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0. 写在前面
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0.2. 如何使用本书
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1. 引言
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1.1. 算法无处不在
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1.2. 算法是什么
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1.3. 小结
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2. 复杂度分析
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2. 复杂度分析
< / label >
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< li class = "md-nav__item" >
< a href = "../../chapter_computational_complexity/performance_evaluation/" class = "md-nav__link" >
2.1. 算法效率评估
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_computational_complexity/time_complexity/" class = "md-nav__link" >
2.2. 时间复杂度
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_computational_complexity/space_complexity/" class = "md-nav__link" >
2.3. 空间复杂度
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_computational_complexity/summary/" class = "md-nav__link" >
2.4. 小结
< / a >
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< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_4" >
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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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< span class = "md-nav__icon md-icon" > < / span >
< / label >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_4_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_4" >
< span class = "md-nav__icon md-icon" > < / span >
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3. 数据结构简介
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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_data_structure/classification_of_data_structure/" class = "md-nav__link" >
3.1. 数据结构分类
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< / a >
< / li >
< li class = "md-nav__item" >
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< a href = "../../chapter_data_structure/basic_data_types/" class = "md-nav__link" >
3.2. 基本数据类型
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_data_structure/number_encoding/" class = "md-nav__link" >
3.3. 数字编码 *
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_data_structure/character_encoding/" class = "md-nav__link" >
3.4. 字符编码 *
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< / a >
< / li >
< 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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< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_5" >
< label class = "md-nav__link" for = "__nav_5" id = "__nav_5_label" tabindex = "0" >
4. 数组与链表
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_5_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_5" >
< span class = "md-nav__icon md-icon" > < / span >
4. 数组与链表
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/array/" class = "md-nav__link" >
4.1. 数组
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/linked_list/" class = "md-nav__link" >
4.2. 链表
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/list/" class = "md-nav__link" >
4.3. 列表
< / a >
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< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/summary/" class = "md-nav__link" >
4.4. 小结
< / a >
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< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_6" >
< label class = "md-nav__link" for = "__nav_6" id = "__nav_6_label" tabindex = "0" >
5. 栈与队列
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_6_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_6" >
< span class = "md-nav__icon md-icon" > < / span >
5. 栈与队列
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/stack/" class = "md-nav__link" >
5.1. 栈
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/queue/" class = "md-nav__link" >
5.2. 队列
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/deque/" class = "md-nav__link" >
5.3. 双向队列
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/summary/" class = "md-nav__link" >
5.4. 小结
< / a >
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< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_7" >
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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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< span class = "md-nav__icon md-icon" > < / span >
< / label >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_7_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_7" >
< span class = "md-nav__icon md-icon" > < / span >
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6. 散列表
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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_hashing/hash_map/" class = "md-nav__link" >
6.1. 哈希表
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_hashing/hash_collision/" class = "md-nav__link" >
6.2. 哈希冲突处理
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< / a >
< / 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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< / a >
< / li >
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< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_8" >
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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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< span class = "md-nav__icon md-icon" > < / span >
< / label >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_8_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_8" >
< span class = "md-nav__icon md-icon" > < / span >
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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
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_tree/binary_search_tree/" class = "md-nav__link" >
7.4. 二叉搜索树
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_tree/avl_tree/" class = "md-nav__link" >
7.5. AVL 树 *
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_tree/summary/" class = "md-nav__link" >
7.6. 小结
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< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_9" >
< label class = "md-nav__link" for = "__nav_9" id = "__nav_9_label" tabindex = "0" >
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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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< / label >
< 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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< / a >
< / li >
< 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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< / a >
< / li >
< 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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< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_10" >
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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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< span class = "md-nav__icon md-icon" > < / span >
< / label >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_10_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_10" >
< span class = "md-nav__icon md-icon" > < / span >
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9. 图
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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_graph/graph/" class = "md-nav__link" >
9.1. 图
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< / a >
< / li >
< 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 >
< 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
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_graph/summary/" class = "md-nav__link" >
9.4. 小结
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< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_11" >
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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 >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_11_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_11" >
< span class = "md-nav__icon md-icon" > < / span >
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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 >
< / li >
< 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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< / a >
< / li >
< 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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< / a >
< / li >
< 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 >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_searching/summary/" class = "md-nav__link" >
10.5. 小结
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< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_12" >
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< label class = "md-nav__link" for = "__nav_12" id = "__nav_12_label" tabindex = "0" >
11. 排序算法
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_12_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_12" >
< span class = "md-nav__icon md-icon" > < / span >
11. 排序算法
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/sorting_algorithm/" class = "md-nav__link" >
11.1. 排序算法
< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/selection_sort/" class = "md-nav__link" >
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11.2. 选择排序（ ）
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/bubble_sort/" class = "md-nav__link" >
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11.3. 冒泡排序
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/insertion_sort/" class = "md-nav__link" >
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11.4. 插入排序
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/quick_sort/" class = "md-nav__link" >
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11.5. 快速排序
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/merge_sort/" class = "md-nav__link" >
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11.6. 归并排序
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/heap_sort/" class = "md-nav__link" >
11.7. 堆排序（ ）
< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_sorting/bucket_sort/" class = "md-nav__link" >
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11.8. 桶排序
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/counting_sort/" class = "md-nav__link" >
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11.9. 计数排序
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/radix_sort/" class = "md-nav__link" >
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11.10. 基数排序
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/summary/" class = "md-nav__link" >
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11.11. 小结
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< / a >
< / li >
< / ul >
< / nav >
< / li >
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< li class = "md-nav__item md-nav__item--active md-nav__item--section md-nav__item--nested" >
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< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_13" checked >
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< label class = "md-nav__link" for = "__nav_13" id = "__nav_13_label" tabindex = "0" >
12. 回溯算法
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< span class = "md-nav__icon md-icon" > < / span >
< / label >
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< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_13_label" aria-expanded = "true" >
< label class = "md-nav__title" for = "__nav_13" >
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< span class = "md-nav__icon md-icon" > < / span >
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12. 回溯算法
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< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../backtracking_algorithm/" class = "md-nav__link" >
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12.1. 回溯算法（ ）
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../permutations_problem/" class = "md-nav__link" >
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12.2. 全排列问题（ ）
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< / a >
< / li >
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12.3. N 皇后问题（ ）
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12.3. N 皇后问题（ ）
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12.3.1. 复杂度分析
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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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12.3.1. 复杂度分析
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< h1 id = "123-n" > 12.3. N 皇后问题< a class = "headerlink" href = "#123-n" title = "Permanent link" > ¶ < / a > < / h1 >
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< p class = "admonition-title" > Question< / p >
< p > 根据国际象棋的规则，皇后可以攻击与之处在同一行或同一列或同一斜线上的棋子。给定 < span class = "arithmatex" > \(n\)< / span > 个皇后和一个 < span class = "arithmatex" > \(n \times n\)< / span > 大小的棋盘，寻找使得所有皇后之间无法相互攻击的摆放方案。< / p >
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< / div >
< p > 如下图所示，当 < span class = "arithmatex" > \(n = 4\)< / span > 时，共可以找到两个解。从回溯算法的角度看，< span class = "arithmatex" > \(n \times n\)< / span > 大小的棋盘共有 < span class = "arithmatex" > \(n^2\)< / span > 个格子，给出了所有的选择 < code > choices< / code > 。在逐个放置皇后的过程中，棋盘状态在不断地变化，每个时刻的棋盘就是状态 < code > state< / code > 。< / p >
< p > < img alt = "4 皇后问题的解" src = "../n_queens_problem.assets/solution_4_queens.png" / > < / p >
< p align = "center" > Fig. 4 皇后问题的解 < / p >
< p > 本题共有三个约束条件：< strong > 多个皇后不能在同一行、同一列和同一对角线< / strong > 。值得注意的是，对角线分为主对角线 < code > \< / code > 和副对角线 < code > /< / code > 两种。< / p >
< p > < img alt = "n 皇后问题的约束条件" src = "../n_queens_problem.assets/n_queens_constraints.png" / > < / p >
< p align = "center" > Fig. n 皇后问题的约束条件 < / p >
< p > 皇后的数量和棋盘的行数都为 < span class = "arithmatex" > \(n\)< / span > ，因此我们容易得到第一个推论：< strong > 棋盘每行都允许且只允许放置一个皇后< / strong > 。这意味着，我们可以采取逐行放置策略：从第一行开始，在每行放置一个皇后，直至最后一行结束。< strong > 此策略起到了剪枝的作用< / strong > ，它避免了同一行出现多个皇后的所有搜索分支。< / p >
< p > 下图展示了 < span class = "arithmatex" > \(4\)< / span > 皇后问题的逐行放置过程。受篇幅限制，下图仅展开了第一行的一个搜索分支。在搜索过程中，我们将不满足列约束和对角线约束的方案都剪枝了。< / p >
< p > < img alt = "逐行放置策略" src = "../n_queens_problem.assets/n_queens_placing.png" / > < / p >
< p align = "center" > Fig. 逐行放置策略 < / p >
< p > 为了实现根据列约束剪枝，我们可以利用一个长度为 < span class = "arithmatex" > \(n\)< / span > 的布尔型数组 < code > cols< / code > 记录每一列是否有皇后。在每次决定放置前，我们通过 < code > cols< / code > 将已有皇后的列剪枝，并在回溯中动态更新 < code > cols< / code > 的状态。< / p >
< p > 那么，如何处理对角线约束呢？设棋盘中某个格子的行列索引为 < code > (row, col)< / code > ，观察矩阵的某条主对角线，< strong > 我们发现该对角线上所有格子的行索引减列索引相等< / strong > ，即 < code > row - col< / code > 为恒定值。换句话说，若两个格子满足 < code > row1 - col1 == row2 - col2< / code > ，则这两个格子一定处在一条主对角线上。< / p >
