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Hello 算法
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2.3. 空间复杂度
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0. 写在前面
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0. 写在前面
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0.1. 关于本书
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0.2. 如何使用本书
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0.3. 小结
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1. 引言
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1. 引言
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1.1. 算法无处不在
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< a href = "../../chapter_introduction/what_is_dsa/" class = "md-nav__link" >
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1.2. 算法是什么
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< a href = "../../chapter_introduction/summary/" class = "md-nav__link" >
1.3. 小结
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< label class = "md-nav__link" for = "__nav_3" id = "__nav_3_label" tabindex = "0" >
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2. 复杂度分析
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< label class = "md-nav__title" for = "__nav_3" >
< span class = "md-nav__icon md-icon" > < / span >
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2. 复杂度分析
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< li class = "md-nav__item" >
< a href = "../performance_evaluation/" class = "md-nav__link" >
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2.1. 算法效率评估
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< a href = "../time_complexity/" class = "md-nav__link" >
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2.2. 时间复杂度
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< input class = "md-nav__toggle md-toggle" type = "checkbox" id = "__toc" >
< label class = "md-nav__link md-nav__link--active" for = "__toc" >
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2.3. 空间复杂度
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< / label >
< a href = "./" class = "md-nav__link md-nav__link--active" >
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2.3. 空间复杂度
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目录
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< li class = "md-nav__item" >
< a href = "#231" class = "md-nav__link" >
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2.3.1. 算法相关空间
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< a href = "#232" class = "md-nav__link" >
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2.3.2. 推算方法
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2.3.3. 常见类型
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< / a >
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< nav class = "md-nav" aria-label = "2.3.3. 常见类型" >
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常数阶 \(O(1)\)
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< a href = "#on" class = "md-nav__link" >
线性阶 \(O(n)\)
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< a href = "#on2" class = "md-nav__link" >
平方阶 \(O(n^2)\)
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< a href = "#o2n" class = "md-nav__link" >
指数阶 \(O(2^n)\)
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< a href = "#olog-n" class = "md-nav__link" >
对数阶 \(O(\log n)\)
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2.3.4. 权衡时间与空间
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< a href = "../summary/" class = "md-nav__link" >
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2.4. 小结
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< label class = "md-nav__link" for = "__nav_4" id = "__nav_4_label" tabindex = "0" >
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3. 数据结构简介
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< label class = "md-nav__title" for = "__nav_4" >
< span class = "md-nav__icon md-icon" > < / span >
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3. 数据结构简介
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< li class = "md-nav__item" >
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3.1. 数据结构分类
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< li class = "md-nav__item" >
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3.2. 基本数据类型
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< a href = "../../chapter_data_structure/number_encoding/" class = "md-nav__link" >
3.3. 数字编码 *
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< a href = "../../chapter_data_structure/character_encoding/" class = "md-nav__link" >
3.4. 字符编码 *
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< li class = "md-nav__item" >
< a href = "../../chapter_data_structure/summary/" class = "md-nav__link" >
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3.5. 小结
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< label class = "md-nav__link" for = "__nav_5" id = "__nav_5_label" tabindex = "0" >
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4. 数组与链表
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< label class = "md-nav__title" for = "__nav_5" >
< span class = "md-nav__icon md-icon" > < / span >
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4. 数组与链表
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< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/array/" class = "md-nav__link" >
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4.1. 数组
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< a href = "../../chapter_array_and_linkedlist/linked_list/" class = "md-nav__link" >
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4.2. 链表
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< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/list/" class = "md-nav__link" >
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4.3. 列表
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< a href = "../../chapter_array_and_linkedlist/summary/" class = "md-nav__link" >
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4.4. 小结
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< label class = "md-nav__link" for = "__nav_6" id = "__nav_6_label" tabindex = "0" >
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5. 栈与队列
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< label class = "md-nav__title" for = "__nav_6" >
< span class = "md-nav__icon md-icon" > < / span >
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5. 栈与队列
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< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/stack/" class = "md-nav__link" >
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5.1. 栈
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< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/queue/" class = "md-nav__link" >
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5.2. 队列
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< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/deque/" class = "md-nav__link" >
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5.3. 双向队列
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< a href = "../../chapter_stack_and_queue/summary/" class = "md-nav__link" >
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5.4. 小结
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< label class = "md-nav__link" for = "__nav_7" id = "__nav_7_label" tabindex = "0" >
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6. 散列表
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< label class = "md-nav__title" for = "__nav_7" >
< span class = "md-nav__icon md-icon" > < / span >
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6. 散列表
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< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
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6.1. 哈希表
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< a href = "../../chapter_hashing/hash_collision/" class = "md-nav__link" >
6.2. 哈希冲突处理
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< / li >
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< li class = "md-nav__item" >
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< a href = "../../chapter_hashing/summary/" class = "md-nav__link" >
6.3. 小结
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< 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" >
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< label class = "md-nav__link" for = "__nav_8" id = "__nav_8_label" tabindex = "0" >
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7. 树
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< / 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 >
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7. 树
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< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
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< a href = "../../chapter_tree/binary_tree/" class = "md-nav__link" >
7.1. 二叉树
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< / a >
< / li >
< li class = "md-nav__item" >
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< a href = "../../chapter_tree/binary_tree_traversal/" class = "md-nav__link" >
7.2. 二叉树遍历
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< / a >
< / li >
< li class = "md-nav__item" >
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< a href = "../../chapter_tree/array_representation_of_tree/" class = "md-nav__link" >
7.3. 二叉树数组表示
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< a href = "../../chapter_tree/binary_search_tree/" class = "md-nav__link" >
7.4. 二叉搜索树
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< li class = "md-nav__item" >
< a href = "../../chapter_tree/avl_tree/" class = "md-nav__link" >
7.5. AVL 树 *
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< li class = "md-nav__item" >
< a href = "../../chapter_tree/summary/" class = "md-nav__link" >
7.6. 小结
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< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_9" >
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< label class = "md-nav__link" for = "__nav_9" id = "__nav_9_label" tabindex = "0" >
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8. 堆
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< 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 >
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8. 堆
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< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
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< a href = "../../chapter_heap/heap/" class = "md-nav__link" >
8.1. 堆
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< li class = "md-nav__item" >
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< a href = "../../chapter_heap/build_heap/" class = "md-nav__link" >
8.2. 建堆操作 *
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< li class = "md-nav__item" >
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< a href = "../../chapter_heap/summary/" class = "md-nav__link" >
8.3. 小结
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< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_10" >
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< label class = "md-nav__link" for = "__nav_10" id = "__nav_10_label" tabindex = "0" >
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9. 图
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< / 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 >
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9. 图
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< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
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< a href = "../../chapter_graph/graph/" class = "md-nav__link" >
9.1. 图
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< / a >
< / li >
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< li class = "md-nav__item" >
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< a href = "../../chapter_graph/graph_operations/" class = "md-nav__link" >
9.2. 图基础操作
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< / a >
< / li >
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< li class = "md-nav__item" >
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< a href = "../../chapter_graph/graph_traversal/" class = "md-nav__link" >
9.3. 图的遍历
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< li class = "md-nav__item" >
< a href = "../../chapter_graph/summary/" class = "md-nav__link" >
9.4. 小结
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< 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" >
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< label class = "md-nav__link" for = "__nav_11" id = "__nav_11_label" tabindex = "0" >
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10. 搜索算法
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< span class = "md-nav__icon md-icon" > < / span >
< / label >
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< label class = "md-nav__title" for = "__nav_11" >
< span class = "md-nav__icon md-icon" > < / span >
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10. 搜索算法
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< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
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< a href = "../../chapter_searching/binary_search/" class = "md-nav__link" >
10.1. 二分查找（ ）
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< / a >
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< li class = "md-nav__item" >
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< a href = "../../chapter_searching/binary_search_edge/" class = "md-nav__link" >
10.2. 二分查找边界（ ）
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< li class = "md-nav__item" >
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< a href = "../../chapter_searching/replace_linear_by_hashing/" class = "md-nav__link" >
10.3. 哈希优化策略
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< li class = "md-nav__item" >
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< a href = "../../chapter_searching/searching_algorithm_revisited/" class = "md-nav__link" >
10.4. 重识搜索算法
< / a >
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< li class = "md-nav__item" >
< a href = "../../chapter_searching/summary/" class = "md-nav__link" >
10.5. 小结
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11. 排序算法
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11. 排序算法
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11.1. 排序算法
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< / a >
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11.2. 选择排序（ ）
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< / a >
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< a href = "../../chapter_sorting/bubble_sort/" class = "md-nav__link" >
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11.3. 冒泡排序
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< a href = "../../chapter_sorting/insertion_sort/" class = "md-nav__link" >
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11.4. 插入排序
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< a href = "../../chapter_sorting/quick_sort/" class = "md-nav__link" >
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11.5. 快速排序
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11.6. 归并排序
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11.7. 堆排序（ ）
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11.8. 桶排序
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11.9. 计数排序
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11.10. 基数排序
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11.11. 小结
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12. 回溯算法
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12. 回溯算法
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12.1. 回溯算法（ ）
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12.3. N 皇后问题（ ）
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13. 附录
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13. 附录
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13.1. 编程环境安装
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13.2. 一起参与创作
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< a href = "../../chapter_reference/" > 参考文献< / a >
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目录
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< a href = "#231" class = "md-nav__link" >
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2.3.1. 算法相关空间
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2.3.2. 推算方法
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2.3.3. 常见类型
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常数阶 \(O(1)\)
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线性阶 \(O(n)\)
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平方阶 \(O(n^2)\)
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指数阶 \(O(2^n)\)
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对数阶 \(O(\log n)\)
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2.3.4. 权衡时间与空间
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< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M10 20H6V4h7v5h5v3.1l2-2V8l-6-6H6c-1.1 0-2 .9-2 2v16c0 1.1.9 2 2 2h4v-2m10.2-7c.1 0 .3.1.4.2l1.3 1.3c.2.2.2.6 0 .8l-1 1-2.1-2.1 1-1c.1-.1.2-.2.4-.2m0 3.9L14.1 23H12v-2.1l6.1-6.1 2.1 2.1Z" / > < / svg >
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< h1 id = "23" > 2.3. 空间复杂度< a class = "headerlink" href = "#23" title = "Permanent link" > ¶ < / a > < / h1 >
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< p > 「空间复杂度 Space Complexity」用于衡量算法使用内存空间随着数据量变大时的增长趋势。这个概念与时间复杂度非常类似。< / p >
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< h2 id = "231" > 2.3.1. 算法相关空间< a class = "headerlink" href = "#231" title = "Permanent link" > ¶ < / a > < / h2 >
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< p > 算法运行过程中使用的内存空间主要包括以下几种：< / p >
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< ul >
< li > 「输入空间」用于存储算法的输入数据；< / li >
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< li > 「暂存空间」用于存储算法运行过程中的变量、对象、函数上下文等数据；< / li >
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< li > 「输出空间」用于存储算法的输出数据；< / li >
< / ul >
< p > 通常情况下，空间复杂度统计范围是「暂存空间」+「输出空间」。< / p >
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< p > 暂存空间可以进一步划分为三个部分：< / p >
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< ul >
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< li > 「暂存数据」用于保存算法运行过程中的各种常量、变量、对象等。< / li >
< li > 「栈帧空间」用于保存调用函数的上下文数据。系统在每次调用函数时都会在栈顶部创建一个栈帧，函数返回后，栈帧空间会被释放。< / li >
< li > 「指令空间」用于保存编译后的程序指令，在实际统计中通常忽略不计。< / li >
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< / ul >
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< p > 因此，在分析一段程序的空间复杂度时，我们一般统计 < strong > 暂存数据、输出数据、栈帧空间< / strong > 三部分。< / p >
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< p > < img alt = "算法使用的相关空间" src = "../space_complexity.assets/space_types.png" / > < / p >
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< p align = "center" > Fig. 算法使用的相关空间 < / p >
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< 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 >
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< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-0-1" name = "__codelineno-0-1" href = "#__codelineno-0-1" > < / a > < span class = "cm" > /* 类 */< / span >
< a id = "__codelineno-0-2" name = "__codelineno-0-2" href = "#__codelineno-0-2" > < / a > < span class = "kd" > class< / span > < span class = "nc" > Node< / 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 = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-0-4" name = "__codelineno-0-4" href = "#__codelineno-0-4" > < / a > < span class = "w" > < / span > < span class = "n" > Node< / span > < span class = "w" > < / span > < span class = "n" > next< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-0-5" name = "__codelineno-0-5" href = "#__codelineno-0-5" > < / a > < span class = "w" > < / span > < span class = "n" > Node< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > x< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > x< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-0-6" name = "__codelineno-0-6" href = "#__codelineno-0-6" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-0-7" name = "__codelineno-0-7" href = "#__codelineno-0-7" > < / a >
< a id = "__codelineno-0-8" name = "__codelineno-0-8" href = "#__codelineno-0-8" > < / a > < span class = "cm" > /* 函数 */< / span >
< a id = "__codelineno-0-9" name = "__codelineno-0-9" href = "#__codelineno-0-9" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > function< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-0-10" name = "__codelineno-0-10" href = "#__codelineno-0-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // do something...< / span >
< a id = "__codelineno-0-11" name = "__codelineno-0-11" href = "#__codelineno-0-11" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-0-12" name = "__codelineno-0-12" href = "#__codelineno-0-12" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-0-13" name = "__codelineno-0-13" href = "#__codelineno-0-13" > < / a >
< a id = "__codelineno-0-14" name = "__codelineno-0-14" href = "#__codelineno-0-14" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > algorithm< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span > < span class = "w" > < / span > < span class = "c1" > // 输入数据< / span >
< a id = "__codelineno-0-15" name = "__codelineno-0-15" href = "#__codelineno-0-15" > < / a > < span class = "w" > < / span > < span class = "kd" > final< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > a< / 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 = "c1" > // 暂存数据（常量）< / span >
< a id = "__codelineno-0-16" name = "__codelineno-0-16" href = "#__codelineno-0-16" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > b< / 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 = "c1" > // 暂存数据（变量）< / span >
< a id = "__codelineno-0-17" name = "__codelineno-0-17" href = "#__codelineno-0-17" > < / a > < span class = "w" > < / span > < span class = "n" > Node< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > Node< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 暂存数据（对象）< / span >
< a id = "__codelineno-0-18" name = "__codelineno-0-18" href = "#__codelineno-0-18" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > c< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > function< / span > < span class = "p" > ();< / span > < span class = "w" > < / span > < span class = "c1" > // 栈帧空间（调用函数）< / span >
< a id = "__codelineno-0-19" name = "__codelineno-0-19" href = "#__codelineno-0-19" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > a< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > b< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > c< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 输出数据< / span >
< a id = "__codelineno-0-20" name = "__codelineno-0-20" href = "#__codelineno-0-20" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-1-1" name = "__codelineno-1-1" href = "#__codelineno-1-1" > < / a > < span class = "cm" > /* 结构体 */< / span >
< a id = "__codelineno-1-2" name = "__codelineno-1-2" href = "#__codelineno-1-2" > < / a > < span class = "k" > struct< / span > < span class = "w" > < / span > < span class = "nc" > Node< / 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 = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-4" name = "__codelineno-1-4" href = "#__codelineno-1-4" > < / a > < span class = "w" > < / span > < span class = "n" > Node< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > next< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-5" name = "__codelineno-1-5" href = "#__codelineno-1-5" > < / a > < span class = "w" > < / span > < span class = "n" > Node< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > x< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > (< / span > < span class = "n" > x< / span > < span class = "p" > ),< / span > < span class = "w" > < / span > < span class = "n" > next< / span > < span class = "p" > (< / span > < span class = "k" > nullptr< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {}< / span >
< a id = "__codelineno-1-6" name = "__codelineno-1-6" href = "#__codelineno-1-6" > < / a > < span class = "p" > };< / span >
< a id = "__codelineno-1-7" name = "__codelineno-1-7" href = "#__codelineno-1-7" > < / a >
< a id = "__codelineno-1-8" name = "__codelineno-1-8" href = "#__codelineno-1-8" > < / a > < span class = "cm" > /* 函数 */< / span >
< a id = "__codelineno-1-9" name = "__codelineno-1-9" href = "#__codelineno-1-9" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > func< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-10" name = "__codelineno-1-10" href = "#__codelineno-1-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // do something...< / span >
< a id = "__codelineno-1-11" name = "__codelineno-1-11" href = "#__codelineno-1-11" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-12" name = "__codelineno-1-12" href = "#__codelineno-1-12" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-1-13" name = "__codelineno-1-13" href = "#__codelineno-1-13" > < / a >
< a id = "__codelineno-1-14" name = "__codelineno-1-14" href = "#__codelineno-1-14" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > algorithm< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span > < span class = "w" > < / span > < span class = "c1" > // 输入数据< / span >
< a id = "__codelineno-1-15" name = "__codelineno-1-15" href = "#__codelineno-1-15" > < / a > < span class = "w" > < / span > < span class = "k" > const< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > a< / 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 = "c1" > // 暂存数据（常量）< / span >
< a id = "__codelineno-1-16" name = "__codelineno-1-16" href = "#__codelineno-1-16" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > b< / 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 = "c1" > // 暂存数据（变量）< / span >
2023-03-12 18:46:10 +08:00
< a id = "__codelineno-1-17" name = "__codelineno-1-17" href = "#__codelineno-1-17" > < / a > < span class = "w" > < / span > < span class = "n" > Node< / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > Node< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 暂存数据（对象）< / span >
< a id = "__codelineno-1-18" name = "__codelineno-1-18" href = "#__codelineno-1-18" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > c< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > func< / span > < span class = "p" > ();< / span > < span class = "w" > < / span > < span class = "c1" > // 栈帧空间（调用函数）< / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-1-19" name = "__codelineno-1-19" href = "#__codelineno-1-19" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > a< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > b< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > c< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 输出数据< / span >
< a id = "__codelineno-1-20" name = "__codelineno-1-20" href = "#__codelineno-1-20" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-04-09 05:30:54 +08:00
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-2-1" name = "__codelineno-2-1" href = "#__codelineno-2-1" > < / a > < span class = "k" > class< / span > < span class = "nc" > Node< / 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" > " " " 类" " " < / span >
2023-03-12 18:46:10 +08:00
< a id = "__codelineno-2-3" name = "__codelineno-2-3" href = "#__codelineno-2-3" > < / a > < span class = "k" > def< / span > < span class = "fm" > __init__< / span > < span class = "p" > (< / span > < span class = "bp" > self< / span > < span class = "p" > ,< / span > < span class = "n" > x< / span > < span class = "p" > :< / span > < span class = "nb" > int< / span > < span class = "p" > ):< / span >
2023-04-09 04:35:05 +08:00
< a id = "__codelineno-2-4" name = "__codelineno-2-4" href = "#__codelineno-2-4" > < / a > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > val< / span > < span class = "p" > :< / span > < span class = "nb" > int< / span > < span class = "o" > =< / span > < span class = "n" > x< / span > < span class = "c1" > # 节点值< / span >
< a id = "__codelineno-2-5" name = "__codelineno-2-5" href = "#__codelineno-2-5" > < / a > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > next< / span > < span class = "p" > :< / span > < span class = "n" > Optional< / span > < span class = "p" > [< / span > < span class = "n" > Node< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "kc" > None< / span > < span class = "c1" > # 指向下一节点的指针（引用）< / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-2-6" name = "__codelineno-2-6" href = "#__codelineno-2-6" > < / a >
2023-04-09 05:30:54 +08:00
< a id = "__codelineno-2-7" name = "__codelineno-2-7" href = "#__codelineno-2-7" > < / a > < span class = "k" > def< / span > < span class = "nf" > function< / span > < span class = "p" > ()< / span > < span class = "o" > -> < / span > < span class = "nb" > int< / span > < span class = "p" > :< / span >
< a id = "__codelineno-2-8" name = "__codelineno-2-8" href = "#__codelineno-2-8" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 函数" " " < / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-2-9" name = "__codelineno-2-9" href = "#__codelineno-2-9" > < / a > < span class = "c1" > # do something...< / span >
< a id = "__codelineno-2-10" name = "__codelineno-2-10" href = "#__codelineno-2-10" > < / a > < span class = "k" > return< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-2-11" name = "__codelineno-2-11" href = "#__codelineno-2-11" > < / a >
2023-03-12 18:46:10 +08:00
< a id = "__codelineno-2-12" name = "__codelineno-2-12" href = "#__codelineno-2-12" > < / a > < span class = "k" > def< / span > < span class = "nf" > algorithm< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "o" > -> < / span > < span class = "nb" > int< / span > < span class = "p" > :< / span > < span class = "c1" > # 输入数据< / span >
2023-05-22 22:01:26 +08:00
< a id = "__codelineno-2-13" name = "__codelineno-2-13" href = "#__codelineno-2-13" > < / a > < span class = "n" > A< / span > < span class = "o" > =< / span > < span class = "mi" > 0< / span > < span class = "c1" > # 暂存数据（常量，一般用大写字母表示）< / span >
< a id = "__codelineno-2-14" name = "__codelineno-2-14" href = "#__codelineno-2-14" > < / a > < span class = "n" > b< / span > < span class = "o" > =< / span > < span class = "mi" > 0< / span > < span class = "c1" > # 暂存数据（变量）< / span >
2023-03-13 22:54:29 +08:00
< a id = "__codelineno-2-15" name = "__codelineno-2-15" href = "#__codelineno-2-15" > < / a > < span class = "n" > node< / span > < span class = "o" > =< / span > < span class = "n" > Node< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span > < span class = "c1" > # 暂存数据（对象）< / span >
2023-05-22 22:01:26 +08:00
< a id = "__codelineno-2-16" name = "__codelineno-2-16" href = "#__codelineno-2-16" > < / a > < span class = "n" > c< / span > < span class = "o" > =< / span > < span class = "n" > function< / span > < span class = "p" > ()< / span > < span class = "c1" > # 栈帧空间（调用函数）< / span >
2023-03-13 22:54:29 +08:00
< a id = "__codelineno-2-17" name = "__codelineno-2-17" href = "#__codelineno-2-17" > < / a > < span class = "k" > return< / span > < span class = "n" > A< / span > < span class = "o" > +< / span > < span class = "n" > b< / span > < span class = "o" > +< / span > < span class = "n" > c< / span > < span class = "c1" > # 输出数据< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-3-1" name = "__codelineno-3-1" href = "#__codelineno-3-1" > < / a > < span class = "cm" > /* 结构体 */< / span >
< a id = "__codelineno-3-2" name = "__codelineno-3-2" href = "#__codelineno-3-2" > < / a > < span class = "kd" > type< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "w" > < / span > < span class = "kd" > struct< / 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 = "nx" > val< / span > < span class = "w" > < / span > < span class = "kt" > int< / span >
< a id = "__codelineno-3-4" name = "__codelineno-3-4" href = "#__codelineno-3-4" > < / a > < span class = "w" > < / span > < span class = "nx" > next< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > node< / 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" > /* 创建 node 结构体 */< / 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" > newNode< / span > < span class = "p" > (< / span > < span class = "nx" > val< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > node< / 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 = "k" > return< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "nx" > node< / span > < span class = "p" > {< / span > < span class = "nx" > val< / span > < span class = "p" > :< / span > < span class = "w" > < / span > < span class = "nx" > val< / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-10" name = "__codelineno-3-10" href = "#__codelineno-3-10" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-3-11" name = "__codelineno-3-11" href = "#__codelineno-3-11" > < / a >
