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< a href = "../../chapter_preface/" > 0. 前言< / a >
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0. 前言
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0.1. 关于本书
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0.2. 如何使用本书
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0.3. 小结
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1. 初识算法
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1.1. 算法无处不在
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1.2. 算法是什么
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1.3. 小结
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2. 复杂度
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2.1. 算法效率评估
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2.2. 时间复杂度
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2.3. 空间复杂度
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2.4. 小结
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3. 数据结构
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3.1. 数据结构分类
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3.2. 基本数据类型
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3.3. 数字编码 *
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3.4. 字符编码 *
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3.5. 小结
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4. 数组与链表
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4.1. 数组
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4.2. 链表
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4.3. 列表
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4.4. 小结
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5. 栈与队列
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5.1. 栈
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5.2. 队列
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5.3. 双向队列
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5.4. 小结
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6. 散列表
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6.1. 哈希表（ ）
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6.2. 哈希冲突（ ）
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6.3. 哈希算法（ ）
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6.4. 小结
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7. 树
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7.1. 二叉树
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7.2. 二叉树遍历
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7.3. 二叉树数组表示
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7.4. 二叉搜索树
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7.5. AVL 树 *
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7.6. 小结
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8. 堆
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8.1. 堆
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8.2. 建堆操作
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8.3. Top-K 问题（ ）
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8.4. 小结
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9. 图
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9.1. 图
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9.2. 图基础操作
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9.3. 图的遍历
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9.4. 小结
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10. 搜索
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10.1. 二分查找
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10.2. 二分查找边界
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10.3. 哈希优化策略
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10.4. 重识搜索算法
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10.5. 小结
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11.2. 选择排序
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11.5. 快速排序
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11.6. 归并排序
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11.7. 堆排序
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11.8. 桶排序
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11.9. 计数排序
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11.10. 基数排序
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11.11. 小结
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12.4. N 皇后问题
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< h1 id = "122" > 12.2. 全排列问题< a class = "headerlink" href = "#122" title = "Permanent link" > ¶ < / a > < / h1 >
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< p > 全排列问题是回溯算法的一个典型应用。它的定义是在给定一个集合（如一个数组或字符串）的情况下，找出这个集合中元素的所有可能的排列。< / p >
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< p > 如下表所示，列举了几个示例数组和其对应的所有排列。< / p >
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< p class = "admonition-title" > Question< / p >
< p > 输入一个整数数组，数组中不包含重复元素，返回所有可能的排列。< / p >
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< p > < strong > 从回溯算法的角度看，我们可以把生成排列的过程想象成一系列选择的结果< / strong > 。假设输入数组为 < span class = "arithmatex" > \([1, 2, 3]\)< / span > ，如果我们先选择 < span class = "arithmatex" > \(1\)< / span > 、再选择 < span class = "arithmatex" > \(3\)< / span > 、最后选择 < span class = "arithmatex" > \(2\)< / span > ，则获得排列 < span class = "arithmatex" > \([1, 3, 2]\)< / span > 。回退表示撤销一个选择，之后继续尝试其他选择。< / p >
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< p > 从回溯算法代码的角度看，候选集合 < code > choices< / code > 是输入数组中的所有元素，状态 < code > state< / code > 是直至目前已被选择的元素。注意，每个元素只允许被选择一次，< strong > 因此在遍历选择时，应当排除已经选择过的元素< / strong > 。< / p >
< p > 如下图所示，我们可以将搜索过程展开成一个递归树，树中的每个节点代表当前状态 < code > state< / code > 。从根节点开始，经过三轮选择后到达叶节点，每个叶节点都对应一个排列。< / p >
< p > < img alt = "全排列的递归树" src = "../permutations_problem.assets/permutations_i.png" / > < / p >
< p align = "center" > Fig. 全排列的递归树 < / p >
< p > 想清楚以上信息之后，我们就可以在框架代码中做“完形填空”了。为了缩短代码行数，我们不单独实现框架代码中的各个函数，而是将他们展开在 < code > backtrack()< / code > 函数中。< / p >
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< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > permutations_i.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：全排列 I */< / 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 = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "o" > []< / span > < span class = "w" > < / span > < span class = "n" > choices< / 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" > selected< / 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" > Integer< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-0-3" name = "__codelineno-0-3" href = "#__codelineno-0-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 当状态长度等于元素数量时，记录解< / span >
< a id = "__codelineno-0-4" name = "__codelineno-0-4" href = "#__codelineno-0-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "na" > size< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > .< / span > < span class = "na" > length< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-0-5" name = "__codelineno-0-5" href = "#__codelineno-0-5" > < / a > < span class = "w" > < / span > < span class = "n" > res< / 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 = "n" > Integer< / span > < span class = "o" > > < / span > < span class = "p" > (< / span > < span class = "n" > state< / 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 = "k" > return< / 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 = "p" > }< / span >