< p > 利用该性质，我们可以借助一个数组 < code > diag1< / code > 来记录每条主对角线上是否有皇后。注意，< span class = "arithmatex" > \(n\)< / span > 维方阵 < code > row - col< / code > 的范围是 < span class = "arithmatex" > \([-n + 1, n - 1]\)< / span > ，因此共有 < span class = "arithmatex" > \(2n - 1\)< / span > 条主对角线。< / p >
< p > < img alt = "处理列约束和对角线约束" src = "../n_queens_problem.assets/n_queens_cols_diagonals.png" / > < / p >
< p align = "center" > Fig. 处理列约束和对角线约束 < / p >
< p > 同理，< strong > 次对角线上的所有格子的 < code > row + col< / code > 是恒定值< / strong > 。我们可以使用同样的方法，借助数组 < code > diag2< / code > 来处理次对角线约束。< / p >
< p > 根据以上分析，我们便可以写出 < span class = "arithmatex" > \(n\)< / span > 皇后的解题代码。< / p >
< div class = "tabbed-set tabbed-alternate" data-tabs = "1:10" > < input checked = "checked" id = "__tabbed_1_1" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_2" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_3" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_4" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_5" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_6" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_7" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_8" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_9" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_10" name = "__tabbed_1" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_1_1" > Java< / label > < label for = "__tabbed_1_2" > C++< / label > < label for = "__tabbed_1_3" > Python< / label > < label for = "__tabbed_1_4" > Go< / label > < label for = "__tabbed_1_5" > JavaScript< / label > < label for = "__tabbed_1_6" > TypeScript< / label > < label for = "__tabbed_1_7" > C< / label > < label for = "__tabbed_1_8" > C#< / label > < label for = "__tabbed_1_9" > Swift< / label > < label for = "__tabbed_1_10" > Zig< / label > < / div >
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< div class = "highlight" > < span class = "filename" > n_queens.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-0-1" name = "__codelineno-0-1" href = "#__codelineno-0-1" > < / a > < span class = "cm" > /* 回溯算法： < / span >
< a id = "__codelineno-0-2" name = "__codelineno-0-2" href = "#__codelineno-0-2" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > backtrack< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > row< / span > < span class = "p" > ,< / span > < span class = "w" > < / 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 = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > String< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < 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" > List< / span > < span class = "o" > < < / span > < span class = "n" > String< / span > < span class = "o" > > > > < / span > < span class = "w" > < / span > < span class = "n" > res< / 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" > boolean< / span > < span class = "o" > []< / span > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > boolean< / span > < span class = "o" > []< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > boolean< / span > < span class = "o" > []< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > )< / span > < span class = "w" > < / 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 = "c1" > // 当放置完所有行时，记录解< / span >
< a id = "__codelineno-0-5" name = "__codelineno-0-5" href = "#__codelineno-0-5" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > row< / 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 = "p" > {< / span >
< a id = "__codelineno-0-6" name = "__codelineno-0-6" href = "#__codelineno-0-6" > < / 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" > String< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "n" > copyState< / 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-0-7" name = "__codelineno-0-7" href = "#__codelineno-0-7" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > String< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > sRow< / span > < span class = "w" > < / span > < span class = "p" > :< / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-0-8" name = "__codelineno-0-8" href = "#__codelineno-0-8" > < / a > < span class = "w" > < / span > < span class = "n" > copyState< / 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" > ArrayList< / span > < span class = "o" > < > < / span > < span class = "p" > (< / span > < span class = "n" > sRow< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-0-9" name = "__codelineno-0-9" href = "#__codelineno-0-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-0-10" name = "__codelineno-0-10" href = "#__codelineno-0-10" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "na" > add< / span > < span class = "p" > (< / span > < span class = "n" > copyState< / span > < span class = "p" > );< / span >
< a id = "__codelineno-0-11" name = "__codelineno-0-11" href = "#__codelineno-0-11" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-0-12" name = "__codelineno-0-12" href = "#__codelineno-0-12" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-0-13" name = "__codelineno-0-13" href = "#__codelineno-0-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有列< / span >
< a id = "__codelineno-0-14" name = "__codelineno-0-14" href = "#__codelineno-0-14" > < / 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" > col< / 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" > col< / 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" > col< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-0-15" name = "__codelineno-0-15" href = "#__codelineno-0-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 计算该格子对应的主对角线和副对角线< / 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" > diag1< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > row< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "n" > col< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-0-17" name = "__codelineno-0-17" href = "#__codelineno-0-17" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > diag2< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > row< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > col< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-0-18" name = "__codelineno-0-18" href = "#__codelineno-0-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：不允许该格子所在 (列 或 主对角线 或 副对角线) 包含皇后< / span >
< a id = "__codelineno-0-19" name = "__codelineno-0-19" href = "#__codelineno-0-19" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > !< / span > < span class = "p" > (< / span > < span class = "n" > cols< / span > < span class = "o" > [< / span > < span class = "n" > col< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "o" > [< / span > < span class = "n" > diag1< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "o" > [< / span > < span class = "n" > diag2< / span > < span class = "o" > ]< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-0-20" name = "__codelineno-0-20" href = "#__codelineno-0-20" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：将皇后放置在该格子< / span >
< a id = "__codelineno-0-21" name = "__codelineno-0-21" href = "#__codelineno-0-21" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "na" > get< / span > < span class = "p" > (< / span > < span class = "n" > row< / span > < span class = "p" > ).< / span > < span class = "na" > set< / span > < span class = "p" > (< / span > < span class = "n" > col< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "s" > " Q" < / span > < span class = "p" > );< / span >
< a id = "__codelineno-0-22" name = "__codelineno-0-22" href = "#__codelineno-0-22" > < / a > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "o" > [< / span > < span class = "n" > col< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "o" > [< / span > < span class = "n" > diag1< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "o" > [< / span > < span class = "n" > diag2< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "kc" > true< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-0-23" name = "__codelineno-0-23" href = "#__codelineno-0-23" > < / a > < span class = "w" > < / span > < span class = "c1" > // 放置下一行< / span >
< a id = "__codelineno-0-24" name = "__codelineno-0-24" href = "#__codelineno-0-24" > < / a > < span class = "w" > < / span > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > row< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > );< / span >
< a id = "__codelineno-0-25" name = "__codelineno-0-25" href = "#__codelineno-0-25" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退：将该格子恢复为空位< / span >
< a id = "__codelineno-0-26" name = "__codelineno-0-26" href = "#__codelineno-0-26" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "na" > get< / span > < span class = "p" > (< / span > < span class = "n" > row< / span > < span class = "p" > ).< / span > < span class = "na" > set< / span > < span class = "p" > (< / span > < span class = "n" > col< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "s" > " #" < / span > < span class = "p" > );< / span >
< a id = "__codelineno-0-27" name = "__codelineno-0-27" href = "#__codelineno-0-27" > < / a > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "o" > [< / span > < span class = "n" > col< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "o" > [< / span > < span class = "n" > diag1< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "o" > [< / span > < span class = "n" > diag2< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "kc" > false< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-0-28" name = "__codelineno-0-28" href = "#__codelineno-0-28" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-0-29" name = "__codelineno-0-29" href = "#__codelineno-0-29" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-0-30" name = "__codelineno-0-30" href = "#__codelineno-0-30" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-0-31" name = "__codelineno-0-31" href = "#__codelineno-0-31" > < / a >
< a id = "__codelineno-0-32" name = "__codelineno-0-32" href = "#__codelineno-0-32" > < / a > < span class = "cm" > /* 求解 N 皇后 */< / span >
< a id = "__codelineno-0-33" name = "__codelineno-0-33" href = "#__codelineno-0-33" > < / a > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > String< / span > < span class = "o" > > > > < / span > < span class = "w" > < / span > < span class = "nf" > nQueens< / 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-0-34" name = "__codelineno-0-34" href = "#__codelineno-0-34" > < / a > < span class = "w" > < / span > < span class = "c1" > // 初始化 n*n 大小的棋盘，其中 ' Q' 代表皇后，' #' 代表空位< / span >
< a id = "__codelineno-0-35" name = "__codelineno-0-35" href = "#__codelineno-0-35" > < / 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" > String< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "n" > state< / 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-0-36" name = "__codelineno-0-36" href = "#__codelineno-0-36" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-0-37" name = "__codelineno-0-37" href = "#__codelineno-0-37" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > String< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > row< / 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-0-38" name = "__codelineno-0-38" href = "#__codelineno-0-38" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > 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-0-39" name = "__codelineno-0-39" href = "#__codelineno-0-39" > < / a > < span class = "w" > < / span > < span class = "n" > row< / span > < span class = "p" > .< / span > < span class = "na" > add< / span > < span class = "p" > (< / span > < span class = "s" > " #" < / span > < span class = "p" > );< / span >
< a id = "__codelineno-0-40" name = "__codelineno-0-40" href = "#__codelineno-0-40" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-0-41" name = "__codelineno-0-41" href = "#__codelineno-0-41" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "na" > add< / span > < span class = "p" > (< / span > < span class = "n" > row< / span > < span class = "p" > );< / span >
< a id = "__codelineno-0-42" name = "__codelineno-0-42" href = "#__codelineno-0-42" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-0-43" name = "__codelineno-0-43" href = "#__codelineno-0-43" > < / a > < span class = "w" > < / span > < span class = "kt" > boolean< / span > < span class = "o" > []< / span > < span class = "w" > < / span > < span class = "n" > cols< / 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" > boolean< / 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" > // 记录列是否有皇后< / span >
< a id = "__codelineno-0-44" name = "__codelineno-0-44" href = "#__codelineno-0-44" > < / a > < span class = "w" > < / span > < span class = "kt" > boolean< / span > < span class = "o" > []< / span > < span class = "w" > < / span > < span class = "n" > diags1< / 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" > boolean< / span > < span class = "o" > [< / span > < span class = "mi" > 2< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "o" > ]< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 记录主对角线是否有皇后< / span >
< a id = "__codelineno-0-45" name = "__codelineno-0-45" href = "#__codelineno-0-45" > < / a > < span class = "w" > < / span > < span class = "kt" > boolean< / span > < span class = "o" > []< / span > < span class = "w" > < / span > < span class = "n" > diags2< / 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" > boolean< / span > < span class = "o" > [< / span > < span class = "mi" > 2< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "o" > ]< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 记录副对角线是否有皇后< / span >
< a id = "__codelineno-0-46" name = "__codelineno-0-46" href = "#__codelineno-0-46" > < / 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" > List< / span > < span class = "o" > < < / span > < span class = "n" > String< / span > < span class = "o" > > > > < / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > ArrayList< / span > < span class = "o" > < > < / span > < span class = "p" > ();< / span >
< a id = "__codelineno-0-47" name = "__codelineno-0-47" href = "#__codelineno-0-47" > < / a >
< a id = "__codelineno-0-48" name = "__codelineno-0-48" href = "#__codelineno-0-48" > < / a > < span class = "w" > < / span > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / 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" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > );< / span >
< a id = "__codelineno-0-49" name = "__codelineno-0-49" href = "#__codelineno-0-49" > < / a >
< a id = "__codelineno-0-50" name = "__codelineno-0-50" href = "#__codelineno-0-50" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-0-51" name = "__codelineno-0-51" href = "#__codelineno-0-51" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > n_queens.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-1-1" name = "__codelineno-1-1" href = "#__codelineno-1-1" > < / a > < span class = "cm" > /* 回溯算法： < / span >