< a id = "__codelineno-3-12" name = "__codelineno-3-12" href = "#__codelineno-3-12" > < / a > < span class = "cm" > /* 函数 */< / span >
< a id = "__codelineno-3-13" name = "__codelineno-3-13" href = "#__codelineno-3-13" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > function< / 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-3-14" name = "__codelineno-3-14" href = "#__codelineno-3-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // do something...< / span >
< a id = "__codelineno-3-15" name = "__codelineno-3-15" href = "#__codelineno-3-15" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-3-16" name = "__codelineno-3-16" href = "#__codelineno-3-16" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-3-17" name = "__codelineno-3-17" href = "#__codelineno-3-17" > < / a >
< a id = "__codelineno-3-18" name = "__codelineno-3-18" href = "#__codelineno-3-18" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > algorithm< / span > < span class = "p" > (< / span > < span class = "nx" > n< / 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 > < span class = "w" > < / span > < span class = "c1" > // 输入数据< / span >
< a id = "__codelineno-3-19" name = "__codelineno-3-19" href = "#__codelineno-3-19" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > a< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "w" > < / span > < span class = "c1" > // 暂存数据（常量）< / span >
< a id = "__codelineno-3-20" name = "__codelineno-3-20" href = "#__codelineno-3-20" > < / a > < span class = "w" > < / span > < span class = "nx" > b< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "w" > < / span > < span class = "c1" > // 暂存数据（变量）< / span >
< a id = "__codelineno-3-21" name = "__codelineno-3-21" href = "#__codelineno-3-21" > < / a > < span class = "w" > < / span > < span class = "nx" > newNode< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "c1" > // 暂存数据（对象）< / span >
< a id = "__codelineno-3-22" name = "__codelineno-3-22" href = "#__codelineno-3-22" > < / a > < span class = "w" > < / span > < span class = "nx" > c< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > function< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "c1" > // 栈帧空间（调用函数）< / span >
< a id = "__codelineno-3-23" name = "__codelineno-3-23" href = "#__codelineno-3-23" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > a< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "nx" > b< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "nx" > c< / span > < span class = "w" > < / span > < span class = "c1" > // 输出数据< / span >
< a id = "__codelineno-3-24" name = "__codelineno-3-24" href = "#__codelineno-3-24" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-4-1" name = "__codelineno-4-1" href = "#__codelineno-4-1" > < / a > < span class = "cm" > /* 类 */< / span >
< a id = "__codelineno-4-2" name = "__codelineno-4-2" href = "#__codelineno-4-2" > < / a > < span class = "kd" > class< / span > < span class = "w" > < / span > < span class = "nx" > Node< / 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 = "nx" > val< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-4-4" name = "__codelineno-4-4" href = "#__codelineno-4-4" > < / a > < span class = "w" > < / span > < span class = "nx" > next< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-4-5" name = "__codelineno-4-5" href = "#__codelineno-4-5" > < / a > < span class = "w" > < / span > < span class = "kr" > constructor< / span > < span class = "p" > (< / span > < span class = "nx" > val< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-04-09 04:35:05 +08:00
< a id = "__codelineno-4-6" name = "__codelineno-4-6" href = "#__codelineno-4-6" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > val< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > val< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "kc" > undefined< / span > < span class = "w" > < / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "w" > < / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "nx" > val< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 节点值< / span >
< a id = "__codelineno-4-7" name = "__codelineno-4-7" href = "#__codelineno-4-7" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > next< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 指向下一节点的引用< / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-4-8" name = "__codelineno-4-8" href = "#__codelineno-4-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-9" name = "__codelineno-4-9" href = "#__codelineno-4-9" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-4-10" name = "__codelineno-4-10" href = "#__codelineno-4-10" > < / a >
< a id = "__codelineno-4-11" name = "__codelineno-4-11" href = "#__codelineno-4-11" > < / a > < span class = "cm" > /* 函数 */< / span >
< a id = "__codelineno-4-12" name = "__codelineno-4-12" href = "#__codelineno-4-12" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > constFunc< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-13" name = "__codelineno-4-13" href = "#__codelineno-4-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // do something< / span >
< a id = "__codelineno-4-14" name = "__codelineno-4-14" href = "#__codelineno-4-14" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-4-15" name = "__codelineno-4-15" href = "#__codelineno-4-15" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-4-16" name = "__codelineno-4-16" href = "#__codelineno-4-16" > < / a >
< a id = "__codelineno-4-17" name = "__codelineno-4-17" href = "#__codelineno-4-17" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > algorithm< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span > < span class = "w" > < / span > < span class = "c1" > // 输入数据< / span >
< a id = "__codelineno-4-18" name = "__codelineno-4-18" href = "#__codelineno-4-18" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > a< / 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 = "c1" > // 暂存数据（常量）< / span >
2023-03-13 22:54:29 +08:00
< a id = "__codelineno-4-19" name = "__codelineno-4-19" href = "#__codelineno-4-19" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > b< / 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 = "c1" > // 暂存数据（变量）< / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-4-20" name = "__codelineno-4-20" href = "#__codelineno-4-20" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "ow" > new< / span > < span class = "w" > < / span > < span class = "nx" > Node< / span > < span class = "p" > (< / span > < span class = "mf" > 0< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 暂存数据（对象）< / span >
< a id = "__codelineno-4-21" name = "__codelineno-4-21" href = "#__codelineno-4-21" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > c< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > constFunc< / span > < span class = "p" > ();< / span > < span class = "w" > < / span > < span class = "c1" > // 栈帧空间（调用函数）< / span >
< a id = "__codelineno-4-22" name = "__codelineno-4-22" href = "#__codelineno-4-22" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > a< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "nx" > b< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "nx" > c< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 输出数据< / span >
< a id = "__codelineno-4-23" name = "__codelineno-4-23" href = "#__codelineno-4-23" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-5-1" name = "__codelineno-5-1" href = "#__codelineno-5-1" > < / a > < span class = "cm" > /* 类 */< / span >
< a id = "__codelineno-5-2" name = "__codelineno-5-2" href = "#__codelineno-5-2" > < / a > < span class = "kd" > class< / span > < span class = "w" > < / span > < span class = "nx" > Node< / 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 = "nx" > val< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-5-4" name = "__codelineno-5-4" href = "#__codelineno-5-4" > < / a > < span class = "w" > < / span > < span class = "nx" > next< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > Node< / span > < span class = "w" > < / span > < span class = "o" > |< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-5-5" name = "__codelineno-5-5" href = "#__codelineno-5-5" > < / a > < span class = "w" > < / span > < span class = "kr" > constructor< / span > < span class = "p" > (< / span > < span class = "nx" > val?< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-04-09 04:35:05 +08:00
< a id = "__codelineno-5-6" name = "__codelineno-5-6" href = "#__codelineno-5-6" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > val< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > val< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "kc" > undefined< / span > < span class = "w" > < / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "nx" > 0< / span > < span class = "w" > < / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > val< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 节点值< / span >
< a id = "__codelineno-5-7" name = "__codelineno-5-7" href = "#__codelineno-5-7" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > next< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 指向下一节点的引用< / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-5-8" name = "__codelineno-5-8" href = "#__codelineno-5-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-5-9" name = "__codelineno-5-9" href = "#__codelineno-5-9" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-5-10" name = "__codelineno-5-10" href = "#__codelineno-5-10" > < / a >
< a id = "__codelineno-5-11" name = "__codelineno-5-11" href = "#__codelineno-5-11" > < / a > < span class = "cm" > /* 函数 */< / span >
< a id = "__codelineno-5-12" name = "__codelineno-5-12" href = "#__codelineno-5-12" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > constFunc< / 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-5-13" name = "__codelineno-5-13" href = "#__codelineno-5-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // do something< / span >
< a id = "__codelineno-5-14" name = "__codelineno-5-14" href = "#__codelineno-5-14" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-5-15" name = "__codelineno-5-15" href = "#__codelineno-5-15" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-5-16" name = "__codelineno-5-16" href = "#__codelineno-5-16" > < / a >
< a id = "__codelineno-5-17" name = "__codelineno-5-17" href = "#__codelineno-5-17" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > algorithm< / span > < span class = "p" > (< / span > < span class = "nx" > n< / 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 > < span class = "w" > < / span > < span class = "c1" > // 输入数据< / span >
< a id = "__codelineno-5-18" name = "__codelineno-5-18" href = "#__codelineno-5-18" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > a< / 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 = "c1" > // 暂存数据（常量）< / span >
2023-03-13 22:54:29 +08:00
< a id = "__codelineno-5-19" name = "__codelineno-5-19" href = "#__codelineno-5-19" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > b< / 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 = "c1" > // 暂存数据（变量）< / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-5-20" name = "__codelineno-5-20" href = "#__codelineno-5-20" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "ow" > new< / span > < span class = "w" > < / span > < span class = "nx" > Node< / span > < span class = "p" > (< / span > < span class = "mf" > 0< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 暂存数据（对象）< / span >
< a id = "__codelineno-5-21" name = "__codelineno-5-21" href = "#__codelineno-5-21" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > c< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > constFunc< / span > < span class = "p" > ();< / span > < span class = "w" > < / span > < span class = "c1" > // 栈帧空间（调用函数）< / span >
< a id = "__codelineno-5-22" name = "__codelineno-5-22" href = "#__codelineno-5-22" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > a< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "nx" > b< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "nx" > c< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 输出数据< / span >
< a id = "__codelineno-5-23" name = "__codelineno-5-23" href = "#__codelineno-5-23" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-04-18 20:19:15 +08:00
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-6-1" name = "__codelineno-6-1" href = "#__codelineno-6-1" > < / a > < span class = "cm" > /* 函数 */< / span >
< a id = "__codelineno-6-2" name = "__codelineno-6-2" href = "#__codelineno-6-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > func< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-6-3" name = "__codelineno-6-3" href = "#__codelineno-6-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // do something...< / span >
< a id = "__codelineno-6-4" name = "__codelineno-6-4" href = "#__codelineno-6-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-6-5" name = "__codelineno-6-5" href = "#__codelineno-6-5" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-6-6" name = "__codelineno-6-6" href = "#__codelineno-6-6" > < / a >
< a id = "__codelineno-6-7" name = "__codelineno-6-7" href = "#__codelineno-6-7" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > algorithm< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span > < span class = "w" > < / span > < span class = "c1" > // 输入数据< / span >
< a id = "__codelineno-6-8" name = "__codelineno-6-8" href = "#__codelineno-6-8" > < / a > < span class = "w" > < / span > < span class = "k" > const< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > a< / 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 = "c1" > // 暂存数据（常量）< / span >
< a id = "__codelineno-6-9" name = "__codelineno-6-9" href = "#__codelineno-6-9" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > b< / 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 = "c1" > // 暂存数据（变量）< / span >
< a id = "__codelineno-6-10" name = "__codelineno-6-10" href = "#__codelineno-6-10" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > c< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > func< / span > < span class = "p" > ();< / span > < span class = "w" > < / span > < span class = "c1" > // 栈帧空间（调用函数）< / span >
< a id = "__codelineno-6-11" name = "__codelineno-6-11" href = "#__codelineno-6-11" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > a< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > b< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > c< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 输出数据< / span >
< a id = "__codelineno-6-12" name = "__codelineno-6-12" href = "#__codelineno-6-12" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-7-1" name = "__codelineno-7-1" href = "#__codelineno-7-1" > < / a > < span class = "cm" > /* 类 */< / span >
< a id = "__codelineno-7-2" name = "__codelineno-7-2" href = "#__codelineno-7-2" > < / a > < span class = "k" > class< / span > < span class = "w" > < / span > < span class = "nc" > Node< / span >
< a id = "__codelineno-7-3" name = "__codelineno-7-3" href = "#__codelineno-7-3" > < / a > < span class = "p" > {< / span >
< a id = "__codelineno-7-4" name = "__codelineno-7-4" href = "#__codelineno-7-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-5" name = "__codelineno-7-5" href = "#__codelineno-7-5" > < / a > < span class = "w" > < / span > < span class = "n" > Node< / span > < span class = "w" > < / span > < span class = "n" > next< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-6" name = "__codelineno-7-6" href = "#__codelineno-7-6" > < / a > < span class = "w" > < / span > < span class = "n" > Node< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > x< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > x< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-7-7" name = "__codelineno-7-7" href = "#__codelineno-7-7" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-7-8" name = "__codelineno-7-8" href = "#__codelineno-7-8" > < / a >
< a id = "__codelineno-7-9" name = "__codelineno-7-9" href = "#__codelineno-7-9" > < / a > < span class = "cm" > /* 函数 */< / span >
< a id = "__codelineno-7-10" name = "__codelineno-7-10" href = "#__codelineno-7-10" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > function< / span > < span class = "p" > ()< / span >
< a id = "__codelineno-7-11" name = "__codelineno-7-11" href = "#__codelineno-7-11" > < / a > < span class = "p" > {< / span >
< a id = "__codelineno-7-12" name = "__codelineno-7-12" href = "#__codelineno-7-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // do something...< / span >
< a id = "__codelineno-7-13" name = "__codelineno-7-13" href = "#__codelineno-7-13" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-14" name = "__codelineno-7-14" href = "#__codelineno-7-14" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-7-15" name = "__codelineno-7-15" href = "#__codelineno-7-15" > < / a >
< a id = "__codelineno-7-16" name = "__codelineno-7-16" href = "#__codelineno-7-16" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > algorithm< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "c1" > // 输入数据< / span >
< a id = "__codelineno-7-17" name = "__codelineno-7-17" href = "#__codelineno-7-17" > < / a > < span class = "p" > {< / span >
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< a id = "__codelineno-7-18" name = "__codelineno-7-18" href = "#__codelineno-7-18" > < / a > < span class = "w" > < / span > < span class = "k" > const< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > a< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 暂存数据（常量）< / span >
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< a id = "__codelineno-7-19" name = "__codelineno-7-19" href = "#__codelineno-7-19" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > b< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 暂存数据（变量）< / span >
< a id = "__codelineno-7-20" name = "__codelineno-7-20" href = "#__codelineno-7-20" > < / a > < span class = "w" > < / span > < span class = "n" > Node< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > Node< / span > < span class = "p" > (< / span > < span class = "m" > 0< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 暂存数据（对象）< / span >
< a id = "__codelineno-7-21" name = "__codelineno-7-21" href = "#__codelineno-7-21" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > c< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > function< / span > < span class = "p" > ();< / span > < span class = "w" > < / span > < span class = "c1" > // 栈帧空间（调用函数）< / span >
< a id = "__codelineno-7-22" name = "__codelineno-7-22" href = "#__codelineno-7-22" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > a< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > b< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > c< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 输出数据< / span >
< a id = "__codelineno-7-23" name = "__codelineno-7-23" href = "#__codelineno-7-23" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-8-1" name = "__codelineno-8-1" href = "#__codelineno-8-1" > < / a > < span class = "cm" > /* 类 */< / span >
< a id = "__codelineno-8-2" name = "__codelineno-8-2" href = "#__codelineno-8-2" > < / a > < span class = "kd" > class< / span > < span class = "nc" > Node< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-3" name = "__codelineno-8-3" href = "#__codelineno-8-3" > < / a > < span class = "kd" > var< / span > < span class = "nv" > val< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / span >
< a id = "__codelineno-8-4" name = "__codelineno-8-4" href = "#__codelineno-8-4" > < / a > < span class = "kd" > var< / span > < span class = "nv" > next< / span > < span class = "p" > :< / span > < span class = "n" > Node< / span > < span class = "p" > ?< / span >
< a id = "__codelineno-8-5" name = "__codelineno-8-5" href = "#__codelineno-8-5" > < / a >
< a id = "__codelineno-8-6" name = "__codelineno-8-6" href = "#__codelineno-8-6" > < / a > < span class = "kd" > init< / span > < span class = "p" > (< / span > < span class = "n" > x< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / span > < span class = "p" > )< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-7" name = "__codelineno-8-7" href = "#__codelineno-8-7" > < / a > < span class = "n" > val< / span > < span class = "p" > =< / span > < span class = "n" > x< / span >
< a id = "__codelineno-8-8" name = "__codelineno-8-8" href = "#__codelineno-8-8" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-9" name = "__codelineno-8-9" href = "#__codelineno-8-9" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-10" name = "__codelineno-8-10" href = "#__codelineno-8-10" > < / a >
< a id = "__codelineno-8-11" name = "__codelineno-8-11" href = "#__codelineno-8-11" > < / a > < span class = "cm" > /* 函数 */< / span >
< a id = "__codelineno-8-12" name = "__codelineno-8-12" href = "#__codelineno-8-12" > < / a > < span class = "kd" > func< / span > < span class = "nf" > function< / span > < span class = "p" > ()< / span > < span class = "p" > -> < / span > < span class = "nb" > Int< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-13" name = "__codelineno-8-13" href = "#__codelineno-8-13" > < / a > < span class = "c1" > // do something...< / span >
< a id = "__codelineno-8-14" name = "__codelineno-8-14" href = "#__codelineno-8-14" > < / a > < span class = "k" > return< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-8-15" name = "__codelineno-8-15" href = "#__codelineno-8-15" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-16" name = "__codelineno-8-16" href = "#__codelineno-8-16" > < / a >
< a id = "__codelineno-8-17" name = "__codelineno-8-17" href = "#__codelineno-8-17" > < / a > < span class = "kd" > func< / span > < span class = "nf" > algorithm< / span > < span class = "p" > (< / span > < span class = "n" > n< / 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 > < span class = "c1" > // 输入数据< / span >
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< a id = "__codelineno-8-18" name = "__codelineno-8-18" href = "#__codelineno-8-18" > < / a > < span class = "kd" > let< / span > < span class = "nv" > a< / span > < span class = "p" > =< / span > < span class = "mi" > 0< / span > < span class = "c1" > // 暂存数据（常量）< / span >
< a id = "__codelineno-8-19" name = "__codelineno-8-19" href = "#__codelineno-8-19" > < / a > < span class = "kd" > var< / span > < span class = "nv" > b< / span > < span class = "p" > =< / span > < span class = "mi" > 0< / span > < span class = "c1" > // 暂存数据（变量）< / span >
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< a id = "__codelineno-8-20" name = "__codelineno-8-20" href = "#__codelineno-8-20" > < / a > < span class = "kd" > let< / span > < span class = "nv" > node< / span > < span class = "p" > =< / span > < span class = "n" > Node< / span > < span class = "p" > (< / span > < span class = "n" > x< / span > < span class = "p" > :< / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span > < span class = "c1" > // 暂存数据（对象）< / span >
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< a id = "__codelineno-8-21" name = "__codelineno-8-21" href = "#__codelineno-8-21" > < / a > < span class = "kd" > let< / span > < span class = "nv" > c< / span > < span class = "p" > =< / span > < span class = "n" > function< / span > < span class = "p" > ()< / span > < span class = "c1" > // 栈帧空间（调用函数）< / span >
< a id = "__codelineno-8-22" name = "__codelineno-8-22" href = "#__codelineno-8-22" > < / a > < span class = "k" > return< / span > < span class = "n" > a< / span > < span class = "o" > +< / span > < span class = "n" > b< / span > < span class = "o" > +< / span > < span class = "n" > c< / span > < span class = "c1" > // 输出数据< / span >
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< a id = "__codelineno-8-23" name = "__codelineno-8-23" href = "#__codelineno-8-23" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-9-1" name = "__codelineno-9-1" href = "#__codelineno-9-1" > < / a >
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
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< h2 id = "232" > 2.3.2. 推算方法< a class = "headerlink" href = "#232" title = "Permanent link" > ¶ < / a > < / h2 >
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< p > 空间复杂度的推算方法与时间复杂度大致相同，只是将统计对象从“计算操作数量”转为“使用空间大小”。与时间复杂度不同的是，< strong > 我们通常只关注「最差空间复杂度」< / strong > ，这是因为内存空间是一项硬性要求，我们必须确保在所有输入数据下都有足够的内存空间预留。< / p >
< p > < strong > 最差空间复杂度中的“最差”有两层含义< / strong > ，分别是输入数据的最差分布和算法运行过程中的最差时间点。< / p >
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< ul >
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< li > < strong > 以最差输入数据为准< / strong > 。当 < span class = "arithmatex" > \(n < 10\)< / span > 时，空间复杂度为 < span class = "arithmatex" > \(O(1)\)< / span > ；但当 < span class = "arithmatex" > \(n > 10\)< / span > 时，初始化的数组 < code > nums< / code > 占用 < span class = "arithmatex" > \(O(n)\)< / span > 空间；因此最差空间复杂度为 < span class = "arithmatex" > \(O(n)\)< / span > ； < / li >
< li > < strong > 以算法运行过程中的峰值内存为准< / strong > 。例如，程序在执行最后一行之前，占用 < span class = "arithmatex" > \(O(1)\)< / span > 空间；当初始化数组 < code > nums< / code > 时，程序占用 < span class = "arithmatex" > \(O(n)\)< / span > 空间；因此最差空间复杂度为 < span class = "arithmatex" > \(O(n)\)< / span > ； < / li >
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< / ul >
< div class = "tabbed-set tabbed-alternate" data-tabs = "2:10" > < input checked = "checked" id = "__tabbed_2_1" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_2" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_3" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_4" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_5" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_6" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_7" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_8" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_9" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_10" name = "__tabbed_2" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_2_1" > Java< / label > < label for = "__tabbed_2_2" > C++< / label > < label for = "__tabbed_2_3" > Python< / label > < label for = "__tabbed_2_4" > Go< / label > < label for = "__tabbed_2_5" > JavaScript< / label > < label for = "__tabbed_2_6" > TypeScript< / label > < label for = "__tabbed_2_7" > C< / label > < label for = "__tabbed_2_8" > C#< / label > < label for = "__tabbed_2_9" > Swift< / label > < label for = "__tabbed_2_10" > Zig< / label > < / div >
< div class = "tabbed-content" >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-10-1" name = "__codelineno-10-1" href = "#__codelineno-10-1" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > algorithm< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-10-2" name = "__codelineno-10-2" href = "#__codelineno-10-2" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > a< / 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 = "c1" > // O(1)< / span >
< a id = "__codelineno-10-3" name = "__codelineno-10-3" href = "#__codelineno-10-3" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "o" > []< / span > < span class = "w" > < / span > < span class = "n" > b< / 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" > 10000< / span > < span class = "o" > ]< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // O(1)< / span >
< a id = "__codelineno-10-4" name = "__codelineno-10-4" href = "#__codelineno-10-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > n< / 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-10-5" name = "__codelineno-10-5" href = "#__codelineno-10-5" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "o" > []< / span > < span class = "w" > < / span > < span class = "n" > nums< / 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 > < span class = "w" > < / span > < span class = "c1" > // O(n)< / span >
< a id = "__codelineno-10-6" name = "__codelineno-10-6" href = "#__codelineno-10-6" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-11-1" name = "__codelineno-11-1" href = "#__codelineno-11-1" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > algorithm< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-2" name = "__codelineno-11-2" href = "#__codelineno-11-2" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > a< / 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 = "c1" > // O(1)< / span >
< a id = "__codelineno-11-3" name = "__codelineno-11-3" href = "#__codelineno-11-3" > < / 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" > b< / span > < span class = "p" > (< / span > < span class = "mi" > 10000< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // O(1)< / span >
< a id = "__codelineno-11-4" name = "__codelineno-11-4" href = "#__codelineno-11-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > n< / 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-11-5" name = "__codelineno-11-5" href = "#__codelineno-11-5" > < / 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" > nums< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // O(n)< / span >
< a id = "__codelineno-11-6" name = "__codelineno-11-6" href = "#__codelineno-11-6" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-03-12 18:46:10 +08:00
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-12-1" name = "__codelineno-12-1" href = "#__codelineno-12-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > algorithm< / span > < span class = "p" > (< / span > < span class = "n" > n< / 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 >
2023-05-22 22:01:26 +08:00
< a id = "__codelineno-12-2" name = "__codelineno-12-2" href = "#__codelineno-12-2" > < / a > < span class = "n" > a< / span > < span class = "o" > =< / span > < span class = "mi" > 0< / span > < span class = "c1" > # O(1)< / span >
< a id = "__codelineno-12-3" name = "__codelineno-12-3" href = "#__codelineno-12-3" > < / a > < span class = "n" > b< / 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" > 10000< / span > < span class = "c1" > # O(1)< / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-12-4" name = "__codelineno-12-4" href = "#__codelineno-12-4" > < / a > < span class = "k" > if< / span > < span class = "n" > n< / span > < span class = "o" > > < / span > < span class = "mi" > 10< / span > < span class = "p" > :< / span >
2023-05-22 22:01:26 +08:00
< a id = "__codelineno-12-5" name = "__codelineno-12-5" href = "#__codelineno-12-5" > < / a > < span class = "n" > nums< / 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 > < span class = "c1" > # O(n)< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-13-1" name = "__codelineno-13-1" href = "#__codelineno-13-1" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > algorithm< / span > < span class = "p" > (< / span > < span class = "nx" > n< / 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-13-2" name = "__codelineno-13-2" href = "#__codelineno-13-2" > < / a > < span class = "w" > < / span > < span class = "nx" > a< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "w" > < / span > < span class = "c1" > // O(1)< / span >
< a id = "__codelineno-13-3" name = "__codelineno-13-3" href = "#__codelineno-13-3" > < / a > < span class = "w" > < / span > < span class = "nx" > b< / 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" > 10000< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "c1" > // O(1)< / span >
< a id = "__codelineno-13-4" name = "__codelineno-13-4" href = "#__codelineno-13-4" > < / a > < span class = "w" > < / span > < span class = "kd" > var< / span > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "w" > < / span > < span class = "p" > []< / span > < span class = "kt" > int< / span >
< a id = "__codelineno-13-5" name = "__codelineno-13-5" href = "#__codelineno-13-5" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "p" > > < / span > < span class = "w" > < / span > < span class = "mi" > 10< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-13-6" name = "__codelineno-13-6" href = "#__codelineno-13-6" > < / a > < span class = "w" > < / span > < span class = "nx" > nums< / 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 > < span class = "w" > < / span > < span class = "c1" > // O(n)< / span >
< a id = "__codelineno-13-7" name = "__codelineno-13-7" href = "#__codelineno-13-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-13-8" name = "__codelineno-13-8" href = "#__codelineno-13-8" > < / a > < span class = "w" > < / span > < span class = "nx" > fmt< / span > < span class = "p" > .< / span > < span class = "nx" > Println< / span > < span class = "p" > (< / span > < span class = "nx" > a< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > b< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "p" > )< / span >
< a id = "__codelineno-13-9" name = "__codelineno-13-9" href = "#__codelineno-13-9" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-14-1" name = "__codelineno-14-1" href = "#__codelineno-14-1" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > algorithm< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-14-2" name = "__codelineno-14-2" href = "#__codelineno-14-2" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > a< / 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 = "c1" > // O(1)< / span >