< a id = "__codelineno-0-8" name = "__codelineno-0-8" href = "#__codelineno-0-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-0-9" name = "__codelineno-0-9" href = "#__codelineno-0-9" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > .< / span > < span class = "na" > length< / 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-0-10" name = "__codelineno-0-10" href = "#__codelineno-0-10" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "o" > [< / span > < span class = "n" > i< / span > < span class = "o" > ]< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-0-11" name = "__codelineno-0-11" href = "#__codelineno-0-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：不允许重复选择元素 且 不允许重复选择相等元素< / span >
< a id = "__codelineno-0-12" name = "__codelineno-0-12" href = "#__codelineno-0-12" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > !< / span > < span class = "n" > selected< / span > < span class = "o" > [< / span > < span class = "n" > i< / span > < span class = "o" > ]< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
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< a id = "__codelineno-0-13" name = "__codelineno-0-13" href = "#__codelineno-0-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新状态< / span >
< a id = "__codelineno-0-14" name = "__codelineno-0-14" href = "#__codelineno-0-14" > < / a > < span class = "w" > < / span > < span class = "n" > selected< / span > < span class = "o" > [< / span > < span class = "n" > i< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "kc" > true< / 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 = "n" > state< / span > < span class = "p" > .< / span > < span class = "na" > add< / span > < span class = "p" > (< / span > < span class = "n" > choice< / span > < span class = "p" > );< / span >
2023-05-03 18:30:04 +08:00
< a id = "__codelineno-0-16" name = "__codelineno-0-16" href = "#__codelineno-0-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-0-17" name = "__codelineno-0-17" href = "#__codelineno-0-17" > < / a > < span class = "w" > < / span > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > selected< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / 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" > // 回退：撤销选择，恢复到之前的状态< / span >
< a id = "__codelineno-0-19" name = "__codelineno-0-19" href = "#__codelineno-0-19" > < / a > < span class = "w" > < / span > < span class = "n" > selected< / span > < span class = "o" > [< / span > < span class = "n" > i< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "kc" > false< / 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 = "n" > state< / span > < span class = "p" > .< / span > < span class = "na" > remove< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "na" > size< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > );< / span >
< a id = "__codelineno-0-21" name = "__codelineno-0-21" href = "#__codelineno-0-21" > < / a > < span class = "w" > < / 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 = "p" > }< / span >
< a id = "__codelineno-0-23" name = "__codelineno-0-23" href = "#__codelineno-0-23" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-0-24" name = "__codelineno-0-24" href = "#__codelineno-0-24" > < / a >
< a id = "__codelineno-0-25" name = "__codelineno-0-25" href = "#__codelineno-0-25" > < / a > < span class = "cm" > /* 全排列 I */< / span >
< a id = "__codelineno-0-26" name = "__codelineno-0-26" href = "#__codelineno-0-26" > < / a > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "nf" > permutationsI< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "o" > []< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-0-27" name = "__codelineno-0-27" href = "#__codelineno-0-27" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "n" > 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 = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / span > < span class = "o" > > > < / 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 = "n" > backtrack< / 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 = "n" > Integer< / span > < span class = "o" > > < / span > < span class = "p" > (),< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > ,< / 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" > nums< / span > < span class = "p" > .< / span > < span class = "na" > length< / span > < span class = "o" > ]< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / 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 = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-0-30" name = "__codelineno-0-30" href = "#__codelineno-0-30" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > permutations_i.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：全排列 I */< / 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 = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "k" > const< / span > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > choices< / 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" > selected< / 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 = "kt" > int< / 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 = "p" > {< / span >
< a id = "__codelineno-1-3" name = "__codelineno-1-3" href = "#__codelineno-1-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 当状态长度等于元素数量时，记录解< / span >
< a id = "__codelineno-1-4" name = "__codelineno-1-4" href = "#__codelineno-1-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > size< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > .< / span > < span class = "n" > size< / span > < span class = "p" > ())< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-5" name = "__codelineno-1-5" href = "#__codelineno-1-5" > < / a > < span class = "w" > < / span > < span class = "n" > 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-1-6" name = "__codelineno-1-6" href = "#__codelineno-1-6" > < / a > < span class = "w" > < / span > < span class = "k" > return< / 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 = "p" > }< / span >
< a id = "__codelineno-1-8" name = "__codelineno-1-8" href = "#__codelineno-1-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-1-9" name = "__codelineno-1-9" href = "#__codelineno-1-9" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > .< / span > < span class = "n" > size< / span > < span class = "p" > ();< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-10" name = "__codelineno-1-10" href = "#__codelineno-1-10" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > [< / span > < span class = "n" > i< / 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" > // 剪枝：不允许重复选择元素 且 不允许重复选择相等元素< / span >
< a id = "__codelineno-1-12" name = "__codelineno-1-12" href = "#__codelineno-1-12" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > !< / span > < span class = "n" > selected< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ])< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
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< a id = "__codelineno-1-13" name = "__codelineno-1-13" href = "#__codelineno-1-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新状态< / span >
