-4-48" href = "#__codelineno-4-48" > < / a > < span class = "w" > < / span > < span class = "c1" > // k = 2 -> exp = 10< / span >
< a id = "__codelineno-4-49" name = "__codelineno-4-49" href = "#__codelineno-4-49" > < / a > < span class = "w" > < / span > < span class = "c1" > // 即 exp = 10^(k-1)< / span >
< a id = "__codelineno-4-50" name = "__codelineno-4-50" href = "#__codelineno-4-50" > < / a > < span class = "w" > < / span > < span class = "nx" > countingSortDigit< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > exp< / span > < span class = "p" > );< / span >
< a id = "__codelineno-4-51" name = "__codelineno-4-51" href = "#__codelineno-4-51" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-52" name = "__codelineno-4-52" href = "#__codelineno-4-52" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > radix_sort.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-5-1" name = "__codelineno-5-1" href = "#__codelineno-5-1" > < / a > < span class = "cm" > /* 获取元素 num 的第 k 位，其中 exp = 10^(k-1) */< / span >
< a id = "__codelineno-5-2" name = "__codelineno-5-2" href = "#__codelineno-5-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > digit< / span > < span class = "p" > (< / span > < span class = "nx" > num< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > exp< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > )< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-3" name = "__codelineno-5-3" href = "#__codelineno-5-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 传入 exp 而非 k 可以避免在此重复执行昂贵的次方计算< / span >
< a id = "__codelineno-5-4" name = "__codelineno-5-4" href = "#__codelineno-5-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nb" > Math< / span > < span class = "p" > .< / span > < span class = "nx" > floor< / span > < span class = "p" > (< / span > < span class = "nx" > num< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "nx" > exp< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > %< / span > < span class = "w" > < / span > < span class = "mf" > 10< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-5-5" name = "__codelineno-5-5" href = "#__codelineno-5-5" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-5-6" name = "__codelineno-5-6" href = "#__codelineno-5-6" > < / a >
< a id = "__codelineno-5-7" name = "__codelineno-5-7" href = "#__codelineno-5-7" > < / a > < span class = "cm" > /* 计数排序（根据 nums 第 k 位排序） */< / span >
< a id = "__codelineno-5-8" name = "__codelineno-5-8" href = "#__codelineno-5-8" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > countingSortDigit< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > [],< / span > < span class = "w" > < / span > < span class = "nx" > exp< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > )< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "ow" > void< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-9" name = "__codelineno-5-9" href = "#__codelineno-5-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 十进制的位范围为 0~9 ，因此需要长度为 10 的桶< / span >
< a id = "__codelineno-5-10" name = "__codelineno-5-10" href = "#__codelineno-5-10" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > counter< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "ow" > new< / span > < span class = "w" > < / span > < span class = "nb" > Array< / span > < span class = "p" > (< / span > < span class = "mf" > 10< / span > < span class = "p" > ).< / span > < span class = "nx" > fill< / span > < span class = "p" > (< / span > < span class = "mf" > 0< / span > < span class = "p" > );< / span >
< a id = "__codelineno-5-11" name = "__codelineno-5-11" href = "#__codelineno-5-11" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "p" > .< / span > < span class = "nx" > length< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-5-12" name = "__codelineno-5-12" href = "#__codelineno-5-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 统计 0~9 各数字的出现次数< / span >
< a id = "__codelineno-5-13" name = "__codelineno-5-13" href = "#__codelineno-5-13" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-14" name = "__codelineno-5-14" href = "#__codelineno-5-14" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > d< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > digit< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "nx" > exp< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 获取 nums[i] 第 k 位，记为 d< / span >
< a id = "__codelineno-5-15" name = "__codelineno-5-15" href = "#__codelineno-5-15" > < / a > < span class = "w" > < / span > < span class = "nx" > counter< / span > < span class = "p" > [< / span > < span class = "nx" > d< / span > < span class = "p" > ]< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 统计数字 d 的出现次数< / span >
< a id = "__codelineno-5-16" name = "__codelineno-5-16" href = "#__codelineno-5-16" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-5-17" name = "__codelineno-5-17" href = "#__codelineno-5-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 求前缀和，将“出现个数”转换为“数组索引”< / span >
< a id = "__codelineno-5-18" name = "__codelineno-5-18" href = "#__codelineno-5-18" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "mf" > 10< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-19" name = "__codelineno-5-19" href = "#__codelineno-5-19" > < / a > < span class = "w" > < / span > < span class = "nx" > counter< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "nx" > counter< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-5-20" name = "__codelineno-5-20" href = "#__codelineno-5-20" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-5-21" name = "__codelineno-5-21" href = "#__codelineno-5-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 倒序遍历，根据桶内统计结果，将各元素填入 res< / span >