< a id = "__codelineno-14-3" name = "__codelineno-14-3" href = "#__codelineno-14-3" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > b< / 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" > 10000< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // O(1)< / span >
< a id = "__codelineno-14-4" name = "__codelineno-14-4" href = "#__codelineno-14-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > n< / 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-14-5" name = "__codelineno-14-5" href = "#__codelineno-14-5" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > nums< / 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 = "w" > < / span > < span class = "c1" > // O(n)< / span >
< a id = "__codelineno-14-6" name = "__codelineno-14-6" href = "#__codelineno-14-6" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-14-7" name = "__codelineno-14-7" href = "#__codelineno-14-7" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-15-1" name = "__codelineno-15-1" href = "#__codelineno-15-1" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > algorithm< / span > < span class = "p" > (< / span > < span class = "nx" > n< / 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-15-2" name = "__codelineno-15-2" href = "#__codelineno-15-2" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > a< / 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 = "c1" > // O(1)< / span >
< a id = "__codelineno-15-3" name = "__codelineno-15-3" href = "#__codelineno-15-3" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > b< / 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" > 10000< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // O(1)< / span >
< a id = "__codelineno-15-4" name = "__codelineno-15-4" href = "#__codelineno-15-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > n< / 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-15-5" name = "__codelineno-15-5" href = "#__codelineno-15-5" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > nums< / 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 = "w" > < / span > < span class = "c1" > // O(n)< / span >
< a id = "__codelineno-15-6" name = "__codelineno-15-6" href = "#__codelineno-15-6" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-15-7" name = "__codelineno-15-7" href = "#__codelineno-15-7" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-04-18 20:19:15 +08:00
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-16-1" name = "__codelineno-16-1" href = "#__codelineno-16-1" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > algorithm< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-16-2" name = "__codelineno-16-2" href = "#__codelineno-16-2" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > a< / 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 = "c1" > // O(1)< / span >
< a id = "__codelineno-16-3" name = "__codelineno-16-3" href = "#__codelineno-16-3" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > b< / span > < span class = "p" > [< / span > < span class = "mi" > 10000< / span > < span class = "p" > ];< / span > < span class = "w" > < / span > < span class = "c1" > // O(1)< / span >
< a id = "__codelineno-16-4" name = "__codelineno-16-4" href = "#__codelineno-16-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > n< / 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-16-5" name = "__codelineno-16-5" href = "#__codelineno-16-5" > < / 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" > nums< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // O(n)< / span >
< a id = "__codelineno-16-6" name = "__codelineno-16-6" href = "#__codelineno-16-6" > < / a > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-17-1" name = "__codelineno-17-1" href = "#__codelineno-17-1" > < / a > < span class = "k" > void< / span > < span class = "w" > < / span > < span class = "nf" > algorithm< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span >
< a id = "__codelineno-17-2" name = "__codelineno-17-2" href = "#__codelineno-17-2" > < / a > < span class = "p" > {< / span >
< a id = "__codelineno-17-3" name = "__codelineno-17-3" href = "#__codelineno-17-3" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > a< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // O(1)< / span >
< a id = "__codelineno-17-4" name = "__codelineno-17-4" href = "#__codelineno-17-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "n" > b< / 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 = "p" > [< / span > < span class = "m" > 10000< / span > < span class = "p" > ];< / span > < span class = "w" > < / span > < span class = "c1" > // O(1)< / span >
< a id = "__codelineno-17-5" name = "__codelineno-17-5" href = "#__codelineno-17-5" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "m" > 10< / span > < span class = "p" > )< / span >
< a id = "__codelineno-17-6" name = "__codelineno-17-6" href = "#__codelineno-17-6" > < / a > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-17-7" name = "__codelineno-17-7" href = "#__codelineno-17-7" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "n" > nums< / 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 = "p" > [< / span > < span class = "n" > n< / span > < span class = "p" > ];< / span > < span class = "w" > < / span > < span class = "c1" > // O(n)< / span >
< a id = "__codelineno-17-8" name = "__codelineno-17-8" href = "#__codelineno-17-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-17-9" name = "__codelineno-17-9" href = "#__codelineno-17-9" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-18-1" name = "__codelineno-18-1" href = "#__codelineno-18-1" > < / a > < span class = "kd" > func< / span > < span class = "nf" > algorithm< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / span > < span class = "p" > )< / span > < span class = "p" > {< / span >
< a id = "__codelineno-18-2" name = "__codelineno-18-2" href = "#__codelineno-18-2" > < / a > < span class = "kd" > let< / span > < span class = "nv" > a< / span > < span class = "p" > =< / span > < span class = "mi" > 0< / span > < span class = "c1" > // O(1)< / span >
< a id = "__codelineno-18-3" name = "__codelineno-18-3" href = "#__codelineno-18-3" > < / a > < span class = "kd" > let< / span > < span class = "nv" > b< / 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" > 10000< / span > < span class = "p" > )< / span > < span class = "c1" > // O(1)< / span >
< a id = "__codelineno-18-4" name = "__codelineno-18-4" href = "#__codelineno-18-4" > < / a > < span class = "k" > if< / span > < span class = "n" > n< / span > < span class = "o" > > < / span > < span class = "mi" > 10< / span > < span class = "p" > {< / span >
< a id = "__codelineno-18-5" name = "__codelineno-18-5" href = "#__codelineno-18-5" > < / a > < span class = "kd" > let< / span > < span class = "nv" > nums< / 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 > < span class = "c1" > // O(n)< / span >
< a id = "__codelineno-18-6" name = "__codelineno-18-6" href = "#__codelineno-18-6" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-18-7" name = "__codelineno-18-7" href = "#__codelineno-18-7" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-19-1" name = "__codelineno-19-1" href = "#__codelineno-19-1" > < / a >
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
2023-04-10 03:12:10 +08:00
< p > < strong > 在递归函数中，需要注意统计栈帧空间< / strong > 。例如，函数 < code > loop()< / code > 在循环中调用了 < span class = "arithmatex" > \(n\)< / span > 次 < code > function()< / code > ，每轮中的 < code > function()< / code > 都返回并释放了栈帧空间，因此空间复杂度仍为 < span class = "arithmatex" > \(O(1)\)< / span > 。而递归函数 < code > recur()< / code > 在运行过程中会同时存在 < span class = "arithmatex" > \(n\)< / span > 个未返回的 < code > recur()< / code > ，从而占用 < span class = "arithmatex" > \(O(n)\)< / span > 的栈帧空间。< / p >
2023-02-08 14:54:41 +08:00
< div class = "tabbed-set tabbed-alternate" data-tabs = "3:10" > < input checked = "checked" id = "__tabbed_3_1" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_2" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_3" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_4" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_5" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_6" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_7" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_8" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_9" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_10" name = "__tabbed_3" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_3_1" > Java< / label > < label for = "__tabbed_3_2" > C++< / label > < label for = "__tabbed_3_3" > Python< / label > < label for = "__tabbed_3_4" > Go< / label > < label for = "__tabbed_3_5" > JavaScript< / label > < label for = "__tabbed_3_6" > TypeScript< / label > < label for = "__tabbed_3_7" > C< / label > < label for = "__tabbed_3_8" > C#< / label > < label for = "__tabbed_3_9" > Swift< / label > < label for = "__tabbed_3_10" > Zig< / label > < / div >
< div class = "tabbed-content" >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-20-1" name = "__codelineno-20-1" href = "#__codelineno-20-1" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > function< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-20-2" name = "__codelineno-20-2" href = "#__codelineno-20-2" > < / a > < span class = "w" > < / span > < span class = "c1" > // do something< / span >
< a id = "__codelineno-20-3" name = "__codelineno-20-3" href = "#__codelineno-20-3" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-20-4" name = "__codelineno-20-4" href = "#__codelineno-20-4" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-20-5" name = "__codelineno-20-5" href = "#__codelineno-20-5" > < / a > < span class = "cm" > /* 循环 O(1) */< / span >
< a id = "__codelineno-20-6" name = "__codelineno-20-6" href = "#__codelineno-20-6" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > loop< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-20-7" name = "__codelineno-20-7" href = "#__codelineno-20-7" > < / 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-20-8" name = "__codelineno-20-8" href = "#__codelineno-20-8" > < / a > < span class = "w" > < / span > < span class = "n" > function< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-20-9" name = "__codelineno-20-9" href = "#__codelineno-20-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-20-10" name = "__codelineno-20-10" href = "#__codelineno-20-10" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-20-11" name = "__codelineno-20-11" href = "#__codelineno-20-11" > < / a > < span class = "cm" > /* 递归 O(n) */< / span >
< a id = "__codelineno-20-12" name = "__codelineno-20-12" href = "#__codelineno-20-12" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > recur< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-20-13" name = "__codelineno-20-13" href = "#__codelineno-20-13" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / 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 = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-20-14" name = "__codelineno-20-14" href = "#__codelineno-20-14" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > recur< / span > < span class = "p" > (< / 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-20-15" name = "__codelineno-20-15" href = "#__codelineno-20-15" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-21-1" name = "__codelineno-21-1" href = "#__codelineno-21-1" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > func< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-21-2" name = "__codelineno-21-2" href = "#__codelineno-21-2" > < / a > < span class = "w" > < / span > < span class = "c1" > // do something< / span >
< a id = "__codelineno-21-3" name = "__codelineno-21-3" href = "#__codelineno-21-3" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-21-4" name = "__codelineno-21-4" href = "#__codelineno-21-4" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-21-5" name = "__codelineno-21-5" href = "#__codelineno-21-5" > < / a > < span class = "cm" > /* 循环 O(1) */< / span >
< a id = "__codelineno-21-6" name = "__codelineno-21-6" href = "#__codelineno-21-6" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > loop< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-21-7" name = "__codelineno-21-7" href = "#__codelineno-21-7" > < / 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-21-8" name = "__codelineno-21-8" href = "#__codelineno-21-8" > < / a > < span class = "w" > < / span > < span class = "n" > func< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-21-9" name = "__codelineno-21-9" href = "#__codelineno-21-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-21-10" name = "__codelineno-21-10" href = "#__codelineno-21-10" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-21-11" name = "__codelineno-21-11" href = "#__codelineno-21-11" > < / a > < span class = "cm" > /* 递归 O(n) */< / span >
< a id = "__codelineno-21-12" name = "__codelineno-21-12" href = "#__codelineno-21-12" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > recur< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-21-13" name = "__codelineno-21-13" href = "#__codelineno-21-13" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / 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 = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-21-14" name = "__codelineno-21-14" href = "#__codelineno-21-14" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > recur< / span > < span class = "p" > (< / 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-21-15" name = "__codelineno-21-15" href = "#__codelineno-21-15" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-03-12 18:46:10 +08:00
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-22-1" name = "__codelineno-22-1" href = "#__codelineno-22-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > function< / span > < span class = "p" > ()< / span > < span class = "o" > -> < / span > < span class = "nb" > int< / span > < span class = "p" > :< / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-22-2" name = "__codelineno-22-2" href = "#__codelineno-22-2" > < / a > < span class = "c1" > # do something< / span >
< a id = "__codelineno-22-3" name = "__codelineno-22-3" href = "#__codelineno-22-3" > < / a > < span class = "k" > return< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-22-4" name = "__codelineno-22-4" href = "#__codelineno-22-4" > < / a >
2023-04-09 05:30:54 +08:00
< a id = "__codelineno-22-5" name = "__codelineno-22-5" href = "#__codelineno-22-5" > < / a > < span class = "k" > def< / span > < span class = "nf" > loop< / span > < span class = "p" > (< / span > < span class = "n" > n< / 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-22-6" name = "__codelineno-22-6" href = "#__codelineno-22-6" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 循环 O(1)" " " < / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-22-7" name = "__codelineno-22-7" href = "#__codelineno-22-7" > < / a > < span class = "k" > for< / span > < span class = "n" > _< / 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-22-8" name = "__codelineno-22-8" href = "#__codelineno-22-8" > < / a > < span class = "n" > function< / span > < span class = "p" > ()< / span >
< a id = "__codelineno-22-9" name = "__codelineno-22-9" href = "#__codelineno-22-9" > < / a >
2023-04-09 05:30:54 +08:00
< a id = "__codelineno-22-10" name = "__codelineno-22-10" href = "#__codelineno-22-10" > < / a > < span class = "k" > def< / span > < span class = "nf" > recur< / span > < span class = "p" > (< / span > < span class = "n" > n< / 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-22-11" name = "__codelineno-22-11" href = "#__codelineno-22-11" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 递归 O(n)" " " < / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-22-12" name = "__codelineno-22-12" href = "#__codelineno-22-12" > < / a > < span class = "k" > if< / span > < span class = "n" > n< / span > < span class = "o" > ==< / span > < span class = "mi" > 1< / span > < span class = "p" > :< / span > < span class = "k" > return< / span >
< a id = "__codelineno-22-13" name = "__codelineno-22-13" href = "#__codelineno-22-13" > < / a > < span class = "k" > return< / span > < span class = "n" > recur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-23-1" name = "__codelineno-23-1" href = "#__codelineno-23-1" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > function< / 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-23-2" name = "__codelineno-23-2" href = "#__codelineno-23-2" > < / a > < span class = "w" > < / span > < span class = "c1" > // do something< / span >
< a id = "__codelineno-23-3" name = "__codelineno-23-3" href = "#__codelineno-23-3" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-23-4" name = "__codelineno-23-4" href = "#__codelineno-23-4" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-23-5" name = "__codelineno-23-5" href = "#__codelineno-23-5" > < / a >
< a id = "__codelineno-23-6" name = "__codelineno-23-6" href = "#__codelineno-23-6" > < / a > < span class = "cm" > /* 循环 O(1) */< / span >
< a id = "__codelineno-23-7" name = "__codelineno-23-7" href = "#__codelineno-23-7" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > loop< / span > < span class = "p" > (< / span > < span class = "nx" > n< / 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-23-8" name = "__codelineno-23-8" href = "#__codelineno-23-8" > < / 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-23-9" name = "__codelineno-23-9" href = "#__codelineno-23-9" > < / a > < span class = "w" > < / span > < span class = "nx" > function< / span > < span class = "p" > ()< / span >
< a id = "__codelineno-23-10" name = "__codelineno-23-10" href = "#__codelineno-23-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-23-11" name = "__codelineno-23-11" href = "#__codelineno-23-11" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-23-12" name = "__codelineno-23-12" href = "#__codelineno-23-12" > < / a >
< a id = "__codelineno-23-13" name = "__codelineno-23-13" href = "#__codelineno-23-13" > < / a > < span class = "cm" > /* 递归 O(n) */< / span >
< a id = "__codelineno-23-14" name = "__codelineno-23-14" href = "#__codelineno-23-14" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > recur< / span > < span class = "p" > (< / span > < span class = "nx" > n< / 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-23-15" name = "__codelineno-23-15" href = "#__codelineno-23-15" > < / a > < span class = "w" > < / span > < span class = "k" > if< / 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 = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-23-16" name = "__codelineno-23-16" href = "#__codelineno-23-16" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span >
< a id = "__codelineno-23-17" name = "__codelineno-23-17" href = "#__codelineno-23-17" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-23-18" name = "__codelineno-23-18" href = "#__codelineno-23-18" > < / a > < span class = "w" > < / span > < span class = "nx" > recur< / span > < span class = "p" > (< / 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 >
< a id = "__codelineno-23-19" name = "__codelineno-23-19" href = "#__codelineno-23-19" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-24-1" name = "__codelineno-24-1" href = "#__codelineno-24-1" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > constFunc< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-24-2" name = "__codelineno-24-2" href = "#__codelineno-24-2" > < / a > < span class = "w" > < / span > < span class = "c1" > // do something< / span >
< a id = "__codelineno-24-3" name = "__codelineno-24-3" href = "#__codelineno-24-3" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-24-4" name = "__codelineno-24-4" href = "#__codelineno-24-4" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-24-5" name = "__codelineno-24-5" href = "#__codelineno-24-5" > < / a > < span class = "cm" > /* 循环 O(1) */< / span >
< a id = "__codelineno-24-6" name = "__codelineno-24-6" href = "#__codelineno-24-6" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > loop< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-24-7" name = "__codelineno-24-7" href = "#__codelineno-24-7" > < / 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-24-8" name = "__codelineno-24-8" href = "#__codelineno-24-8" > < / a > < span class = "w" > < / span > < span class = "nx" > constFunc< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-24-9" name = "__codelineno-24-9" href = "#__codelineno-24-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-24-10" name = "__codelineno-24-10" href = "#__codelineno-24-10" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-24-11" name = "__codelineno-24-11" href = "#__codelineno-24-11" > < / a > < span class = "cm" > /* 递归 O(n) */< / span >
< a id = "__codelineno-24-12" name = "__codelineno-24-12" href = "#__codelineno-24-12" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > recur< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-24-13" name = "__codelineno-24-13" href = "#__codelineno-24-13" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / 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 = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-24-14" name = "__codelineno-24-14" href = "#__codelineno-24-14" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > recur< / span > < span class = "p" > (< / 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 >
< a id = "__codelineno-24-15" name = "__codelineno-24-15" href = "#__codelineno-24-15" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-25-1" name = "__codelineno-25-1" href = "#__codelineno-25-1" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > constFunc< / 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-25-2" name = "__codelineno-25-2" href = "#__codelineno-25-2" > < / a > < span class = "w" > < / span > < span class = "c1" > // do something< / span >
< a id = "__codelineno-25-3" name = "__codelineno-25-3" href = "#__codelineno-25-3" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-25-4" name = "__codelineno-25-4" href = "#__codelineno-25-4" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-25-5" name = "__codelineno-25-5" href = "#__codelineno-25-5" > < / a > < span class = "cm" > /* 循环 O(1) */< / span >
< a id = "__codelineno-25-6" name = "__codelineno-25-6" href = "#__codelineno-25-6" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > loop< / span > < span class = "p" > (< / span > < span class = "nx" > n< / 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-25-7" name = "__codelineno-25-7" href = "#__codelineno-25-7" > < / 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-25-8" name = "__codelineno-25-8" href = "#__codelineno-25-8" > < / a > < span class = "w" > < / span > < span class = "nx" > constFunc< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-25-9" name = "__codelineno-25-9" href = "#__codelineno-25-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-25-10" name = "__codelineno-25-10" href = "#__codelineno-25-10" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-25-11" name = "__codelineno-25-11" href = "#__codelineno-25-11" > < / a > < span class = "cm" > /* 递归 O(n) */< / span >
< a id = "__codelineno-25-12" name = "__codelineno-25-12" href = "#__codelineno-25-12" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > recur< / span > < span class = "p" > (< / span > < span class = "nx" > n< / 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-25-13" name = "__codelineno-25-13" href = "#__codelineno-25-13" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / 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 = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-25-14" name = "__codelineno-25-14" href = "#__codelineno-25-14" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > recur< / span > < span class = "p" > (< / 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 >
< a id = "__codelineno-25-15" name = "__codelineno-25-15" href = "#__codelineno-25-15" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-04-18 20:19:15 +08:00
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-26-1" name = "__codelineno-26-1" href = "#__codelineno-26-1" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > func< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-26-2" name = "__codelineno-26-2" href = "#__codelineno-26-2" > < / a > < span class = "w" > < / span > < span class = "c1" > // do something< / span >
< a id = "__codelineno-26-3" name = "__codelineno-26-3" href = "#__codelineno-26-3" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-26-4" name = "__codelineno-26-4" href = "#__codelineno-26-4" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-26-5" name = "__codelineno-26-5" href = "#__codelineno-26-5" > < / a > < span class = "cm" > /* 循环 O(1) */< / span >
< a id = "__codelineno-26-6" name = "__codelineno-26-6" href = "#__codelineno-26-6" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > loop< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-26-7" name = "__codelineno-26-7" href = "#__codelineno-26-7" > < / 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-26-8" name = "__codelineno-26-8" href = "#__codelineno-26-8" > < / a > < span class = "w" > < / span > < span class = "n" > func< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-26-9" name = "__codelineno-26-9" href = "#__codelineno-26-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-26-10" name = "__codelineno-26-10" href = "#__codelineno-26-10" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-26-11" name = "__codelineno-26-11" href = "#__codelineno-26-11" > < / a > < span class = "cm" > /* 递归 O(n) */< / span >
< a id = "__codelineno-26-12" name = "__codelineno-26-12" href = "#__codelineno-26-12" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > recur< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-26-13" name = "__codelineno-26-13" href = "#__codelineno-26-13" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / 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 = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-26-14" name = "__codelineno-26-14" href = "#__codelineno-26-14" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > recur< / span > < span class = "p" > (< / 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-26-15" name = "__codelineno-26-15" href = "#__codelineno-26-15" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-27-1" name = "__codelineno-27-1" href = "#__codelineno-27-1" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > function< / span > < span class = "p" > ()< / span >
< a id = "__codelineno-27-2" name = "__codelineno-27-2" href = "#__codelineno-27-2" > < / a > < span class = "p" > {< / span >
< a id = "__codelineno-27-3" name = "__codelineno-27-3" href = "#__codelineno-27-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // do something< / span >
< a id = "__codelineno-27-4" name = "__codelineno-27-4" href = "#__codelineno-27-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-27-5" name = "__codelineno-27-5" href = "#__codelineno-27-5" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-27-6" name = "__codelineno-27-6" href = "#__codelineno-27-6" > < / a > < span class = "cm" > /* 循环 O(1) */< / span >
< a id = "__codelineno-27-7" name = "__codelineno-27-7" href = "#__codelineno-27-7" > < / a > < span class = "k" > void< / span > < span class = "w" > < / span > < span class = "nf" > loop< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span >
< a id = "__codelineno-27-8" name = "__codelineno-27-8" href = "#__codelineno-27-8" > < / a > < span class = "p" > {< / span >
< a id = "__codelineno-27-9" name = "__codelineno-27-9" href = "#__codelineno-27-9" > < / 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 = "m" > 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-27-10" name = "__codelineno-27-10" href = "#__codelineno-27-10" > < / a > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-27-11" name = "__codelineno-27-11" href = "#__codelineno-27-11" > < / a > < span class = "w" > < / span > < span class = "n" > function< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-27-12" name = "__codelineno-27-12" href = "#__codelineno-27-12" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-27-13" name = "__codelineno-27-13" href = "#__codelineno-27-13" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-27-14" name = "__codelineno-27-14" href = "#__codelineno-27-14" > < / a > < span class = "cm" > /* 递归 O(n) */< / span >
< a id = "__codelineno-27-15" name = "__codelineno-27-15" href = "#__codelineno-27-15" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > recur< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span >
< a id = "__codelineno-27-16" name = "__codelineno-27-16" href = "#__codelineno-27-16" > < / a > < span class = "p" > {< / span >
< a id = "__codelineno-27-17" name = "__codelineno-27-17" href = "#__codelineno-27-17" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-27-18" name = "__codelineno-27-18" href = "#__codelineno-27-18" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nf" > recur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > );< / span >
< a id = "__codelineno-27-19" name = "__codelineno-27-19" href = "#__codelineno-27-19" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-28-1" name = "__codelineno-28-1" href = "#__codelineno-28-1" > < / a > < span class = "p" > @< / span > < span class = "n" > discardableResult< / span >
< a id = "__codelineno-28-2" name = "__codelineno-28-2" href = "#__codelineno-28-2" > < / a > < span class = "kd" > func< / span > < span class = "nf" > function< / span > < span class = "p" > ()< / span > < span class = "p" > -> < / span > < span class = "nb" > Int< / span > < span class = "p" > {< / span >
< a id = "__codelineno-28-3" name = "__codelineno-28-3" href = "#__codelineno-28-3" > < / a > < span class = "c1" > // do something< / span >
< a id = "__codelineno-28-4" name = "__codelineno-28-4" href = "#__codelineno-28-4" > < / a > < span class = "k" > return< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-28-5" name = "__codelineno-28-5" href = "#__codelineno-28-5" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-28-6" name = "__codelineno-28-6" href = "#__codelineno-28-6" > < / a >
< a id = "__codelineno-28-7" name = "__codelineno-28-7" href = "#__codelineno-28-7" > < / a > < span class = "cm" > /* 循环 O(1) */< / span >
< a id = "__codelineno-28-8" name = "__codelineno-28-8" href = "#__codelineno-28-8" > < / a > < span class = "kd" > func< / span > < span class = "nf" > loop< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / span > < span class = "p" > )< / span > < span class = "p" > {< / span >
< a id = "__codelineno-28-9" name = "__codelineno-28-9" href = "#__codelineno-28-9" > < / a > < span class = "k" > for< / span > < span class = "kc" > _< / span > < span class = "k" > in< / span > < span class = "mi" > 0< / span > < span class = "p" > ..< / span > < span class = "o" > < < / span > < span class = "n" > n< / span > < span class = "p" > {< / span >
< a id = "__codelineno-28-10" name = "__codelineno-28-10" href = "#__codelineno-28-10" > < / a > < span class = "n" > function< / span > < span class = "p" > ()< / span >
< a id = "__codelineno-28-11" name = "__codelineno-28-11" href = "#__codelineno-28-11" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-28-12" name = "__codelineno-28-12" href = "#__codelineno-28-12" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-28-13" name = "__codelineno-28-13" href = "#__codelineno-28-13" > < / a >
< a id = "__codelineno-28-14" name = "__codelineno-28-14" href = "#__codelineno-28-14" > < / a > < span class = "cm" > /* 递归 O(n) */< / span >
< a id = "__codelineno-28-15" name = "__codelineno-28-15" href = "#__codelineno-28-15" > < / a > < span class = "kd" > func< / span > < span class = "nf" > recur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / span > < span class = "p" > )< / span > < span class = "p" > {< / span >
< a id = "__codelineno-28-16" name = "__codelineno-28-16" href = "#__codelineno-28-16" > < / a > < span class = "k" > if< / span > < span class = "n" > n< / span > < span class = "p" > ==< / span > < span class = "mi" > 1< / span > < span class = "p" > {< / span >
< a id = "__codelineno-28-17" name = "__codelineno-28-17" href = "#__codelineno-28-17" > < / a > < span class = "k" > return< / span >
< a id = "__codelineno-28-18" name = "__codelineno-28-18" href = "#__codelineno-28-18" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-28-19" name = "__codelineno-28-19" href = "#__codelineno-28-19" > < / a > < span class = "n" > recur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > :< / span > < span class = "n" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span >