< a id = "__codelineno-1-14" name = "__codelineno-1-14" href = "#__codelineno-1-14" > < / a > < span class = "w" > < / span > < span class = "n" > selected< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > true< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-15" name = "__codelineno-1-15" href = "#__codelineno-1-15" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > push_back< / span > < span class = "p" > (< / span > < span class = "n" > choice< / span > < span class = "p" > );< / span >
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< a id = "__codelineno-1-16" name = "__codelineno-1-16" href = "#__codelineno-1-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-1-17" name = "__codelineno-1-17" href = "#__codelineno-1-17" > < / a > < span class = "w" > < / span > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > selected< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / 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 = "c1" > // 回退：撤销选择，恢复到之前的状态< / span >
< a id = "__codelineno-1-19" name = "__codelineno-1-19" href = "#__codelineno-1-19" > < / a > < span class = "w" > < / span > < span class = "n" > selected< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > false< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-20" name = "__codelineno-1-20" href = "#__codelineno-1-20" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > pop_back< / 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 = "p" > }< / span >
< a id = "__codelineno-1-22" name = "__codelineno-1-22" href = "#__codelineno-1-22" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-1-23" name = "__codelineno-1-23" href = "#__codelineno-1-23" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-1-24" name = "__codelineno-1-24" href = "#__codelineno-1-24" > < / a >
< a id = "__codelineno-1-25" name = "__codelineno-1-25" href = "#__codelineno-1-25" > < / a > < span class = "cm" > /* 全排列 I */< / span >
< a id = "__codelineno-1-26" name = "__codelineno-1-26" href = "#__codelineno-1-26" > < / a > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "n" > permutationsI< / span > < span class = "p" > (< / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-27" name = "__codelineno-1-27" href = "#__codelineno-1-27" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-28" name = "__codelineno-1-28" href = "#__codelineno-1-28" > < / 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" > selected< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > .< / span > < span class = "n" > size< / span > < span class = "p" > (),< / span > < span class = "w" > < / span > < span class = "nb" > false< / span > < span class = "p" > );< / span >
< a id = "__codelineno-1-29" name = "__codelineno-1-29" href = "#__codelineno-1-29" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "n" > res< / 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 = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > selected< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-1-31" name = "__codelineno-1-31" href = "#__codelineno-1-31" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-32" name = "__codelineno-1-32" href = "#__codelineno-1-32" > < / a > < span class = "p" > }< / span >
2023-04-24 03:30:35 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > permutations_i.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" > state< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > int< / span > < span class = "p" > ],< / span > < span class = "n" > choices< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > int< / span > < span class = "p" > ],< / span > < span class = "n" > selected< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > bool< / span > < span class = "p" > ],< / span > < 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" > int< / span > < span class = "p" > ]]< / span >
< a id = "__codelineno-2-3" name = "__codelineno-2-3" href = "#__codelineno-2-3" > < / a > < span class = "p" > ):< / span >
< a id = "__codelineno-2-4" name = "__codelineno-2-4" href = "#__codelineno-2-4" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 回溯算法：全排列 I" " " < / span >
< a id = "__codelineno-2-5" name = "__codelineno-2-5" href = "#__codelineno-2-5" > < / a > < span class = "c1" > # 当状态长度等于元素数量时，记录解< / span >
< a id = "__codelineno-2-6" name = "__codelineno-2-6" href = "#__codelineno-2-6" > < / a > < span class = "k" > if< / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > )< / span > < span class = "o" > ==< / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "n" > choices< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-2-7" name = "__codelineno-2-7" href = "#__codelineno-2-7" > < / 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" > state< / span > < span class = "p" > ))< / span >
< a id = "__codelineno-2-8" name = "__codelineno-2-8" href = "#__codelineno-2-8" > < / a > < span class = "k" > return< / span >
< a id = "__codelineno-2-9" name = "__codelineno-2-9" href = "#__codelineno-2-9" > < / a > < span class = "c1" > # 遍历所有选择< / span >
< a id = "__codelineno-2-10" name = "__codelineno-2-10" href = "#__codelineno-2-10" > < / a > < span class = "k" > for< / span > < span class = "n" > i< / span > < span class = "p" > ,< / span > < span class = "n" > choice< / span > < span class = "ow" > in< / span > < span class = "nb" > enumerate< / span > < span class = "p" > (< / span > < span class = "n" > choices< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-2-11" name = "__codelineno-2-11" href = "#__codelineno-2-11" > < / a > < span class = "c1" > # 剪枝：不允许重复选择元素< / span >
< a id = "__codelineno-2-12" name = "__codelineno-2-12" href = "#__codelineno-2-12" > < / a > < span class = "k" > if< / span > < span class = "ow" > not< / span > < span class = "n" > selected< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]:< / span >
2023-04-27 01:28:42 +08:00
< a id = "__codelineno-2-13" name = "__codelineno-2-13" href = "#__codelineno-2-13" > < / a > < span class = "c1" > # 尝试：做出选择，更新状态< / span >
< a id = "__codelineno-2-14" name = "__codelineno-2-14" href = "#__codelineno-2-14" > < / a > < span class = "n" > selected< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "kc" > True< / span >
< a id = "__codelineno-2-15" name = "__codelineno-2-15" href = "#__codelineno-2-15" > < / a > < span class = "n" > state< / span > < span class = "o" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > choice< / span > < span class = "p" > )< / span >
2023-05-03 18:30:04 +08:00
< a id = "__codelineno-2-16" name = "__codelineno-2-16" href = "#__codelineno-2-16" > < / a > < span class = "c1" > # 进行下一轮选择< / span >
< a id = "__codelineno-2-17" name = "__codelineno-2-17" href = "#__codelineno-2-17" > < / a > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span > < span class = "n" > selected< / span > < span class = "p" > ,< / span > < span class = "n" > res< / span > < span class = "p" > )< / span >
< a id = "__codelineno-2-18" name = "__codelineno-2-18" href = "#__codelineno-2-18" > < / a > < span class = "c1" > # 回退：撤销选择，恢复到之前的状态< / span >
< a id = "__codelineno-2-19" name = "__codelineno-2-19" href = "#__codelineno-2-19" > < / a > < span class = "n" > selected< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "kc" > False< / span >
< a id = "__codelineno-2-20" name = "__codelineno-2-20" href = "#__codelineno-2-20" > < / a > < span class = "n" > state< / span > < span class = "o" > .< / span > < span class = "n" > pop< / span > < span class = "p" > ()< / span >
< a id = "__codelineno-2-21" name = "__codelineno-2-21" href = "#__codelineno-2-21" > < / a >