< a id = "__codelineno-5-22" name = "__codelineno-5-22" href = "#__codelineno-5-22" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "ow" > new< / span > < span class = "w" > < / span > < span class = "nb" > Array< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "p" > ).< / span > < span class = "nx" > fill< / span > < span class = "p" > (< / span > < span class = "mf" > 0< / span > < span class = "p" > );< / span >
< a id = "__codelineno-5-23" name = "__codelineno-5-23" href = "#__codelineno-5-23" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > > =< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > --< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-24" name = "__codelineno-5-24" href = "#__codelineno-5-24" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > d< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > digit< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "nx" > exp< / span > < span class = "p" > );< / span >
< a id = "__codelineno-5-25" name = "__codelineno-5-25" href = "#__codelineno-5-25" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > j< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > counter< / span > < span class = "p" > [< / span > < span class = "nx" > d< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 获取 d 在数组中的索引 j< / span >
< a id = "__codelineno-5-26" name = "__codelineno-5-26" href = "#__codelineno-5-26" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > [< / span > < span class = "nx" > j< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ];< / span > < span class = "w" > < / span > < span class = "c1" > // 将当前元素填入索引 j< / span >
< a id = "__codelineno-5-27" name = "__codelineno-5-27" href = "#__codelineno-5-27" > < / a > < span class = "w" > < / span > < span class = "nx" > counter< / span > < span class = "p" > [< / span > < span class = "nx" > d< / span > < span class = "p" > ]< / span > < span class = "o" > --< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 将 d 的数量减 1< / span >
< a id = "__codelineno-5-28" name = "__codelineno-5-28" href = "#__codelineno-5-28" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-5-29" name = "__codelineno-5-29" href = "#__codelineno-5-29" > < / a > < span class = "w" > < / span > < span class = "c1" > // 使用结果覆盖原数组 nums< / span >
< a id = "__codelineno-5-30" name = "__codelineno-5-30" href = "#__codelineno-5-30" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-31" name = "__codelineno-5-31" href = "#__codelineno-5-31" > < / a > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-5-32" name = "__codelineno-5-32" href = "#__codelineno-5-32" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-5-33" name = "__codelineno-5-33" href = "#__codelineno-5-33" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-5-34" name = "__codelineno-5-34" href = "#__codelineno-5-34" > < / a >
< a id = "__codelineno-5-35" name = "__codelineno-5-35" href = "#__codelineno-5-35" > < / a > < span class = "cm" > /* 基数排序 */< / span >
< a id = "__codelineno-5-36" name = "__codelineno-5-36" href = "#__codelineno-5-36" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > radixSort< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > [])< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "ow" > void< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-37" name = "__codelineno-5-37" href = "#__codelineno-5-37" > < / a > < span class = "w" > < / span > < span class = "c1" > // 获取数组的最大元素，用于判断最大位数< / span >
< a id = "__codelineno-5-38" name = "__codelineno-5-38" href = "#__codelineno-5-38" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > m< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > Number< / span > < span class = "p" > .< / span > < span class = "nx" > MIN_VALUE< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-5-39" name = "__codelineno-5-39" href = "#__codelineno-5-39" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > num< / span > < span class = "w" > < / span > < span class = "k" > of< / span > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-40" name = "__codelineno-5-40" href = "#__codelineno-5-40" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > num< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "nx" > m< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-41" name = "__codelineno-5-41" href = "#__codelineno-5-41" > < / a > < span class = "w" > < / span > < span class = "nx" > m< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > num< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-5-42" name = "__codelineno-5-42" href = "#__codelineno-5-42" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-5-43" name = "__codelineno-5-43" href = "#__codelineno-5-43" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-5-44" name = "__codelineno-5-44" href = "#__codelineno-5-44" > < / a > < span class = "w" > < / span > < span class = "c1" > // 按照从低位到高位的顺序遍历< / span >
< a id = "__codelineno-5-45" name = "__codelineno-5-45" href = "#__codelineno-5-45" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > exp< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > exp< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "nx" > m< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > exp< / span > < span class = "w" > < / span > < span class = "o" > *=< / span > < span class = "w" > < / span > < span class = "mf" > 10< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-46" name = "__codelineno-5-46" href = "#__codelineno-5-46" > < / a > < span class = "w" > < / span > < span class = "c1" > // 对数组元素的第 k 位执行计数排序< / span >