< a id = "__codelineno-28-20" name = "__codelineno-28-20" href = "#__codelineno-28-20" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-29-1" name = "__codelineno-29-1" href = "#__codelineno-29-1" > < / a >
< / code > < / pre > < / div >
< / div >
< / div >
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< h2 id = "233" > 2.3.3. 常见类型< a class = "headerlink" href = "#233" title = "Permanent link" > ¶ < / a > < / h2 >
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< p > 设输入数据大小为 < span class = "arithmatex" > \(n\)< / span > ，常见的空间复杂度类型有（从低到高排列）< / p >
< div class = "arithmatex" > \[
\begin{aligned}
O(1) < O(\log n) < O(n) < O(n^2) < O(2^n) \newline
\text{常数阶} < \text{对数阶} < \text{线性阶} < \text{平方阶} < \text{指数阶}
\end{aligned}
\]< / div >
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< p > < img alt = "空间复杂度的常见类型" src = "../space_complexity.assets/space_complexity_common_types.png" / > < / p >
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< p align = "center" > Fig. 空间复杂度的常见类型 < / p >
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< div class = "admonition tip" >
< p class = "admonition-title" > Tip< / p >
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< p > 部分示例代码需要一些前置知识，包括数组、链表、二叉树、递归算法等。如果遇到看不懂的地方无需担心，可以在学习完后面章节后再来复习，现阶段我们先专注于理解空间复杂度的含义和推算方法。< / p >
2023-02-08 14:54:41 +08:00
< / div >
< h3 id = "o1" > 常数阶 < span class = "arithmatex" > \(O(1)\)< / span > < a class = "headerlink" href = "#o1" title = "Permanent link" > ¶ < / a > < / h3 >
< p > 常数阶常见于数量与输入数据大小 < span class = "arithmatex" > \(n\)< / span > 无关的常量、变量、对象。< / p >
< p > 需要注意的是，在循环中初始化变量或调用函数而占用的内存，在进入下一循环后就会被释放，即不会累积占用空间，空间复杂度仍为 < span class = "arithmatex" > \(O(1)\)< / span > 。< / p >
< div class = "tabbed-set tabbed-alternate" data-tabs = "4:10" > < input checked = "checked" id = "__tabbed_4_1" name = "__tabbed_4" type = "radio" / > < input id = "__tabbed_4_2" name = "__tabbed_4" type = "radio" / > < input id = "__tabbed_4_3" name = "__tabbed_4" type = "radio" / > < input id = "__tabbed_4_4" name = "__tabbed_4" type = "radio" / > < input id = "__tabbed_4_5" name = "__tabbed_4" type = "radio" / > < input id = "__tabbed_4_6" name = "__tabbed_4" type = "radio" / > < input id = "__tabbed_4_7" name = "__tabbed_4" type = "radio" / > < input id = "__tabbed_4_8" name = "__tabbed_4" type = "radio" / > < input id = "__tabbed_4_9" name = "__tabbed_4" type = "radio" / > < input id = "__tabbed_4_10" name = "__tabbed_4" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_4_1" > Java< / label > < label for = "__tabbed_4_2" > C++< / label > < label for = "__tabbed_4_3" > Python< / label > < label for = "__tabbed_4_4" > Go< / label > < label for = "__tabbed_4_5" > JavaScript< / label > < label for = "__tabbed_4_6" > TypeScript< / label > < label for = "__tabbed_4_7" > C< / label > < label for = "__tabbed_4_8" > C#< / label > < label for = "__tabbed_4_9" > Swift< / label > < label for = "__tabbed_4_10" > Zig< / label > < / div >
< div class = "tabbed-content" >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-30-1" name = "__codelineno-30-1" href = "#__codelineno-30-1" > < / a > < span class = "cm" > /* 常数阶 */< / span >
< a id = "__codelineno-30-2" name = "__codelineno-30-2" href = "#__codelineno-30-2" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > constant< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-30-3" name = "__codelineno-30-3" href = "#__codelineno-30-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 常量、变量、对象占用 O(1) 空间< / span >
< a id = "__codelineno-30-4" name = "__codelineno-30-4" href = "#__codelineno-30-4" > < / a > < span class = "w" > < / span > < span class = "kd" > final< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > a< / 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-30-5" name = "__codelineno-30-5" href = "#__codelineno-30-5" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > b< / 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-30-6" name = "__codelineno-30-6" href = "#__codelineno-30-6" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "o" > []< / span > < span class = "w" > < / span > < span class = "n" > nums< / 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" > 10000< / span > < span class = "o" > ]< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-30-7" name = "__codelineno-30-7" href = "#__codelineno-30-7" > < / a > < span class = "w" > < / span > < span class = "n" > ListNode< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > ListNode< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > );< / span >
< a id = "__codelineno-30-8" name = "__codelineno-30-8" href = "#__codelineno-30-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环中的变量占用 O(1) 空间< / span >
< a id = "__codelineno-30-9" name = "__codelineno-30-9" href = "#__codelineno-30-9" > < / 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-30-10" name = "__codelineno-30-10" href = "#__codelineno-30-10" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > c< / 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-30-11" name = "__codelineno-30-11" href = "#__codelineno-30-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-30-12" name = "__codelineno-30-12" href = "#__codelineno-30-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环中的函数占用 O(1) 空间< / span >
< a id = "__codelineno-30-13" name = "__codelineno-30-13" href = "#__codelineno-30-13" > < / 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-30-14" name = "__codelineno-30-14" href = "#__codelineno-30-14" > < / a > < span class = "w" > < / span > < span class = "n" > function< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-30-15" name = "__codelineno-30-15" href = "#__codelineno-30-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-30-16" name = "__codelineno-30-16" href = "#__codelineno-30-16" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-31-1" name = "__codelineno-31-1" href = "#__codelineno-31-1" > < / a > < span class = "cm" > /* 常数阶 */< / span >
< a id = "__codelineno-31-2" name = "__codelineno-31-2" href = "#__codelineno-31-2" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > constant< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-31-3" name = "__codelineno-31-3" href = "#__codelineno-31-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 常量、变量、对象占用 O(1) 空间< / span >
< a id = "__codelineno-31-4" name = "__codelineno-31-4" href = "#__codelineno-31-4" > < / a > < span class = "w" > < / span > < span class = "k" > const< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > a< / 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-31-5" name = "__codelineno-31-5" href = "#__codelineno-31-5" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > b< / 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-31-6" name = "__codelineno-31-6" href = "#__codelineno-31-6" > < / 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" > nums< / span > < span class = "p" > (< / span > < span class = "mi" > 10000< / span > < span class = "p" > );< / span >
< a id = "__codelineno-31-7" name = "__codelineno-31-7" href = "#__codelineno-31-7" > < / a > < span class = "w" > < / span > < span class = "n" > ListNode< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > );< / span >
< a id = "__codelineno-31-8" name = "__codelineno-31-8" href = "#__codelineno-31-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环中的变量占用 O(1) 空间< / span >
< a id = "__codelineno-31-9" name = "__codelineno-31-9" href = "#__codelineno-31-9" > < / 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-31-10" name = "__codelineno-31-10" href = "#__codelineno-31-10" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > c< / 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-31-11" name = "__codelineno-31-11" href = "#__codelineno-31-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-31-12" name = "__codelineno-31-12" href = "#__codelineno-31-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环中的函数占用 O(1) 空间< / span >
< a id = "__codelineno-31-13" name = "__codelineno-31-13" href = "#__codelineno-31-13" > < / 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-31-14" name = "__codelineno-31-14" href = "#__codelineno-31-14" > < / a > < span class = "w" > < / span > < span class = "n" > func< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-31-15" name = "__codelineno-31-15" href = "#__codelineno-31-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-31-16" name = "__codelineno-31-16" href = "#__codelineno-31-16" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-03-12 18:46:10 +08:00
< div class = "highlight" > < span class = "filename" > space_complexity.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-32-1" name = "__codelineno-32-1" href = "#__codelineno-32-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > constant< / span > < span class = "p" > (< / span > < span class = "n" > n< / 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 >
2023-04-09 05:12:29 +08:00
< a id = "__codelineno-32-2" name = "__codelineno-32-2" href = "#__codelineno-32-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 常数阶" " " < / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-32-3" name = "__codelineno-32-3" href = "#__codelineno-32-3" > < / a > < span class = "c1" > # 常量、变量、对象占用 O(1) 空间< / span >
2023-05-22 22:01:26 +08:00
< a id = "__codelineno-32-4" name = "__codelineno-32-4" href = "#__codelineno-32-4" > < / a > < span class = "n" > a< / span > < span class = "o" > =< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-32-5" name = "__codelineno-32-5" href = "#__codelineno-32-5" > < / a > < span class = "n" > nums< / 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" > 10000< / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-32-6" name = "__codelineno-32-6" href = "#__codelineno-32-6" > < / a > < span class = "n" > node< / span > < span class = "o" > =< / span > < span class = "n" > ListNode< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span >
< a id = "__codelineno-32-7" name = "__codelineno-32-7" href = "#__codelineno-32-7" > < / a > < span class = "c1" > # 循环中的变量占用 O(1) 空间< / span >
< a id = "__codelineno-32-8" name = "__codelineno-32-8" href = "#__codelineno-32-8" > < / a > < span class = "k" > for< / span > < span class = "n" > _< / span > < span class = "ow" > in< / span > < span class = "nb" > range< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > ):< / span >
2023-05-22 22:01:26 +08:00
< a id = "__codelineno-32-9" name = "__codelineno-32-9" href = "#__codelineno-32-9" > < / a > < span class = "n" > c< / span > < span class = "o" > =< / span > < span class = "mi" > 0< / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-32-10" name = "__codelineno-32-10" href = "#__codelineno-32-10" > < / a > < span class = "c1" > # 循环中的函数占用 O(1) 空间< / span >
< a id = "__codelineno-32-11" name = "__codelineno-32-11" href = "#__codelineno-32-11" > < / a > < span class = "k" > for< / span > < span class = "n" > _< / 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-32-12" name = "__codelineno-32-12" href = "#__codelineno-32-12" > < / a > < span class = "n" > function< / span > < span class = "p" > ()< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-33-1" name = "__codelineno-33-1" href = "#__codelineno-33-1" > < / a > < span class = "cm" > /* 常数阶 */< / span >
< a id = "__codelineno-33-2" name = "__codelineno-33-2" href = "#__codelineno-33-2" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > spaceConstant< / span > < span class = "p" > (< / span > < span class = "nx" > n< / 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-33-3" name = "__codelineno-33-3" href = "#__codelineno-33-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 常量、变量、对象占用 O(1) 空间< / span >
< a id = "__codelineno-33-4" name = "__codelineno-33-4" href = "#__codelineno-33-4" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > a< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-33-5" name = "__codelineno-33-5" href = "#__codelineno-33-5" > < / a > < span class = "w" > < / span > < span class = "nx" > b< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-33-6" name = "__codelineno-33-6" href = "#__codelineno-33-6" > < / a > < span class = "w" > < / span > < span class = "nx" > nums< / 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" > 10000< / span > < span class = "p" > )< / span >
< a id = "__codelineno-33-7" name = "__codelineno-33-7" href = "#__codelineno-33-7" > < / a > < span class = "w" > < / span > < span class = "nx" > ListNode< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > newNode< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span >
< a id = "__codelineno-33-8" name = "__codelineno-33-8" href = "#__codelineno-33-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环中的变量占用 O(1) 空间< / span >
< a id = "__codelineno-33-9" name = "__codelineno-33-9" href = "#__codelineno-33-9" > < / a > < span class = "w" > < / span > < span class = "kd" > var< / span > < span class = "w" > < / span > < span class = "nx" > c< / span > < span class = "w" > < / span > < span class = "kt" > int< / span >
< a id = "__codelineno-33-10" name = "__codelineno-33-10" href = "#__codelineno-33-10" > < / 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-33-11" name = "__codelineno-33-11" href = "#__codelineno-33-11" > < / a > < span class = "w" > < / span > < span class = "nx" > c< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-33-12" name = "__codelineno-33-12" href = "#__codelineno-33-12" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-33-13" name = "__codelineno-33-13" href = "#__codelineno-33-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环中的函数占用 O(1) 空间< / span >
< a id = "__codelineno-33-14" name = "__codelineno-33-14" href = "#__codelineno-33-14" > < / 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-33-15" name = "__codelineno-33-15" href = "#__codelineno-33-15" > < / a > < span class = "w" > < / span > < span class = "nx" > function< / span > < span class = "p" > ()< / span >
< a id = "__codelineno-33-16" name = "__codelineno-33-16" href = "#__codelineno-33-16" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-33-17" name = "__codelineno-33-17" href = "#__codelineno-33-17" > < / a > < span class = "w" > < / span > < span class = "nx" > fmt< / span > < span class = "p" > .< / span > < span class = "nx" > Println< / span > < span class = "p" > (< / span > < span class = "nx" > a< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > b< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > c< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > ListNode< / span > < span class = "p" > )< / span >
< a id = "__codelineno-33-18" name = "__codelineno-33-18" href = "#__codelineno-33-18" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-34-1" name = "__codelineno-34-1" href = "#__codelineno-34-1" > < / a > < span class = "cm" > /* 常数阶 */< / span >
< a id = "__codelineno-34-2" name = "__codelineno-34-2" href = "#__codelineno-34-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > constant< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-34-3" name = "__codelineno-34-3" href = "#__codelineno-34-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 常量、变量、对象占用 O(1) 空间< / span >
< a id = "__codelineno-34-4" name = "__codelineno-34-4" href = "#__codelineno-34-4" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > a< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-34-5" name = "__codelineno-34-5" href = "#__codelineno-34-5" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > b< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-34-6" name = "__codelineno-34-6" href = "#__codelineno-34-6" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > nums< / 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" > 10000< / span > < span class = "p" > );< / span >
< a id = "__codelineno-34-7" name = "__codelineno-34-7" href = "#__codelineno-34-7" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "ow" > new< / span > < span class = "w" > < / span > < span class = "nx" > ListNode< / span > < span class = "p" > (< / span > < span class = "mf" > 0< / span > < span class = "p" > );< / span >
< a id = "__codelineno-34-8" name = "__codelineno-34-8" href = "#__codelineno-34-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环中的变量占用 O(1) 空间< / span >
< a id = "__codelineno-34-9" name = "__codelineno-34-9" href = "#__codelineno-34-9" > < / 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-34-10" name = "__codelineno-34-10" href = "#__codelineno-34-10" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > c< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-34-11" name = "__codelineno-34-11" href = "#__codelineno-34-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-34-12" name = "__codelineno-34-12" href = "#__codelineno-34-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环中的函数占用 O(1) 空间< / span >
< a id = "__codelineno-34-13" name = "__codelineno-34-13" href = "#__codelineno-34-13" > < / 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-34-14" name = "__codelineno-34-14" href = "#__codelineno-34-14" > < / a > < span class = "w" > < / span > < span class = "nx" > constFunc< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-34-15" name = "__codelineno-34-15" href = "#__codelineno-34-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-34-16" name = "__codelineno-34-16" href = "#__codelineno-34-16" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-35-1" name = "__codelineno-35-1" href = "#__codelineno-35-1" > < / a > < span class = "cm" > /* 常数阶 */< / span >
< a id = "__codelineno-35-2" name = "__codelineno-35-2" href = "#__codelineno-35-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > constant< / span > < span class = "p" > (< / span > < span class = "nx" > n< / 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-35-3" name = "__codelineno-35-3" href = "#__codelineno-35-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 常量、变量、对象占用 O(1) 空间< / span >
< a id = "__codelineno-35-4" name = "__codelineno-35-4" href = "#__codelineno-35-4" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > a< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-35-5" name = "__codelineno-35-5" href = "#__codelineno-35-5" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > b< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-35-6" name = "__codelineno-35-6" href = "#__codelineno-35-6" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > nums< / 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" > 10000< / span > < span class = "p" > );< / span >
< a id = "__codelineno-35-7" name = "__codelineno-35-7" href = "#__codelineno-35-7" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > node< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "ow" > new< / span > < span class = "w" > < / span > < span class = "nx" > ListNode< / span > < span class = "p" > (< / span > < span class = "mf" > 0< / span > < span class = "p" > );< / span >
< a id = "__codelineno-35-8" name = "__codelineno-35-8" href = "#__codelineno-35-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环中的变量占用 O(1) 空间< / span >
< a id = "__codelineno-35-9" name = "__codelineno-35-9" href = "#__codelineno-35-9" > < / 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-35-10" name = "__codelineno-35-10" href = "#__codelineno-35-10" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > c< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-35-11" name = "__codelineno-35-11" href = "#__codelineno-35-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-35-12" name = "__codelineno-35-12" href = "#__codelineno-35-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环中的函数占用 O(1) 空间< / span >
< a id = "__codelineno-35-13" name = "__codelineno-35-13" href = "#__codelineno-35-13" > < / 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-35-14" name = "__codelineno-35-14" href = "#__codelineno-35-14" > < / a > < span class = "w" > < / span > < span class = "nx" > constFunc< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-35-15" name = "__codelineno-35-15" href = "#__codelineno-35-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-35-16" name = "__codelineno-35-16" href = "#__codelineno-35-16" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-04-18 20:19:15 +08:00
< div class = "highlight" > < span class = "filename" > space_complexity.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-36-1" name = "__codelineno-36-1" href = "#__codelineno-36-1" > < / a > < span class = "cm" > /* 常数阶 */< / span >
< a id = "__codelineno-36-2" name = "__codelineno-36-2" href = "#__codelineno-36-2" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > constant< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-36-3" name = "__codelineno-36-3" href = "#__codelineno-36-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 常量、变量、对象占用 O(1) 空间< / span >
< a id = "__codelineno-36-4" name = "__codelineno-36-4" href = "#__codelineno-36-4" > < / a > < span class = "w" > < / span > < span class = "k" > const< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > a< / 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-36-5" name = "__codelineno-36-5" href = "#__codelineno-36-5" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > b< / 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-36-6" name = "__codelineno-36-6" href = "#__codelineno-36-6" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > [< / span > < span class = "mi" > 1000< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-36-7" name = "__codelineno-36-7" href = "#__codelineno-36-7" > < / a > < span class = "w" > < / span > < span class = "n" > ListNode< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > newListNode< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > );< / span >
< a id = "__codelineno-36-8" name = "__codelineno-36-8" href = "#__codelineno-36-8" > < / a > < span class = "w" > < / span > < span class = "n" > free< / span > < span class = "p" > (< / span > < span class = "n" > node< / span > < span class = "p" > );< / span >
< a id = "__codelineno-36-9" name = "__codelineno-36-9" href = "#__codelineno-36-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环中的变量占用 O(1) 空间< / span >
< a id = "__codelineno-36-10" name = "__codelineno-36-10" href = "#__codelineno-36-10" > < / 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-36-11" name = "__codelineno-36-11" href = "#__codelineno-36-11" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > c< / 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-36-12" name = "__codelineno-36-12" href = "#__codelineno-36-12" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-36-13" name = "__codelineno-36-13" href = "#__codelineno-36-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环中的函数占用 O(1) 空间< / span >
< a id = "__codelineno-36-14" name = "__codelineno-36-14" href = "#__codelineno-36-14" > < / 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-36-15" name = "__codelineno-36-15" href = "#__codelineno-36-15" > < / a > < span class = "w" > < / span > < span class = "n" > func< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-36-16" name = "__codelineno-36-16" href = "#__codelineno-36-16" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-36-17" name = "__codelineno-36-17" href = "#__codelineno-36-17" > < / a > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-37-1" name = "__codelineno-37-1" href = "#__codelineno-37-1" > < / a > < span class = "cm" > /* 常数阶 */< / span >
2023-04-23 14:58:11 +08:00
< a id = "__codelineno-37-2" name = "__codelineno-37-2" href = "#__codelineno-37-2" > < / a > < span class = "k" > void< / span > < span class = "w" > < / span > < span class = "nf" > constant< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-37-3" name = "__codelineno-37-3" href = "#__codelineno-37-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 常量、变量、对象占用 O(1) 空间< / span >
< a id = "__codelineno-37-4" name = "__codelineno-37-4" href = "#__codelineno-37-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > a< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-37-5" name = "__codelineno-37-5" href = "#__codelineno-37-5" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > b< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-37-6" name = "__codelineno-37-6" href = "#__codelineno-37-6" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "n" > nums< / 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 = "p" > [< / span > < span class = "m" > 10000< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-37-7" name = "__codelineno-37-7" href = "#__codelineno-37-7" > < / a > < span class = "w" > < / span > < span class = "n" > ListNode< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > ListNode< / span > < span class = "p" > (< / span > < span class = "m" > 0< / span > < span class = "p" > );< / span >
< a id = "__codelineno-37-8" name = "__codelineno-37-8" href = "#__codelineno-37-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环中的变量占用 O(1) 空间< / span >
< a id = "__codelineno-37-9" name = "__codelineno-37-9" href = "#__codelineno-37-9" > < / 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 = "m" > 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-37-10" name = "__codelineno-37-10" href = "#__codelineno-37-10" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > c< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-37-11" name = "__codelineno-37-11" href = "#__codelineno-37-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-37-12" name = "__codelineno-37-12" href = "#__codelineno-37-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环中的函数占用 O(1) 空间< / span >
< a id = "__codelineno-37-13" name = "__codelineno-37-13" href = "#__codelineno-37-13" > < / 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 = "m" > 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-37-14" name = "__codelineno-37-14" href = "#__codelineno-37-14" > < / a > < span class = "w" > < / span > < span class = "n" > function< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-37-15" name = "__codelineno-37-15" href = "#__codelineno-37-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-37-16" name = "__codelineno-37-16" href = "#__codelineno-37-16" > < / a > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-38-1" name = "__codelineno-38-1" href = "#__codelineno-38-1" > < / a > < span class = "cm" > /* 常数阶 */< / span >
< a id = "__codelineno-38-2" name = "__codelineno-38-2" href = "#__codelineno-38-2" > < / a > < span class = "kd" > func< / span > < span class = "nf" > constant< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / span > < span class = "p" > )< / span > < span class = "p" > {< / span >
< a id = "__codelineno-38-3" name = "__codelineno-38-3" href = "#__codelineno-38-3" > < / a > < span class = "c1" > // 常量、变量、对象占用 O(1) 空间< / span >
< a id = "__codelineno-38-4" name = "__codelineno-38-4" href = "#__codelineno-38-4" > < / a > < span class = "kd" > let< / span > < span class = "nv" > a< / span > < span class = "p" > =< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-38-5" name = "__codelineno-38-5" href = "#__codelineno-38-5" > < / a > < span class = "kd" > var< / span > < span class = "nv" > b< / span > < span class = "p" > =< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-38-6" name = "__codelineno-38-6" href = "#__codelineno-38-6" > < / a > < span class = "kd" > let< / span > < span class = "nv" > nums< / 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" > 10000< / span > < span class = "p" > )< / span >
< a id = "__codelineno-38-7" name = "__codelineno-38-7" href = "#__codelineno-38-7" > < / a > < span class = "kd" > let< / span > < span class = "nv" > node< / span > < span class = "p" > =< / span > < span class = "n" > ListNode< / span > < span class = "p" > (< / span > < span class = "n" > x< / span > < span class = "p" > :< / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span >
< a id = "__codelineno-38-8" name = "__codelineno-38-8" href = "#__codelineno-38-8" > < / a > < span class = "c1" > // 循环中的变量占用 O(1) 空间< / span >
< a id = "__codelineno-38-9" name = "__codelineno-38-9" href = "#__codelineno-38-9" > < / a > < span class = "k" > for< / span > < span class = "kc" > _< / span > < span class = "k" > in< / span > < span class = "mi" > 0< / span > < span class = "p" > ..< / span > < span class = "o" > < < / span > < span class = "n" > n< / span > < span class = "p" > {< / span >
< a id = "__codelineno-38-10" name = "__codelineno-38-10" href = "#__codelineno-38-10" > < / a > < span class = "kd" > let< / span > < span class = "nv" > c< / span > < span class = "p" > =< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-38-11" name = "__codelineno-38-11" href = "#__codelineno-38-11" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-38-12" name = "__codelineno-38-12" href = "#__codelineno-38-12" > < / a > < span class = "c1" > // 循环中的函数占用 O(1) 空间< / span >
< a id = "__codelineno-38-13" name = "__codelineno-38-13" href = "#__codelineno-38-13" > < / a > < span class = "k" > for< / span > < span class = "kc" > _< / span > < span class = "k" > in< / span > < span class = "mi" > 0< / span > < span class = "p" > ..< / span > < span class = "o" > < < / span > < span class = "n" > n< / span > < span class = "p" > {< / span >
< a id = "__codelineno-38-14" name = "__codelineno-38-14" href = "#__codelineno-38-14" > < / a > < span class = "n" > function< / span > < span class = "p" > ()< / span >
< a id = "__codelineno-38-15" name = "__codelineno-38-15" href = "#__codelineno-38-15" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-38-16" name = "__codelineno-38-16" href = "#__codelineno-38-16" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-39-1" name = "__codelineno-39-1" href = "#__codelineno-39-1" > < / a > < span class = "c1" > // 常数阶< / span >
< a id = "__codelineno-39-2" name = "__codelineno-39-2" href = "#__codelineno-39-2" > < / a > < span class = "k" > fn< / span > < span class = "w" > < / span > < span class = "n" > constant< / span > < span class = "p" > (< / span > < span class = "n" > n< / 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" > void< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-39-3" name = "__codelineno-39-3" href = "#__codelineno-39-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 常量、变量、对象占用 O(1) 空间< / span >
< a id = "__codelineno-39-4" name = "__codelineno-39-4" href = "#__codelineno-39-4" > < / a > < span class = "w" > < / span > < span class = "kr" > const< / span > < span class = "w" > < / span > < span class = "n" > a< / 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" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-39-5" name = "__codelineno-39-5" href = "#__codelineno-39-5" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > b< / 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" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-39-6" name = "__codelineno-39-6" href = "#__codelineno-39-6" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [< / span > < span class = "n" > _< / span > < span class = "p" > ]< / span > < span class = "kt" > i32< / span > < span class = "p" > {< / span > < span class = "mi" > 0< / span > < span class = "p" > }< / span > < span class = "o" > **< / span > < span class = "mi" > 10000< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-39-7" name = "__codelineno-39-7" href = "#__codelineno-39-7" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > inc< / span > < span class = "p" > .< / span > < span class = "n" > ListNode< / span > < span class = "p" > (< / span > < span class = "kt" > i32< / span > < span class = "p" > ){.< / span > < span class = "n" > val< / 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-39-8" name = "__codelineno-39-8" href = "#__codelineno-39-8" > < / 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" > i32< / 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-39-9" name = "__codelineno-39-9" href = "#__codelineno-39-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环中的变量占用 O(1) 空间< / span >
< a id = "__codelineno-39-10" name = "__codelineno-39-10" href = "#__codelineno-39-10" > < / 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-39-11" name = "__codelineno-39-11" href = "#__codelineno-39-11" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > c< / 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" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-39-12" name = "__codelineno-39-12" href = "#__codelineno-39-12" > < / a > < span class = "w" > < / span > < span class = "n" > _< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > c< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-39-13" name = "__codelineno-39-13" href = "#__codelineno-39-13" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-39-14" name = "__codelineno-39-14" href = "#__codelineno-39-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环中的函数占用 O(1) 空间< / span >