< a id = "__codelineno-1-2" name = "__codelineno-1-2" href = "#__codelineno-1-2" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > backtrack< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > row< / span > < span class = "p" > ,< / span > < span class = "w" > < / 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 = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > string< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > string< / span > < span class = "o" > > > > < / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > bool< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > cols< / 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 = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > bool< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > bool< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > diags2< / span > < span class = "p" > )< / span > < span class = "w" > < / 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 = "c1" > // 当放置完所有行时，记录解< / span >
< a id = "__codelineno-1-5" name = "__codelineno-1-5" href = "#__codelineno-1-5" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > row< / 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 = "p" > {< / span >
< a id = "__codelineno-1-6" name = "__codelineno-1-6" href = "#__codelineno-1-6" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > push_back< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > );< / span >
< a id = "__codelineno-1-7" name = "__codelineno-1-7" href = "#__codelineno-1-7" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-8" name = "__codelineno-1-8" href = "#__codelineno-1-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-1-9" name = "__codelineno-1-9" href = "#__codelineno-1-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有列< / span >
< a id = "__codelineno-1-10" name = "__codelineno-1-10" href = "#__codelineno-1-10" > < / 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" > col< / 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" > col< / 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" > col< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-11" name = "__codelineno-1-11" href = "#__codelineno-1-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 计算该格子对应的主对角线和副对角线< / span >
< a id = "__codelineno-1-12" name = "__codelineno-1-12" href = "#__codelineno-1-12" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > diag1< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > row< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "n" > col< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-13" name = "__codelineno-1-13" href = "#__codelineno-1-13" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > diag2< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > row< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > col< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-14" name = "__codelineno-1-14" href = "#__codelineno-1-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：不允许该格子所在 (列 或 主对角线 或 副对角线) 包含皇后< / span >
< a id = "__codelineno-1-15" name = "__codelineno-1-15" href = "#__codelineno-1-15" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > !< / span > < span class = "p" > (< / span > < span class = "n" > cols< / span > < span class = "p" > [< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > [< / span > < span class = "n" > diag1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > [< / span > < span class = "n" > diag2< / span > < span class = "p" > ]))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-16" name = "__codelineno-1-16" href = "#__codelineno-1-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：将皇后放置在该格子< / span >
< a id = "__codelineno-1-17" name = "__codelineno-1-17" href = "#__codelineno-1-17" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > [< / span > < span class = "n" > row< / span > < span class = "p" > ][< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "s" > " Q" < / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-18" name = "__codelineno-1-18" href = "#__codelineno-1-18" > < / a > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "p" > [< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > [< / span > < span class = "n" > diag1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > [< / span > < span class = "n" > diag2< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > true< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-19" name = "__codelineno-1-19" href = "#__codelineno-1-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 放置下一行< / span >
< a id = "__codelineno-1-20" name = "__codelineno-1-20" href = "#__codelineno-1-20" > < / a > < span class = "w" > < / span > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > row< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > );< / span >
< a id = "__codelineno-1-21" name = "__codelineno-1-21" href = "#__codelineno-1-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退：将该格子恢复为空位< / span >
< a id = "__codelineno-1-22" name = "__codelineno-1-22" href = "#__codelineno-1-22" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > [< / span > < span class = "n" > row< / span > < span class = "p" > ][< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "s" > " #" < / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-23" name = "__codelineno-1-23" href = "#__codelineno-1-23" > < / a > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "p" > [< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > [< / span > < span class = "n" > diag1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > [< / span > < span class = "n" > diag2< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > false< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-24" name = "__codelineno-1-24" href = "#__codelineno-1-24" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-1-25" name = "__codelineno-1-25" href = "#__codelineno-1-25" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-1-26" name = "__codelineno-1-26" href = "#__codelineno-1-26" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-1-27" name = "__codelineno-1-27" href = "#__codelineno-1-27" > < / a >
< a id = "__codelineno-1-28" name = "__codelineno-1-28" href = "#__codelineno-1-28" > < / a > < span class = "cm" > /* 求解 N 皇后 */< / span >
< a id = "__codelineno-1-29" name = "__codelineno-1-29" href = "#__codelineno-1-29" > < / a > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > string< / span > < span class = "o" > > > > < / span > < span class = "w" > < / span > < span class = "n" > nQueens< / 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-1-30" name = "__codelineno-1-30" href = "#__codelineno-1-30" > < / a > < span class = "w" > < / span > < span class = "c1" > // 初始化 n*n 大小的棋盘，其中 ' Q' 代表皇后，' #' 代表空位< / span >
< a id = "__codelineno-1-31" name = "__codelineno-1-31" href = "#__codelineno-1-31" > < / 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 = "n" > string< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > string< / span > < span class = "o" > > < / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "s" > " #" < / span > < span class = "p" > ));< / span >
< a id = "__codelineno-1-32" name = "__codelineno-1-32" href = "#__codelineno-1-32" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > bool< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nb" > false< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 记录列是否有皇后< / span >
< a id = "__codelineno-1-33" name = "__codelineno-1-33" href = "#__codelineno-1-33" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > bool< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > (< / span > < span class = "mi" > 2< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nb" > false< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 记录主对角线是否有皇后< / span >
< a id = "__codelineno-1-34" name = "__codelineno-1-34" href = "#__codelineno-1-34" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > bool< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > (< / span > < span class = "mi" > 2< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nb" > false< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 记录副对角线是否有皇后< / span >
< a id = "__codelineno-1-35" name = "__codelineno-1-35" href = "#__codelineno-1-35" > < / 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 = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > string< / span > < span class = "o" > > > > < / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-36" name = "__codelineno-1-36" href = "#__codelineno-1-36" > < / a >
< a id = "__codelineno-1-37" name = "__codelineno-1-37" href = "#__codelineno-1-37" > < / a > < span class = "w" > < / span > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / 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" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > );< / span >
< a id = "__codelineno-1-38" name = "__codelineno-1-38" href = "#__codelineno-1-38" > < / a >
< a id = "__codelineno-1-39" name = "__codelineno-1-39" href = "#__codelineno-1-39" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-40" name = "__codelineno-1-40" href = "#__codelineno-1-40" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > n_queens.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-2-1" name = "__codelineno-2-1" href = "#__codelineno-2-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > backtrack< / span > < span class = "p" > (< / span >
< a id = "__codelineno-2-2" name = "__codelineno-2-2" href = "#__codelineno-2-2" > < / a > < span class = "n" > row< / span > < span class = "p" > :< / span > < span class = "nb" > int< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-2-3" name = "__codelineno-2-3" href = "#__codelineno-2-3" > < / a > < span class = "n" > n< / span > < span class = "p" > :< / span > < span class = "nb" > int< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-2-4" name = "__codelineno-2-4" href = "#__codelineno-2-4" > < / a > < span class = "n" > state< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > str< / span > < span class = "p" > ]],< / span >
2023-05-04 05:32:16 +08:00
< a id = "__codelineno-2-5" name = "__codelineno-2-5" href = "#__codelineno-2-5" > < / a > < span class = "n" > res< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > str< / span > < span class = "p" > ]]],< / span >
< a id = "__codelineno-2-6" name = "__codelineno-2-6" href = "#__codelineno-2-6" > < / a > < span class = "n" > cols< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > bool< / span > < span class = "p" > ],< / span >
< a id = "__codelineno-2-7" name = "__codelineno-2-7" href = "#__codelineno-2-7" > < / a > < span class = "n" > diags1< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > bool< / span > < span class = "p" > ],< / span >
< a id = "__codelineno-2-8" name = "__codelineno-2-8" href = "#__codelineno-2-8" > < / a > < span class = "n" > diags2< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > bool< / span > < span class = "p" > ],< / span >
2023-05-04 05:22:36 +08:00
< a id = "__codelineno-2-9" name = "__codelineno-2-9" href = "#__codelineno-2-9" > < / a > < span class = "p" > ):< / span >
< a id = "__codelineno-2-10" name = "__codelineno-2-10" href = "#__codelineno-2-10" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 回溯算法： " " " < / span >
< a id = "__codelineno-2-11" name = "__codelineno-2-11" href = "#__codelineno-2-11" > < / a > < span class = "c1" > # 当放置完所有行时，记录解< / span >
< a id = "__codelineno-2-12" name = "__codelineno-2-12" href = "#__codelineno-2-12" > < / a > < span class = "k" > if< / span > < span class = "n" > row< / span > < span class = "o" > ==< / span > < span class = "n" > n< / span > < span class = "p" > :< / span >
< a id = "__codelineno-2-13" name = "__codelineno-2-13" href = "#__codelineno-2-13" > < / a > < span class = "n" > res< / span > < span class = "o" > .< / span > < span class = "n" > append< / span > < span class = "p" > ([< / span > < span class = "nb" > list< / span > < span class = "p" > (< / span > < span class = "n" > row< / span > < span class = "p" > )< / span > < span class = "k" > for< / span > < span class = "n" > row< / span > < span class = "ow" > in< / span > < span class = "n" > state< / span > < span class = "p" > ])< / span >
< a id = "__codelineno-2-14" name = "__codelineno-2-14" href = "#__codelineno-2-14" > < / a > < span class = "k" > return< / span >
< a id = "__codelineno-2-15" name = "__codelineno-2-15" href = "#__codelineno-2-15" > < / a > < span class = "c1" > # 遍历所有列< / span >
< a id = "__codelineno-2-16" name = "__codelineno-2-16" href = "#__codelineno-2-16" > < / a > < span class = "k" > for< / span > < span class = "n" > col< / span > < span class = "ow" > in< / span > < span class = "nb" > range< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-2-17" name = "__codelineno-2-17" href = "#__codelineno-2-17" > < / a > < span class = "c1" > # 计算该格子对应的主对角线和副对角线< / span >
< a id = "__codelineno-2-18" name = "__codelineno-2-18" href = "#__codelineno-2-18" > < / a > < span class = "n" > diag1< / span > < span class = "o" > =< / span > < span class = "n" > row< / span > < span class = "o" > -< / span > < span class = "n" > col< / span > < span class = "o" > +< / span > < span class = "n" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-2-19" name = "__codelineno-2-19" href = "#__codelineno-2-19" > < / a > < span class = "n" > diag2< / span > < span class = "o" > =< / span > < span class = "n" > row< / span > < span class = "o" > +< / span > < span class = "n" > col< / span >
< a id = "__codelineno-2-20" name = "__codelineno-2-20" href = "#__codelineno-2-20" > < / a > < span class = "c1" > # 剪枝：不允许该格子所在 (列 或 主对角线 或 副对角线) 包含皇后< / span >
< a id = "__codelineno-2-21" name = "__codelineno-2-21" href = "#__codelineno-2-21" > < / a > < span class = "k" > if< / span > < span class = "ow" > not< / span > < span class = "p" > (< / span > < span class = "n" > cols< / span > < span class = "p" > [< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "ow" > or< / span > < span class = "n" > diags1< / span > < span class = "p" > [< / span > < span class = "n" > diag1< / span > < span class = "p" > ]< / span > < span class = "ow" > or< / span > < span class = "n" > diags2< / span > < span class = "p" > [< / span > < span class = "n" > diag2< / span > < span class = "p" > ]):< / span >
< a id = "__codelineno-2-22" name = "__codelineno-2-22" href = "#__codelineno-2-22" > < / a > < span class = "c1" > # 尝试：将皇后放置在该格子< / span >
< a id = "__codelineno-2-23" name = "__codelineno-2-23" href = "#__codelineno-2-23" > < / a > < span class = "n" > state< / span > < span class = "p" > [< / span > < span class = "n" > row< / span > < span class = "p" > ][< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "s2" > " Q" < / span >