< a id = "__codelineno-5-47" name = "__codelineno-5-47" href = "#__codelineno-5-47" > < / a > < span class = "w" > < / span > < span class = "c1" > // k = 1 -> exp = 1< / span >
< a id = "__codelineno-5-48" name = "__codelineno-5-48" href = "#__codelineno-5-48" > < / a > < span class = "w" > < / span > < span class = "c1" > // k = 2 -> exp = 10< / span >
< a id = "__codelineno-5-49" name = "__codelineno-5-49" href = "#__codelineno-5-49" > < / a > < span class = "w" > < / span > < span class = "c1" > // 即 exp = 10^(k-1)< / span >
< a id = "__codelineno-5-50" name = "__codelineno-5-50" href = "#__codelineno-5-50" > < / a > < span class = "w" > < / span > < span class = "nx" > countingSortDigit< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > exp< / span > < span class = "p" > );< / span >
< a id = "__codelineno-5-51" name = "__codelineno-5-51" href = "#__codelineno-5-51" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-5-52" name = "__codelineno-5-52" href = "#__codelineno-5-52" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > radix_sort.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-6-1" name = "__codelineno-6-1" href = "#__codelineno-6-1" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > digit< / span > < span class = "p" > }< / span >
< a id = "__codelineno-6-2" name = "__codelineno-6-2" href = "#__codelineno-6-2" > < / a >
< a id = "__codelineno-6-3" name = "__codelineno-6-3" href = "#__codelineno-6-3" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > countingSortDigit< / span > < span class = "p" > }< / span >
< a id = "__codelineno-6-4" name = "__codelineno-6-4" href = "#__codelineno-6-4" > < / a >
< a id = "__codelineno-6-5" name = "__codelineno-6-5" href = "#__codelineno-6-5" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > radixSort< / span > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > radix_sort.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-7-1" name = "__codelineno-7-1" href = "#__codelineno-7-1" > < / a > < span class = "na" > [class]< / span > < span class = "p" > {< / span > < span class = "n" > radix_sort< / span > < span class = "p" > }< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > digit< / span > < span class = "p" > }< / span >
< a id = "__codelineno-7-2" name = "__codelineno-7-2" href = "#__codelineno-7-2" > < / a >
< a id = "__codelineno-7-3" name = "__codelineno-7-3" href = "#__codelineno-7-3" > < / a > < span class = "na" > [class]< / span > < span class = "p" > {< / span > < span class = "n" > radix_sort< / span > < span class = "p" > }< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > countingSortDigit< / span > < span class = "p" > }< / span >
< a id = "__codelineno-7-4" name = "__codelineno-7-4" href = "#__codelineno-7-4" > < / a >
< a id = "__codelineno-7-5" name = "__codelineno-7-5" href = "#__codelineno-7-5" > < / a > < span class = "na" > [class]< / span > < span class = "p" > {< / span > < span class = "n" > radix_sort< / span > < span class = "p" > }< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > radixSort< / span > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > radix_sort.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-8-1" name = "__codelineno-8-1" href = "#__codelineno-8-1" > < / a > < span class = "cm" > /* 获取元素 num 的第 k 位，其中 exp = 10^(k-1) */< / span >
< a id = "__codelineno-8-2" name = "__codelineno-8-2" href = "#__codelineno-8-2" > < / a > < span class = "kd" > func< / span > < span class = "nf" > digit< / span > < span class = "p" > (< / span > < span class = "n" > num< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / span > < span class = "p" > ,< / span > < span class = "n" > exp< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / span > < span class = "p" > )< / span > < span class = "p" > -> < / span > < span class = "nb" > Int< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-3" name = "__codelineno-8-3" href = "#__codelineno-8-3" > < / a > < span class = "c1" > // 传入 exp 而非 k 可以避免在此重复执行昂贵的次方计算< / span >
< a id = "__codelineno-8-4" name = "__codelineno-8-4" href = "#__codelineno-8-4" > < / a > < span class = "p" > (< / span > < span class = "n" > num< / span > < span class = "o" > /< / span > < span class = "n" > exp< / span > < span class = "p" > )< / span > < span class = "o" > %< / span > < span class = "mi" > 10< / span >
< a id = "__codelineno-8-5" name = "__codelineno-8-5" href = "#__codelineno-8-5" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-6" name = "__codelineno-8-6" href = "#__codelineno-8-6" > < / a >
< a id = "__codelineno-8-7" name = "__codelineno-8-7" href = "#__codelineno-8-7" > < / a > < span class = "cm" > /* 计数排序（根据 nums 第 k 位排序） */< / span >
< a id = "__codelineno-8-8" name = "__codelineno-8-8" href = "#__codelineno-8-8" > < / a > < span class = "kd" > func< / span > < span class = "nf" > countingSortDigit< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > :< / span > < span class = "kr" > inout< / span > < span class = "p" > [< / span > < span class = "nb" > Int< / span > < span class = "p" > ],< / span > < span class = "n" > exp< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / span > < span class = "p" > )< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-9" name = "__codelineno-8-9" href = "#__codelineno-8-9" > < / a > < span class = "c1" > // 十进制的位范围为 0~9 ，因此需要长度为 10 的桶< / span >