< a id = "__codelineno-39-15" name = "__codelineno-39-15" href = "#__codelineno-39-15" > < / 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-39-16" name = "__codelineno-39-16" href = "#__codelineno-39-16" > < / 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-39-17" name = "__codelineno-39-17" href = "#__codelineno-39-17" > < / a > < span class = "w" > < / span > < span class = "n" > _< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > function< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-39-18" name = "__codelineno-39-18" href = "#__codelineno-39-18" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-39-19" name = "__codelineno-39-19" href = "#__codelineno-39-19" > < / a > < span class = "w" > < / span > < span class = "n" > _< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > a< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-39-20" name = "__codelineno-39-20" href = "#__codelineno-39-20" > < / a > < span class = "w" > < / span > < span class = "n" > _< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > b< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-39-21" name = "__codelineno-39-21" href = "#__codelineno-39-21" > < / a > < span class = "w" > < / span > < span class = "n" > _< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-39-22" name = "__codelineno-39-22" href = "#__codelineno-39-22" > < / a > < span class = "w" > < / span > < span class = "n" > _< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-39-23" name = "__codelineno-39-23" href = "#__codelineno-39-23" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< h3 id = "on" > 线性阶 < span class = "arithmatex" > \(O(n)\)< / span > < a class = "headerlink" href = "#on" title = "Permanent link" > ¶ < / a > < / h3 >
< p > 线性阶常见于元素数量与 < span class = "arithmatex" > \(n\)< / span > 成正比的数组、链表、栈、队列等。< / p >
< div class = "tabbed-set tabbed-alternate" data-tabs = "5:10" > < input checked = "checked" id = "__tabbed_5_1" name = "__tabbed_5" type = "radio" / > < input id = "__tabbed_5_2" name = "__tabbed_5" type = "radio" / > < input id = "__tabbed_5_3" name = "__tabbed_5" type = "radio" / > < input id = "__tabbed_5_4" name = "__tabbed_5" type = "radio" / > < input id = "__tabbed_5_5" name = "__tabbed_5" type = "radio" / > < input id = "__tabbed_5_6" name = "__tabbed_5" type = "radio" / > < input id = "__tabbed_5_7" name = "__tabbed_5" type = "radio" / > < input id = "__tabbed_5_8" name = "__tabbed_5" type = "radio" / > < input id = "__tabbed_5_9" name = "__tabbed_5" type = "radio" / > < input id = "__tabbed_5_10" name = "__tabbed_5" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_5_1" > Java< / label > < label for = "__tabbed_5_2" > C++< / label > < label for = "__tabbed_5_3" > Python< / label > < label for = "__tabbed_5_4" > Go< / label > < label for = "__tabbed_5_5" > JavaScript< / label > < label for = "__tabbed_5_6" > TypeScript< / label > < label for = "__tabbed_5_7" > C< / label > < label for = "__tabbed_5_8" > C#< / label > < label for = "__tabbed_5_9" > Swift< / label > < label for = "__tabbed_5_10" > Zig< / label > < / div >
< div class = "tabbed-content" >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-40-1" name = "__codelineno-40-1" href = "#__codelineno-40-1" > < / a > < span class = "cm" > /* 线性阶 */< / span >
< a id = "__codelineno-40-2" name = "__codelineno-40-2" href = "#__codelineno-40-2" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > linear< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-40-3" name = "__codelineno-40-3" href = "#__codelineno-40-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 长度为 n 的数组占用 O(n) 空间< / span >
< a id = "__codelineno-40-4" name = "__codelineno-40-4" href = "#__codelineno-40-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "o" > []< / span > < span class = "w" > < / span > < span class = "n" > nums< / 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-40-5" name = "__codelineno-40-5" href = "#__codelineno-40-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 长度为 n 的列表占用 O(n) 空间< / span >
< a id = "__codelineno-40-6" name = "__codelineno-40-6" href = "#__codelineno-40-6" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > ListNode< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > nodes< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > ArrayList< / span > < span class = "o" > < > < / span > < span class = "p" > ();< / span >
< a id = "__codelineno-40-7" name = "__codelineno-40-7" href = "#__codelineno-40-7" > < / 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-40-8" name = "__codelineno-40-8" href = "#__codelineno-40-8" > < / a > < span class = "w" > < / span > < span class = "n" > nodes< / span > < span class = "p" > .< / span > < span class = "na" > add< / span > < span class = "p" > (< / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > ListNode< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-40-9" name = "__codelineno-40-9" href = "#__codelineno-40-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-40-10" name = "__codelineno-40-10" href = "#__codelineno-40-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 长度为 n 的哈希表占用 O(n) 空间< / span >
< a id = "__codelineno-40-11" name = "__codelineno-40-11" href = "#__codelineno-40-11" > < / a > < span class = "w" > < / span > < span class = "n" > Map< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > String< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > map< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > HashMap< / span > < span class = "o" > < > < / span > < span class = "p" > ();< / span >
< a id = "__codelineno-40-12" name = "__codelineno-40-12" href = "#__codelineno-40-12" > < / 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-40-13" name = "__codelineno-40-13" href = "#__codelineno-40-13" > < / a > < span class = "w" > < / span > < span class = "n" > map< / span > < span class = "p" > .< / span > < span class = "na" > put< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > String< / span > < span class = "p" > .< / span > < span class = "na" > valueOf< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-40-14" name = "__codelineno-40-14" href = "#__codelineno-40-14" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-40-15" name = "__codelineno-40-15" href = "#__codelineno-40-15" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-41-1" name = "__codelineno-41-1" href = "#__codelineno-41-1" > < / a > < span class = "cm" > /* 线性阶 */< / span >
< a id = "__codelineno-41-2" name = "__codelineno-41-2" href = "#__codelineno-41-2" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > linear< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-41-3" name = "__codelineno-41-3" href = "#__codelineno-41-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 长度为 n 的数组占用 O(n) 空间< / span >
< a id = "__codelineno-41-4" name = "__codelineno-41-4" href = "#__codelineno-41-4" > < / 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" > nums< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > );< / span >
< a id = "__codelineno-41-5" name = "__codelineno-41-5" href = "#__codelineno-41-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 长度为 n 的列表占用 O(n) 空间< / span >
< a id = "__codelineno-41-6" name = "__codelineno-41-6" href = "#__codelineno-41-6" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > ListNode< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > nodes< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-41-7" name = "__codelineno-41-7" href = "#__codelineno-41-7" > < / 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-41-8" name = "__codelineno-41-8" href = "#__codelineno-41-8" > < / a > < span class = "w" > < / span > < span class = "n" > nodes< / span > < span class = "p" > .< / span > < span class = "n" > push_back< / span > < span class = "p" > (< / span > < span class = "n" > ListNode< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-41-9" name = "__codelineno-41-9" href = "#__codelineno-41-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-41-10" name = "__codelineno-41-10" href = "#__codelineno-41-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 长度为 n 的哈希表占用 O(n) 空间< / span >
< a id = "__codelineno-41-11" name = "__codelineno-41-11" href = "#__codelineno-41-11" > < / a > < span class = "w" > < / span > < span class = "n" > unordered_map< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > string< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > map< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-41-12" name = "__codelineno-41-12" href = "#__codelineno-41-12" > < / 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-41-13" name = "__codelineno-41-13" href = "#__codelineno-41-13" > < / a > < span class = "w" > < / span > < span class = "n" > map< / 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" > to_string< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > );< / span >
< a id = "__codelineno-41-14" name = "__codelineno-41-14" href = "#__codelineno-41-14" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-41-15" name = "__codelineno-41-15" href = "#__codelineno-41-15" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-03-12 18:46:10 +08:00
< div class = "highlight" > < span class = "filename" > space_complexity.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-42-1" name = "__codelineno-42-1" href = "#__codelineno-42-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > linear< / span > < span class = "p" > (< / span > < span class = "n" > n< / 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 >
2023-04-09 05:12:29 +08:00
< a id = "__codelineno-42-2" name = "__codelineno-42-2" href = "#__codelineno-42-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 线性阶" " " < / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-42-3" name = "__codelineno-42-3" href = "#__codelineno-42-3" > < / a > < span class = "c1" > # 长度为 n 的列表占用 O(n) 空间< / span >
2023-05-22 22:01:26 +08:00
< a id = "__codelineno-42-4" name = "__codelineno-42-4" href = "#__codelineno-42-4" > < / a > < span class = "n" > nums< / 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 >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-42-5" name = "__codelineno-42-5" href = "#__codelineno-42-5" > < / a > < span class = "c1" > # 长度为 n 的哈希表占用 O(n) 空间< / span >
2023-03-23 18:57:04 +08:00
< a id = "__codelineno-42-6" name = "__codelineno-42-6" href = "#__codelineno-42-6" > < / a > < span class = "n" > mapp< / span > < span class = "o" > =< / span > < span class = "nb" > dict< / span > < span class = "p" > [< / span > < span class = "nb" > int< / span > < span class = "p" > ,< / span > < span class = "nb" > str< / span > < span class = "p" > ]()< / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-42-7" name = "__codelineno-42-7" href = "#__codelineno-42-7" > < / 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-42-8" name = "__codelineno-42-8" href = "#__codelineno-42-8" > < / a > < span class = "n" > mapp< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "nb" > str< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > )< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-43-1" name = "__codelineno-43-1" href = "#__codelineno-43-1" > < / a > < span class = "cm" > /* 线性阶 */< / span >
< a id = "__codelineno-43-2" name = "__codelineno-43-2" href = "#__codelineno-43-2" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > spaceLinear< / span > < span class = "p" > (< / span > < span class = "nx" > n< / 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-43-3" name = "__codelineno-43-3" href = "#__codelineno-43-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 长度为 n 的数组占用 O(n) 空间< / span >
< a id = "__codelineno-43-4" name = "__codelineno-43-4" href = "#__codelineno-43-4" > < / a > < span class = "w" > < / span > < span class = "nx" > _< / span > < span class = "w" > < / span > < span class = "p" > =< / 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-43-5" name = "__codelineno-43-5" href = "#__codelineno-43-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 长度为 n 的列表占用 O(n) 空间< / span >
< a id = "__codelineno-43-6" name = "__codelineno-43-6" href = "#__codelineno-43-6" > < / a > < span class = "w" > < / span > < span class = "kd" > var< / span > < span class = "w" > < / span > < span class = "nx" > nodes< / span > < span class = "w" > < / span > < span class = "p" > []< / span > < span class = "o" > *< / span > < span class = "nx" > node< / span >
< a id = "__codelineno-43-7" name = "__codelineno-43-7" href = "#__codelineno-43-7" > < / 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-43-8" name = "__codelineno-43-8" href = "#__codelineno-43-8" > < / a > < span class = "w" > < / span > < span class = "nx" > nodes< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nb" > append< / span > < span class = "p" > (< / span > < span class = "nx" > nodes< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > newNode< / span > < span class = "p" > (< / span > < span class = "nx" > i< / span > < span class = "p" > ))< / span >
< a id = "__codelineno-43-9" name = "__codelineno-43-9" href = "#__codelineno-43-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-43-10" name = "__codelineno-43-10" href = "#__codelineno-43-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 长度为 n 的哈希表占用 O(n) 空间< / span >
< a id = "__codelineno-43-11" name = "__codelineno-43-11" href = "#__codelineno-43-11" > < / a > < span class = "w" > < / span > < span class = "nx" > m< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nb" > make< / span > < span class = "p" > (< / span > < span class = "kd" > map< / span > < span class = "p" > [< / span > < span class = "kt" > int< / span > < span class = "p" > ]< / span > < span class = "kt" > string< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > )< / span >
< a id = "__codelineno-43-12" name = "__codelineno-43-12" href = "#__codelineno-43-12" > < / 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-43-13" name = "__codelineno-43-13" href = "#__codelineno-43-13" > < / a > < span class = "w" > < / span > < span class = "nx" > m< / 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" > strconv< / span > < span class = "p" > .< / span > < span class = "nx" > Itoa< / span > < span class = "p" > (< / span > < span class = "nx" > i< / span > < span class = "p" > )< / span >
< a id = "__codelineno-43-14" name = "__codelineno-43-14" href = "#__codelineno-43-14" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-43-15" name = "__codelineno-43-15" href = "#__codelineno-43-15" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-44-1" name = "__codelineno-44-1" href = "#__codelineno-44-1" > < / a > < span class = "cm" > /* 线性阶 */< / span >
< a id = "__codelineno-44-2" name = "__codelineno-44-2" href = "#__codelineno-44-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > linear< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-44-3" name = "__codelineno-44-3" href = "#__codelineno-44-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 长度为 n 的数组占用 O(n) 空间< / span >
< a id = "__codelineno-44-4" name = "__codelineno-44-4" href = "#__codelineno-44-4" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > nums< / 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 >
< a id = "__codelineno-44-5" name = "__codelineno-44-5" href = "#__codelineno-44-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 长度为 n 的列表占用 O(n) 空间< / span >
< a id = "__codelineno-44-6" name = "__codelineno-44-6" href = "#__codelineno-44-6" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > nodes< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [];< / span >
< a id = "__codelineno-44-7" name = "__codelineno-44-7" href = "#__codelineno-44-7" > < / 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-44-8" name = "__codelineno-44-8" href = "#__codelineno-44-8" > < / a > < span class = "w" > < / span > < span class = "nx" > nodes< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > (< / span > < span class = "ow" > new< / span > < span class = "w" > < / span > < span class = "nx" > ListNode< / span > < span class = "p" > (< / span > < span class = "nx" > i< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-44-9" name = "__codelineno-44-9" href = "#__codelineno-44-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-44-10" name = "__codelineno-44-10" href = "#__codelineno-44-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 长度为 n 的哈希表占用 O(n) 空间< / span >
< a id = "__codelineno-44-11" name = "__codelineno-44-11" href = "#__codelineno-44-11" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > map< / 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" > Map< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-44-12" name = "__codelineno-44-12" href = "#__codelineno-44-12" > < / 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-44-13" name = "__codelineno-44-13" href = "#__codelineno-44-13" > < / a > < span class = "w" > < / span > < span class = "nx" > map< / span > < span class = "p" > .< / span > < span class = "nx" > set< / span > < span class = "p" > (< / span > < span class = "nx" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "p" > .< / span > < span class = "nx" > toString< / span > < span class = "p" > ());< / span >
< a id = "__codelineno-44-14" name = "__codelineno-44-14" href = "#__codelineno-44-14" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-44-15" name = "__codelineno-44-15" href = "#__codelineno-44-15" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-45-1" name = "__codelineno-45-1" href = "#__codelineno-45-1" > < / a > < span class = "cm" > /* 线性阶 */< / span >
< a id = "__codelineno-45-2" name = "__codelineno-45-2" href = "#__codelineno-45-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > linear< / span > < span class = "p" > (< / span > < span class = "nx" > n< / 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-45-3" name = "__codelineno-45-3" href = "#__codelineno-45-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 长度为 n 的数组占用 O(n) 空间< / span >
< a id = "__codelineno-45-4" name = "__codelineno-45-4" href = "#__codelineno-45-4" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > nums< / 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 >
< a id = "__codelineno-45-5" name = "__codelineno-45-5" href = "#__codelineno-45-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 长度为 n 的列表占用 O(n) 空间< / span >
< a id = "__codelineno-45-6" name = "__codelineno-45-6" href = "#__codelineno-45-6" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > nodes< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > ListNode< / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [];< / span >
< a id = "__codelineno-45-7" name = "__codelineno-45-7" href = "#__codelineno-45-7" > < / 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-45-8" name = "__codelineno-45-8" href = "#__codelineno-45-8" > < / a > < span class = "w" > < / span > < span class = "nx" > nodes< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > (< / span > < span class = "ow" > new< / span > < span class = "w" > < / span > < span class = "nx" > ListNode< / span > < span class = "p" > (< / span > < span class = "nx" > i< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-45-9" name = "__codelineno-45-9" href = "#__codelineno-45-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-45-10" name = "__codelineno-45-10" href = "#__codelineno-45-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 长度为 n 的哈希表占用 O(n) 空间< / span >
< a id = "__codelineno-45-11" name = "__codelineno-45-11" href = "#__codelineno-45-11" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > map< / 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" > Map< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-45-12" name = "__codelineno-45-12" href = "#__codelineno-45-12" > < / 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-45-13" name = "__codelineno-45-13" href = "#__codelineno-45-13" > < / a > < span class = "w" > < / span > < span class = "nx" > map< / span > < span class = "p" > .< / span > < span class = "nx" > set< / span > < span class = "p" > (< / span > < span class = "nx" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "p" > .< / span > < span class = "nx" > toString< / span > < span class = "p" > ());< / span >
< a id = "__codelineno-45-14" name = "__codelineno-45-14" href = "#__codelineno-45-14" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-45-15" name = "__codelineno-45-15" href = "#__codelineno-45-15" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-04-18 21:19:05 +08:00
< div class = "highlight" > < span class = "filename" > space_complexity.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-46-1" name = "__codelineno-46-1" href = "#__codelineno-46-1" > < / a > < span class = "cm" > /* 哈希表 */< / span >
< a id = "__codelineno-46-2" name = "__codelineno-46-2" href = "#__codelineno-46-2" > < / a > < span class = "k" > struct< / span > < span class = "w" > < / span > < span class = "nc" > hashTable< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-46-3" name = "__codelineno-46-3" href = "#__codelineno-46-3" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > key< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-46-4" name = "__codelineno-46-4" href = "#__codelineno-46-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-46-5" name = "__codelineno-46-5" href = "#__codelineno-46-5" > < / a > < span class = "w" > < / span > < span class = "n" > UT_hash_handle< / span > < span class = "w" > < / span > < span class = "n" > hh< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 基于 uthash.h 实现< / span >
< a id = "__codelineno-46-6" name = "__codelineno-46-6" href = "#__codelineno-46-6" > < / a > < span class = "p" > };< / span >
< a id = "__codelineno-46-7" name = "__codelineno-46-7" href = "#__codelineno-46-7" > < / a >
2023-04-22 01:35:59 +08:00
< a id = "__codelineno-46-8" name = "__codelineno-46-8" href = "#__codelineno-46-8" > < / a > < span class = "k" > typedef< / span > < span class = "w" > < / span > < span class = "k" > struct< / span > < span class = "w" > < / span > < span class = "nc" > hashTable< / span > < span class = "w" > < / span > < span class = "n" > hashTable< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-46-9" name = "__codelineno-46-9" href = "#__codelineno-46-9" > < / a >
< a id = "__codelineno-46-10" name = "__codelineno-46-10" href = "#__codelineno-46-10" > < / a > < span class = "cm" > /* 线性阶 */< / span >
< a id = "__codelineno-46-11" name = "__codelineno-46-11" href = "#__codelineno-46-11" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > linear< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-46-12" name = "__codelineno-46-12" href = "#__codelineno-46-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 长度为 n 的数组占用 O(n) 空间< / span >
< a id = "__codelineno-46-13" name = "__codelineno-46-13" href = "#__codelineno-46-13" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > nums< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > malloc< / span > < span class = "p" > (< / span > < span class = "k" > sizeof< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > );< / span >
< a id = "__codelineno-46-14" name = "__codelineno-46-14" href = "#__codelineno-46-14" > < / a > < span class = "w" > < / span > < span class = "n" > free< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > );< / span >
< a id = "__codelineno-46-15" name = "__codelineno-46-15" href = "#__codelineno-46-15" > < / a >
< a id = "__codelineno-46-16" name = "__codelineno-46-16" href = "#__codelineno-46-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 长度为 n 的列表占用 O(n) 空间< / span >
< a id = "__codelineno-46-17" name = "__codelineno-46-17" href = "#__codelineno-46-17" > < / a > < span class = "w" > < / span > < span class = "n" > ListNode< / span > < span class = "w" > < / span > < span class = "o" > **< / span > < span class = "n" > nodes< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > malloc< / span > < span class = "p" > (< / span > < span class = "k" > sizeof< / span > < span class = "p" > (< / span > < span class = "n" > ListNode< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > );< / span >
< a id = "__codelineno-46-18" name = "__codelineno-46-18" href = "#__codelineno-46-18" > < / 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" > 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-46-19" name = "__codelineno-46-19" href = "#__codelineno-46-19" > < / a > < span class = "w" > < / span > < span class = "n" > nodes< / 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" > newListNode< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > );< / span >
< a id = "__codelineno-46-20" name = "__codelineno-46-20" href = "#__codelineno-46-20" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-46-21" name = "__codelineno-46-21" href = "#__codelineno-46-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 内存释放< / span >
< a id = "__codelineno-46-22" name = "__codelineno-46-22" href = "#__codelineno-46-22" > < / 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-46-23" name = "__codelineno-46-23" href = "#__codelineno-46-23" > < / a > < span class = "w" > < / span > < span class = "n" > free< / span > < span class = "p" > (< / span > < span class = "n" > nodes< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]);< / span >
< a id = "__codelineno-46-24" name = "__codelineno-46-24" href = "#__codelineno-46-24" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-46-25" name = "__codelineno-46-25" href = "#__codelineno-46-25" > < / a > < span class = "w" > < / span > < span class = "n" > free< / span > < span class = "p" > (< / span > < span class = "n" > nodes< / span > < span class = "p" > );< / span >
< a id = "__codelineno-46-26" name = "__codelineno-46-26" href = "#__codelineno-46-26" > < / a >
< a id = "__codelineno-46-27" name = "__codelineno-46-27" href = "#__codelineno-46-27" > < / a > < span class = "w" > < / span > < span class = "c1" > // 长度为 n 的哈希表占用 O(n) 空间< / span >
< a id = "__codelineno-46-28" name = "__codelineno-46-28" href = "#__codelineno-46-28" > < / a > < span class = "w" > < / span > < span class = "n" > hashTable< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > h< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > NULL< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-46-29" name = "__codelineno-46-29" href = "#__codelineno-46-29" > < / 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-46-30" name = "__codelineno-46-30" href = "#__codelineno-46-30" > < / a > < span class = "w" > < / span > < span class = "n" > hashTable< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > tmp< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > malloc< / span > < span class = "p" > (< / span > < span class = "k" > sizeof< / span > < span class = "p" > (< / span > < span class = "n" > hashTable< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-46-31" name = "__codelineno-46-31" href = "#__codelineno-46-31" > < / a > < span class = "w" > < / span > < span class = "n" > tmp< / span > < span class = "o" > -> < / span > < span class = "n" > key< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-46-32" name = "__codelineno-46-32" href = "#__codelineno-46-32" > < / a > < span class = "w" > < / span > < span class = "n" > tmp< / span > < span class = "o" > -> < / span > < span class = "n" > val< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-46-33" name = "__codelineno-46-33" href = "#__codelineno-46-33" > < / a > < span class = "w" > < / span > < span class = "n" > HASH_ADD_INT< / span > < span class = "p" > (< / span > < span class = "n" > h< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > key< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > tmp< / span > < span class = "p" > );< / span >
< a id = "__codelineno-46-34" name = "__codelineno-46-34" href = "#__codelineno-46-34" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-46-35" name = "__codelineno-46-35" href = "#__codelineno-46-35" > < / a >
< a id = "__codelineno-46-36" name = "__codelineno-46-36" href = "#__codelineno-46-36" > < / a > < span class = "w" > < / span > < span class = "c1" > // 内存释放< / span >
< a id = "__codelineno-46-37" name = "__codelineno-46-37" href = "#__codelineno-46-37" > < / a > < span class = "w" > < / span > < span class = "n" > hashTable< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > curr< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > tmp< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-46-38" name = "__codelineno-46-38" href = "#__codelineno-46-38" > < / a > < span class = "w" > < / span > < span class = "n" > HASH_ITER< / span > < span class = "p" > (< / span > < span class = "n" > hh< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > h< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > curr< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > tmp< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-46-39" name = "__codelineno-46-39" href = "#__codelineno-46-39" > < / a > < span class = "w" > < / span > < span class = "n" > HASH_DEL< / span > < span class = "p" > (< / span > < span class = "n" > h< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > curr< / span > < span class = "p" > );< / span >
< a id = "__codelineno-46-40" name = "__codelineno-46-40" href = "#__codelineno-46-40" > < / a > < span class = "w" > < / span > < span class = "n" > free< / span > < span class = "p" > (< / span > < span class = "n" > curr< / span > < span class = "p" > );< / span >
< a id = "__codelineno-46-41" name = "__codelineno-46-41" href = "#__codelineno-46-41" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-46-42" name = "__codelineno-46-42" href = "#__codelineno-46-42" > < / a > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-47-1" name = "__codelineno-47-1" href = "#__codelineno-47-1" > < / a > < span class = "cm" > /* 线性阶 */< / span >
2023-04-23 14:58:11 +08:00
< a id = "__codelineno-47-2" name = "__codelineno-47-2" href = "#__codelineno-47-2" > < / a > < span class = "k" > void< / span > < span class = "w" > < / span > < span class = "nf" > linear< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-47-3" name = "__codelineno-47-3" href = "#__codelineno-47-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 长度为 n 的数组占用 O(n) 空间< / span >
< a id = "__codelineno-47-4" name = "__codelineno-47-4" href = "#__codelineno-47-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "n" > nums< / 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 = "p" > [< / span > < span class = "n" > n< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-47-5" name = "__codelineno-47-5" href = "#__codelineno-47-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 长度为 n 的列表占用 O(n) 空间< / span >
< a id = "__codelineno-47-6" name = "__codelineno-47-6" href = "#__codelineno-47-6" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > ListNode< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > nodes< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-47-7" name = "__codelineno-47-7" href = "#__codelineno-47-7" > < / 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 = "m" > 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-47-8" name = "__codelineno-47-8" href = "#__codelineno-47-8" > < / a > < span class = "w" > < / span > < span class = "n" > nodes< / span > < span class = "p" > .< / span > < span class = "n" > Add< / span > < span class = "p" > (< / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > ListNode< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-47-9" name = "__codelineno-47-9" href = "#__codelineno-47-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-47-10" name = "__codelineno-47-10" href = "#__codelineno-47-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 长度为 n 的哈希表占用 O(n) 空间< / span >
< a id = "__codelineno-47-11" name = "__codelineno-47-11" href = "#__codelineno-47-11" > < / a > < span class = "w" > < / span > < span class = "n" > Dictionary< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > string< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > map< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-47-12" name = "__codelineno-47-12" href = "#__codelineno-47-12" > < / 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 = "m" > 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-47-13" name = "__codelineno-47-13" href = "#__codelineno-47-13" > < / a > < span class = "w" > < / span > < span class = "n" > map< / span > < span class = "p" > .< / span > < span class = "n" > Add< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > .< / span > < span class = "n" > ToString< / span > < span class = "p" > ());< / span >
< a id = "__codelineno-47-14" name = "__codelineno-47-14" href = "#__codelineno-47-14" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-47-15" name = "__codelineno-47-15" href = "#__codelineno-47-15" > < / a > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-48-1" name = "__codelineno-48-1" href = "#__codelineno-48-1" > < / a > < span class = "cm" > /* 线性阶 */< / span >