< a id = "__codelineno-2-22" name = "__codelineno-2-22" href = "#__codelineno-2-22" > < / a > < span class = "k" > def< / span > < span class = "nf" > permutations_i< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > int< / span > < span class = "p" > ])< / span > < span class = "o" > -> < / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > int< / span > < span class = "p" > ]]:< / span >
< a id = "__codelineno-2-23" name = "__codelineno-2-23" href = "#__codelineno-2-23" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 全排列 I" " " < / span >
< a id = "__codelineno-2-24" name = "__codelineno-2-24" href = "#__codelineno-2-24" > < / a > < span class = "n" > res< / span > < span class = "o" > =< / span > < span class = "p" > []< / span >
< a id = "__codelineno-2-25" name = "__codelineno-2-25" href = "#__codelineno-2-25" > < / a > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "o" > =< / span > < span class = "p" > [],< / span > < span class = "n" > choices< / span > < span class = "o" > =< / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "n" > selected< / span > < span class = "o" > =< / span > < span class = "p" > [< / span > < span class = "kc" > False< / span > < span class = "p" > ]< / span > < span class = "o" > *< / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > ),< / span > < span class = "n" > res< / span > < span class = "o" > =< / span > < span class = "n" > res< / span > < span class = "p" > )< / span >
< a id = "__codelineno-2-26" name = "__codelineno-2-26" href = "#__codelineno-2-26" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
2023-04-24 03:30:35 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-05-16 14:51:45 +08:00
< div class = "highlight" > < span class = "filename" > permutations_i.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：全排列 I */< / 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" > backtrackI< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > []< / span > < span class = "kt" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choices< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > []< / span > < span class = "kt" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > selected< / 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 = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > [][]< / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-3" name = "__codelineno-3-3" href = "#__codelineno-3-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 当状态长度等于元素数量时，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 = "nb" > len< / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > state< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > choices< / span > < span class = "p" > )< / 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" > append< / span > < span class = "p" > ([]< / span > < span class = "kt" > int< / span > < span class = "p" > {},< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > state< / span > < span class = "o" > ...< / 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 = "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-3-7" name = "__codelineno-3-7" href = "#__codelineno-3-7" > < / a > < span class = "w" > < / 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 = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-3-9" name = "__codelineno-3-9" href = "#__codelineno-3-9" > < / 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 = "nb" > len< / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > choices< / 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-3-10" name = "__codelineno-3-10" href = "#__codelineno-3-10" > < / a > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > choices< / span > < span class = "p" > )[< / span > < span class = "nx" > i< / 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 = "c1" > // 剪枝：不允许重复选择元素 且 不允许重复选择相等元素< / span >
< a id = "__codelineno-3-12" name = "__codelineno-3-12" href = "#__codelineno-3-12" > < / 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" > selected< / span > < span class = "p" > )[< / span > < span class = "nx" > i< / span > < span class = "p" > ]< / span > < 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" > // 尝试：做出选择，更新状态< / span >
< a id = "__codelineno-3-14" name = "__codelineno-3-14" href = "#__codelineno-3-14" > < / a > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > selected< / 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 = "kc" > true< / span >
< a id = "__codelineno-3-15" name = "__codelineno-3-15" href = "#__codelineno-3-15" > < / a > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > state< / 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" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-16" name = "__codelineno-3-16" href = "#__codelineno-3-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-3-17" name = "__codelineno-3-17" href = "#__codelineno-3-17" > < / a > < span class = "w" > < / span > < span class = "nx" > backtrackI< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > selected< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-18" name = "__codelineno-3-18" href = "#__codelineno-3-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退：撤销选择，恢复到之前的状态< / span >
< a id = "__codelineno-3-19" name = "__codelineno-3-19" href = "#__codelineno-3-19" > < / a > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > selected< / 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 = "kc" > false< / span >
< a id = "__codelineno-3-20" name = "__codelineno-3-20" href = "#__codelineno-3-20" > < / a > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > state< / span > < span class = "w" > < / 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 = "nb" > len< / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > state< / span > < span class = "p" > )< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-3-21" name = "__codelineno-3-21" href = "#__codelineno-3-21" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-22" name = "__codelineno-3-22" href = "#__codelineno-3-22" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-23" name = "__codelineno-3-23" href = "#__codelineno-3-23" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-3-24" name = "__codelineno-3-24" href = "#__codelineno-3-24" > < / a >
< a id = "__codelineno-3-25" name = "__codelineno-3-25" href = "#__codelineno-3-25" > < / a > < span class = "cm" > /* 全排列 I */< / span >
< a id = "__codelineno-3-26" name = "__codelineno-3-26" href = "#__codelineno-3-26" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > permutationsI< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "w" > < / span > < span class = "p" > []< / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > [][]< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-27" name = "__codelineno-3-27" href = "#__codelineno-3-27" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nb" > make< / span > < span class = "p" > ([][]< / span > < span class = "kt" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-28" name = "__codelineno-3-28" href = "#__codelineno-3-28" > < / 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" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 0< / 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 = "nx" > selected< / 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 = "nb" > len< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "p" > ))< / span >