< a id = "__codelineno-2-24" name = "__codelineno-2-24" href = "#__codelineno-2-24" > < / a > < span class = "n" > cols< / span > < span class = "p" > [< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "n" > diags1< / span > < span class = "p" > [< / span > < span class = "n" > diag1< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "n" > diags2< / span > < span class = "p" > [< / span > < span class = "n" > diag2< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "kc" > True< / span >
< a id = "__codelineno-2-25" name = "__codelineno-2-25" href = "#__codelineno-2-25" > < / a > < span class = "c1" > # 放置下一行< / span >
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< a id = "__codelineno-2-26" name = "__codelineno-2-26" href = "#__codelineno-2-26" > < / a > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > row< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "n" > cols< / span > < span class = "p" > ,< / span > < span class = "n" > diags1< / span > < span class = "p" > ,< / span > < span class = "n" > diags2< / span > < span class = "p" > )< / span >
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< a id = "__codelineno-2-27" name = "__codelineno-2-27" href = "#__codelineno-2-27" > < / a > < span class = "c1" > # 回退：将该格子恢复为空位< / span >
< a id = "__codelineno-2-28" name = "__codelineno-2-28" href = "#__codelineno-2-28" > < / a > < span class = "n" > state< / span > < span class = "p" > [< / span > < span class = "n" > row< / span > < span class = "p" > ][< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "s2" > " #" < / span >
< a id = "__codelineno-2-29" name = "__codelineno-2-29" href = "#__codelineno-2-29" > < / a > < span class = "n" > cols< / span > < span class = "p" > [< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "n" > diags1< / span > < span class = "p" > [< / span > < span class = "n" > diag1< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "n" > diags2< / span > < span class = "p" > [< / span > < span class = "n" > diag2< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "kc" > False< / span >
< a id = "__codelineno-2-30" name = "__codelineno-2-30" href = "#__codelineno-2-30" > < / a >
< a id = "__codelineno-2-31" name = "__codelineno-2-31" href = "#__codelineno-2-31" > < / a > < span class = "k" > def< / span > < span class = "nf" > n_queens< / 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" > list< / span > < span class = "p" > [< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > str< / span > < span class = "p" > ]]]:< / span >
< a id = "__codelineno-2-32" name = "__codelineno-2-32" href = "#__codelineno-2-32" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 求解 N 皇后" " " < / span >
< a id = "__codelineno-2-33" name = "__codelineno-2-33" href = "#__codelineno-2-33" > < / a > < span class = "c1" > # 初始化 n*n 大小的棋盘，其中 ' Q' 代表皇后，' #' 代表空位< / span >
< a id = "__codelineno-2-34" name = "__codelineno-2-34" href = "#__codelineno-2-34" > < / a > < span class = "n" > state< / span > < span class = "o" > =< / span > < span class = "p" > [[< / span > < span class = "s2" > " #" < / 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 > < 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-2-35" name = "__codelineno-2-35" href = "#__codelineno-2-35" > < / a > < span class = "n" > cols< / span > < span class = "o" > =< / span > < span class = "p" > [< / span > < span class = "kc" > False< / span > < span class = "p" > ]< / span > < span class = "o" > *< / span > < span class = "n" > n< / span > < span class = "c1" > # 记录列是否有皇后< / span >
< a id = "__codelineno-2-36" name = "__codelineno-2-36" href = "#__codelineno-2-36" > < / a > < span class = "n" > diags1< / span > < span class = "o" > =< / span > < span class = "p" > [< / span > < span class = "kc" > False< / span > < span class = "p" > ]< / span > < span class = "o" > *< / span > < span class = "p" > (< / span > < span class = "mi" > 2< / span > < span class = "o" > *< / span > < span class = "n" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "c1" > # 记录主对角线是否有皇后< / span >
< a id = "__codelineno-2-37" name = "__codelineno-2-37" href = "#__codelineno-2-37" > < / a > < span class = "n" > diags2< / span > < span class = "o" > =< / span > < span class = "p" > [< / span > < span class = "kc" > False< / span > < span class = "p" > ]< / span > < span class = "o" > *< / span > < span class = "p" > (< / span > < span class = "mi" > 2< / span > < span class = "o" > *< / span > < span class = "n" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "c1" > # 记录副对角线是否有皇后< / span >
< a id = "__codelineno-2-38" name = "__codelineno-2-38" href = "#__codelineno-2-38" > < / a > < span class = "n" > res< / span > < span class = "o" > =< / span > < span class = "p" > []< / span >
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< a id = "__codelineno-2-39" name = "__codelineno-2-39" href = "#__codelineno-2-39" > < / a > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "n" > cols< / span > < span class = "p" > ,< / span > < span class = "n" > diags1< / span > < span class = "p" > ,< / span > < span class = "n" > diags2< / span > < span class = "p" > )< / span >
2023-05-04 05:22:36 +08:00
< a id = "__codelineno-2-40" name = "__codelineno-2-40" href = "#__codelineno-2-40" > < / a >
< a id = "__codelineno-2-41" name = "__codelineno-2-41" href = "#__codelineno-2-41" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > n_queens.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-3-1" name = "__codelineno-3-1" href = "#__codelineno-3-1" > < / a > < span class = "cm" > /* 回溯算法： < / span >
< a id = "__codelineno-3-2" name = "__codelineno-3-2" href = "#__codelineno-3-2" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > (< / span > < span class = "nx" > row< / span > < span class = "p" > ,< / span > < span class = "w" > < / 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 = "nx" > state< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > [][]< / span > < span class = "kt" > string< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > [][][]< / span > < span class = "kt" > string< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > diags2< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > []< / span > < span class = "kt" > bool< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-3" name = "__codelineno-3-3" href = "#__codelineno-3-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 当放置完所有行时，记录解< / span >
< a id = "__codelineno-3-4" name = "__codelineno-3-4" href = "#__codelineno-3-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > row< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-5" name = "__codelineno-3-5" href = "#__codelineno-3-5" > < / a > < span class = "w" > < / span > < span class = "nx" > newState< / 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" > string< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > state< / span > < span class = "p" > ))< / span >
< a id = "__codelineno-3-6" name = "__codelineno-3-6" href = "#__codelineno-3-6" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > _< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "k" > range< / span > < span class = "w" > < / span > < span class = "nx" > newState< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-7" name = "__codelineno-3-7" href = "#__codelineno-3-7" > < / a > < span class = "w" > < / span > < span class = "nx" > newState< / 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" > string< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nb" > len< / span > < span class = "p" > ((< / span > < span class = "o" > *< / span > < span class = "nx" > state< / span > < span class = "p" > )[< / span > < span class = "mi" > 0< / span > < span class = "p" > ]))< / span >
< a id = "__codelineno-3-8" name = "__codelineno-3-8" href = "#__codelineno-3-8" > < / a > < span class = "w" > < / span > < span class = "nb" > copy< / span > < span class = "p" > (< / span > < span class = "nx" > newState< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > state< / span > < span class = "p" > )[< / span > < span class = "nx" > i< / span > < span class = "p" > ])< / span >
< a id = "__codelineno-3-9" name = "__codelineno-3-9" href = "#__codelineno-3-9" > < / a >
< a id = "__codelineno-3-10" name = "__codelineno-3-10" href = "#__codelineno-3-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-11" name = "__codelineno-3-11" href = "#__codelineno-3-11" > < / a > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nb" > append< / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > newState< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-12" name = "__codelineno-3-12" href = "#__codelineno-3-12" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-13" name = "__codelineno-3-13" href = "#__codelineno-3-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有列< / span >
< a id = "__codelineno-3-14" name = "__codelineno-3-14" href = "#__codelineno-3-14" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > col< / 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" > col< / 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" > col< / span > < span class = "o" > ++< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-15" name = "__codelineno-3-15" href = "#__codelineno-3-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 计算该格子对应的主对角线和副对角线< / span >
< a id = "__codelineno-3-16" name = "__codelineno-3-16" href = "#__codelineno-3-16" > < / a > < span class = "w" > < / span > < span class = "nx" > diag1< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > row< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "nx" > col< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-3-17" name = "__codelineno-3-17" href = "#__codelineno-3-17" > < / a > < span class = "w" > < / span > < span class = "nx" > diag2< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > row< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "nx" > col< / span >
< a id = "__codelineno-3-18" name = "__codelineno-3-18" href = "#__codelineno-3-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：不允许该格子所在 (列 或 主对角线 或 副对角线) 包含皇后< / span >
< a id = "__codelineno-3-19" name = "__codelineno-3-19" href = "#__codelineno-3-19" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > !((< / span > < span class = "o" > *< / span > < span class = "nx" > cols< / span > < span class = "p" > )[< / span > < span class = "nx" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > diags1< / span > < span class = "p" > )[< / span > < span class = "nx" > diag1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > diags2< / span > < span class = "p" > )[< / span > < span class = "nx" > diag2< / span > < span class = "p" > ])< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-20" name = "__codelineno-3-20" href = "#__codelineno-3-20" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：将皇后放置在该格子< / span >
< a id = "__codelineno-3-21" name = "__codelineno-3-21" href = "#__codelineno-3-21" > < / a > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > state< / span > < span class = "p" > )[< / span > < span class = "nx" > row< / span > < span class = "p" > ][< / span > < span class = "nx" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "s" > " Q" < / span >
< a id = "__codelineno-3-22" name = "__codelineno-3-22" href = "#__codelineno-3-22" > < / a > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > cols< / span > < span class = "p" > )[< / span > < span class = "nx" > col< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > diags1< / span > < span class = "p" > )[< / span > < span class = "nx" > diag1< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > diags2< / span > < span class = "p" > )[< / span > < span class = "nx" > diag2< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "kc" > true< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > true< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > true< / span >
< a id = "__codelineno-3-23" name = "__codelineno-3-23" href = "#__codelineno-3-23" > < / a > < span class = "w" > < / span > < span class = "c1" > // 放置下一行< / span >
< a id = "__codelineno-3-24" name = "__codelineno-3-24" href = "#__codelineno-3-24" > < / a > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > (< / span > < span class = "nx" > row< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / 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" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > diags2< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-25" name = "__codelineno-3-25" href = "#__codelineno-3-25" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退：将该格子恢复为空位< / span >
< a id = "__codelineno-3-26" name = "__codelineno-3-26" href = "#__codelineno-3-26" > < / a > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > state< / span > < span class = "p" > )[< / span > < span class = "nx" > row< / span > < span class = "p" > ][< / span > < span class = "nx" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "s" > " #" < / span >
< a id = "__codelineno-3-27" name = "__codelineno-3-27" href = "#__codelineno-3-27" > < / a > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > cols< / span > < span class = "p" > )[< / span > < span class = "nx" > col< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > diags1< / span > < span class = "p" > )[< / span > < span class = "nx" > diag1< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > diags2< / span > < span class = "p" > )[< / span > < span class = "nx" > diag2< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "kc" > false< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > false< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > false< / span >
< a id = "__codelineno-3-28" name = "__codelineno-3-28" href = "#__codelineno-3-28" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-29" name = "__codelineno-3-29" href = "#__codelineno-3-29" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-30" name = "__codelineno-3-30" href = "#__codelineno-3-30" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-3-31" name = "__codelineno-3-31" href = "#__codelineno-3-31" > < / a >
< a id = "__codelineno-3-32" name = "__codelineno-3-32" href = "#__codelineno-3-32" > < / a > < span class = "cm" > /* 回溯算法： < / span >
< a id = "__codelineno-3-33" name = "__codelineno-3-33" href = "#__codelineno-3-33" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > (< / span > < span class = "nx" > row< / span > < span class = "p" > ,< / span > < span class = "w" > < / 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 = "nx" > state< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > [][]< / span > < span class = "kt" > string< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > [][][]< / span > < span class = "kt" > string< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > diags2< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > []< / span > < span class = "kt" > bool< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-34" name = "__codelineno-3-34" href = "#__codelineno-3-34" > < / a > < span class = "w" > < / span > < span class = "c1" > // 当放置完所有行时，记录解< / span >