< a id = "__codelineno-8-10" name = "__codelineno-8-10" href = "#__codelineno-8-10" > < / a > < span class = "kd" > var< / span > < span class = "nv" > counter< / span > < span class = "p" > =< / span > < span class = "nb" > Array< / span > < span class = "p" > (< / span > < span class = "n" > repeating< / span > < span class = "p" > :< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "bp" > count< / span > < span class = "p" > :< / span > < span class = "mi" > 10< / span > < span class = "p" > )< / span >
< a id = "__codelineno-8-11" name = "__codelineno-8-11" href = "#__codelineno-8-11" > < / a > < span class = "kd" > let< / span > < span class = "nv" > n< / span > < span class = "p" > =< / span > < span class = "n" > nums< / span > < span class = "p" > .< / span > < span class = "bp" > count< / span >
< a id = "__codelineno-8-12" name = "__codelineno-8-12" href = "#__codelineno-8-12" > < / a > < span class = "c1" > // 统计 0~9 各数字的出现次数< / span >
< a id = "__codelineno-8-13" name = "__codelineno-8-13" href = "#__codelineno-8-13" > < / a > < span class = "k" > for< / span > < span class = "n" > i< / span > < span class = "k" > in< / span > < span class = "n" > nums< / span > < span class = "p" > .< / span > < span class = "bp" > indices< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-14" name = "__codelineno-8-14" href = "#__codelineno-8-14" > < / a > < span class = "kd" > let< / span > < span class = "nv" > d< / span > < span class = "p" > =< / span > < span class = "n" > digit< / span > < span class = "p" > (< / span > < span class = "n" > num< / span > < span class = "p" > :< / span > < span class = "n" > nums< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ],< / span > < span class = "n" > exp< / span > < span class = "p" > :< / span > < span class = "n" > exp< / span > < span class = "p" > )< / span > < span class = "c1" > // 获取 nums[i] 第 k 位，记为 d< / span >
< a id = "__codelineno-8-15" name = "__codelineno-8-15" href = "#__codelineno-8-15" > < / a > < span class = "n" > counter< / span > < span class = "p" > [< / span > < span class = "n" > d< / span > < span class = "p" > ]< / span > < span class = "o" > +=< / span > < span class = "mi" > 1< / span > < span class = "c1" > // 统计数字 d 的出现次数< / span >
< a id = "__codelineno-8-16" name = "__codelineno-8-16" href = "#__codelineno-8-16" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-17" name = "__codelineno-8-17" href = "#__codelineno-8-17" > < / a > < span class = "c1" > // 求前缀和，将“出现个数”转换为“数组索引”< / span >
< a id = "__codelineno-8-18" name = "__codelineno-8-18" href = "#__codelineno-8-18" > < / a > < span class = "k" > for< / span > < span class = "n" > i< / span > < span class = "k" > in< / span > < span class = "mi" > 1< / span > < span class = "p" > ..< / span > < span class = "o" > < < / span > < span class = "mi" > 10< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-19" name = "__codelineno-8-19" href = "#__codelineno-8-19" > < / a > < span class = "n" > counter< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "o" > +=< / span > < span class = "n" > counter< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-8-20" name = "__codelineno-8-20" href = "#__codelineno-8-20" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-21" name = "__codelineno-8-21" href = "#__codelineno-8-21" > < / a > < span class = "c1" > // 倒序遍历，根据桶内统计结果，将各元素填入 res< / span >
< a id = "__codelineno-8-22" name = "__codelineno-8-22" href = "#__codelineno-8-22" > < / a > < span class = "kd" > var< / span > < span class = "nv" > res< / span > < span class = "p" > =< / span > < span class = "nb" > Array< / span > < span class = "p" > (< / span > < span class = "n" > repeating< / span > < span class = "p" > :< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "bp" > count< / span > < span class = "p" > :< / span > < span class = "n" > n< / span > < span class = "p" > )< / span >
< a id = "__codelineno-8-23" name = "__codelineno-8-23" href = "#__codelineno-8-23" > < / a > < span class = "k" > for< / span > < span class = "n" > i< / span > < span class = "k" > in< / span > < span class = "bp" > stride< / span > < span class = "p" > (< / span > < span class = "n" > from< / span > < span class = "p" > :< / span > < span class = "n" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "n" > through< / span > < span class = "p" > :< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "n" > by< / span > < span class = "p" > :< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-24" name = "__codelineno-8-24" href = "#__codelineno-8-24" > < / a > < span class = "kd" > let< / span > < span class = "nv" > d< / span > < span class = "p" > =< / span > < span class = "n" > digit< / span > < span class = "p" > (< / span > < span class = "n" > num< / span > < span class = "p" > :< / span > < span class = "n" > nums< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ],< / span > < span class = "n" > exp< / span > < span class = "p" > :< / span > < span class = "n" > exp< / span > < span class = "p" > )< / span >
< a id = "__codelineno-8-25" name = "__codelineno-8-25" href = "#__codelineno-8-25" > < / a > < span class = "kd" > let< / span > < span class = "nv" > j< / span > < span class = "p" > =< / span > < span class = "n" > counter< / span > < span class = "p" > [< / span > < span class = "n" > d< / span > < span class = "p" > ]< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "c1" > // 获取 d 在数组中的索引 j< / span >