< a id = "__codelineno-3-30" name = "__codelineno-3-30" href = "#__codelineno-3-30" > < / a > < span class = "w" > < / span > < span class = "nx" > backtrackI< / span > < span class = "p" > (< / 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" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "nx" > selected< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "nx" > res< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-31" name = "__codelineno-3-31" href = "#__codelineno-3-31" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span >
< a id = "__codelineno-3-32" name = "__codelineno-3-32" href = "#__codelineno-3-32" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > permutations_i.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：全排列 I */< / 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" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > selected< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / 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" > // 当状态长度等于元素数量时，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" > state< / span > < span class = "p" > .< / span > < span class = "nx" > length< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "nx" > choices< / span > < span class = "p" > .< / span > < span class = "nx" > length< / 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 >
< 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" > // 遍历所有选择< / span >
< a id = "__codelineno-4-9" name = "__codelineno-4-9" href = "#__codelineno-4-9" > < / a > < span class = "w" > < / span > < span class = "nx" > choices< / span > < span class = "p" > .< / span > < span class = "nx" > forEach< / span > < span class = "p" > ((< / span > < span class = "nx" > choice< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "p" > )< / span > < span class = "w" > < / 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" > // 剪枝：不允许重复选择元素 且 不允许重复选择相等元素< / span >
< a id = "__codelineno-4-11" name = "__codelineno-4-11" href = "#__codelineno-4-11" > < / 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" > selected< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ])< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-12" name = "__codelineno-4-12" href = "#__codelineno-4-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新状态< / span >
< a id = "__codelineno-4-13" name = "__codelineno-4-13" href = "#__codelineno-4-13" > < / a > < span class = "w" > < / span > < span class = "nx" > selected< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "kc" > true< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-4-14" name = "__codelineno-4-14" href = "#__codelineno-4-14" > < / a > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > (< / span > < span class = "nx" > choice< / 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" > // 进行下一轮选择< / span >
< a id = "__codelineno-4-16" name = "__codelineno-4-16" href = "#__codelineno-4-16" > < / a > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > selected< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-4-17" name = "__codelineno-4-17" href = "#__codelineno-4-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退：撤销选择，恢复到之前的状态< / span >
< a id = "__codelineno-4-18" name = "__codelineno-4-18" href = "#__codelineno-4-18" > < / a > < span class = "w" > < / span > < span class = "nx" > selected< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "kc" > false< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-4-19" name = "__codelineno-4-19" href = "#__codelineno-4-19" > < / a > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "p" > .< / span > < span class = "nx" > pop< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-4-20" name = "__codelineno-4-20" href = "#__codelineno-4-20" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-21" name = "__codelineno-4-21" href = "#__codelineno-4-21" > < / a > < span class = "w" > < / span > < span class = "p" > });< / span >
< a id = "__codelineno-4-22" name = "__codelineno-4-22" href = "#__codelineno-4-22" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-4-23" name = "__codelineno-4-23" href = "#__codelineno-4-23" > < / a >
< a id = "__codelineno-4-24" name = "__codelineno-4-24" href = "#__codelineno-4-24" > < / a > < span class = "cm" > /* 全排列 I */< / span >
< a id = "__codelineno-4-25" name = "__codelineno-4-25" href = "#__codelineno-4-25" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > permutationsI< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-26" name = "__codelineno-4-26" href = "#__codelineno-4-26" > < / 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-4-27" name = "__codelineno-4-27" href = "#__codelineno-4-27" > < / a > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > ([],< / span > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nb" > Array< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "p" > .< / span > < span class = "nx" > length< / 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 = "nx" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-4-28" name = "__codelineno-4-28" href = "#__codelineno-4-28" > < / 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-4-29" name = "__codelineno-4-29" href = "#__codelineno-4-29" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > permutations_i.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：全排列 I */< / 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" > state< / 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" > choices< / 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" > selected< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > boolean< / 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" > number< / span > < span class = "p" > [][]< / span >
< a id = "__codelineno-5-7" name = "__codelineno-5-7" href = "#__codelineno-5-7" > < / 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-5-8" name = "__codelineno-5-8" href = "#__codelineno-5-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 当状态长度等于元素数量时，记录解< / span >
< a id = "__codelineno-5-9" name = "__codelineno-5-9" href = "#__codelineno-5-9" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > .< / span > < span class = "nx" > length< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "nx" > choices< / span > < span class = "p" > .< / span > < span class = "nx" > length< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-10" name = "__codelineno-5-10" href = "#__codelineno-5-10" > < / 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 >
< a id = "__codelineno-5-11" name = "__codelineno-5-11" href = "#__codelineno-5-11" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-5-12" name = "__codelineno-5-12" href = "#__codelineno-5-12" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-5-13" name = "__codelineno-5-13" href = "#__codelineno-5-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-5-14" name = "__codelineno-5-14" href = "#__codelineno-5-14" > < / a > < span class = "w" > < / span > < span class = "nx" > choices< / span > < span class = "p" > .< / span > < span class = "nx" > forEach< / span > < span class = "p" > ((< / span > < span class = "nx" > choice< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > => < / span > < span class = "w" > < / 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 = "c1" > // 剪枝：不允许重复选择元素 且 不允许重复选择相等元素< / span >