< a id = "__codelineno-3-35" name = "__codelineno-3-35" href = "#__codelineno-3-35" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > row< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-36" name = "__codelineno-3-36" href = "#__codelineno-3-36" > < / a > < span class = "w" > < / span > < span class = "nx" > newState< / 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" > string< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > state< / span > < span class = "p" > ))< / span >
< a id = "__codelineno-3-37" name = "__codelineno-3-37" href = "#__codelineno-3-37" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > _< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "k" > range< / span > < span class = "w" > < / span > < span class = "nx" > newState< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-38" name = "__codelineno-3-38" href = "#__codelineno-3-38" > < / a > < span class = "w" > < / span > < span class = "nx" > newState< / 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" > string< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nb" > len< / span > < span class = "p" > ((< / span > < span class = "o" > *< / span > < span class = "nx" > state< / span > < span class = "p" > )[< / span > < span class = "mi" > 0< / span > < span class = "p" > ]))< / span >
< a id = "__codelineno-3-39" name = "__codelineno-3-39" href = "#__codelineno-3-39" > < / a > < span class = "w" > < / span > < span class = "nb" > copy< / span > < span class = "p" > (< / span > < span class = "nx" > newState< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > state< / span > < span class = "p" > )[< / span > < span class = "nx" > i< / span > < span class = "p" > ])< / span >
< a id = "__codelineno-3-40" name = "__codelineno-3-40" href = "#__codelineno-3-40" > < / a >
< a id = "__codelineno-3-41" name = "__codelineno-3-41" href = "#__codelineno-3-41" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-42" name = "__codelineno-3-42" href = "#__codelineno-3-42" > < / a > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nb" > append< / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > newState< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-43" name = "__codelineno-3-43" href = "#__codelineno-3-43" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-44" name = "__codelineno-3-44" href = "#__codelineno-3-44" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有列< / span >
< a id = "__codelineno-3-45" name = "__codelineno-3-45" href = "#__codelineno-3-45" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > col< / 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" > col< / 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" > col< / span > < span class = "o" > ++< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-46" name = "__codelineno-3-46" href = "#__codelineno-3-46" > < / a > < span class = "w" > < / span > < span class = "c1" > // 计算该格子对应的主对角线和副对角线< / span >
< a id = "__codelineno-3-47" name = "__codelineno-3-47" href = "#__codelineno-3-47" > < / a > < span class = "w" > < / span > < span class = "nx" > diag1< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > row< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "nx" > col< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-3-48" name = "__codelineno-3-48" href = "#__codelineno-3-48" > < / a > < span class = "w" > < / span > < span class = "nx" > diag2< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > row< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "nx" > col< / span >
< a id = "__codelineno-3-49" name = "__codelineno-3-49" href = "#__codelineno-3-49" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：不允许该格子所在 (列 或 主对角线 或 副对角线) 包含皇后< / span >
< a id = "__codelineno-3-50" name = "__codelineno-3-50" href = "#__codelineno-3-50" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > !((< / span > < span class = "o" > *< / span > < span class = "nx" > cols< / span > < span class = "p" > )[< / span > < span class = "nx" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > diags1< / span > < span class = "p" > )[< / span > < span class = "nx" > diag1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > diags2< / span > < span class = "p" > )[< / span > < span class = "nx" > diag2< / span > < span class = "p" > ])< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-51" name = "__codelineno-3-51" href = "#__codelineno-3-51" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：将皇后放置在该格子< / span >
< a id = "__codelineno-3-52" name = "__codelineno-3-52" href = "#__codelineno-3-52" > < / a > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > state< / span > < span class = "p" > )[< / span > < span class = "nx" > row< / span > < span class = "p" > ][< / span > < span class = "nx" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "s" > " Q" < / span >
< a id = "__codelineno-3-53" name = "__codelineno-3-53" href = "#__codelineno-3-53" > < / a > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > cols< / span > < span class = "p" > )[< / span > < span class = "nx" > col< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > diags1< / span > < span class = "p" > )[< / span > < span class = "nx" > diag1< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > diags2< / span > < span class = "p" > )[< / span > < span class = "nx" > diag2< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "kc" > true< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > true< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > true< / span >
< a id = "__codelineno-3-54" name = "__codelineno-3-54" href = "#__codelineno-3-54" > < / a > < span class = "w" > < / span > < span class = "c1" > // 放置下一行< / span >
< a id = "__codelineno-3-55" name = "__codelineno-3-55" href = "#__codelineno-3-55" > < / a > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > (< / span > < span class = "nx" > row< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / 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" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > diags2< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-56" name = "__codelineno-3-56" href = "#__codelineno-3-56" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退：将该格子恢复为空位< / span >
< a id = "__codelineno-3-57" name = "__codelineno-3-57" href = "#__codelineno-3-57" > < / a > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > state< / span > < span class = "p" > )[< / span > < span class = "nx" > row< / span > < span class = "p" > ][< / span > < span class = "nx" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "s" > " #" < / span >
< a id = "__codelineno-3-58" name = "__codelineno-3-58" href = "#__codelineno-3-58" > < / a > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > cols< / span > < span class = "p" > )[< / span > < span class = "nx" > col< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > diags1< / span > < span class = "p" > )[< / span > < span class = "nx" > diag1< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > diags2< / span > < span class = "p" > )[< / span > < span class = "nx" > diag2< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "kc" > false< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > false< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > false< / span >
< a id = "__codelineno-3-59" name = "__codelineno-3-59" href = "#__codelineno-3-59" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-60" name = "__codelineno-3-60" href = "#__codelineno-3-60" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-61" name = "__codelineno-3-61" href = "#__codelineno-3-61" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-3-62" name = "__codelineno-3-62" href = "#__codelineno-3-62" > < / a >
< a id = "__codelineno-3-63" name = "__codelineno-3-63" href = "#__codelineno-3-63" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > nQueens< / 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 > < span class = "kt" > string< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-64" name = "__codelineno-3-64" href = "#__codelineno-3-64" > < / a > < span class = "w" > < / span > < span class = "c1" > // 初始化 n*n 大小的棋盘，其中 ' Q' 代表皇后，' #' 代表空位< / span >
< a id = "__codelineno-3-65" name = "__codelineno-3-65" href = "#__codelineno-3-65" > < / a > < span class = "w" > < / span > < span class = "nx" > state< / 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" > string< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-66" name = "__codelineno-3-66" href = "#__codelineno-3-66" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "p" > < < / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-67" name = "__codelineno-3-67" href = "#__codelineno-3-67" > < / a > < span class = "w" > < / span > < span class = "nx" > row< / 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" > string< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-68" name = "__codelineno-3-68" href = "#__codelineno-3-68" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "p" > < < / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-69" name = "__codelineno-3-69" href = "#__codelineno-3-69" > < / a > < span class = "w" > < / span > < span class = "nx" > row< / 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 = "s" > " #" < / span >
< a id = "__codelineno-3-70" name = "__codelineno-3-70" href = "#__codelineno-3-70" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-71" name = "__codelineno-3-71" href = "#__codelineno-3-71" > < / a > < span class = "w" > < / span > < span class = "nx" > state< / 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" > row< / span >
< a id = "__codelineno-3-72" name = "__codelineno-3-72" href = "#__codelineno-3-72" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-73" name = "__codelineno-3-73" href = "#__codelineno-3-73" > < / a > < span class = "w" > < / span > < span class = "c1" > // 记录列是否有皇后< / span >
< a id = "__codelineno-3-74" name = "__codelineno-3-74" href = "#__codelineno-3-74" > < / a > < span class = "w" > < / span > < span class = "nx" > cols< / 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" > bool< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-75" name = "__codelineno-3-75" href = "#__codelineno-3-75" > < / a > < span class = "w" > < / span > < span class = "nx" > diags1< / 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" > bool< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 2< / span > < span class = "o" > *< / span > < span class = "nx" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-76" name = "__codelineno-3-76" href = "#__codelineno-3-76" > < / a > < span class = "w" > < / span > < span class = "nx" > diags2< / 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" > bool< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 2< / span > < span class = "o" > *< / span > < span class = "nx" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-77" name = "__codelineno-3-77" href = "#__codelineno-3-77" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nb" > make< / span > < span class = "p" > ([][][]< / span > < span class = "kt" > string< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-78" name = "__codelineno-3-78" href = "#__codelineno-3-78" > < / a > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "nx" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "nx" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "nx" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "nx" > diags2< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-79" name = "__codelineno-3-79" href = "#__codelineno-3-79" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span >
< a id = "__codelineno-3-80" name = "__codelineno-3-80" href = "#__codelineno-3-80" > < / a > < span class = "p" > }< / span >
2023-05-04 05:22:36 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-05-16 14:51:45 +08:00
< div class = "highlight" > < span class = "filename" > n_queens.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-4-1" name = "__codelineno-4-1" href = "#__codelineno-4-1" > < / a > < span class = "cm" > /* 回溯算法： < / span >
< a id = "__codelineno-4-2" name = "__codelineno-4-2" href = "#__codelineno-4-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > (< / span > < span class = "nx" > row< / 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" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > diags2< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-3" name = "__codelineno-4-3" href = "#__codelineno-4-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 当放置完所有行时，记录解< / span >
< a id = "__codelineno-4-4" name = "__codelineno-4-4" href = "#__codelineno-4-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > row< / 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 = "p" > {< / span >
< a id = "__codelineno-4-5" name = "__codelineno-4-5" href = "#__codelineno-4-5" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > .< / span > < span class = "nx" > map< / span > < span class = "p" > ((< / span > < span class = "nx" > row< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > => < / span > < span class = "w" > < / span > < span class = "nx" > row< / span > < span class = "p" > .< / span > < span class = "nx" > slice< / span > < span class = "p" > ()));< / span >
< a id = "__codelineno-4-6" name = "__codelineno-4-6" href = "#__codelineno-4-6" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-4-7" name = "__codelineno-4-7" href = "#__codelineno-4-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-8" name = "__codelineno-4-8" href = "#__codelineno-4-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有列< / span >
< a id = "__codelineno-4-9" name = "__codelineno-4-9" href = "#__codelineno-4-9" > < / 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" > col< / 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" > col< / 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" > col< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-10" name = "__codelineno-4-10" href = "#__codelineno-4-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 计算该格子对应的主对角线和副对角线< / span >
< a id = "__codelineno-4-11" name = "__codelineno-4-11" href = "#__codelineno-4-11" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > diag1< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > row< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "nx" > col< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-4-12" name = "__codelineno-4-12" href = "#__codelineno-4-12" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > diag2< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > row< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "nx" > col< / 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" > // 剪枝：不允许该格子所在 (列 或 主对角线 或 副对角线) 包含皇后< / span >