< a id = "__codelineno-48-2" name = "__codelineno-48-2" href = "#__codelineno-48-2" > < / a > < span class = "kd" > func< / span > < span class = "nf" > linear< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / span > < span class = "p" > )< / span > < span class = "p" > {< / span >
< a id = "__codelineno-48-3" name = "__codelineno-48-3" href = "#__codelineno-48-3" > < / a > < span class = "c1" > // 长度为 n 的数组占用 O(n) 空间< / span >
< a id = "__codelineno-48-4" name = "__codelineno-48-4" href = "#__codelineno-48-4" > < / a > < span class = "kd" > let< / span > < span class = "nv" > nums< / 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-48-5" name = "__codelineno-48-5" href = "#__codelineno-48-5" > < / a > < span class = "c1" > // 长度为 n 的列表占用 O(n) 空间< / span >
< a id = "__codelineno-48-6" name = "__codelineno-48-6" href = "#__codelineno-48-6" > < / a > < span class = "kd" > let< / span > < span class = "nv" > nodes< / span > < span class = "p" > =< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > ..< / span > < span class = "o" > < < / span > < span class = "n" > n< / span > < span class = "p" > ).< / span > < span class = "bp" > map< / span > < span class = "p" > {< / span > < span class = "n" > ListNode< / span > < span class = "p" > (< / span > < span class = "n" > x< / span > < span class = "p" > :< / span > < span class = "nv" > $0< / span > < span class = "p" > )< / span > < span class = "p" > }< / span >
< a id = "__codelineno-48-7" name = "__codelineno-48-7" href = "#__codelineno-48-7" > < / a > < span class = "c1" > // 长度为 n 的哈希表占用 O(n) 空间< / span >
< a id = "__codelineno-48-8" name = "__codelineno-48-8" href = "#__codelineno-48-8" > < / a > < span class = "kd" > let< / span > < span class = "nv" > map< / span > < span class = "p" > =< / span > < span class = "nb" > Dictionary< / span > < span class = "p" > (< / span > < span class = "n" > uniqueKeysWithValues< / span > < span class = "p" > :< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > ..< / span > < span class = "o" > < < / span > < span class = "n" > n< / span > < span class = "p" > ).< / span > < span class = "bp" > map< / span > < span class = "p" > {< / span > < span class = "p" > (< / span > < span class = "nv" > $0< / span > < span class = "p" > ,< / span > < span class = "s" > " < / span > < span class = "si" > \(< / span > < span class = "nv" > $0< / span > < span class = "si" > )< / span > < span class = "s" > " < / span > < span class = "p" > )< / span > < span class = "p" > })< / span >
< a id = "__codelineno-48-9" name = "__codelineno-48-9" href = "#__codelineno-48-9" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-49-1" name = "__codelineno-49-1" href = "#__codelineno-49-1" > < / a > < span class = "c1" > // 线性阶< / span >
< a id = "__codelineno-49-2" name = "__codelineno-49-2" href = "#__codelineno-49-2" > < / a > < span class = "k" > fn< / span > < span class = "w" > < / span > < span class = "n" > linear< / span > < span class = "p" > (< / span > < span class = "kr" > comptime< / span > < span class = "w" > < / span > < span class = "n" > n< / 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-49-3" name = "__codelineno-49-3" href = "#__codelineno-49-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 长度为 n 的数组占用 O(n) 空间< / span >
< a id = "__codelineno-49-4" name = "__codelineno-49-4" href = "#__codelineno-49-4" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [< / span > < span class = "n" > _< / span > < span class = "p" > ]< / span > < span class = "kt" > i32< / span > < span class = "p" > {< / span > < span class = "mi" > 0< / span > < span class = "p" > }< / span > < span class = "o" > **< / span > < span class = "n" > n< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-49-5" name = "__codelineno-49-5" href = "#__codelineno-49-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 长度为 n 的列表占用 O(n) 空间< / span >
< a id = "__codelineno-49-6" name = "__codelineno-49-6" href = "#__codelineno-49-6" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > nodes< / 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" > ArrayList< / span > < span class = "p" > (< / span > < span class = "kt" > i32< / 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-49-7" name = "__codelineno-49-7" href = "#__codelineno-49-7" > < / a > < span class = "w" > < / span > < span class = "k" > defer< / span > < span class = "w" > < / span > < span class = "n" > nodes< / span > < span class = "p" > .< / span > < span class = "n" > deinit< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-49-8" name = "__codelineno-49-8" href = "#__codelineno-49-8" > < / 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" > i32< / 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-49-9" name = "__codelineno-49-9" href = "#__codelineno-49-9" > < / 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-49-10" name = "__codelineno-49-10" href = "#__codelineno-49-10" > < / a > < span class = "w" > < / span > < span class = "k" > try< / span > < span class = "w" > < / span > < span class = "n" > nodes< / span > < span class = "p" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > );< / span >
< a id = "__codelineno-49-11" name = "__codelineno-49-11" href = "#__codelineno-49-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-49-12" name = "__codelineno-49-12" href = "#__codelineno-49-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 长度为 n 的哈希表占用 O(n) 空间< / span >
< a id = "__codelineno-49-13" name = "__codelineno-49-13" href = "#__codelineno-49-13" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > map< / 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" > AutoArrayHashMap< / span > < span class = "p" > (< / span > < span class = "kt" > i32< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "p" > []< / span > < span class = "kr" > const< / span > < span class = "w" > < / span > < span class = "kt" > u8< / 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-49-14" name = "__codelineno-49-14" href = "#__codelineno-49-14" > < / a > < span class = "w" > < / span > < span class = "k" > defer< / span > < span class = "w" > < / span > < span class = "n" > map< / span > < span class = "p" > .< / span > < span class = "n" > deinit< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-49-15" name = "__codelineno-49-15" href = "#__codelineno-49-15" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > j< / 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" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-49-16" name = "__codelineno-49-16" href = "#__codelineno-49-16" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > j< / 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" > j< / 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-49-17" name = "__codelineno-49-17" href = "#__codelineno-49-17" > < / a > < span class = "w" > < / span > < span class = "kr" > const< / span > < span class = "w" > < / span > < span class = "n" > string< / 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" > std< / span > < span class = "p" > .< / span > < span class = "n" > fmt< / span > < span class = "p" > .< / span > < span class = "n" > allocPrint< / 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 > < span class = "w" > < / span > < span class = "s" > " {d}" < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "p" > .{< / span > < span class = "n" > j< / span > < span class = "p" > });< / span >
< a id = "__codelineno-49-18" name = "__codelineno-49-18" href = "#__codelineno-49-18" > < / a > < span class = "w" > < / span > < span class = "k" > defer< / 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" > page_allocator< / span > < span class = "p" > .< / span > < span class = "n" > free< / span > < span class = "p" > (< / span > < span class = "n" > string< / span > < span class = "p" > );< / span >
< a id = "__codelineno-49-19" name = "__codelineno-49-19" href = "#__codelineno-49-19" > < / a > < span class = "w" > < / span > < span class = "k" > try< / span > < span class = "w" > < / span > < span class = "n" > map< / span > < span class = "p" > .< / span > < span class = "n" > put< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > string< / span > < span class = "p" > );< / span >
< a id = "__codelineno-49-20" name = "__codelineno-49-20" href = "#__codelineno-49-20" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-49-21" name = "__codelineno-49-21" href = "#__codelineno-49-21" > < / a > < span class = "w" > < / span > < span class = "n" > _< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-49-22" name = "__codelineno-49-22" href = "#__codelineno-49-22" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< p > 以下递归函数会同时存在 < span class = "arithmatex" > \(n\)< / span > 个未返回的 < code > algorithm()< / code > 函数，使用 < span class = "arithmatex" > \(O(n)\)< / span > 大小的栈帧空间。< / p >
< div class = "tabbed-set tabbed-alternate" data-tabs = "6:10" > < input checked = "checked" id = "__tabbed_6_1" name = "__tabbed_6" type = "radio" / > < input id = "__tabbed_6_2" name = "__tabbed_6" type = "radio" / > < input id = "__tabbed_6_3" name = "__tabbed_6" type = "radio" / > < input id = "__tabbed_6_4" name = "__tabbed_6" type = "radio" / > < input id = "__tabbed_6_5" name = "__tabbed_6" type = "radio" / > < input id = "__tabbed_6_6" name = "__tabbed_6" type = "radio" / > < input id = "__tabbed_6_7" name = "__tabbed_6" type = "radio" / > < input id = "__tabbed_6_8" name = "__tabbed_6" type = "radio" / > < input id = "__tabbed_6_9" name = "__tabbed_6" type = "radio" / > < input id = "__tabbed_6_10" name = "__tabbed_6" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_6_1" > Java< / label > < label for = "__tabbed_6_2" > C++< / label > < label for = "__tabbed_6_3" > Python< / label > < label for = "__tabbed_6_4" > Go< / label > < label for = "__tabbed_6_5" > JavaScript< / label > < label for = "__tabbed_6_6" > TypeScript< / label > < label for = "__tabbed_6_7" > C< / label > < label for = "__tabbed_6_8" > C#< / label > < label for = "__tabbed_6_9" > Swift< / label > < label for = "__tabbed_6_10" > Zig< / label > < / div >
< div class = "tabbed-content" >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-50-1" name = "__codelineno-50-1" href = "#__codelineno-50-1" > < / a > < span class = "cm" > /* 线性阶（递归实现） */< / span >
< a id = "__codelineno-50-2" name = "__codelineno-50-2" href = "#__codelineno-50-2" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > linearRecur< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-50-3" name = "__codelineno-50-3" href = "#__codelineno-50-3" > < / a > < span class = "w" > < / span > < span class = "n" > System< / span > < span class = "p" > .< / span > < span class = "na" > out< / span > < span class = "p" > .< / span > < span class = "na" > println< / span > < span class = "p" > (< / span > < span class = "s" > " 递归 n = " < / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > );< / span >
2023-04-14 04:01:48 +08:00
< a id = "__codelineno-50-4" name = "__codelineno-50-4" href = "#__codelineno-50-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / 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-50-5" name = "__codelineno-50-5" href = "#__codelineno-50-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-50-6" name = "__codelineno-50-6" href = "#__codelineno-50-6" > < / a > < span class = "w" > < / span > < span class = "n" > linearRecur< / span > < span class = "p" > (< / 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-50-7" name = "__codelineno-50-7" href = "#__codelineno-50-7" > < / a > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-51-1" name = "__codelineno-51-1" href = "#__codelineno-51-1" > < / a > < span class = "cm" > /* 线性阶（递归实现） */< / span >
< a id = "__codelineno-51-2" name = "__codelineno-51-2" href = "#__codelineno-51-2" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > linearRecur< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-51-3" name = "__codelineno-51-3" href = "#__codelineno-51-3" > < / a > < span class = "w" > < / span > < span class = "n" > cout< / span > < span class = "w" > < / span > < span class = "o" > < < < / span > < span class = "w" > < / span > < span class = "s" > " 递归 n = " < / 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 = "n" > endl< / span > < span class = "p" > ;< / span >
2023-04-14 04:01:48 +08:00
< a id = "__codelineno-51-4" name = "__codelineno-51-4" href = "#__codelineno-51-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / 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-51-5" name = "__codelineno-51-5" href = "#__codelineno-51-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-51-6" name = "__codelineno-51-6" href = "#__codelineno-51-6" > < / a > < span class = "w" > < / span > < span class = "n" > linearRecur< / span > < span class = "p" > (< / 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-51-7" name = "__codelineno-51-7" href = "#__codelineno-51-7" > < / a > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-03-12 18:46:10 +08:00
< div class = "highlight" > < span class = "filename" > space_complexity.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-52-1" name = "__codelineno-52-1" href = "#__codelineno-52-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > linear_recur< / span > < span class = "p" > (< / span > < span class = "n" > n< / 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 >
2023-04-09 05:12:29 +08:00
< a id = "__codelineno-52-2" name = "__codelineno-52-2" href = "#__codelineno-52-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 线性阶（递归实现）" " " < / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-52-3" name = "__codelineno-52-3" href = "#__codelineno-52-3" > < / a > < span class = "nb" > print< / span > < span class = "p" > (< / span > < span class = "s2" > " 递归 n =" < / span > < span class = "p" > ,< / span > < span class = "n" > n< / span > < span class = "p" > )< / span >
2023-04-09 05:12:29 +08:00
< a id = "__codelineno-52-4" name = "__codelineno-52-4" href = "#__codelineno-52-4" > < / a > < span class = "k" > if< / span > < span class = "n" > n< / span > < span class = "o" > ==< / span > < span class = "mi" > 1< / span > < span class = "p" > :< / span >
< a id = "__codelineno-52-5" name = "__codelineno-52-5" href = "#__codelineno-52-5" > < / a > < span class = "k" > return< / span >
< a id = "__codelineno-52-6" name = "__codelineno-52-6" href = "#__codelineno-52-6" > < / a > < span class = "n" > linear_recur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-53-1" name = "__codelineno-53-1" href = "#__codelineno-53-1" > < / a > < span class = "cm" > /* 线性阶（递归实现） */< / span >
< a id = "__codelineno-53-2" name = "__codelineno-53-2" href = "#__codelineno-53-2" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > spaceLinearRecur< / span > < span class = "p" > (< / span > < span class = "nx" > n< / 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-53-3" name = "__codelineno-53-3" href = "#__codelineno-53-3" > < / a > < span class = "w" > < / span > < span class = "nx" > fmt< / span > < span class = "p" > .< / span > < span class = "nx" > Println< / span > < span class = "p" > (< / span > < span class = "s" > " 递归 n =" < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > )< / span >
< a id = "__codelineno-53-4" name = "__codelineno-53-4" href = "#__codelineno-53-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / 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 = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-53-5" name = "__codelineno-53-5" href = "#__codelineno-53-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span >
< a id = "__codelineno-53-6" name = "__codelineno-53-6" href = "#__codelineno-53-6" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-53-7" name = "__codelineno-53-7" href = "#__codelineno-53-7" > < / a > < span class = "w" > < / span > < span class = "nx" > spaceLinearRecur< / span > < span class = "p" > (< / 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 >
< a id = "__codelineno-53-8" name = "__codelineno-53-8" href = "#__codelineno-53-8" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-54-1" name = "__codelineno-54-1" href = "#__codelineno-54-1" > < / a > < span class = "cm" > /* 线性阶（递归实现） */< / span >
< a id = "__codelineno-54-2" name = "__codelineno-54-2" href = "#__codelineno-54-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > linearRecur< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-54-3" name = "__codelineno-54-3" href = "#__codelineno-54-3" > < / a > < span class = "w" > < / span > < span class = "nx" > console< / span > < span class = "p" > .< / span > < span class = "nx" > log< / span > < span class = "p" > (< / span > < span class = "sb" > `递归 n = < / span > < span class = "si" > ${< / span > < span class = "nx" > n< / span > < span class = "si" > }< / span > < span class = "sb" > `< / span > < span class = "p" > );< / span >
< a id = "__codelineno-54-4" name = "__codelineno-54-4" href = "#__codelineno-54-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / 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 = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-54-5" name = "__codelineno-54-5" href = "#__codelineno-54-5" > < / a > < span class = "w" > < / span > < span class = "nx" > linearRecur< / span > < span class = "p" > (< / 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 >
< a id = "__codelineno-54-6" name = "__codelineno-54-6" href = "#__codelineno-54-6" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-55-1" name = "__codelineno-55-1" href = "#__codelineno-55-1" > < / a > < span class = "cm" > /* 线性阶（递归实现） */< / span >
< a id = "__codelineno-55-2" name = "__codelineno-55-2" href = "#__codelineno-55-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > linearRecur< / span > < span class = "p" > (< / span > < span class = "nx" > n< / 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-55-3" name = "__codelineno-55-3" href = "#__codelineno-55-3" > < / a > < span class = "w" > < / span > < span class = "nx" > console< / span > < span class = "p" > .< / span > < span class = "nx" > log< / span > < span class = "p" > (< / span > < span class = "sb" > `递归 n = < / span > < span class = "si" > ${< / span > < span class = "nx" > n< / span > < span class = "si" > }< / span > < span class = "sb" > `< / span > < span class = "p" > );< / span >
< a id = "__codelineno-55-4" name = "__codelineno-55-4" href = "#__codelineno-55-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / 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 = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-55-5" name = "__codelineno-55-5" href = "#__codelineno-55-5" > < / a > < span class = "w" > < / span > < span class = "nx" > linearRecur< / span > < span class = "p" > (< / 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 >
< a id = "__codelineno-55-6" name = "__codelineno-55-6" href = "#__codelineno-55-6" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-04-18 20:19:15 +08:00
< div class = "highlight" > < span class = "filename" > space_complexity.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-56-1" name = "__codelineno-56-1" href = "#__codelineno-56-1" > < / a > < span class = "cm" > /* 线性阶（递归实现） */< / span >
< a id = "__codelineno-56-2" name = "__codelineno-56-2" href = "#__codelineno-56-2" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > linearRecur< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-56-3" name = "__codelineno-56-3" href = "#__codelineno-56-3" > < / a > < span class = "w" > < / span > < span class = "n" > printf< / span > < span class = "p" > (< / span > < span class = "s" > " 递归 n = %d< / span > < span class = "se" > \r\n< / span > < span class = "s" > " < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > );< / span >
< a id = "__codelineno-56-4" name = "__codelineno-56-4" href = "#__codelineno-56-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / 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-56-5" name = "__codelineno-56-5" href = "#__codelineno-56-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-56-6" name = "__codelineno-56-6" href = "#__codelineno-56-6" > < / a > < span class = "w" > < / span > < span class = "n" > linearRecur< / span > < span class = "p" > (< / 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-56-7" name = "__codelineno-56-7" href = "#__codelineno-56-7" > < / a > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-57-1" name = "__codelineno-57-1" href = "#__codelineno-57-1" > < / a > < span class = "cm" > /* 线性阶（递归实现） */< / span >
2023-04-23 14:58:11 +08:00
< a id = "__codelineno-57-2" name = "__codelineno-57-2" href = "#__codelineno-57-2" > < / a > < span class = "k" > void< / span > < span class = "w" > < / span > < span class = "nf" > linearRecur< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-57-3" name = "__codelineno-57-3" href = "#__codelineno-57-3" > < / a > < span class = "w" > < / span > < span class = "n" > Console< / span > < span class = "p" > .< / span > < span class = "n" > WriteLine< / span > < span class = "p" > (< / span > < span class = "s" > " 递归 n = " < / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > );< / span >
< a id = "__codelineno-57-4" name = "__codelineno-57-4" href = "#__codelineno-57-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-57-5" name = "__codelineno-57-5" href = "#__codelineno-57-5" > < / a > < span class = "w" > < / span > < span class = "n" > linearRecur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > );< / span >
< a id = "__codelineno-57-6" name = "__codelineno-57-6" href = "#__codelineno-57-6" > < / a > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-58-1" name = "__codelineno-58-1" href = "#__codelineno-58-1" > < / a > < span class = "cm" > /* 线性阶（递归实现） */< / span >
< a id = "__codelineno-58-2" name = "__codelineno-58-2" href = "#__codelineno-58-2" > < / a > < span class = "kd" > func< / span > < span class = "nf" > linearRecur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / span > < span class = "p" > )< / span > < span class = "p" > {< / span >
< a id = "__codelineno-58-3" name = "__codelineno-58-3" href = "#__codelineno-58-3" > < / a > < span class = "bp" > print< / span > < span class = "p" > (< / span > < span class = "s" > " 递归 n = < / span > < span class = "si" > \(< / span > < span class = "n" > n< / span > < span class = "si" > )< / span > < span class = "s" > " < / span > < span class = "p" > )< / span >
< a id = "__codelineno-58-4" name = "__codelineno-58-4" href = "#__codelineno-58-4" > < / a > < span class = "k" > if< / span > < span class = "n" > n< / span > < span class = "p" > ==< / span > < span class = "mi" > 1< / span > < span class = "p" > {< / span >
< a id = "__codelineno-58-5" name = "__codelineno-58-5" href = "#__codelineno-58-5" > < / a > < span class = "k" > return< / span >
< a id = "__codelineno-58-6" name = "__codelineno-58-6" href = "#__codelineno-58-6" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-58-7" name = "__codelineno-58-7" href = "#__codelineno-58-7" > < / a > < span class = "n" > linearRecur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > :< / span > < span class = "n" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span >
< a id = "__codelineno-58-8" name = "__codelineno-58-8" href = "#__codelineno-58-8" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-59-1" name = "__codelineno-59-1" href = "#__codelineno-59-1" > < / a > < span class = "c1" > // 线性阶（递归实现）< / span >
< a id = "__codelineno-59-2" name = "__codelineno-59-2" href = "#__codelineno-59-2" > < / a > < span class = "k" > fn< / span > < span class = "w" > < / span > < span class = "n" > linearRecur< / span > < span class = "p" > (< / span > < span class = "kr" > comptime< / span > < span class = "w" > < / span > < span class = "n" > n< / 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" > void< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-59-3" name = "__codelineno-59-3" href = "#__codelineno-59-3" > < / a > < span class = "w" > < / span > < span class = "n" > std< / span > < span class = "p" > .< / span > < span class = "n" > debug< / span > < span class = "p" > .< / span > < span class = "n" > print< / span > < span class = "p" > (< / span > < span class = "s" > " 递归 n = {}< / span > < span class = "se" > \n< / span > < span class = "s" > " < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "p" > .{< / span > < span class = "n" > n< / span > < span class = "p" > });< / span >
< a id = "__codelineno-59-4" name = "__codelineno-59-4" href = "#__codelineno-59-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / 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 = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-59-5" name = "__codelineno-59-5" href = "#__codelineno-59-5" > < / a > < span class = "w" > < / span > < span class = "n" > linearRecur< / span > < span class = "p" > (< / 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-59-6" name = "__codelineno-59-6" href = "#__codelineno-59-6" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
2023-02-26 18:18:03 +08:00
< p > < img alt = "递归函数产生的线性阶空间复杂度" src = "../space_complexity.assets/space_complexity_recursive_linear.png" / > < / p >
2023-02-26 19:53:32 +08:00
< p align = "center" > Fig. 递归函数产生的线性阶空间复杂度 < / p >
2023-02-08 14:54:41 +08:00
< h3 id = "on2" > 平方阶 < span class = "arithmatex" > \(O(n^2)\)< / span > < a class = "headerlink" href = "#on2" title = "Permanent link" > ¶ < / a > < / h3 >
2023-04-07 22:32:13 +08:00
< p > 平方阶常见于矩阵和图，元素数量与 < span class = "arithmatex" > \(n\)< / span > 成平方关系。< / p >
2023-02-08 14:54:41 +08:00
< div class = "tabbed-set tabbed-alternate" data-tabs = "7:10" > < input checked = "checked" id = "__tabbed_7_1" name = "__tabbed_7" type = "radio" / > < input id = "__tabbed_7_2" name = "__tabbed_7" type = "radio" / > < input id = "__tabbed_7_3" name = "__tabbed_7" type = "radio" / > < input id = "__tabbed_7_4" name = "__tabbed_7" type = "radio" / > < input id = "__tabbed_7_5" name = "__tabbed_7" type = "radio" / > < input id = "__tabbed_7_6" name = "__tabbed_7" type = "radio" / > < input id = "__tabbed_7_7" name = "__tabbed_7" type = "radio" / > < input id = "__tabbed_7_8" name = "__tabbed_7" type = "radio" / > < input id = "__tabbed_7_9" name = "__tabbed_7" type = "radio" / > < input id = "__tabbed_7_10" name = "__tabbed_7" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_7_1" > Java< / label > < label for = "__tabbed_7_2" > C++< / label > < label for = "__tabbed_7_3" > Python< / label > < label for = "__tabbed_7_4" > Go< / label > < label for = "__tabbed_7_5" > JavaScript< / label > < label for = "__tabbed_7_6" > TypeScript< / label > < label for = "__tabbed_7_7" > C< / label > < label for = "__tabbed_7_8" > C#< / label > < label for = "__tabbed_7_9" > Swift< / label > < label for = "__tabbed_7_10" > Zig< / label > < / div >
< div class = "tabbed-content" >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-60-1" name = "__codelineno-60-1" href = "#__codelineno-60-1" > < / a > < span class = "cm" > /* 平方阶 */< / span >
< a id = "__codelineno-60-2" name = "__codelineno-60-2" href = "#__codelineno-60-2" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > quadratic< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-60-3" name = "__codelineno-60-3" href = "#__codelineno-60-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 矩阵占用 O(n^2) 空间< / span >
< a id = "__codelineno-60-4" name = "__codelineno-60-4" href = "#__codelineno-60-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "o" > [][]< / span > < span class = "w" > < / span > < span class = "n" > numMatrix< / 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 = "n" > n< / span > < span class = "o" > ]< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-60-5" name = "__codelineno-60-5" href = "#__codelineno-60-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 二维列表占用 O(n^2) 空间< / span >
< a id = "__codelineno-60-6" name = "__codelineno-60-6" href = "#__codelineno-60-6" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "n" > numList< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > ArrayList< / span > < span class = "o" > < > < / span > < span class = "p" > ();< / span >
< a id = "__codelineno-60-7" name = "__codelineno-60-7" href = "#__codelineno-60-7" > < / 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-60-8" name = "__codelineno-60-8" href = "#__codelineno-60-8" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > tmp< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > ArrayList< / span > < span class = "o" > < > < / span > < span class = "p" > ();< / span >
< a id = "__codelineno-60-9" name = "__codelineno-60-9" href = "#__codelineno-60-9" > < / 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" > j< / 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" > j< / 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" > j< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-60-10" name = "__codelineno-60-10" href = "#__codelineno-60-10" > < / a > < span class = "w" > < / span > < span class = "n" > tmp< / span > < span class = "p" > .< / span > < span class = "na" > add< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > );< / span >
< a id = "__codelineno-60-11" name = "__codelineno-60-11" href = "#__codelineno-60-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-60-12" name = "__codelineno-60-12" href = "#__codelineno-60-12" > < / a > < span class = "w" > < / span > < span class = "n" > numList< / span > < span class = "p" > .< / span > < span class = "na" > add< / span > < span class = "p" > (< / span > < span class = "n" > tmp< / span > < span class = "p" > );< / span >
< a id = "__codelineno-60-13" name = "__codelineno-60-13" href = "#__codelineno-60-13" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-60-14" name = "__codelineno-60-14" href = "#__codelineno-60-14" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-61-1" name = "__codelineno-61-1" href = "#__codelineno-61-1" > < / a > < span class = "cm" > /* 平方阶 */< / span >
< a id = "__codelineno-61-2" name = "__codelineno-61-2" href = "#__codelineno-61-2" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > quadratic< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-61-3" name = "__codelineno-61-3" href = "#__codelineno-61-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 二维列表占用 O(n^2) 空间< / span >
< a id = "__codelineno-61-4" name = "__codelineno-61-4" href = "#__codelineno-61-4" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / 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" > numMatrix< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-61-5" name = "__codelineno-61-5" href = "#__codelineno-61-5" > < / 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-61-6" name = "__codelineno-61-6" href = "#__codelineno-61-6" > < / 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" > tmp< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-61-7" name = "__codelineno-61-7" href = "#__codelineno-61-7" > < / 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" > j< / 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" > j< / 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" > j< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-61-8" name = "__codelineno-61-8" href = "#__codelineno-61-8" > < / a > < span class = "w" > < / span > < span class = "n" > tmp< / span > < span class = "p" > .< / span > < span class = "n" > push_back< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > );< / span >
< a id = "__codelineno-61-9" name = "__codelineno-61-9" href = "#__codelineno-61-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-61-10" name = "__codelineno-61-10" href = "#__codelineno-61-10" > < / a > < span class = "w" > < / span > < span class = "n" > numMatrix< / span > < span class = "p" > .< / span > < span class = "n" > push_back< / span > < span class = "p" > (< / span > < span class = "n" > tmp< / span > < span class = "p" > );< / span >
< a id = "__codelineno-61-11" name = "__codelineno-61-11" href = "#__codelineno-61-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-61-12" name = "__codelineno-61-12" href = "#__codelineno-61-12" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-03-12 18:46:10 +08:00
< div class = "highlight" > < span class = "filename" > space_complexity.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-62-1" name = "__codelineno-62-1" href = "#__codelineno-62-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > quadratic< / span > < span class = "p" > (< / span > < span class = "n" > n< / 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 >
2023-04-09 05:12:29 +08:00
< a id = "__codelineno-62-2" name = "__codelineno-62-2" href = "#__codelineno-62-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 平方阶" " " < / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-62-3" name = "__codelineno-62-3" href = "#__codelineno-62-3" > < / a > < span class = "c1" > # 二维列表占用 O(n^2) 空间< / span >
2023-05-22 22:01:26 +08:00