< a id = "__codelineno-8-26" name = "__codelineno-8-26" href = "#__codelineno-8-26" > < / a > < span class = "n" > res< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "n" > nums< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "c1" > // 将当前元素填入索引 j< / span >
< a id = "__codelineno-8-27" name = "__codelineno-8-27" href = "#__codelineno-8-27" > < / a > < span class = "n" > counter< / span > < span class = "p" > [< / span > < span class = "n" > d< / span > < span class = "p" > ]< / span > < span class = "o" > -=< / span > < span class = "mi" > 1< / span > < span class = "c1" > // 将 d 的数量减 1< / span >
< a id = "__codelineno-8-28" name = "__codelineno-8-28" href = "#__codelineno-8-28" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-29" name = "__codelineno-8-29" href = "#__codelineno-8-29" > < / a > < span class = "c1" > // 使用结果覆盖原数组 nums< / span >
< a id = "__codelineno-8-30" name = "__codelineno-8-30" href = "#__codelineno-8-30" > < / a > < span class = "k" > for< / span > < span class = "n" > i< / span > < span class = "k" > in< / span > < span class = "n" > nums< / span > < span class = "p" > .< / span > < span class = "bp" > indices< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-31" name = "__codelineno-8-31" href = "#__codelineno-8-31" > < / a > < span class = "n" > nums< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "n" > res< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-8-32" name = "__codelineno-8-32" href = "#__codelineno-8-32" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-33" name = "__codelineno-8-33" href = "#__codelineno-8-33" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-34" name = "__codelineno-8-34" href = "#__codelineno-8-34" > < / a >
< a id = "__codelineno-8-35" name = "__codelineno-8-35" href = "#__codelineno-8-35" > < / a > < span class = "cm" > /* 基数排序 */< / span >
< a id = "__codelineno-8-36" name = "__codelineno-8-36" href = "#__codelineno-8-36" > < / a > < span class = "kd" > func< / span > < span class = "nf" > radixSort< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > :< / span > < span class = "kr" > inout< / span > < span class = "p" > [< / span > < span class = "nb" > Int< / span > < span class = "p" > ])< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-37" name = "__codelineno-8-37" href = "#__codelineno-8-37" > < / a > < span class = "c1" > // 获取数组的最大元素，用于判断最大位数< / span >
< a id = "__codelineno-8-38" name = "__codelineno-8-38" href = "#__codelineno-8-38" > < / a > < span class = "kd" > var< / span > < span class = "nv" > m< / span > < span class = "p" > =< / span > < span class = "nb" > Int< / span > < span class = "p" > .< / span > < span class = "bp" > min< / span >
< a id = "__codelineno-8-39" name = "__codelineno-8-39" href = "#__codelineno-8-39" > < / a > < span class = "k" > for< / span > < span class = "n" > num< / span > < span class = "k" > in< / span > < span class = "n" > nums< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-40" name = "__codelineno-8-40" href = "#__codelineno-8-40" > < / a > < span class = "k" > if< / span > < span class = "n" > num< / span > < span class = "o" > > < / span > < span class = "n" > m< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-41" name = "__codelineno-8-41" href = "#__codelineno-8-41" > < / a > < span class = "n" > m< / span > < span class = "p" > =< / span > < span class = "n" > num< / span >
< a id = "__codelineno-8-42" name = "__codelineno-8-42" href = "#__codelineno-8-42" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-43" name = "__codelineno-8-43" href = "#__codelineno-8-43" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-44" name = "__codelineno-8-44" href = "#__codelineno-8-44" > < / a > < span class = "c1" > // 按照从低位到高位的顺序遍历< / span >
< a id = "__codelineno-8-45" name = "__codelineno-8-45" href = "#__codelineno-8-45" > < / a > < span class = "k" > for< / span > < span class = "n" > exp< / span > < span class = "k" > in< / span > < span class = "n" > sequence< / span > < span class = "p" > (< / span > < span class = "bp" > first< / span > < span class = "p" > :< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "n" > next< / span > < span class = "p" > :< / span > < span class = "p" > {< / span > < span class = "n" > m< / span > < span class = "o" > > =< / span > < span class = "p" > (< / span > < span class = "nv" > $0< / span > < span class = "o" > *< / span > < span class = "mi" > 10< / span > < span class = "p" > )< / span > < span class = "p" > ?< / span > < span class = "nv" > $0< / span > < span class = "o" > *< / span > < span class = "mi" > 10< / span > < span class = "p" > :< / span > < span class = "kc" > nil< / span > < span class = "p" > })< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-46" name = "__codelineno-8-46" href = "#__codelineno-8-46" > < / a > < span class = "c1" > // 对数组元素的第 k 位执行计数排序< / span >
< a id = "__codelineno-8-47" name = "__codelineno-8-47" href = "#__codelineno-8-47" > < / a > < span class = "c1" > // k = 1 -> exp = 1< / span >
< a id = "__codelineno-8-48" name = "__codelineno-8-48" href = "#__codelineno-8-48" > < / a > < span class = "c1" > // k = 2 -> exp = 10< / span >
< a id = "__codelineno-8-49" name = "__codelineno-8-49" href = "#__codelineno-8-49" > < / a > < span class = "c1" > // 即 exp = 10^(k-1)< / span >
< a id = "__codelineno-8-50" name = "__codelineno-8-50" href = "#__codelineno-8-50" > < / a > < span class = "n" > countingSortDigit< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "n" > exp< / span > < span class = "p" > :< / span > < span class = "n" > exp< / span > < span class = "p" > )< / span >