< a id = "__codelineno-4-14" name = "__codelineno-4-14" href = "#__codelineno-4-14" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > !< / span > < span class = "p" > (< / span > < span class = "nx" > cols< / span > < span class = "p" > [< / span > < span class = "nx" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "nx" > diags1< / span > < span class = "p" > [< / span > < span class = "nx" > diag1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "nx" > diags2< / span > < span class = "p" > [< / span > < span class = "nx" > diag2< / span > < span class = "p" > ]))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-15" name = "__codelineno-4-15" href = "#__codelineno-4-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：将皇后放置在该格子< / span >
< a id = "__codelineno-4-16" name = "__codelineno-4-16" href = "#__codelineno-4-16" > < / a > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "p" > [< / span > < span class = "nx" > row< / span > < span class = "p" > ][< / span > < span class = "nx" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "s1" > ' Q' < / span > < span class = "p" > ;< / span >
< a id = "__codelineno-4-17" name = "__codelineno-4-17" href = "#__codelineno-4-17" > < / a > < span class = "w" > < / span > < span class = "nx" > cols< / span > < span class = "p" > [< / span > < span class = "nx" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > diags1< / span > < span class = "p" > [< / span > < span class = "nx" > diag1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > diags2< / span > < span class = "p" > [< / span > < span class = "nx" > diag2< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "kc" > true< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-4-18" name = "__codelineno-4-18" href = "#__codelineno-4-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 放置下一行< / span >
< a id = "__codelineno-4-19" name = "__codelineno-4-19" href = "#__codelineno-4-19" > < / a > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > (< / span > < span class = "nx" > row< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > diags2< / span > < span class = "p" > );< / span >
< a id = "__codelineno-4-20" name = "__codelineno-4-20" href = "#__codelineno-4-20" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退：将该格子恢复为空位< / span >
< a id = "__codelineno-4-21" name = "__codelineno-4-21" href = "#__codelineno-4-21" > < / a > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "p" > [< / span > < span class = "nx" > row< / span > < span class = "p" > ][< / span > < span class = "nx" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "s1" > ' #' < / span > < span class = "p" > ;< / span >
< a id = "__codelineno-4-22" name = "__codelineno-4-22" href = "#__codelineno-4-22" > < / a > < span class = "w" > < / span > < span class = "nx" > cols< / span > < span class = "p" > [< / span > < span class = "nx" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > diags1< / span > < span class = "p" > [< / span > < span class = "nx" > diag1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > diags2< / span > < span class = "p" > [< / span > < span class = "nx" > diag2< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "kc" > false< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-4-23" name = "__codelineno-4-23" href = "#__codelineno-4-23" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-24" name = "__codelineno-4-24" href = "#__codelineno-4-24" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-25" name = "__codelineno-4-25" href = "#__codelineno-4-25" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-4-26" name = "__codelineno-4-26" href = "#__codelineno-4-26" > < / a >
< a id = "__codelineno-4-27" name = "__codelineno-4-27" href = "#__codelineno-4-27" > < / a > < span class = "cm" > /* 求解 N 皇后 */< / span >
< a id = "__codelineno-4-28" name = "__codelineno-4-28" href = "#__codelineno-4-28" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > nQueens< / 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-4-29" name = "__codelineno-4-29" href = "#__codelineno-4-29" > < / a > < span class = "w" > < / span > < span class = "c1" > // 初始化 n*n 大小的棋盘，其中 ' Q' 代表皇后，' #' 代表空位< / span >
< a id = "__codelineno-4-30" name = "__codelineno-4-30" href = "#__codelineno-4-30" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > Array< / span > < span class = "p" > .< / span > < span class = "kr" > from< / span > < span class = "p" > ({< / span > < span class = "w" > < / span > < span class = "nx" > length< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "p" > },< / span > < span class = "w" > < / 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 = "s1" > ' #' < / span > < span class = "p" > ));< / span >
< a id = "__codelineno-4-31" name = "__codelineno-4-31" href = "#__codelineno-4-31" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > cols< / 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 > < span class = "nx" > fill< / span > < span class = "p" > (< / span > < span class = "kc" > false< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 记录列是否有皇后< / span >
< a id = "__codelineno-4-32" name = "__codelineno-4-32" href = "#__codelineno-4-32" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > diags1< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > Array< / span > < span class = "p" > (< / span > < span class = "mf" > 2< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ).< / span > < span class = "nx" > fill< / span > < span class = "p" > (< / span > < span class = "kc" > false< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 记录主对角线是否有皇后< / span >
< a id = "__codelineno-4-33" name = "__codelineno-4-33" href = "#__codelineno-4-33" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > diags2< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > Array< / span > < span class = "p" > (< / span > < span class = "mf" > 2< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ).< / span > < span class = "nx" > fill< / span > < span class = "p" > (< / span > < span class = "kc" > false< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 记录副对角线是否有皇后< / span >
< a id = "__codelineno-4-34" name = "__codelineno-4-34" href = "#__codelineno-4-34" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [];< / span >
< a id = "__codelineno-4-35" name = "__codelineno-4-35" href = "#__codelineno-4-35" > < / a >
< a id = "__codelineno-4-36" name = "__codelineno-4-36" href = "#__codelineno-4-36" > < / a > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > (< / span > < span class = "mf" > 0< / 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" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > diags2< / span > < span class = "p" > );< / span >
< a id = "__codelineno-4-37" name = "__codelineno-4-37" href = "#__codelineno-4-37" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-4-38" name = "__codelineno-4-38" href = "#__codelineno-4-38" > < / a > < span class = "p" > }< / span >
2023-05-04 05:22:36 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-05-16 14:51:45 +08:00
< div class = "highlight" > < span class = "filename" > n_queens.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-5-1" name = "__codelineno-5-1" href = "#__codelineno-5-1" > < / a > < span class = "cm" > /* 回溯算法： < / span >
< a id = "__codelineno-5-2" name = "__codelineno-5-2" href = "#__codelineno-5-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > backtrack< / 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" > row< / 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" > n< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / 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 = "nx" > state< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > string< / span > < span class = "p" > [][],< / span >
< a id = "__codelineno-5-6" name = "__codelineno-5-6" href = "#__codelineno-5-6" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > string< / span > < span class = "p" > [][][],< / span >
< a id = "__codelineno-5-7" name = "__codelineno-5-7" href = "#__codelineno-5-7" > < / a > < span class = "w" > < / span > < span class = "nx" > cols< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > boolean< / span > < span class = "p" > [],< / span >
< a id = "__codelineno-5-8" name = "__codelineno-5-8" href = "#__codelineno-5-8" > < / a > < span class = "w" > < / span > < span class = "nx" > diags1< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > boolean< / span > < span class = "p" > [],< / span >
< a id = "__codelineno-5-9" name = "__codelineno-5-9" href = "#__codelineno-5-9" > < / a > < span class = "w" > < / span > < span class = "nx" > diags2< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > boolean< / span > < span class = "p" > []< / span >
< a id = "__codelineno-5-10" name = "__codelineno-5-10" href = "#__codelineno-5-10" > < / a > < span class = "p" > )< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "ow" > void< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-11" name = "__codelineno-5-11" href = "#__codelineno-5-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 当放置完所有行时，记录解< / span >
< a id = "__codelineno-5-12" name = "__codelineno-5-12" href = "#__codelineno-5-12" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > row< / 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 = "p" > {< / span >
< a id = "__codelineno-5-13" name = "__codelineno-5-13" href = "#__codelineno-5-13" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > .< / span > < span class = "nx" > map< / span > < span class = "p" > ((< / span > < span class = "nx" > row< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > => < / span > < span class = "w" > < / span > < span class = "nx" > row< / span > < span class = "p" > .< / span > < span class = "nx" > slice< / span > < span class = "p" > ()));< / span >
< a id = "__codelineno-5-14" name = "__codelineno-5-14" href = "#__codelineno-5-14" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-5-15" name = "__codelineno-5-15" href = "#__codelineno-5-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-5-16" name = "__codelineno-5-16" href = "#__codelineno-5-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有列< / span >
< a id = "__codelineno-5-17" name = "__codelineno-5-17" href = "#__codelineno-5-17" > < / 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" > col< / 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" > col< / 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" > col< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-18" name = "__codelineno-5-18" href = "#__codelineno-5-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 计算该格子对应的主对角线和副对角线< / span >
< a id = "__codelineno-5-19" name = "__codelineno-5-19" href = "#__codelineno-5-19" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > diag1< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > row< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "nx" > col< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ;< / span >
< 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" > diag2< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > row< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "nx" > col< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-5-21" name = "__codelineno-5-21" href = "#__codelineno-5-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：不允许该格子所在 (列 或 主对角线 或 副对角线) 包含皇后< / span >
< a id = "__codelineno-5-22" name = "__codelineno-5-22" href = "#__codelineno-5-22" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > !< / span > < span class = "p" > (< / span > < span class = "nx" > cols< / span > < span class = "p" > [< / span > < span class = "nx" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "nx" > diags1< / span > < span class = "p" > [< / span > < span class = "nx" > diag1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "nx" > diags2< / span > < span class = "p" > [< / span > < span class = "nx" > diag2< / span > < span class = "p" > ]))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-23" name = "__codelineno-5-23" href = "#__codelineno-5-23" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：将皇后放置在该格子< / span >
< a id = "__codelineno-5-24" name = "__codelineno-5-24" href = "#__codelineno-5-24" > < / a > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "p" > [< / span > < span class = "nx" > row< / span > < span class = "p" > ][< / span > < span class = "nx" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "s1" > ' Q' < / span > < span class = "p" > ;< / span >
< a id = "__codelineno-5-25" name = "__codelineno-5-25" href = "#__codelineno-5-25" > < / a > < span class = "w" > < / span > < span class = "nx" > cols< / span > < span class = "p" > [< / span > < span class = "nx" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > diags1< / span > < span class = "p" > [< / span > < span class = "nx" > diag1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > diags2< / span > < span class = "p" > [< / span > < span class = "nx" > diag2< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "kc" > true< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-5-26" name = "__codelineno-5-26" href = "#__codelineno-5-26" > < / a > < span class = "w" > < / span > < span class = "c1" > // 放置下一行< / span >
< a id = "__codelineno-5-27" name = "__codelineno-5-27" href = "#__codelineno-5-27" > < / a > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > (< / span > < span class = "nx" > row< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > diags2< / span > < span class = "p" > );< / span >
< a id = "__codelineno-5-28" name = "__codelineno-5-28" href = "#__codelineno-5-28" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退：将该格子恢复为空位< / span >
< a id = "__codelineno-5-29" name = "__codelineno-5-29" href = "#__codelineno-5-29" > < / a > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "p" > [< / span > < span class = "nx" > row< / span > < span class = "p" > ][< / span > < span class = "nx" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "s1" > ' #' < / span > < span class = "p" > ;< / span >
< a id = "__codelineno-5-30" name = "__codelineno-5-30" href = "#__codelineno-5-30" > < / a > < span class = "w" > < / span > < span class = "nx" > cols< / span > < span class = "p" > [< / span > < span class = "nx" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > diags1< / span > < span class = "p" > [< / span > < span class = "nx" > diag1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > diags2< / span > < span class = "p" > [< / span > < span class = "nx" > diag2< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "kc" > false< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-5-31" name = "__codelineno-5-31" href = "#__codelineno-5-31" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-5-32" name = "__codelineno-5-32" href = "#__codelineno-5-32" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-5-33" name = "__codelineno-5-33" href = "#__codelineno-5-33" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-5-34" name = "__codelineno-5-34" href = "#__codelineno-5-34" > < / a >