< a id = "__codelineno-62-4" name = "__codelineno-62-4" href = "#__codelineno-62-4" > < / a > < span class = "n" > num_matrix< / 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 > < span class = "k" > for< / span > < span class = "n" > _< / span > < span class = "ow" > in< / span > < span class = "nb" > range< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > )]< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-63-1" name = "__codelineno-63-1" href = "#__codelineno-63-1" > < / a > < span class = "cm" > /* 平方阶 */< / span >
< a id = "__codelineno-63-2" name = "__codelineno-63-2" href = "#__codelineno-63-2" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > spaceQuadratic< / span > < span class = "p" > (< / span > < span class = "nx" > n< / 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-63-3" name = "__codelineno-63-3" href = "#__codelineno-63-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 矩阵占用 O(n^2) 空间< / span >
< a id = "__codelineno-63-4" name = "__codelineno-63-4" href = "#__codelineno-63-4" > < / a > < span class = "w" > < / span > < span class = "nx" > numMatrix< / 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-63-5" name = "__codelineno-63-5" href = "#__codelineno-63-5" > < / 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-63-6" name = "__codelineno-63-6" href = "#__codelineno-63-6" > < / a > < span class = "w" > < / span > < span class = "nx" > numMatrix< / 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 = "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-63-7" name = "__codelineno-63-7" href = "#__codelineno-63-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-63-8" name = "__codelineno-63-8" href = "#__codelineno-63-8" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-64-1" name = "__codelineno-64-1" href = "#__codelineno-64-1" > < / a > < span class = "cm" > /* 平方阶 */< / span >
< a id = "__codelineno-64-2" name = "__codelineno-64-2" href = "#__codelineno-64-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > quadratic< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-64-3" name = "__codelineno-64-3" href = "#__codelineno-64-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 矩阵占用 O(n^2) 空间< / span >
2023-04-17 21:57:50 +08:00
< a id = "__codelineno-64-4" name = "__codelineno-64-4" href = "#__codelineno-64-4" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > numMatrix< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > Array< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "p" > )< / span >
< a id = "__codelineno-64-5" name = "__codelineno-64-5" href = "#__codelineno-64-5" > < / a > < span class = "w" > < / span > < span class = "p" > .< / span > < span class = "nx" > fill< / span > < span class = "p" > (< / span > < span class = "kc" > null< / span > < span class = "p" > )< / span >
< a id = "__codelineno-64-6" name = "__codelineno-64-6" href = "#__codelineno-64-6" > < / a > < span class = "w" > < / span > < span class = "p" > .< / span > < span class = "nx" > map< / span > < span class = "p" > (()< / span > < span class = "w" > < / span > < span class = "p" > => < / 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 = "kc" > null< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-64-7" name = "__codelineno-64-7" href = "#__codelineno-64-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 二维列表占用 O(n^2) 空间< / span >
< a id = "__codelineno-64-8" name = "__codelineno-64-8" href = "#__codelineno-64-8" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > numList< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [];< / span >
< a id = "__codelineno-64-9" name = "__codelineno-64-9" href = "#__codelineno-64-9" > < / 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-64-10" name = "__codelineno-64-10" href = "#__codelineno-64-10" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > tmp< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [];< / span >
< a id = "__codelineno-64-11" name = "__codelineno-64-11" href = "#__codelineno-64-11" > < / 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" > j< / 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" > j< / 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" > j< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-64-12" name = "__codelineno-64-12" href = "#__codelineno-64-12" > < / a > < span class = "w" > < / span > < span class = "nx" > tmp< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > (< / span > < span class = "mf" > 0< / span > < span class = "p" > );< / span >
< a id = "__codelineno-64-13" name = "__codelineno-64-13" href = "#__codelineno-64-13" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-64-14" name = "__codelineno-64-14" href = "#__codelineno-64-14" > < / a > < span class = "w" > < / span > < span class = "nx" > numList< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > (< / span > < span class = "nx" > tmp< / span > < span class = "p" > );< / span >
< a id = "__codelineno-64-15" name = "__codelineno-64-15" href = "#__codelineno-64-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-64-16" name = "__codelineno-64-16" href = "#__codelineno-64-16" > < / a > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-65-1" name = "__codelineno-65-1" href = "#__codelineno-65-1" > < / a > < span class = "cm" > /* 平方阶 */< / span >
< a id = "__codelineno-65-2" name = "__codelineno-65-2" href = "#__codelineno-65-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > quadratic< / span > < span class = "p" > (< / span > < span class = "nx" > n< / 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-65-3" name = "__codelineno-65-3" href = "#__codelineno-65-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 矩阵占用 O(n^2) 空间< / span >
2023-03-03 02:46:43 +08:00
< a id = "__codelineno-65-4" name = "__codelineno-65-4" href = "#__codelineno-65-4" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > numMatrix< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > Array< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "p" > )< / span >
< a id = "__codelineno-65-5" name = "__codelineno-65-5" href = "#__codelineno-65-5" > < / a > < span class = "w" > < / span > < span class = "p" > .< / span > < span class = "nx" > fill< / span > < span class = "p" > (< / span > < span class = "kc" > null< / span > < span class = "p" > )< / span >
< a id = "__codelineno-65-6" name = "__codelineno-65-6" href = "#__codelineno-65-6" > < / a > < span class = "w" > < / span > < span class = "p" > .< / span > < span class = "nx" > map< / span > < span class = "p" > (()< / span > < span class = "w" > < / span > < span class = "p" > => < / 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 = "kc" > null< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-65-7" name = "__codelineno-65-7" href = "#__codelineno-65-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 二维列表占用 O(n^2) 空间< / span >
< a id = "__codelineno-65-8" name = "__codelineno-65-8" href = "#__codelineno-65-8" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > numList< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [];< / span >
< a id = "__codelineno-65-9" name = "__codelineno-65-9" href = "#__codelineno-65-9" > < / 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-65-10" name = "__codelineno-65-10" href = "#__codelineno-65-10" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > tmp< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [];< / span >
< a id = "__codelineno-65-11" name = "__codelineno-65-11" href = "#__codelineno-65-11" > < / 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" > j< / 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" > j< / 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" > j< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-65-12" name = "__codelineno-65-12" href = "#__codelineno-65-12" > < / a > < span class = "w" > < / span > < span class = "nx" > tmp< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > (< / span > < span class = "mf" > 0< / span > < span class = "p" > );< / span >
< a id = "__codelineno-65-13" name = "__codelineno-65-13" href = "#__codelineno-65-13" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-65-14" name = "__codelineno-65-14" href = "#__codelineno-65-14" > < / a > < span class = "w" > < / span > < span class = "nx" > numList< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > (< / span > < span class = "nx" > tmp< / span > < span class = "p" > );< / span >
< a id = "__codelineno-65-15" name = "__codelineno-65-15" href = "#__codelineno-65-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-65-16" name = "__codelineno-65-16" href = "#__codelineno-65-16" > < / a > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-04-18 20:19:15 +08:00
< div class = "highlight" > < span class = "filename" > space_complexity.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-66-1" name = "__codelineno-66-1" href = "#__codelineno-66-1" > < / a > < span class = "cm" > /* 平方阶 */< / span >
< a id = "__codelineno-66-2" name = "__codelineno-66-2" href = "#__codelineno-66-2" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > quadratic< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-66-3" name = "__codelineno-66-3" href = "#__codelineno-66-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 二维列表占用 O(n^2) 空间< / span >
< a id = "__codelineno-66-4" name = "__codelineno-66-4" href = "#__codelineno-66-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "o" > **< / span > < span class = "n" > numMatrix< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > malloc< / span > < span class = "p" > (< / span > < span class = "k" > sizeof< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > );< / span >
< a id = "__codelineno-66-5" name = "__codelineno-66-5" href = "#__codelineno-66-5" > < / 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-66-6" name = "__codelineno-66-6" href = "#__codelineno-66-6" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > tmp< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > malloc< / span > < span class = "p" > (< / span > < span class = "k" > sizeof< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > );< / span >
< a id = "__codelineno-66-7" name = "__codelineno-66-7" href = "#__codelineno-66-7" > < / 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" > j< / 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" > j< / 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" > j< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-66-8" name = "__codelineno-66-8" href = "#__codelineno-66-8" > < / a > < span class = "w" > < / span > < span class = "n" > tmp< / 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 = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-66-9" name = "__codelineno-66-9" href = "#__codelineno-66-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-66-10" name = "__codelineno-66-10" href = "#__codelineno-66-10" > < / a > < span class = "w" > < / span > < span class = "n" > numMatrix< / 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" > tmp< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-66-11" name = "__codelineno-66-11" href = "#__codelineno-66-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-66-12" name = "__codelineno-66-12" href = "#__codelineno-66-12" > < / a >
< a id = "__codelineno-66-13" name = "__codelineno-66-13" href = "#__codelineno-66-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 内存释放< / span >
< a id = "__codelineno-66-14" name = "__codelineno-66-14" href = "#__codelineno-66-14" > < / 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-66-15" name = "__codelineno-66-15" href = "#__codelineno-66-15" > < / a > < span class = "w" > < / span > < span class = "n" > free< / span > < span class = "p" > (< / span > < span class = "n" > numMatrix< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]);< / span >
< a id = "__codelineno-66-16" name = "__codelineno-66-16" href = "#__codelineno-66-16" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-66-17" name = "__codelineno-66-17" href = "#__codelineno-66-17" > < / a > < span class = "w" > < / span > < span class = "n" > free< / span > < span class = "p" > (< / span > < span class = "n" > numMatrix< / span > < span class = "p" > );< / span >
< a id = "__codelineno-66-18" name = "__codelineno-66-18" href = "#__codelineno-66-18" > < / a > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-67-1" name = "__codelineno-67-1" href = "#__codelineno-67-1" > < / a > < span class = "cm" > /* 平方阶 */< / span >
2023-04-23 14:58:11 +08:00
< a id = "__codelineno-67-2" name = "__codelineno-67-2" href = "#__codelineno-67-2" > < / a > < span class = "k" > void< / span > < span class = "w" > < / span > < span class = "nf" > quadratic< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-67-3" name = "__codelineno-67-3" href = "#__codelineno-67-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 矩阵占用 O(n^2) 空间< / span >
< a id = "__codelineno-67-4" name = "__codelineno-67-4" href = "#__codelineno-67-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > [,]< / span > < span class = "w" > < / span > < span class = "n" > numMatrix< / 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 = "p" > [< / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-67-5" name = "__codelineno-67-5" href = "#__codelineno-67-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 二维列表占用 O(n^2) 空间< / span >
< a id = "__codelineno-67-6" name = "__codelineno-67-6" href = "#__codelineno-67-6" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "n" > numList< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-67-7" name = "__codelineno-67-7" href = "#__codelineno-67-7" > < / 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 = "m" > 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-67-8" name = "__codelineno-67-8" href = "#__codelineno-67-8" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > tmp< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-67-9" name = "__codelineno-67-9" href = "#__codelineno-67-9" > < / 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" > j< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > ;< / 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" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-67-10" name = "__codelineno-67-10" href = "#__codelineno-67-10" > < / a > < span class = "w" > < / span > < span class = "n" > tmp< / span > < span class = "p" > .< / span > < span class = "n" > Add< / span > < span class = "p" > (< / span > < span class = "m" > 0< / span > < span class = "p" > );< / span >
< a id = "__codelineno-67-11" name = "__codelineno-67-11" href = "#__codelineno-67-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-67-12" name = "__codelineno-67-12" href = "#__codelineno-67-12" > < / a > < span class = "w" > < / span > < span class = "n" > numList< / span > < span class = "p" > .< / span > < span class = "n" > Add< / span > < span class = "p" > (< / span > < span class = "n" > tmp< / span > < span class = "p" > );< / span >
< a id = "__codelineno-67-13" name = "__codelineno-67-13" href = "#__codelineno-67-13" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-67-14" name = "__codelineno-67-14" href = "#__codelineno-67-14" > < / a > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-68-1" name = "__codelineno-68-1" href = "#__codelineno-68-1" > < / a > < span class = "cm" > /* 平方阶 */< / span >
< a id = "__codelineno-68-2" name = "__codelineno-68-2" href = "#__codelineno-68-2" > < / a > < span class = "kd" > func< / span > < span class = "nf" > quadratic< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / span > < span class = "p" > )< / span > < span class = "p" > {< / span >
< a id = "__codelineno-68-3" name = "__codelineno-68-3" href = "#__codelineno-68-3" > < / a > < span class = "c1" > // 二维列表占用 O(n^2) 空间< / span >
< a id = "__codelineno-68-4" name = "__codelineno-68-4" href = "#__codelineno-68-4" > < / a > < span class = "kd" > let< / span > < span class = "nv" > numList< / 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 = "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 > < span class = "bp" > count< / span > < span class = "p" > :< / span > < span class = "n" > n< / span > < span class = "p" > )< / span >
< a id = "__codelineno-68-5" name = "__codelineno-68-5" href = "#__codelineno-68-5" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-69-1" name = "__codelineno-69-1" href = "#__codelineno-69-1" > < / a > < span class = "c1" > // 平方阶< / span >
< a id = "__codelineno-69-2" name = "__codelineno-69-2" href = "#__codelineno-69-2" > < / a > < span class = "k" > fn< / span > < span class = "w" > < / span > < span class = "n" > quadratic< / span > < span class = "p" > (< / span > < span class = "n" > n< / 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-69-3" name = "__codelineno-69-3" href = "#__codelineno-69-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 二维列表占用 O(n^2) 空间< / span >
< a id = "__codelineno-69-4" name = "__codelineno-69-4" href = "#__codelineno-69-4" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > nodes< / 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" > ArrayList< / span > < span class = "p" > (< / span > < span class = "n" > std< / span > < span class = "p" > .< / span > < span class = "n" > ArrayList< / span > < span class = "p" > (< / span > < span class = "kt" > i32< / 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-69-5" name = "__codelineno-69-5" href = "#__codelineno-69-5" > < / a > < span class = "w" > < / span > < span class = "k" > defer< / span > < span class = "w" > < / span > < span class = "n" > nodes< / span > < span class = "p" > .< / span > < span class = "n" > deinit< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-69-6" name = "__codelineno-69-6" href = "#__codelineno-69-6" > < / 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" > i32< / 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-69-7" name = "__codelineno-69-7" href = "#__codelineno-69-7" > < / 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-69-8" name = "__codelineno-69-8" href = "#__codelineno-69-8" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > tmp< / 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" > ArrayList< / span > < span class = "p" > (< / span > < span class = "kt" > i32< / 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-69-9" name = "__codelineno-69-9" href = "#__codelineno-69-9" > < / a > < span class = "w" > < / span > < span class = "k" > defer< / span > < span class = "w" > < / span > < span class = "n" > tmp< / span > < span class = "p" > .< / span > < span class = "n" > deinit< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-69-10" name = "__codelineno-69-10" href = "#__codelineno-69-10" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > j< / 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" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-69-11" name = "__codelineno-69-11" href = "#__codelineno-69-11" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > j< / 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" > j< / 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-69-12" name = "__codelineno-69-12" href = "#__codelineno-69-12" > < / a > < span class = "w" > < / span > < span class = "k" > try< / span > < span class = "w" > < / span > < span class = "n" > tmp< / span > < span class = "p" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > );< / span >
< a id = "__codelineno-69-13" name = "__codelineno-69-13" href = "#__codelineno-69-13" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-69-14" name = "__codelineno-69-14" href = "#__codelineno-69-14" > < / a > < span class = "w" > < / span > < span class = "k" > try< / span > < span class = "w" > < / span > < span class = "n" > nodes< / span > < span class = "p" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > tmp< / span > < span class = "p" > );< / span >
< a id = "__codelineno-69-15" name = "__codelineno-69-15" href = "#__codelineno-69-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-69-16" name = "__codelineno-69-16" href = "#__codelineno-69-16" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
2023-04-10 03:12:10 +08:00
< p > 在以下递归函数中，同时存在 < span class = "arithmatex" > \(n\)< / span > 个未返回的 < code > algorithm()< / code > ，并且每个函数中都初始化了一个数组，长度分别为 < span class = "arithmatex" > \(n, n-1, n-2, ..., 2, 1\)< / span > ，平均长度为 < span class = "arithmatex" > \(\frac{n}{2}\)< / span > ，因此总体占用 < span class = "arithmatex" > \(O(n^2)\)< / span > 空间。< / p >
2023-02-08 14:54:41 +08:00
< div class = "tabbed-set tabbed-alternate" data-tabs = "8:10" > < input checked = "checked" id = "__tabbed_8_1" name = "__tabbed_8" type = "radio" / > < input id = "__tabbed_8_2" name = "__tabbed_8" type = "radio" / > < input id = "__tabbed_8_3" name = "__tabbed_8" type = "radio" / > < input id = "__tabbed_8_4" name = "__tabbed_8" type = "radio" / > < input id = "__tabbed_8_5" name = "__tabbed_8" type = "radio" / > < input id = "__tabbed_8_6" name = "__tabbed_8" type = "radio" / > < input id = "__tabbed_8_7" name = "__tabbed_8" type = "radio" / > < input id = "__tabbed_8_8" name = "__tabbed_8" type = "radio" / > < input id = "__tabbed_8_9" name = "__tabbed_8" type = "radio" / > < input id = "__tabbed_8_10" name = "__tabbed_8" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_8_1" > Java< / label > < label for = "__tabbed_8_2" > C++< / label > < label for = "__tabbed_8_3" > Python< / label > < label for = "__tabbed_8_4" > Go< / label > < label for = "__tabbed_8_5" > JavaScript< / label > < label for = "__tabbed_8_6" > TypeScript< / label > < label for = "__tabbed_8_7" > C< / label > < label for = "__tabbed_8_8" > C#< / label > < label for = "__tabbed_8_9" > Swift< / label > < label for = "__tabbed_8_10" > Zig< / label > < / div >
< div class = "tabbed-content" >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-70-1" name = "__codelineno-70-1" href = "#__codelineno-70-1" > < / a > < span class = "cm" > /* 平方阶（递归实现） */< / span >
< a id = "__codelineno-70-2" name = "__codelineno-70-2" href = "#__codelineno-70-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > quadraticRecur< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-04-14 04:01:48 +08:00
< a id = "__codelineno-70-3" name = "__codelineno-70-3" href = "#__codelineno-70-3" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > n< / 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-70-4" name = "__codelineno-70-4" href = "#__codelineno-70-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-70-5" name = "__codelineno-70-5" href = "#__codelineno-70-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 数组 nums 长度为 n, n-1, ..., 2, 1< / span >
< a id = "__codelineno-70-6" name = "__codelineno-70-6" href = "#__codelineno-70-6" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "o" > []< / span > < span class = "w" > < / span > < span class = "n" > nums< / 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-70-7" name = "__codelineno-70-7" href = "#__codelineno-70-7" > < / a > < span class = "w" > < / span > < span class = "n" > System< / span > < span class = "p" > .< / span > < span class = "na" > out< / span > < span class = "p" > .< / span > < span class = "na" > println< / span > < span class = "p" > (< / span > < span class = "s" > " 递归 n = " < / 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 = "s" > " 中的 nums 长度 = " < / 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-70-8" name = "__codelineno-70-8" href = "#__codelineno-70-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > quadraticRecur< / span > < span class = "p" > (< / 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-70-9" name = "__codelineno-70-9" href = "#__codelineno-70-9" > < / a > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-71-1" name = "__codelineno-71-1" href = "#__codelineno-71-1" > < / a > < span class = "cm" > /* 平方阶（递归实现） */< / span >
< a id = "__codelineno-71-2" name = "__codelineno-71-2" href = "#__codelineno-71-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > quadraticRecur< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-04-14 04:01:48 +08:00
< a id = "__codelineno-71-3" name = "__codelineno-71-3" href = "#__codelineno-71-3" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > n< / 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-71-4" name = "__codelineno-71-4" href = "#__codelineno-71-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-71-5" name = "__codelineno-71-5" href = "#__codelineno-71-5" > < / 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" > nums< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > );< / span >
< a id = "__codelineno-71-6" name = "__codelineno-71-6" href = "#__codelineno-71-6" > < / a > < span class = "w" > < / span > < span class = "n" > cout< / span > < span class = "w" > < / span > < span class = "o" > < < < / span > < span class = "w" > < / span > < span class = "s" > " 递归 n = " < / 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 = "s" > " 中的 nums 长度 = " < / 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 > < span class = "w" > < / span > < span class = "o" > < < < / span > < span class = "w" > < / span > < span class = "n" > endl< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-71-7" name = "__codelineno-71-7" href = "#__codelineno-71-7" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > quadraticRecur< / span > < span class = "p" > (< / 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-71-8" name = "__codelineno-71-8" href = "#__codelineno-71-8" > < / a > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-03-12 18:46:10 +08:00
< div class = "highlight" > < span class = "filename" > space_complexity.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-72-1" name = "__codelineno-72-1" href = "#__codelineno-72-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > quadratic_recur< / span > < span class = "p" > (< / span > < span class = "n" > n< / 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 >
2023-04-09 05:12:29 +08:00
< a id = "__codelineno-72-2" name = "__codelineno-72-2" href = "#__codelineno-72-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 平方阶（递归实现）" " " < / span >
< a id = "__codelineno-72-3" name = "__codelineno-72-3" href = "#__codelineno-72-3" > < / a > < span class = "k" > if< / span > < span class = "n" > n< / span > < span class = "o" > < =< / span > < span class = "mi" > 0< / span > < span class = "p" > :< / span >
< a id = "__codelineno-72-4" name = "__codelineno-72-4" href = "#__codelineno-72-4" > < / a > < span class = "k" > return< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-72-5" name = "__codelineno-72-5" href = "#__codelineno-72-5" > < / a > < span class = "c1" > # 数组 nums 长度为 n, n-1, ..., 2, 1< / span >
2023-05-22 22:01:26 +08:00
< a id = "__codelineno-72-6" name = "__codelineno-72-6" href = "#__codelineno-72-6" > < / a > < span class = "n" > nums< / 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 >
2023-04-09 05:12:29 +08:00
< a id = "__codelineno-72-7" name = "__codelineno-72-7" href = "#__codelineno-72-7" > < / a > < span class = "k" > return< / span > < span class = "n" > quadratic_recur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-73-1" name = "__codelineno-73-1" href = "#__codelineno-73-1" > < / a > < span class = "cm" > /* 平方阶（递归实现） */< / span >
< a id = "__codelineno-73-2" name = "__codelineno-73-2" href = "#__codelineno-73-2" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > spaceQuadraticRecur< / span > < span class = "p" > (< / span > < span class = "nx" > n< / 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-73-3" name = "__codelineno-73-3" href = "#__codelineno-73-3" > < / a > < span class = "w" > < / span > < span class = "k" > if< / 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" > 0< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-73-4" name = "__codelineno-73-4" href = "#__codelineno-73-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-73-5" name = "__codelineno-73-5" href = "#__codelineno-73-5" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
2023-02-09 04:43:20 +08:00
< a id = "__codelineno-73-6" name = "__codelineno-73-6" href = "#__codelineno-73-6" > < / a > < span class = "w" > < / span > < span class = "nx" > nums< / 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-73-7" name = "__codelineno-73-7" href = "#__codelineno-73-7" > < / a > < span class = "w" > < / span > < span class = "nx" > fmt< / span > < span class = "p" > .< / span > < span class = "nx" > Printf< / span > < span class = "p" > (< / span > < span class = "s" > " 递归 n = %d 中的 nums 长度 = %d \n" < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "p" > ))< / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-73-8" name = "__codelineno-73-8" href = "#__codelineno-73-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > spaceQuadraticRecur< / span > < span class = "p" > (< / 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 >
< a id = "__codelineno-73-9" name = "__codelineno-73-9" href = "#__codelineno-73-9" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-74-1" name = "__codelineno-74-1" href = "#__codelineno-74-1" > < / a > < span class = "cm" > /* 平方阶（递归实现） */< / span >
< a id = "__codelineno-74-2" name = "__codelineno-74-2" href = "#__codelineno-74-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > quadraticRecur< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-74-3" name = "__codelineno-74-3" href = "#__codelineno-74-3" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > n< / 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 = "k" > return< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-74-4" name = "__codelineno-74-4" href = "#__codelineno-74-4" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > nums< / 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 >
< a id = "__codelineno-74-5" name = "__codelineno-74-5" href = "#__codelineno-74-5" > < / a > < span class = "w" > < / span > < span class = "nx" > console< / span > < span class = "p" > .< / span > < span class = "nx" > log< / span > < span class = "p" > (< / span > < span class = "sb" > `递归 n = < / span > < span class = "si" > ${< / span > < span class = "nx" > n< / span > < span class = "si" > }< / span > < span class = "sb" > 中的 nums 长度 = < / span > < span class = "si" > ${< / span > < span class = "nx" > nums< / span > < span class = "p" > .< / span > < span class = "nx" > length< / span > < span class = "si" > }< / span > < span class = "sb" > `< / span > < span class = "p" > );< / span >
< a id = "__codelineno-74-6" name = "__codelineno-74-6" href = "#__codelineno-74-6" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > quadraticRecur< / span > < span class = "p" > (< / 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 >
< a id = "__codelineno-74-7" name = "__codelineno-74-7" href = "#__codelineno-74-7" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-75-1" name = "__codelineno-75-1" href = "#__codelineno-75-1" > < / a > < span class = "cm" > /* 平方阶（递归实现） */< / span >
< a id = "__codelineno-75-2" name = "__codelineno-75-2" href = "#__codelineno-75-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > quadraticRecur< / span > < span class = "p" > (< / span > < span class = "nx" > n< / 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-75-3" name = "__codelineno-75-3" href = "#__codelineno-75-3" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > n< / 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 = "k" > return< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-75-4" name = "__codelineno-75-4" href = "#__codelineno-75-4" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > nums< / 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 >
< a id = "__codelineno-75-5" name = "__codelineno-75-5" href = "#__codelineno-75-5" > < / a > < span class = "w" > < / span > < span class = "nx" > console< / span > < span class = "p" > .< / span > < span class = "nx" > log< / span > < span class = "p" > (< / span > < span class = "sb" > `递归 n = < / span > < span class = "si" > ${< / span > < span class = "nx" > n< / span > < span class = "si" > }< / span > < span class = "sb" > 中的 nums 长度 = < / span > < span class = "si" > ${< / span > < span class = "nx" > nums< / span > < span class = "p" > .< / span > < span class = "nx" > length< / span > < span class = "si" > }< / span > < span class = "sb" > `< / span > < span class = "p" > );< / span >
< a id = "__codelineno-75-6" name = "__codelineno-75-6" href = "#__codelineno-75-6" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > quadraticRecur< / span > < span class = "p" > (< / 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 >
< a id = "__codelineno-75-7" name = "__codelineno-75-7" href = "#__codelineno-75-7" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-04-18 20:19:15 +08:00
< div class = "highlight" > < span class = "filename" > space_complexity.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-76-1" name = "__codelineno-76-1" href = "#__codelineno-76-1" > < / a > < span class = "cm" > /* 平方阶（递归实现） */< / span >