< a id = "__codelineno-8-51" name = "__codelineno-8-51" href = "#__codelineno-8-51" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-52" name = "__codelineno-8-52" href = "#__codelineno-8-52" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > radix_sort.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-9-1" name = "__codelineno-9-1" href = "#__codelineno-9-1" > < / a > < span class = "c1" > // 获取元素 num 的第 k 位，其中 exp = 10^(k-1)< / span >
< a id = "__codelineno-9-2" name = "__codelineno-9-2" href = "#__codelineno-9-2" > < / a > < span class = "k" > fn< / span > < span class = "w" > < / span > < span class = "n" > digit< / span > < span class = "p" > (< / span > < span class = "n" > num< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > i32< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > exp< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > i32< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "kt" > i32< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-3" name = "__codelineno-9-3" href = "#__codelineno-9-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 传入 exp 而非 k 可以避免在此重复执行昂贵的次方计算< / span >
< a id = "__codelineno-9-4" name = "__codelineno-9-4" href = "#__codelineno-9-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nb" > @mod< / span > < span class = "p" > (< / span > < span class = "nb" > @divFloor< / span > < span class = "p" > (< / span > < span class = "n" > num< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > exp< / span > < span class = "p" > ),< / span > < span class = "w" > < / span > < span class = "mi" > 10< / span > < span class = "p" > );< / span >
< a id = "__codelineno-9-5" name = "__codelineno-9-5" href = "#__codelineno-9-5" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-9-6" name = "__codelineno-9-6" href = "#__codelineno-9-6" > < / a >
< a id = "__codelineno-9-7" name = "__codelineno-9-7" href = "#__codelineno-9-7" > < / a > < span class = "c1" > // 计数排序（根据 nums 第 k 位排序）< / span >
< a id = "__codelineno-9-8" name = "__codelineno-9-8" href = "#__codelineno-9-8" > < / a > < span class = "k" > fn< / span > < span class = "w" > < / span > < span class = "n" > countingSortDigit< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "p" > []< / span > < span class = "kt" > i32< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > exp< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > i32< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > !< / span > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-9" name = "__codelineno-9-9" href = "#__codelineno-9-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 十进制的位范围为 0~9 ，因此需要长度为 10 的桶< / span >
< a id = "__codelineno-9-10" name = "__codelineno-9-10" href = "#__codelineno-9-10" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > mem_arena< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > std< / span > < span class = "p" > .< / span > < span class = "n" > heap< / span > < span class = "p" > .< / span > < span class = "n" > ArenaAllocator< / span > < span class = "p" > .< / span > < span class = "n" > init< / span > < span class = "p" > (< / span > < span class = "n" > std< / span > < span class = "p" > .< / span > < span class = "n" > heap< / span > < span class = "p" > .< / span > < span class = "n" > page_allocator< / span > < span class = "p" > );< / span >
< a id = "__codelineno-9-11" name = "__codelineno-9-11" href = "#__codelineno-9-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // defer mem_arena.deinit();< / span >
< a id = "__codelineno-9-12" name = "__codelineno-9-12" href = "#__codelineno-9-12" > < / a > < span class = "w" > < / span > < span class = "kr" > const< / span > < span class = "w" > < / span > < span class = "n" > mem_allocator< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > mem_arena< / span > < span class = "p" > .< / span > < span class = "n" > allocator< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-9-13" name = "__codelineno-9-13" href = "#__codelineno-9-13" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > counter< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > try< / span > < span class = "w" > < / span > < span class = "n" > mem_allocator< / span > < span class = "p" > .< / span > < span class = "n" > alloc< / span > < span class = "p" > (< / span > < span class = "kt" > usize< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 10< / span > < span class = "p" > );< / span >
< a id = "__codelineno-9-14" name = "__codelineno-9-14" href = "#__codelineno-9-14" > < / a > < span class = "w" > < / span > < span class = "n" > std< / span > < span class = "p" > .< / span > < span class = "n" > mem< / span > < span class = "p" > .< / span > < span class = "n" > set< / span > < span class = "p" > (< / span > < span class = "kt" > usize< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > counter< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > );< / span >
< a id = "__codelineno-9-15" name = "__codelineno-9-15" href = "#__codelineno-9-15" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > .< / span > < span class = "n" > len< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-9-16" name = "__codelineno-9-16" href = "#__codelineno-9-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 统计 0~9 各数字的出现次数< / span >