< a id = "__codelineno-5-16" name = "__codelineno-5-16" href = "#__codelineno-5-16" > < / 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" > selected< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ])< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-17" name = "__codelineno-5-17" href = "#__codelineno-5-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新状态< / span >
< a id = "__codelineno-5-18" name = "__codelineno-5-18" href = "#__codelineno-5-18" > < / a > < span class = "w" > < / span > < span class = "nx" > selected< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "kc" > true< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-5-19" name = "__codelineno-5-19" href = "#__codelineno-5-19" > < / a > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > (< / span > < span class = "nx" > choice< / 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 = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-5-21" name = "__codelineno-5-21" href = "#__codelineno-5-21" > < / a > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > selected< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-5-22" name = "__codelineno-5-22" href = "#__codelineno-5-22" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退：撤销选择，恢复到之前的状态< / span >
< a id = "__codelineno-5-23" name = "__codelineno-5-23" href = "#__codelineno-5-23" > < / a > < span class = "w" > < / span > < span class = "nx" > selected< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "kc" > false< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-5-24" name = "__codelineno-5-24" href = "#__codelineno-5-24" > < / a > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "p" > .< / span > < span class = "nx" > pop< / 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 = "p" > }< / span >
< a id = "__codelineno-5-26" name = "__codelineno-5-26" href = "#__codelineno-5-26" > < / a > < span class = "w" > < / span > < span class = "p" > });< / span >
< a id = "__codelineno-5-27" name = "__codelineno-5-27" href = "#__codelineno-5-27" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-5-28" name = "__codelineno-5-28" href = "#__codelineno-5-28" > < / a >
< a id = "__codelineno-5-29" name = "__codelineno-5-29" href = "#__codelineno-5-29" > < / a > < span class = "cm" > /* 全排列 I */< / span >
< a id = "__codelineno-5-30" name = "__codelineno-5-30" href = "#__codelineno-5-30" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > permutationsI< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > [])< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > [][]< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-31" name = "__codelineno-5-31" href = "#__codelineno-5-31" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > [][]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [];< / span >
< a id = "__codelineno-5-32" name = "__codelineno-5-32" href = "#__codelineno-5-32" > < / a > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > ([],< / span > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nb" > Array< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "p" > .< / span > < span class = "nx" > length< / 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 = "nx" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-5-33" name = "__codelineno-5-33" href = "#__codelineno-5-33" > < / 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-5-34" name = "__codelineno-5-34" href = "#__codelineno-5-34" > < / a > < span class = "p" > }< / span >
2023-04-24 03:30:35 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > permutations_i.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 >
2023-04-27 01:28:42 +08:00
< 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" > permutationsI< / span > < span class = "p" > }< / span >
2023-04-24 03:30:35 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-04-27 01:28:42 +08:00
< div class = "highlight" > < span class = "filename" > permutations_i.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：全排列 I */< / 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 = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "n" > choices< / 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" > selected< / 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" > int< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > )< / span > < span class = "w" > < / 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 = "c1" > // 当状态长度等于元素数量时，记录解< / span >
< a id = "__codelineno-7-4" name = "__codelineno-7-4" href = "#__codelineno-7-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > Count< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > .< / span > < span class = "n" > Length< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-5" name = "__codelineno-7-5" href = "#__codelineno-7-5" > < / a > < span class = "w" > < / span > < span class = "n" > res< / 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" > int< / span > < span class = "o" > > < / span > < span class = "p" > (< / span > < span class = "n" > state< / 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 = "k" > return< / 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 = "p" > }< / span >
< a id = "__codelineno-7-8" name = "__codelineno-7-8" href = "#__codelineno-7-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-7-9" name = "__codelineno-7-9" href = "#__codelineno-7-9" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > .< / span > < span class = "n" > Length< / 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-7-10" name = "__codelineno-7-10" href = "#__codelineno-7-10" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > [< / span > < span class = "n" > i< / 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 = "c1" > // 剪枝：不允许重复选择元素 且 不允许重复选择相等元素< / span >
< a id = "__codelineno-7-12" name = "__codelineno-7-12" href = "#__codelineno-7-12" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > !< / span > < span class = "n" > selected< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ])< / span > < 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" > // 尝试：做出选择，更新状态< / span >
< a id = "__codelineno-7-14" name = "__codelineno-7-14" href = "#__codelineno-7-14" > < / a > < span class = "w" > < / span > < span class = "n" > selected< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > true< / 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 = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > Add< / span > < span class = "p" > (< / span > < span class = "n" > choice< / span > < span class = "p" > );< / span >
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< a id = "__codelineno-7-16" name = "__codelineno-7-16" href = "#__codelineno-7-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-7-17" name = "__codelineno-7-17" href = "#__codelineno-7-17" > < / a > < span class = "w" > < / span > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > selected< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / 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" > // 回退：撤销选择，恢复到之前的状态< / span >