< a id = "__codelineno-76-2" name = "__codelineno-76-2" href = "#__codelineno-76-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > quadraticRecur< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-76-3" name = "__codelineno-76-3" href = "#__codelineno-76-3" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > n< / 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-76-4" name = "__codelineno-76-4" href = "#__codelineno-76-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-76-5" name = "__codelineno-76-5" href = "#__codelineno-76-5" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > nums< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > malloc< / span > < span class = "p" > (< / span > < span class = "k" > sizeof< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > );< / span >
< a id = "__codelineno-76-6" name = "__codelineno-76-6" href = "#__codelineno-76-6" > < / a > < span class = "w" > < / span > < span class = "n" > printf< / span > < span class = "p" > (< / span > < span class = "s" > " 递归 n = %d 中的 nums 长度 = %d< / span > < span class = "se" > \r\n< / span > < span class = "s" > " < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > );< / span >
< a id = "__codelineno-76-7" name = "__codelineno-76-7" href = "#__codelineno-76-7" > < / a > < span class = "w" > < / span > < span class = "n" > free< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > );< / span >
< a id = "__codelineno-76-8" name = "__codelineno-76-8" href = "#__codelineno-76-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > quadraticRecur< / span > < span class = "p" > (< / 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-76-9" name = "__codelineno-76-9" href = "#__codelineno-76-9" > < / a > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-77-1" name = "__codelineno-77-1" href = "#__codelineno-77-1" > < / a > < span class = "cm" > /* 平方阶（递归实现） */< / span >
2023-04-23 14:58:11 +08:00
< a id = "__codelineno-77-2" name = "__codelineno-77-2" href = "#__codelineno-77-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > quadraticRecur< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-77-3" name = "__codelineno-77-3" href = "#__codelineno-77-3" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-77-4" name = "__codelineno-77-4" href = "#__codelineno-77-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "n" > nums< / 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 = "p" > [< / span > < span class = "n" > n< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-77-5" name = "__codelineno-77-5" href = "#__codelineno-77-5" > < / a > < span class = "w" > < / span > < span class = "n" > Console< / span > < span class = "p" > .< / span > < span class = "n" > WriteLine< / span > < span class = "p" > (< / span > < span class = "s" > " 递归 n = " < / 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 = "s" > " 中的 nums 长度 = " < / 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" > Length< / span > < span class = "p" > );< / span >
< a id = "__codelineno-77-6" name = "__codelineno-77-6" href = "#__codelineno-77-6" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nf" > quadraticRecur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > );< / span >
< a id = "__codelineno-77-7" name = "__codelineno-77-7" href = "#__codelineno-77-7" > < / a > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-78-1" name = "__codelineno-78-1" href = "#__codelineno-78-1" > < / a > < span class = "cm" > /* 平方阶（递归实现） */< / span >
2023-02-08 20:30:33 +08:00
< a id = "__codelineno-78-2" name = "__codelineno-78-2" href = "#__codelineno-78-2" > < / a > < span class = "p" > @< / span > < span class = "n" > discardableResult< / span >
< a id = "__codelineno-78-3" name = "__codelineno-78-3" href = "#__codelineno-78-3" > < / a > < span class = "kd" > func< / span > < span class = "nf" > quadraticRecur< / span > < span class = "p" > (< / span > < span class = "n" > n< / 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-78-4" name = "__codelineno-78-4" href = "#__codelineno-78-4" > < / a > < span class = "k" > if< / span > < span class = "n" > n< / span > < span class = "o" > < =< / span > < span class = "mi" > 0< / span > < span class = "p" > {< / span >
< a id = "__codelineno-78-5" name = "__codelineno-78-5" href = "#__codelineno-78-5" > < / a > < span class = "k" > return< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-78-6" name = "__codelineno-78-6" href = "#__codelineno-78-6" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-78-7" name = "__codelineno-78-7" href = "#__codelineno-78-7" > < / a > < span class = "c1" > // 数组 nums 长度为 n, n-1, ..., 2, 1< / span >
< a id = "__codelineno-78-8" name = "__codelineno-78-8" href = "#__codelineno-78-8" > < / a > < span class = "kd" > let< / span > < span class = "nv" > nums< / 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-78-9" name = "__codelineno-78-9" href = "#__codelineno-78-9" > < / a > < span class = "bp" > print< / span > < span class = "p" > (< / span > < span class = "s" > " 递归 n = < / span > < span class = "si" > \(< / span > < span class = "n" > n< / span > < span class = "si" > )< / span > < span class = "s" > 中的 nums 长度 = < / span > < span class = "si" > \(< / span > < span class = "n" > nums< / span > < span class = "p" > .< / span > < span class = "bp" > count< / span > < span class = "si" > )< / span > < span class = "s" > " < / span > < span class = "p" > )< / span >
< a id = "__codelineno-78-10" name = "__codelineno-78-10" href = "#__codelineno-78-10" > < / a > < span class = "k" > return< / span > < span class = "n" > quadraticRecur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > :< / span > < span class = "n" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span >
< a id = "__codelineno-78-11" name = "__codelineno-78-11" href = "#__codelineno-78-11" > < / a > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-79-1" name = "__codelineno-79-1" href = "#__codelineno-79-1" > < / a > < span class = "c1" > // 平方阶（递归实现）< / span >
< a id = "__codelineno-79-2" name = "__codelineno-79-2" href = "#__codelineno-79-2" > < / a > < span class = "k" > fn< / span > < span class = "w" > < / span > < span class = "n" > quadraticRecur< / span > < span class = "p" > (< / span > < span class = "kr" > comptime< / span > < span class = "w" > < / span > < span class = "n" > n< / 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-79-3" name = "__codelineno-79-3" href = "#__codelineno-79-3" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > n< / 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" > return< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-79-4" name = "__codelineno-79-4" href = "#__codelineno-79-4" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [< / span > < span class = "n" > _< / span > < span class = "p" > ]< / span > < span class = "kt" > i32< / span > < span class = "p" > {< / span > < span class = "mi" > 0< / span > < span class = "p" > }< / span > < span class = "o" > **< / span > < span class = "n" > n< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-79-5" name = "__codelineno-79-5" href = "#__codelineno-79-5" > < / a > < span class = "w" > < / span > < span class = "n" > std< / span > < span class = "p" > .< / span > < span class = "n" > debug< / span > < span class = "p" > .< / span > < span class = "n" > print< / span > < span class = "p" > (< / span > < span class = "s" > " 递归 n = {} 中的 nums 长度 = {}< / span > < span class = "se" > \n< / span > < span class = "s" > " < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "p" > .{< / span > < span class = "n" > n< / span > < span class = "p" > ,< / 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-79-6" name = "__codelineno-79-6" href = "#__codelineno-79-6" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > quadraticRecur< / span > < span class = "p" > (< / 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-79-7" name = "__codelineno-79-7" href = "#__codelineno-79-7" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
2023-02-26 18:18:03 +08:00
< p > < img alt = "递归函数产生的平方阶空间复杂度" src = "../space_complexity.assets/space_complexity_recursive_quadratic.png" / > < / p >
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< p align = "center" > Fig. 递归函数产生的平方阶空间复杂度 < / p >
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< h3 id = "o2n" > 指数阶 < span class = "arithmatex" > \(O(2^n)\)< / span > < a class = "headerlink" href = "#o2n" title = "Permanent link" > ¶ < / a > < / h3 >
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< p > 指数阶常见于二叉树。高度为 < span class = "arithmatex" > \(n\)< / span > 的「满二叉树」的节点数量为 < span class = "arithmatex" > \(2^n - 1\)< / span > ，占用 < span class = "arithmatex" > \(O(2^n)\)< / span > 空间。< / p >
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< div class = "tabbed-set tabbed-alternate" data-tabs = "9:10" > < input checked = "checked" id = "__tabbed_9_1" name = "__tabbed_9" type = "radio" / > < input id = "__tabbed_9_2" name = "__tabbed_9" type = "radio" / > < input id = "__tabbed_9_3" name = "__tabbed_9" type = "radio" / > < input id = "__tabbed_9_4" name = "__tabbed_9" type = "radio" / > < input id = "__tabbed_9_5" name = "__tabbed_9" type = "radio" / > < input id = "__tabbed_9_6" name = "__tabbed_9" type = "radio" / > < input id = "__tabbed_9_7" name = "__tabbed_9" type = "radio" / > < input id = "__tabbed_9_8" name = "__tabbed_9" type = "radio" / > < input id = "__tabbed_9_9" name = "__tabbed_9" type = "radio" / > < input id = "__tabbed_9_10" name = "__tabbed_9" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_9_1" > Java< / label > < label for = "__tabbed_9_2" > C++< / label > < label for = "__tabbed_9_3" > Python< / label > < label for = "__tabbed_9_4" > Go< / label > < label for = "__tabbed_9_5" > JavaScript< / label > < label for = "__tabbed_9_6" > TypeScript< / label > < label for = "__tabbed_9_7" > C< / label > < label for = "__tabbed_9_8" > C#< / label > < label for = "__tabbed_9_9" > Swift< / label > < label for = "__tabbed_9_10" > Zig< / label > < / div >
< div class = "tabbed-content" >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-80-1" name = "__codelineno-80-1" href = "#__codelineno-80-1" > < / a > < span class = "cm" > /* 指数阶（建立满二叉树） */< / span >
< a id = "__codelineno-80-2" name = "__codelineno-80-2" href = "#__codelineno-80-2" > < / a > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "nf" > buildTree< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-04-14 04:01:48 +08:00
< a id = "__codelineno-80-3" name = "__codelineno-80-3" href = "#__codelineno-80-3" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > n< / 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-80-4" name = "__codelineno-80-4" href = "#__codelineno-80-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-80-5" name = "__codelineno-80-5" href = "#__codelineno-80-5" > < / a > < span class = "w" > < / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "n" > root< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > TreeNode< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > );< / span >
< a id = "__codelineno-80-6" name = "__codelineno-80-6" href = "#__codelineno-80-6" > < / a > < span class = "w" > < / span > < span class = "n" > root< / span > < span class = "p" > .< / span > < span class = "na" > left< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > buildTree< / span > < span class = "p" > (< / 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-80-7" name = "__codelineno-80-7" href = "#__codelineno-80-7" > < / a > < span class = "w" > < / span > < span class = "n" > root< / span > < span class = "p" > .< / span > < span class = "na" > right< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > buildTree< / span > < span class = "p" > (< / 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-80-8" name = "__codelineno-80-8" href = "#__codelineno-80-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > root< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-80-9" name = "__codelineno-80-9" href = "#__codelineno-80-9" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-81-1" name = "__codelineno-81-1" href = "#__codelineno-81-1" > < / a > < span class = "cm" > /* 指数阶（建立满二叉树） */< / span >
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< a id = "__codelineno-81-2" name = "__codelineno-81-2" href = "#__codelineno-81-2" > < / a > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nf" > buildTree< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-81-3" name = "__codelineno-81-3" href = "#__codelineno-81-3" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > n< / 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-81-4" name = "__codelineno-81-4" href = "#__codelineno-81-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "k" > nullptr< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-81-5" name = "__codelineno-81-5" href = "#__codelineno-81-5" > < / a > < span class = "w" > < / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > root< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > TreeNode< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > );< / span >
< a id = "__codelineno-81-6" name = "__codelineno-81-6" href = "#__codelineno-81-6" > < / a > < span class = "w" > < / span > < span class = "n" > root< / span > < span class = "o" > -> < / span > < span class = "n" > left< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > buildTree< / span > < span class = "p" > (< / 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-81-7" name = "__codelineno-81-7" href = "#__codelineno-81-7" > < / a > < span class = "w" > < / span > < span class = "n" > root< / span > < span class = "o" > -> < / span > < span class = "n" > right< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > buildTree< / span > < span class = "p" > (< / 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-81-8" name = "__codelineno-81-8" href = "#__codelineno-81-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > root< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-81-9" name = "__codelineno-81-9" href = "#__codelineno-81-9" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > space_complexity.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-82-1" name = "__codelineno-82-1" href = "#__codelineno-82-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > build_tree< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > :< / span > < span class = "nb" > int< / span > < span class = "p" > )< / span > < span class = "o" > -> < / span > < span class = "n" > TreeNode< / span > < span class = "o" > |< / span > < span class = "kc" > None< / span > < span class = "p" > :< / span >
2023-04-09 05:12:29 +08:00
< a id = "__codelineno-82-2" name = "__codelineno-82-2" href = "#__codelineno-82-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 指数阶（建立满二叉树）" " " < / span >
< a id = "__codelineno-82-3" name = "__codelineno-82-3" href = "#__codelineno-82-3" > < / a > < span class = "k" > if< / span > < span class = "n" > n< / span > < span class = "o" > ==< / span > < span class = "mi" > 0< / span > < span class = "p" > :< / span >
< a id = "__codelineno-82-4" name = "__codelineno-82-4" href = "#__codelineno-82-4" > < / a > < span class = "k" > return< / span > < span class = "kc" > None< / span >
< a id = "__codelineno-82-5" name = "__codelineno-82-5" href = "#__codelineno-82-5" > < / a > < span class = "n" > root< / span > < span class = "o" > =< / span > < span class = "n" > TreeNode< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span >
< a id = "__codelineno-82-6" name = "__codelineno-82-6" href = "#__codelineno-82-6" > < / a > < span class = "n" > root< / span > < span class = "o" > .< / span > < span class = "n" > left< / span > < span class = "o" > =< / span > < span class = "n" > build_tree< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span >
< a id = "__codelineno-82-7" name = "__codelineno-82-7" href = "#__codelineno-82-7" > < / a > < span class = "n" > root< / span > < span class = "o" > .< / span > < span class = "n" > right< / span > < span class = "o" > =< / span > < span class = "n" > build_tree< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span >
< a id = "__codelineno-82-8" name = "__codelineno-82-8" href = "#__codelineno-82-8" > < / a > < span class = "k" > return< / span > < span class = "n" > root< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-83-1" name = "__codelineno-83-1" href = "#__codelineno-83-1" > < / a > < span class = "cm" > /* 指数阶（建立满二叉树） */< / span >
< a id = "__codelineno-83-2" name = "__codelineno-83-2" href = "#__codelineno-83-2" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > buildTree< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > treeNode< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-83-3" name = "__codelineno-83-3" href = "#__codelineno-83-3" > < / a > < span class = "w" > < / span > < span class = "k" > if< / 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" > 0< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-83-4" name = "__codelineno-83-4" href = "#__codelineno-83-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "kc" > nil< / span >
< a id = "__codelineno-83-5" name = "__codelineno-83-5" href = "#__codelineno-83-5" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-83-6" name = "__codelineno-83-6" href = "#__codelineno-83-6" > < / a > < span class = "w" > < / span > < span class = "nx" > root< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > newTreeNode< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span >
< a id = "__codelineno-83-7" name = "__codelineno-83-7" href = "#__codelineno-83-7" > < / a > < span class = "w" > < / span > < span class = "nx" > root< / span > < span class = "p" > .< / span > < span class = "nx" > left< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > buildTree< / span > < span class = "p" > (< / 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 >
< a id = "__codelineno-83-8" name = "__codelineno-83-8" href = "#__codelineno-83-8" > < / a > < span class = "w" > < / span > < span class = "nx" > root< / span > < span class = "p" > .< / span > < span class = "nx" > right< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > buildTree< / span > < span class = "p" > (< / 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 >
< a id = "__codelineno-83-9" name = "__codelineno-83-9" href = "#__codelineno-83-9" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > root< / span >
< a id = "__codelineno-83-10" name = "__codelineno-83-10" href = "#__codelineno-83-10" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-84-1" name = "__codelineno-84-1" href = "#__codelineno-84-1" > < / a > < span class = "cm" > /* 指数阶（建立满二叉树） */< / span >
< a id = "__codelineno-84-2" name = "__codelineno-84-2" href = "#__codelineno-84-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > buildTree< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-84-3" name = "__codelineno-84-3" href = "#__codelineno-84-3" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > n< / 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 = "k" > return< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-84-4" name = "__codelineno-84-4" href = "#__codelineno-84-4" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > root< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "ow" > new< / span > < span class = "w" > < / span > < span class = "nx" > TreeNode< / span > < span class = "p" > (< / span > < span class = "mf" > 0< / span > < span class = "p" > );< / span >
< a id = "__codelineno-84-5" name = "__codelineno-84-5" href = "#__codelineno-84-5" > < / a > < span class = "w" > < / span > < span class = "nx" > root< / span > < span class = "p" > .< / span > < span class = "nx" > left< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > buildTree< / span > < span class = "p" > (< / 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 >
< a id = "__codelineno-84-6" name = "__codelineno-84-6" href = "#__codelineno-84-6" > < / a > < span class = "w" > < / span > < span class = "nx" > root< / span > < span class = "p" > .< / span > < span class = "nx" > right< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > buildTree< / span > < span class = "p" > (< / 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 >
< a id = "__codelineno-84-7" name = "__codelineno-84-7" href = "#__codelineno-84-7" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > root< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-84-8" name = "__codelineno-84-8" href = "#__codelineno-84-8" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-85-1" name = "__codelineno-85-1" href = "#__codelineno-85-1" > < / a > < span class = "cm" > /* 指数阶（建立满二叉树） */< / span >
< a id = "__codelineno-85-2" name = "__codelineno-85-2" href = "#__codelineno-85-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > buildTree< / span > < span class = "p" > (< / span > < span class = "nx" > n< / 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 = "nx" > TreeNode< / span > < span class = "w" > < / span > < span class = "o" > |< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-85-3" name = "__codelineno-85-3" href = "#__codelineno-85-3" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > n< / 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 = "k" > return< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-85-4" name = "__codelineno-85-4" href = "#__codelineno-85-4" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > root< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "ow" > new< / span > < span class = "w" > < / span > < span class = "nx" > TreeNode< / span > < span class = "p" > (< / span > < span class = "mf" > 0< / span > < span class = "p" > );< / span >
< a id = "__codelineno-85-5" name = "__codelineno-85-5" href = "#__codelineno-85-5" > < / a > < span class = "w" > < / span > < span class = "nx" > root< / span > < span class = "p" > .< / span > < span class = "nx" > left< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > buildTree< / span > < span class = "p" > (< / 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 >
< a id = "__codelineno-85-6" name = "__codelineno-85-6" href = "#__codelineno-85-6" > < / a > < span class = "w" > < / span > < span class = "nx" > root< / span > < span class = "p" > .< / span > < span class = "nx" > right< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > buildTree< / span > < span class = "p" > (< / 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 >
< a id = "__codelineno-85-7" name = "__codelineno-85-7" href = "#__codelineno-85-7" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > root< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-85-8" name = "__codelineno-85-8" href = "#__codelineno-85-8" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-04-18 20:19:15 +08:00
< div class = "highlight" > < span class = "filename" > space_complexity.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-86-1" name = "__codelineno-86-1" href = "#__codelineno-86-1" > < / a > < span class = "cm" > /* 指数阶（建立满二叉树） */< / span >
< a id = "__codelineno-86-2" name = "__codelineno-86-2" href = "#__codelineno-86-2" > < / a > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nf" > buildTree< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-86-3" name = "__codelineno-86-3" href = "#__codelineno-86-3" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > n< / 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-86-4" name = "__codelineno-86-4" href = "#__codelineno-86-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nb" > NULL< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-86-5" name = "__codelineno-86-5" href = "#__codelineno-86-5" > < / a > < span class = "w" > < / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > root< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > newTreeNode< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > );< / span >
< a id = "__codelineno-86-6" name = "__codelineno-86-6" href = "#__codelineno-86-6" > < / a > < span class = "w" > < / span > < span class = "n" > root< / span > < span class = "o" > -> < / span > < span class = "n" > left< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > buildTree< / span > < span class = "p" > (< / 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-86-7" name = "__codelineno-86-7" href = "#__codelineno-86-7" > < / a > < span class = "w" > < / span > < span class = "n" > root< / span > < span class = "o" > -> < / span > < span class = "n" > right< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > buildTree< / span > < span class = "p" > (< / 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-86-8" name = "__codelineno-86-8" href = "#__codelineno-86-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > root< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-86-9" name = "__codelineno-86-9" href = "#__codelineno-86-9" > < / a > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-87-1" name = "__codelineno-87-1" href = "#__codelineno-87-1" > < / a > < span class = "cm" > /* 指数阶（建立满二叉树） */< / span >
2023-04-23 14:58:11 +08:00
< a id = "__codelineno-87-2" name = "__codelineno-87-2" href = "#__codelineno-87-2" > < / a > < span class = "n" > TreeNode< / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "n" > buildTree< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-87-3" name = "__codelineno-87-3" href = "#__codelineno-87-3" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "k" > null< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-87-4" name = "__codelineno-87-4" href = "#__codelineno-87-4" > < / a > < span class = "w" > < / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "n" > root< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > TreeNode< / span > < span class = "p" > (< / span > < span class = "m" > 0< / span > < span class = "p" > );< / span >
< a id = "__codelineno-87-5" name = "__codelineno-87-5" href = "#__codelineno-87-5" > < / a > < span class = "w" > < / span > < span class = "n" > root< / span > < span class = "p" > .< / span > < span class = "n" > left< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > buildTree< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > );< / span >
< a id = "__codelineno-87-6" name = "__codelineno-87-6" href = "#__codelineno-87-6" > < / a > < span class = "w" > < / span > < span class = "n" > root< / span > < span class = "p" > .< / span > < span class = "n" > right< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > buildTree< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > );< / span >
< a id = "__codelineno-87-7" name = "__codelineno-87-7" href = "#__codelineno-87-7" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > root< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-87-8" name = "__codelineno-87-8" href = "#__codelineno-87-8" > < / a > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-88-1" name = "__codelineno-88-1" href = "#__codelineno-88-1" > < / a > < span class = "cm" > /* 指数阶（建立满二叉树） */< / span >
< a id = "__codelineno-88-2" name = "__codelineno-88-2" href = "#__codelineno-88-2" > < / a > < span class = "kd" > func< / span > < span class = "nf" > buildTree< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / span > < span class = "p" > )< / span > < span class = "p" > -> < / span > < span class = "n" > TreeNode< / span > < span class = "p" > ?< / span > < span class = "p" > {< / span >
< a id = "__codelineno-88-3" name = "__codelineno-88-3" href = "#__codelineno-88-3" > < / a > < span class = "k" > if< / span > < span class = "n" > n< / span > < span class = "p" > ==< / span > < span class = "mi" > 0< / span > < span class = "p" > {< / span >
< a id = "__codelineno-88-4" name = "__codelineno-88-4" href = "#__codelineno-88-4" > < / a > < span class = "k" > return< / span > < span class = "kc" > nil< / span >
< a id = "__codelineno-88-5" name = "__codelineno-88-5" href = "#__codelineno-88-5" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-88-6" name = "__codelineno-88-6" href = "#__codelineno-88-6" > < / a > < span class = "kd" > let< / span > < span class = "nv" > root< / span > < span class = "p" > =< / span > < span class = "n" > TreeNode< / span > < span class = "p" > (< / span > < span class = "n" > x< / span > < span class = "p" > :< / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span >
< a id = "__codelineno-88-7" name = "__codelineno-88-7" href = "#__codelineno-88-7" > < / a > < span class = "n" > root< / span > < span class = "p" > .< / span > < span class = "kr" > left< / span > < span class = "p" > =< / span > < span class = "n" > buildTree< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > :< / span > < span class = "n" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span >
< a id = "__codelineno-88-8" name = "__codelineno-88-8" href = "#__codelineno-88-8" > < / a > < span class = "n" > root< / span > < span class = "p" > .< / span > < span class = "kr" > right< / span > < span class = "p" > =< / span > < span class = "n" > buildTree< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > :< / span > < span class = "n" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span >
< a id = "__codelineno-88-9" name = "__codelineno-88-9" href = "#__codelineno-88-9" > < / a > < span class = "k" > return< / span > < span class = "n" > root< / span >
< a id = "__codelineno-88-10" name = "__codelineno-88-10" href = "#__codelineno-88-10" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > space_complexity.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-89-1" name = "__codelineno-89-1" href = "#__codelineno-89-1" > < / a > < span class = "c1" > // 指数阶（建立满二叉树）< / span >
< a id = "__codelineno-89-2" name = "__codelineno-89-2" href = "#__codelineno-89-2" > < / a > < span class = "k" > fn< / span > < span class = "w" > < / span > < span class = "n" > buildTree< / span > < span class = "p" > (< / span > < span class = "n" > mem_allocator< / span > < span class = "o" > :< / span > < 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" > Allocator< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > n< / 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 = "n" > inc< / span > < span class = "p" > .< / span > < span class = "n" > TreeNode< / span > < span class = "p" > (< / span > < span class = "kt" > i32< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-89-3" name = "__codelineno-89-3" href = "#__codelineno-89-3" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > n< / 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" > return< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-89-4" name = "__codelineno-89-4" href = "#__codelineno-89-4" > < / a > < span class = "w" > < / span > < span class = "kr" > const< / span > < span class = "w" > < / span > < span class = "n" > root< / 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" > create< / span > < span class = "p" > (< / span > < span class = "n" > inc< / span > < span class = "p" > .< / span > < span class = "n" > TreeNode< / span > < span class = "p" > (< / span > < span class = "kt" > i32< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-89-5" name = "__codelineno-89-5" href = "#__codelineno-89-5" > < / a > < span class = "w" > < / span > < span class = "n" > root< / span > < span class = "p" > .< / span > < span class = "n" > init< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > );< / span >
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< p > < img alt = "满二叉树产生的指数阶空间复杂度" src = "../space_complexity.assets/space_complexity_exponential.png" / > < / p >
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< p align = "center" > Fig. 满二叉树产生的指数阶空间复杂度 < / p >
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< h3 id = "olog-n" > 对数阶 < span class = "arithmatex" > \(O(\log n)\)< / span > < a class = "headerlink" href = "#olog-n" title = "Permanent link" > ¶ < / a > < / h3 >
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< p > 对数阶常见于分治算法和数据类型转换等。< / p >
< p > 例如“归并排序”算法，输入长度为 < span class = "arithmatex" > \(n\)< / span > 的数组，每轮递归将数组从中点划分为两半，形成高度为 < span class = "arithmatex" > \(\log n\)< / span > 的递归树，使用 < span class = "arithmatex" > \(O(\log n)\)< / span > 栈帧空间。< / p >
< p > 再例如“数字转化为字符串”，输入任意正整数 < span class = "arithmatex" > \(n\)< / span > ，它的位数为 < span class = "arithmatex" > \(\log_{10} n\)< / span > ，即对应字符串长度为 < span class = "arithmatex" > \(\log_{10} n\)< / span > ，因此空间复杂度为 < span class = "arithmatex" > \(O(\log_{10} n) = O(\log n)\)< / span > 。< / p >
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< h2 id = "234" > 2.3.4. 权衡时间与空间< a class = "headerlink" href = "#234" title = "Permanent link" > ¶ < / a > < / h2 >
< p > 理想情况下，我们希望算法的时间复杂度和空间复杂度都能达到最优。然而在实际情况中，同时优化时间复杂度和空间复杂度通常是非常困难的。< / p >
< p > < strong > 降低时间复杂度通常需要以提升空间复杂度为代价，反之亦然< / strong > 。我们将牺牲内存空间来提升算法运行速度的思路称为“以空间换时间”；反之，则称为“以时间换空间”。< / p >
< p > 选择哪种思路取决于我们更看重哪个方面。在大多数情况下，时间比空间更宝贵，因此以空间换时间通常是更常用的策略。当然，在数据量很大的情况下，控制空间复杂度也是非常重要的。< / p >
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