< a id = "__codelineno-9-17" name = "__codelineno-9-17" href = "#__codelineno-9-17" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > |< / span > < span class = "n" > num< / span > < span class = "o" > |< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-18" name = "__codelineno-9-18" href = "#__codelineno-9-18" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > d< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > @bitCast< / span > < span class = "p" > (< / span > < span class = "kt" > u32< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > digit< / span > < span class = "p" > (< / span > < span class = "n" > num< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > exp< / span > < span class = "p" > ));< / span > < span class = "w" > < / span > < span class = "c1" > // 获取 nums[i] 第 k 位，记为 d< / span >
< a id = "__codelineno-9-19" name = "__codelineno-9-19" href = "#__codelineno-9-19" > < / a > < span class = "w" > < / span > < span class = "n" > counter< / span > < span class = "p" > [< / span > < span class = "n" > d< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 统计数字 d 的出现次数< / span >
< a id = "__codelineno-9-20" name = "__codelineno-9-20" href = "#__codelineno-9-20" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-9-21" name = "__codelineno-9-21" href = "#__codelineno-9-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 求前缀和，将“出现个数”转换为“数组索引”< / span >
< a id = "__codelineno-9-22" name = "__codelineno-9-22" href = "#__codelineno-9-22" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > usize< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-9-23" name = "__codelineno-9-23" href = "#__codelineno-9-23" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "mi" > 10< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-24" name = "__codelineno-9-24" href = "#__codelineno-9-24" > < / a > < span class = "w" > < / span > < span class = "n" > counter< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > counter< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-9-25" name = "__codelineno-9-25" href = "#__codelineno-9-25" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-9-26" name = "__codelineno-9-26" href = "#__codelineno-9-26" > < / a > < span class = "w" > < / span > < span class = "c1" > // 倒序遍历，根据桶内统计结果，将各元素填入 res< / span >
< a id = "__codelineno-9-27" name = "__codelineno-9-27" href = "#__codelineno-9-27" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > try< / span > < span class = "w" > < / span > < span class = "n" > mem_allocator< / span > < span class = "p" > .< / span > < span class = "n" > alloc< / span > < span class = "p" > (< / span > < span class = "kt" > i32< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > );< / span >
< a id = "__codelineno-9-28" name = "__codelineno-9-28" href = "#__codelineno-9-28" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-9-29" name = "__codelineno-9-29" href = "#__codelineno-9-29" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > -=< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-30" name = "__codelineno-9-30" href = "#__codelineno-9-30" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > d< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > @bitCast< / span > < span class = "p" > (< / span > < span class = "kt" > u32< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > digit< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "n" > exp< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-9-31" name = "__codelineno-9-31" href = "#__codelineno-9-31" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > counter< / span > < span class = "p" > [< / span > < span class = "n" > d< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 获取 d 在数组中的索引 j< / span >
< a id = "__codelineno-9-32" name = "__codelineno-9-32" href = "#__codelineno-9-32" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ];< / span > < span class = "w" > < / span > < span class = "c1" > // 将当前元素填入索引 j< / span >
< a id = "__codelineno-9-33" name = "__codelineno-9-33" href = "#__codelineno-9-33" > < / a > < span class = "w" > < / span > < span class = "n" > counter< / span > < span class = "p" > [< / span > < span class = "n" > d< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > -=< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 将 d 的数量减 1< / span >
< a id = "__codelineno-9-34" name = "__codelineno-9-34" href = "#__codelineno-9-34" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > break< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-9-35" name = "__codelineno-9-35" href = "#__codelineno-9-35" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-9-36" name = "__codelineno-9-36" href = "#__codelineno-9-36" > < / a > < span class = "w" > < / span > < span class = "c1" > // 使用结果覆盖原数组 nums< / span >
< a id = "__codelineno-9-37" name = "__codelineno-9-37" href = "#__codelineno-9-37" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-9-38" name = "__codelineno-9-38" href = "#__codelineno-9-38" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-39" name = "__codelineno-9-39" href = "#__codelineno-9-39" > < / a > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-9-40" name = "__codelineno-9-40" href = "#__codelineno-9-40" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-9-41" name = "__codelineno-9-41" href = "#__codelineno-9-41" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-9-42" name = "__codelineno-9-42" href = "#__codelineno-9-42" > < / a >
< a id = "__codelineno-9-43" name = "__codelineno-9-43" href = "#__codelineno-9-43" > < / a > < span class = "c1" > // 基数排序< / span >