< a id = "__codelineno-7-19" name = "__codelineno-7-19" href = "#__codelineno-7-19" > < / a > < span class = "w" > < / span > < span class = "n" > selected< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > false< / 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 = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > RemoveAt< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > Count< / 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-7-21" name = "__codelineno-7-21" href = "#__codelineno-7-21" > < / a > < span class = "w" > < / 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 = "p" > }< / span >
< a id = "__codelineno-7-23" name = "__codelineno-7-23" href = "#__codelineno-7-23" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-7-24" name = "__codelineno-7-24" href = "#__codelineno-7-24" > < / a >
< a id = "__codelineno-7-25" name = "__codelineno-7-25" href = "#__codelineno-7-25" > < / a > < span class = "cm" > /* 全排列 I */< / span >
< a id = "__codelineno-7-26" name = "__codelineno-7-26" href = "#__codelineno-7-26" > < / a > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "n" > permutationsI< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-27" name = "__codelineno-7-27" href = "#__codelineno-7-27" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "n" > 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 = "kt" > int< / span > < span class = "o" > > > < / 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 = "n" > backtrack< / 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" > int< / span > < span class = "o" > > < / span > < span class = "p" > (),< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > ,< / 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" > nums< / span > < span class = "p" > .< / span > < span class = "n" > Length< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "n" > res< / 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 = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-30" name = "__codelineno-7-30" href = "#__codelineno-7-30" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > permutations_i.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：全排列 I */< / 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" > state< / span > < span class = "p" > :< / span > < span class = "kr" > inout< / span > < span class = "p" > [< / span > < span class = "nb" > Int< / span > < span class = "p" > ],< / span > < span class = "n" > choices< / span > < span class = "p" > :< / span > < span class = "p" > [< / span > < span class = "nb" > Int< / span > < span class = "p" > ],< / span > < span class = "n" > selected< / 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" > res< / span > < span class = "p" > :< / span > < span class = "kr" > inout< / span > < span class = "p" > [[< / span > < span class = "nb" > Int< / span > < span class = "p" > ]])< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-3" name = "__codelineno-8-3" href = "#__codelineno-8-3" > < / a > < span class = "c1" > // 当状态长度等于元素数量时，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" > state< / span > < span class = "p" > .< / span > < span class = "bp" > count< / span > < span class = "p" > ==< / span > < span class = "n" > choices< / span > < span class = "p" > .< / span > < span class = "bp" > count< / 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" > // 遍历所有选择< / span >
< a id = "__codelineno-8-9" name = "__codelineno-8-9" href = "#__codelineno-8-9" > < / a > < span class = "k" > for< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > ,< / span > < span class = "n" > choice< / span > < span class = "p" > )< / span > < span class = "k" > in< / span > < span class = "n" > choices< / span > < span class = "p" > .< / span > < span class = "n" > enumerated< / span > < span class = "p" > ()< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-10" name = "__codelineno-8-10" href = "#__codelineno-8-10" > < / a > < span class = "c1" > // 剪枝：不允许重复选择元素 且 不允许重复选择相等元素< / span >
< a id = "__codelineno-8-11" name = "__codelineno-8-11" href = "#__codelineno-8-11" > < / a > < span class = "k" > if< / span > < span class = "o" > !< / span > < span class = "n" > selected< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-12" name = "__codelineno-8-12" href = "#__codelineno-8-12" > < / a > < span class = "c1" > // 尝试：做出选择，更新状态< / span >
< a id = "__codelineno-8-13" name = "__codelineno-8-13" href = "#__codelineno-8-13" > < / a > < span class = "n" > selected< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "kc" > true< / span >
< a id = "__codelineno-8-14" name = "__codelineno-8-14" href = "#__codelineno-8-14" > < / a > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > choice< / span > < span class = "p" > )< / span >
< a id = "__codelineno-8-15" name = "__codelineno-8-15" href = "#__codelineno-8-15" > < / a > < span class = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-8-16" name = "__codelineno-8-16" href = "#__codelineno-8-16" > < / a > < span class = "n" > backtrack< / 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" > choices< / span > < span class = "p" > :< / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span > < span class = "n" > selected< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > selected< / 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 >
< a id = "__codelineno-8-17" name = "__codelineno-8-17" href = "#__codelineno-8-17" > < / a > < span class = "c1" > // 回退：撤销选择，恢复到之前的状态< / span >
< a id = "__codelineno-8-18" name = "__codelineno-8-18" href = "#__codelineno-8-18" > < / a > < span class = "n" > selected< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "kc" > false< / span >
< a id = "__codelineno-8-19" name = "__codelineno-8-19" href = "#__codelineno-8-19" > < / a > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "bp" > removeLast< / span > < span class = "p" > ()< / span >
< a id = "__codelineno-8-20" name = "__codelineno-8-20" href = "#__codelineno-8-20" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-21" name = "__codelineno-8-21" href = "#__codelineno-8-21" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-22" name = "__codelineno-8-22" href = "#__codelineno-8-22" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-23" name = "__codelineno-8-23" href = "#__codelineno-8-23" > < / a >
< a id = "__codelineno-8-24" name = "__codelineno-8-24" href = "#__codelineno-8-24" > < / a > < span class = "cm" > /* 全排列 I */< / span >
< a id = "__codelineno-8-25" name = "__codelineno-8-25" href = "#__codelineno-8-25" > < / a > < span class = "kd" > func< / span > < span class = "nf" > permutationsI< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > :< / 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" > Int< / span > < span class = "p" > ]]< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-26" name = "__codelineno-8-26" href = "#__codelineno-8-26" > < / a > < span class = "kd" > var< / span > < span class = "nv" > state< / span > < span class = "p" > :< / span > < span class = "p" > [< / span > < span class = "nb" > Int< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "p" > []< / span >
< a id = "__codelineno-8-27" name = "__codelineno-8-27" href = "#__codelineno-8-27" > < / a > < span class = "kd" > var< / span > < span class = "nv" > selected< / 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" > nums< / span > < span class = "p" > .< / span > < span class = "bp" > count< / span > < span class = "p" > )< / span >