< a id = "__codelineno-5-35" name = "__codelineno-5-35" href = "#__codelineno-5-35" > < / a > < span class = "cm" > /* 求解 N 皇后 */< / span >
< a id = "__codelineno-5-36" name = "__codelineno-5-36" href = "#__codelineno-5-36" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > nQueens< / 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" > string< / span > < span class = "p" > [][][]< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-37" name = "__codelineno-5-37" href = "#__codelineno-5-37" > < / a > < span class = "w" > < / span > < span class = "c1" > // 初始化 n*n 大小的棋盘，其中 ' Q' 代表皇后，' #' 代表空位< / span >
< a id = "__codelineno-5-38" name = "__codelineno-5-38" href = "#__codelineno-5-38" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > Array< / span > < span class = "p" > .< / span > < span class = "kr" > from< / span > < span class = "p" > ({< / span > < span class = "w" > < / span > < span class = "nx" > length< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > n< / span > < span class = "w" > < / span > < span class = "p" > },< / span > < span class = "w" > < / 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 = "s1" > ' #' < / span > < span class = "p" > ));< / span >
< a id = "__codelineno-5-39" name = "__codelineno-5-39" href = "#__codelineno-5-39" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > cols< / 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 > < span class = "nx" > fill< / span > < span class = "p" > (< / span > < span class = "kc" > false< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 记录列是否有皇后< / span >
< a id = "__codelineno-5-40" name = "__codelineno-5-40" href = "#__codelineno-5-40" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > diags1< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > Array< / span > < span class = "p" > (< / span > < span class = "mf" > 2< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ).< / span > < span class = "nx" > fill< / span > < span class = "p" > (< / span > < span class = "kc" > false< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 记录主对角线是否有皇后< / span >
< a id = "__codelineno-5-41" name = "__codelineno-5-41" href = "#__codelineno-5-41" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > diags2< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > Array< / span > < span class = "p" > (< / span > < span class = "mf" > 2< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ).< / span > < span class = "nx" > fill< / span > < span class = "p" > (< / span > < span class = "kc" > false< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 记录副对角线是否有皇后< / span >
< a id = "__codelineno-5-42" name = "__codelineno-5-42" href = "#__codelineno-5-42" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > string< / span > < span class = "p" > [][][]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [];< / span >
< a id = "__codelineno-5-43" name = "__codelineno-5-43" href = "#__codelineno-5-43" > < / a >
< a id = "__codelineno-5-44" name = "__codelineno-5-44" href = "#__codelineno-5-44" > < / a > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > (< / span > < span class = "mf" > 0< / 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" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > diags2< / span > < span class = "p" > );< / span >
< a id = "__codelineno-5-45" name = "__codelineno-5-45" href = "#__codelineno-5-45" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-5-46" name = "__codelineno-5-46" href = "#__codelineno-5-46" > < / a > < span class = "p" > }< / span >
2023-05-04 05:22:36 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > n_queens.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-6-1" name = "__codelineno-6-1" href = "#__codelineno-6-1" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > backtrack< / span > < span class = "p" > }< / span >
< a id = "__codelineno-6-2" name = "__codelineno-6-2" href = "#__codelineno-6-2" > < / a >
< a id = "__codelineno-6-3" name = "__codelineno-6-3" href = "#__codelineno-6-3" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > nQueens< / span > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-05-05 03:41:48 +08:00
< div class = "highlight" > < span class = "filename" > n_queens.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-7-1" name = "__codelineno-7-1" href = "#__codelineno-7-1" > < / a > < span class = "cm" > /* 回溯算法： < / span >
< a id = "__codelineno-7-2" name = "__codelineno-7-2" href = "#__codelineno-7-2" > < / a > < span class = "k" > void< / span > < span class = "w" > < / span > < span class = "nf" > backtrack< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > row< / span > < span class = "p" > ,< / span > < span class = "w" > < / 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 = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > string< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < 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" > List< / span > < span class = "o" > < < / span > < span class = "kt" > string< / span > < span class = "o" > > > > < / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-7-3" name = "__codelineno-7-3" href = "#__codelineno-7-3" > < / a > < span class = "w" > < / span > < span class = "kt" > bool< / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > bool< / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > bool< / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-4" name = "__codelineno-7-4" href = "#__codelineno-7-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 当放置完所有行时，记录解< / span >
< a id = "__codelineno-7-5" name = "__codelineno-7-5" href = "#__codelineno-7-5" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > row< / 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 = "p" > {< / span >
< a id = "__codelineno-7-6" name = "__codelineno-7-6" href = "#__codelineno-7-6" > < / 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" > string< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "n" > copyState< / 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" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > string< / span > < span class = "o" > > > < / span > < span class = "p" > ();< / span >
< a id = "__codelineno-7-7" name = "__codelineno-7-7" href = "#__codelineno-7-7" > < / a > < span class = "w" > < / span > < span class = "k" > foreach< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > string< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > sRow< / span > < span class = "w" > < / span > < span class = "k" > in< / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-8" name = "__codelineno-7-8" href = "#__codelineno-7-8" > < / a > < span class = "w" > < / span > < span class = "n" > copyState< / 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" > List< / span > < span class = "o" > < < / span > < span class = "kt" > string< / span > < span class = "o" > > < / span > < span class = "p" > (< / span > < span class = "n" > sRow< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-7-9" name = "__codelineno-7-9" href = "#__codelineno-7-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-7-10" name = "__codelineno-7-10" href = "#__codelineno-7-10" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > Add< / span > < span class = "p" > (< / span > < span class = "n" > copyState< / span > < span class = "p" > );< / span >
< a id = "__codelineno-7-11" name = "__codelineno-7-11" href = "#__codelineno-7-11" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-12" name = "__codelineno-7-12" href = "#__codelineno-7-12" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-7-13" name = "__codelineno-7-13" href = "#__codelineno-7-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有列< / span >
< a id = "__codelineno-7-14" name = "__codelineno-7-14" href = "#__codelineno-7-14" > < / 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" > col< / 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" > col< / 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" > col< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-15" name = "__codelineno-7-15" href = "#__codelineno-7-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 计算该格子对应的主对角线和副对角线< / span >
< a id = "__codelineno-7-16" name = "__codelineno-7-16" href = "#__codelineno-7-16" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > diag1< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > row< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "n" > col< / 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 = "m" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-17" name = "__codelineno-7-17" href = "#__codelineno-7-17" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > diag2< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > row< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > col< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-18" name = "__codelineno-7-18" href = "#__codelineno-7-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：不允许该格子所在 (列 或 主对角线 或 副对角线) 包含皇后< / span >
< a id = "__codelineno-7-19" name = "__codelineno-7-19" href = "#__codelineno-7-19" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > !< / span > < span class = "p" > (< / span > < span class = "n" > cols< / span > < span class = "p" > [< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > [< / span > < span class = "n" > diag1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > [< / span > < span class = "n" > diag2< / span > < span class = "p" > ]))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-20" name = "__codelineno-7-20" href = "#__codelineno-7-20" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：将皇后放置在该格子< / span >
< a id = "__codelineno-7-21" name = "__codelineno-7-21" href = "#__codelineno-7-21" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > [< / span > < span class = "n" > row< / span > < span class = "p" > ][< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "s" > " Q" < / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-22" name = "__codelineno-7-22" href = "#__codelineno-7-22" > < / a > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "p" > [< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > [< / span > < span class = "n" > diag1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > [< / span > < span class = "n" > diag2< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > true< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-23" name = "__codelineno-7-23" href = "#__codelineno-7-23" > < / a > < span class = "w" > < / span > < span class = "c1" > // 放置下一行< / span >
< a id = "__codelineno-7-24" name = "__codelineno-7-24" href = "#__codelineno-7-24" > < / a > < span class = "w" > < / span > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > row< / 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 = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > );< / span >
< a id = "__codelineno-7-25" name = "__codelineno-7-25" href = "#__codelineno-7-25" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退：将该格子恢复为空位< / span >
< a id = "__codelineno-7-26" name = "__codelineno-7-26" href = "#__codelineno-7-26" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > [< / span > < span class = "n" > row< / span > < span class = "p" > ][< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "s" > " #" < / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-27" name = "__codelineno-7-27" href = "#__codelineno-7-27" > < / a > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "p" > [< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > [< / span > < span class = "n" > diag1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > [< / span > < span class = "n" > diag2< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > false< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-28" name = "__codelineno-7-28" href = "#__codelineno-7-28" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-7-29" name = "__codelineno-7-29" href = "#__codelineno-7-29" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-7-30" name = "__codelineno-7-30" href = "#__codelineno-7-30" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-7-31" name = "__codelineno-7-31" href = "#__codelineno-7-31" > < / a >
< a id = "__codelineno-7-32" name = "__codelineno-7-32" href = "#__codelineno-7-32" > < / a > < span class = "cm" > /* 求解 N 皇后 */< / span >
< a id = "__codelineno-7-33" name = "__codelineno-7-33" href = "#__codelineno-7-33" > < / a > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > string< / span > < span class = "o" > > > > < / span > < span class = "w" > < / span > < span class = "n" > nQueens< / 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-7-34" name = "__codelineno-7-34" href = "#__codelineno-7-34" > < / a > < span class = "w" > < / span > < span class = "c1" > // 初始化 n*n 大小的棋盘，其中 ' Q' 代表皇后，' #' 代表空位< / span >
< a id = "__codelineno-7-35" name = "__codelineno-7-35" href = "#__codelineno-7-35" > < / 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" > string< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "n" > state< / 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" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > string< / span > < span class = "o" > > > < / span > < span class = "p" > ();< / span >
< a id = "__codelineno-7-36" name = "__codelineno-7-36" href = "#__codelineno-7-36" > < / 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-7-37" name = "__codelineno-7-37" href = "#__codelineno-7-37" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > string< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > row< / 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" > List< / span > < span class = "o" > < < / span > < span class = "kt" > string< / span > < span class = "o" > > < / span > < span class = "p" > ();< / span >
< a id = "__codelineno-7-38" name = "__codelineno-7-38" href = "#__codelineno-7-38" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > 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-7-39" name = "__codelineno-7-39" href = "#__codelineno-7-39" > < / a > < span class = "w" > < / span > < span class = "n" > row< / span > < span class = "p" > .< / span > < span class = "n" > Add< / span > < span class = "p" > (< / span > < span class = "s" > " #" < / span > < span class = "p" > );< / span >
< a id = "__codelineno-7-40" name = "__codelineno-7-40" href = "#__codelineno-7-40" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-7-41" name = "__codelineno-7-41" href = "#__codelineno-7-41" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > Add< / span > < span class = "p" > (< / span > < span class = "n" > row< / span > < span class = "p" > );< / span >