< a id = "__codelineno-9-44" name = "__codelineno-9-44" href = "#__codelineno-9-44" > < / a > < span class = "k" > fn< / span > < span class = "w" > < / span > < span class = "n" > radixSort< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "p" > []< / span > < span class = "kt" > i32< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > !< / span > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-45" name = "__codelineno-9-45" href = "#__codelineno-9-45" > < / a > < span class = "w" > < / span > < span class = "c1" > // 获取数组的最大元素，用于判断最大位数< / span >
< a id = "__codelineno-9-46" name = "__codelineno-9-46" href = "#__codelineno-9-46" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > m< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > i32< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > std< / span > < span class = "p" > .< / span > < span class = "n" > math< / span > < span class = "p" > .< / span > < span class = "n" > minInt< / span > < span class = "p" > (< / span > < span class = "kt" > i32< / span > < span class = "p" > );< / span >
< a id = "__codelineno-9-47" name = "__codelineno-9-47" href = "#__codelineno-9-47" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > |< / span > < span class = "n" > num< / span > < span class = "o" > |< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-48" name = "__codelineno-9-48" href = "#__codelineno-9-48" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > num< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > m< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "n" > m< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > num< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-9-49" name = "__codelineno-9-49" href = "#__codelineno-9-49" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-9-50" name = "__codelineno-9-50" href = "#__codelineno-9-50" > < / a > < span class = "w" > < / span > < span class = "c1" > // 按照从低位到高位的顺序遍历< / span >
< a id = "__codelineno-9-51" name = "__codelineno-9-51" href = "#__codelineno-9-51" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > exp< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > i32< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-9-52" name = "__codelineno-9-52" href = "#__codelineno-9-52" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > exp< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > m< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > exp< / span > < span class = "w" > < / span > < span class = "o" > *=< / span > < span class = "w" > < / span > < span class = "mi" > 10< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-53" name = "__codelineno-9-53" href = "#__codelineno-9-53" > < / a > < span class = "w" > < / span > < span class = "c1" > // 对数组元素的第 k 位执行计数排序< / span >
< a id = "__codelineno-9-54" name = "__codelineno-9-54" href = "#__codelineno-9-54" > < / a > < span class = "w" > < / span > < span class = "c1" > // k = 1 -> exp = 1< / span >
< a id = "__codelineno-9-55" name = "__codelineno-9-55" href = "#__codelineno-9-55" > < / a > < span class = "w" > < / span > < span class = "c1" > // k = 2 -> exp = 10< / span >
< a id = "__codelineno-9-56" name = "__codelineno-9-56" href = "#__codelineno-9-56" > < / a > < span class = "w" > < / span > < span class = "c1" > // 即 exp = 10^(k-1)< / span >
< a id = "__codelineno-9-57" name = "__codelineno-9-57" href = "#__codelineno-9-57" > < / a > < span class = "w" > < / span > < span class = "k" > try< / span > < span class = "w" > < / span > < span class = "n" > countingSortDigit< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > exp< / span > < span class = "p" > );< / span > < span class = "w" > < / span >
< a id = "__codelineno-9-58" name = "__codelineno-9-58" href = "#__codelineno-9-58" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-9-59" name = "__codelineno-9-59" href = "#__codelineno-9-59" > < / a > < span class = "p" > }< / span > < span class = "w" > < / span >
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< div class = "admonition question" >
< p class = "admonition-title" > 为什么从最低位开始排序？< / p >
< p > 在连续的排序轮次中，后一轮排序会覆盖前一轮排序的结果。举例来说，如果第一轮排序结果 < span class = "arithmatex" > \(a < b\)< / span > ，而第二轮排序结果 < span class = "arithmatex" > \(a > b\)< / span > ，那么第二轮的结果将取代第一轮的结果。由于数字的高位优先级高于低位，我们应该先排序低位再排序高位。< / p >
< / div >
< h2 id = "1182" > 11.8.2. 算法特性< a class = "headerlink" href = "#1182" title = "Permanent link" > ¶ < / a > < / h2 >
< p > < strong > 时间复杂度 < span class = "arithmatex" > \(O(nk)\)< / span > < / strong > ：设数据量为 < span class = "arithmatex" > \(n\)< / span > 、数据为 < span class = "arithmatex" > \(d\)< / span > 进制、最大位数为 < span class = "arithmatex" > \(k\)< / span > ，则对某一位执行计数排序使用 < span class = "arithmatex" > \(O(n + d)\)< / span > 时间，排序所有 < span class = "arithmatex" > \(k\)< / span > 位使用 < span class = "arithmatex" > \(O((n + d)k)\)< / span > 时间。通常情况下，< span class = "arithmatex" > \(d\)< / span > 和 < span class = "arithmatex" > \(k\)< / span > 都相对较小，时间复杂度趋向 < span class = "arithmatex" > \(O(n)\)< / span > 。< / p >
< p > < strong > 空间复杂度 < span class = "arithmatex" > \(O(n + d)\)< / span > < / strong > ：与计数排序相同，基数排序需要借助长度为 < span class = "arithmatex" > \(n\)< / span > 和 < span class = "arithmatex" > \(d\)< / span > 的数组 < code > res< / code > 和 < code > counter< / code > ，因此它是一种“非原地排序”。< / p >
< p > 基数排序与计数排序一样，都属于稳定排序。相较于计数排序，基数排序适用于数值范围较大的情况，< strong > 但前提是数据必须可以表示为固定位数的格式，且位数不能过大< / strong > 。例如，浮点数不适合使用基数排序，因为其位数 < span class = "arithmatex" > \(k\)< / span > 过大，可能导致时间复杂度 < span class = "arithmatex" > \(O(nk) \gg O(n^2)\)< / span > 。< / p >
< h2 id = "__comments" > 评论< / h2 >
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