< a id = "__codelineno-7-42" name = "__codelineno-7-42" href = "#__codelineno-7-42" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-7-43" name = "__codelineno-7-43" href = "#__codelineno-7-43" > < / a > < span class = "w" > < / span > < span class = "kt" > bool< / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "n" > cols< / 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" > bool< / span > < span class = "p" > [< / span > < span class = "n" > n< / span > < span class = "p" > ];< / span > < span class = "w" > < / span > < span class = "c1" > // 记录列是否有皇后< / span >
< a id = "__codelineno-7-44" name = "__codelineno-7-44" href = "#__codelineno-7-44" > < / a > < span class = "w" > < / span > < span class = "kt" > bool< / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "n" > diags1< / 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" > bool< / span > < span class = "p" > [< / span > < span class = "m" > 2< / 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 = "m" > 1< / span > < span class = "p" > ];< / span > < span class = "w" > < / span > < span class = "c1" > // 记录主对角线是否有皇后< / span >
< a id = "__codelineno-7-45" name = "__codelineno-7-45" href = "#__codelineno-7-45" > < / a > < span class = "w" > < / span > < span class = "kt" > bool< / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "n" > diags2< / 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" > bool< / span > < span class = "p" > [< / span > < span class = "m" > 2< / 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 = "m" > 1< / span > < span class = "p" > ];< / span > < span class = "w" > < / span > < span class = "c1" > // 记录副对角线是否有皇后< / span >
< a id = "__codelineno-7-46" name = "__codelineno-7-46" href = "#__codelineno-7-46" > < / 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" > List< / span > < span class = "o" > < < / span > < span class = "kt" > string< / span > < span class = "o" > > > > < / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > string< / span > < span class = "o" > > > > < / span > < span class = "p" > ();< / span >
< a id = "__codelineno-7-47" name = "__codelineno-7-47" href = "#__codelineno-7-47" > < / a >
< a id = "__codelineno-7-48" name = "__codelineno-7-48" href = "#__codelineno-7-48" > < / a > < span class = "w" > < / span > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "m" > 0< / 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" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > cols< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > diags1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > diags2< / span > < span class = "p" > );< / span >
< a id = "__codelineno-7-49" name = "__codelineno-7-49" href = "#__codelineno-7-49" > < / a >
< a id = "__codelineno-7-50" name = "__codelineno-7-50" href = "#__codelineno-7-50" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-51" name = "__codelineno-7-51" href = "#__codelineno-7-51" > < / a > < span class = "p" > }< / span >
2023-05-04 05:22:36 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-05-16 14:51:45 +08:00
< div class = "highlight" > < span class = "filename" > n_queens.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-8-1" name = "__codelineno-8-1" href = "#__codelineno-8-1" > < / a > < span class = "cm" > /* 回溯算法： < / span >
< a id = "__codelineno-8-2" name = "__codelineno-8-2" href = "#__codelineno-8-2" > < / a > < span class = "kd" > func< / span > < span class = "nf" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > row< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / 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 = "n" > state< / span > < span class = "p" > :< / span > < span class = "kr" > inout< / span > < span class = "p" > [[< / span > < span class = "nb" > String< / span > < span class = "p" > ]],< / span > < span class = "n" > res< / span > < span class = "p" > :< / span > < span class = "kr" > inout< / span > < span class = "p" > [[[< / span > < span class = "nb" > String< / span > < span class = "p" > ]]],< / span > < span class = "n" > cols< / span > < span class = "p" > :< / span > < span class = "kr" > inout< / span > < span class = "p" > [< / span > < span class = "nb" > Bool< / span > < span class = "p" > ],< / span > < span class = "n" > diags1< / span > < span class = "p" > :< / span > < span class = "kr" > inout< / span > < span class = "p" > [< / span > < span class = "nb" > Bool< / span > < span class = "p" > ],< / span > < span class = "n" > diags2< / span > < span class = "p" > :< / span > < span class = "kr" > inout< / span > < span class = "p" > [< / span > < span class = "nb" > Bool< / span > < span class = "p" > ])< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-3" name = "__codelineno-8-3" href = "#__codelineno-8-3" > < / a > < span class = "c1" > // 当放置完所有行时，记录解< / span >
< a id = "__codelineno-8-4" name = "__codelineno-8-4" href = "#__codelineno-8-4" > < / a > < span class = "k" > if< / span > < span class = "n" > row< / span > < span class = "p" > ==< / span > < span class = "n" > n< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-5" name = "__codelineno-8-5" href = "#__codelineno-8-5" > < / a > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > )< / span >
< a id = "__codelineno-8-6" name = "__codelineno-8-6" href = "#__codelineno-8-6" > < / a > < span class = "k" > return< / span >
< a id = "__codelineno-8-7" name = "__codelineno-8-7" href = "#__codelineno-8-7" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-8" name = "__codelineno-8-8" href = "#__codelineno-8-8" > < / a > < span class = "c1" > // 遍历所有列< / span >
< a id = "__codelineno-8-9" name = "__codelineno-8-9" href = "#__codelineno-8-9" > < / a > < span class = "k" > for< / span > < span class = "n" > col< / 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-8-10" name = "__codelineno-8-10" href = "#__codelineno-8-10" > < / a > < span class = "c1" > // 计算该格子对应的主对角线和副对角线< / span >
< a id = "__codelineno-8-11" name = "__codelineno-8-11" href = "#__codelineno-8-11" > < / a > < span class = "kd" > let< / span > < span class = "nv" > diag1< / span > < span class = "p" > =< / span > < span class = "n" > row< / span > < span class = "o" > -< / span > < span class = "n" > col< / span > < span class = "o" > +< / span > < span class = "n" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-8-12" name = "__codelineno-8-12" href = "#__codelineno-8-12" > < / a > < span class = "kd" > let< / span > < span class = "nv" > diag2< / span > < span class = "p" > =< / span > < span class = "n" > row< / span > < span class = "o" > +< / span > < span class = "n" > col< / span >
< a id = "__codelineno-8-13" name = "__codelineno-8-13" href = "#__codelineno-8-13" > < / a > < span class = "c1" > // 剪枝：不允许该格子所在 (列 或 主对角线 或 副对角线) 包含皇后< / span >
< a id = "__codelineno-8-14" name = "__codelineno-8-14" href = "#__codelineno-8-14" > < / a > < span class = "k" > if< / span > < span class = "o" > !< / span > < span class = "p" > (< / span > < span class = "n" > cols< / span > < span class = "p" > [< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "o" > ||< / span > < span class = "n" > diags1< / span > < span class = "p" > [< / span > < span class = "n" > diag1< / span > < span class = "p" > ]< / span > < span class = "o" > ||< / span > < span class = "n" > diags2< / span > < span class = "p" > [< / span > < span class = "n" > diag2< / span > < span class = "p" > ])< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-15" name = "__codelineno-8-15" href = "#__codelineno-8-15" > < / a > < span class = "c1" > // 尝试：将皇后放置在该格子< / span >
< a id = "__codelineno-8-16" name = "__codelineno-8-16" href = "#__codelineno-8-16" > < / a > < span class = "n" > state< / span > < span class = "p" > [< / span > < span class = "n" > row< / span > < span class = "p" > ][< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "s" > " Q" < / span >
< a id = "__codelineno-8-17" name = "__codelineno-8-17" href = "#__codelineno-8-17" > < / a > < span class = "n" > cols< / span > < span class = "p" > [< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "kc" > true< / span >
< a id = "__codelineno-8-18" name = "__codelineno-8-18" href = "#__codelineno-8-18" > < / a > < span class = "n" > diags1< / span > < span class = "p" > [< / span > < span class = "n" > diag1< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "kc" > true< / span >
< a id = "__codelineno-8-19" name = "__codelineno-8-19" href = "#__codelineno-8-19" > < / a > < span class = "n" > diags2< / span > < span class = "p" > [< / span > < span class = "n" > diag2< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "kc" > true< / span >
< a id = "__codelineno-8-20" name = "__codelineno-8-20" href = "#__codelineno-8-20" > < / a > < span class = "c1" > // 放置下一行< / span >
< a id = "__codelineno-8-21" name = "__codelineno-8-21" href = "#__codelineno-8-21" > < / a > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > row< / span > < span class = "p" > :< / span > < span class = "n" > row< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "n" > n< / span > < span class = "p" > :< / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "n" > state< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "n" > res< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "n" > cols< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > cols< / span > < span class = "p" > ,< / span > < span class = "n" > diags1< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > diags1< / span > < span class = "p" > ,< / span > < span class = "n" > diags2< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > diags2< / span > < span class = "p" > )< / span >
< a id = "__codelineno-8-22" name = "__codelineno-8-22" href = "#__codelineno-8-22" > < / a > < span class = "c1" > // 回退：将该格子恢复为空位< / span >
< a id = "__codelineno-8-23" name = "__codelineno-8-23" href = "#__codelineno-8-23" > < / a > < span class = "n" > state< / span > < span class = "p" > [< / span > < span class = "n" > row< / span > < span class = "p" > ][< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "s" > " #" < / span >
< a id = "__codelineno-8-24" name = "__codelineno-8-24" href = "#__codelineno-8-24" > < / a > < span class = "n" > cols< / span > < span class = "p" > [< / span > < span class = "n" > col< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "kc" > false< / span >
< a id = "__codelineno-8-25" name = "__codelineno-8-25" href = "#__codelineno-8-25" > < / a > < span class = "n" > diags1< / span > < span class = "p" > [< / span > < span class = "n" > diag1< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "kc" > false< / span >
< a id = "__codelineno-8-26" name = "__codelineno-8-26" href = "#__codelineno-8-26" > < / a > < span class = "n" > diags2< / span > < span class = "p" > [< / span > < span class = "n" > diag2< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "kc" > false< / span >
< a id = "__codelineno-8-27" name = "__codelineno-8-27" href = "#__codelineno-8-27" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-28" name = "__codelineno-8-28" href = "#__codelineno-8-28" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-29" name = "__codelineno-8-29" href = "#__codelineno-8-29" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-30" name = "__codelineno-8-30" href = "#__codelineno-8-30" > < / a >
< a id = "__codelineno-8-31" name = "__codelineno-8-31" href = "#__codelineno-8-31" > < / a > < span class = "cm" > /* 求解 N 皇后 */< / span >
< a id = "__codelineno-8-32" name = "__codelineno-8-32" href = "#__codelineno-8-32" > < / a > < span class = "kd" > func< / span > < span class = "nf" > nQueens< / 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 = "p" > [[[< / span > < span class = "nb" > String< / span > < span class = "p" > ]]]< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-33" name = "__codelineno-8-33" href = "#__codelineno-8-33" > < / a > < span class = "c1" > // 初始化 n*n 大小的棋盘，其中 ' Q' 代表皇后，' #' 代表空位< / span >
< a id = "__codelineno-8-34" name = "__codelineno-8-34" href = "#__codelineno-8-34" > < / a > < span class = "kd" > var< / span > < span class = "nv" > state< / 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 = "s" > " #" < / 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-8-35" name = "__codelineno-8-35" href = "#__codelineno-8-35" > < / a > < span class = "kd" > var< / span > < span class = "nv" > cols< / 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 = "kc" > false< / 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" > // 记录列是否有皇后< / span >
< a id = "__codelineno-8-36" name = "__codelineno-8-36" href = "#__codelineno-8-36" > < / a > < span class = "kd" > var< / span > < span class = "nv" > diags1< / 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 = "kc" > false< / span > < span class = "p" > ,< / span > < span class = "bp" > count< / span > < span class = "p" > :< / span > < span class = "mi" > 2< / span > < span class = "o" > *< / span > < span class = "n" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "c1" > // 记录主对角线是否有皇后< / span >
< a id = "__codelineno-8-37" name = "__codelineno-8-37" href = "#__codelineno-8-37" > < / a > < span class = "kd" > var< / span > < span class = "nv" > diags2< / 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 = "kc" > false< / span > < span class = "p" > ,< / span > < span class = "bp" > count< / span > < span class = "p" > :< / span > < span class = "mi" > 2< / span > < span class = "o" > *< / span > < span class = "n" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "c1" > // 记录副对角线是否有皇后< / span >
< a id = "__codelineno-8-38" name = "__codelineno-8-38" href = "#__codelineno-8-38" > < / a > < span class = "kd" > var< / span > < span class = "nv" > res< / span > < span class = "p" > :< / span > < span class = "p" > [[[< / span > < span class = "nb" > String< / span > < span class = "p" > ]]]< / span > < span class = "p" > =< / span > < span class = "p" > []< / span >
< a id = "__codelineno-8-39" name = "__codelineno-8-39" href = "#__codelineno-8-39" > < / a >
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< h2 id = "1231" > 12.3.1. 复杂度分析< a class = "headerlink" href = "#1231" title = "Permanent link" > ¶ < / a > < / h2 >
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< p > 逐行放置 < span class = "arithmatex" > \(n\)< / span > 次，考虑列约束，则从第一行到最后一行分别有 < span class = "arithmatex" > \(n, n-1, \cdots, 2, 1\)< / span > 个选择，< strong > 因此时间复杂度为 < span class = "arithmatex" > \(O(n!)\)< / span > < / strong > 。实际上，根据对角线约束的剪枝也能够大幅地缩小搜索空间，因而搜索效率往往优于以上时间复杂度。< / p >
< p > < code > state< / code > 使用 < span class = "arithmatex" > \(O(n^2)\)< / span > 空间，< code > cols< / code > , < code > diags1< / code > , < code > diags2< / code > 皆使用 < span class = "arithmatex" > \(O(n)\)< / span > 空间。最大递归深度为 < span class = "arithmatex" > \(n\)< / span > ，使用 < span class = "arithmatex" > \(O(n)\)< / span > 栈帧空间。因此，< strong > 空间复杂度为 < span class = "arithmatex" > \(O(n^2)\)< / span > < / strong > 。< / p >
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