< a id = "__codelineno-8-28" name = "__codelineno-8-28" href = "#__codelineno-8-28" > < / a > < span class = "kd" > var< / span > < span class = "nv" > res< / span > < span class = "p" > :< / span > < span class = "p" > [[< / span > < span class = "nb" > Int< / span > < span class = "p" > ]]< / span > < span class = "p" > =< / span > < span class = "p" > []< / span >
< a id = "__codelineno-8-29" name = "__codelineno-8-29" href = "#__codelineno-8-29" > < / a > < span class = "n" > backtrack< / 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" > choices< / span > < span class = "p" > :< / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "n" > selected< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > selected< / 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 >
< a id = "__codelineno-8-30" name = "__codelineno-8-30" href = "#__codelineno-8-30" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
< a id = "__codelineno-8-31" name = "__codelineno-8-31" href = "#__codelineno-8-31" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > permutations_i.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-9-1" name = "__codelineno-9-1" href = "#__codelineno-9-1" > < / 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 >
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< a id = "__codelineno-9-2" name = "__codelineno-9-2" href = "#__codelineno-9-2" > < / a >
< a id = "__codelineno-9-3" name = "__codelineno-9-3" href = "#__codelineno-9-3" > < / 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" > permutationsI< / span > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
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< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > permutations_i.dart< / span > < pre > < span > < / span > < code > < a id = "__codelineno-10-1" name = "__codelineno-10-1" href = "#__codelineno-10-1" > < / 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-10-2" name = "__codelineno-10-2" href = "#__codelineno-10-2" > < / a >
< a id = "__codelineno-10-3" name = "__codelineno-10-3" href = "#__codelineno-10-3" > < / 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" > permutationsI< / span > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
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< / div >
< / div >
< p > 需要重点关注的是，我们引入了一个布尔型数组 < code > selected< / code > ，它的长度与输入数组长度相等，其中 < code > selected[i]< / code > 表示 < code > choices[i]< / code > 是否已被选择。我们利用 < code > selected< / code > 避免某个元素被重复选择，从而实现剪枝。< / p >
< p > 如下图所示，假设我们第一轮选择 1 ，第二轮选择 3 ，第三轮选择 2 ，则需要在第二轮剪掉元素 1 的分支，在第三轮剪掉元素 1, 3 的分支。< strong > 从本质上理解，此剪枝操作可将搜索空间大小从 < span class = "arithmatex" > \(O(n^n)\)< / span > 降低至 < span class = "arithmatex" > \(O(n!)\)< / span > < / strong > 。< / p >
< p > < img alt = "全排列剪枝示例" src = "../permutations_problem.assets/permutations_i_pruning.png" / > < / p >
< p align = "center" > Fig. 全排列剪枝示例 < / p >
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< h2 id = "1222" > 12.2.2. 考虑重复的情况< a class = "headerlink" href = "#1222" title = "Permanent link" > ¶ < / a > < / h2 >
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< div class = "admonition question" >
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< p class = "admonition-title" > Question< / p >
< p > 输入一个整数数组，< strong > 数组中可能包含重复元素< / strong > ，返回所有不重复的排列。< / p >
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< / div >
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< p > 假设输入数组为 < span class = "arithmatex" > \([1, 1, 2]\)< / span > 。为了方便区分两个重复的元素 < span class = "arithmatex" > \(1\)< / span > ，接下来我们将第二个元素记为 < span class = "arithmatex" > \(\hat{1}\)< / span > 。如下图所示，上述方法生成的排列有一半都是重复的。< / p >
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< p > < img alt = "重复排列" src = "../permutations_problem.assets/permutations_ii.png" / > < / p >
< p align = "center" > Fig. 重复排列 < / p >
< p > 那么，如何去除重复的排列呢？最直接地，我们可以借助一个哈希表，直接对排列结果进行去重。然而，这样做不够优雅，因为生成重复排列的搜索分支是没有必要的，应当被提前识别并剪枝，这样可以提升算法效率。< / p >
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< p > 观察发现，在第一轮中，选择 < span class = "arithmatex" > \(1\)< / span > 或选择 < span class = "arithmatex" > \(\hat{1}\)< / span > 是等价的，因为在这两个选择之下生成的所有排列都是重复的。因此，我们应该把 < span class = "arithmatex" > \(\hat{1}\)< / span > 剪枝掉。同理，在第一轮选择 < span class = "arithmatex" > \(2\)< / span > 后，第二轮选择中的 < span class = "arithmatex" > \(1\)< / span > 和 < span class = "arithmatex" > \(\hat{1}\)< / span > 也会产生重复分支，因此也需要将第二轮的 < span class = "arithmatex" > \(\hat{1}\)< / span > 剪枝。< / p >
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< p > < img alt = "重复排列剪枝" src = "../permutations_problem.assets/permutations_ii_pruning.png" / > < / p >
< p align = "center" > Fig. 重复排列剪枝 < / p >
< p > 本质上看，< strong > 我们的目标是实现在某一轮选择中，多个相等的元素仅被选择一次< / strong > 。因此，在上一题的代码的基础上，我们考虑在每一轮选择中开启一个哈希表 < code > duplicated< / code > ，用于记录该轮中已经尝试过的元素，并将重复元素剪枝。< / p >
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< div class = "tabbed-set tabbed-alternate" data-tabs = "2:11" > < input checked = "checked" id = "__tabbed_2_1" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_2" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_3" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_4" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_5" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_6" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_7" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_8" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_9" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_10" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_11" name = "__tabbed_2" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_2_1" > Java< / label > < label for = "__tabbed_2_2" > C++< / label > < label for = "__tabbed_2_3" > Python< / label > < label for = "__tabbed_2_4" > Go< / label > < label for = "__tabbed_2_5" > JavaScript< / label > < label for = "__tabbed_2_6" > TypeScript< / label > < label for = "__tabbed_2_7" > C< / label > < label for = "__tabbed_2_8" > C#< / label > < label for = "__tabbed_2_9" > Swift< / label > < label for = "__tabbed_2_10" > Zig< / label > < label for = "__tabbed_2_11" > Dart< / label > < / div >
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< div class = "tabbed-content" >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > permutations_ii.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-11-1" name = "__codelineno-11-1" href = "#__codelineno-11-1" > < / a > < span class = "cm" > /* 回溯算法：全排列 II */< / span >
< a id = "__codelineno-11-2" name = "__codelineno-11-2" href = "#__codelineno-11-2" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "o" > []< / span > < span class = "w" > < / span > < span class = "n" > choices< / 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" > selected< / 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" > Integer< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
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< a id = "__codelineno-11-3" name = "__codelineno-11-3" href = "#__codelineno-11-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 当状态长度等于元素数量时，记录解< / span >
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< a id = "__codelineno-11-4" name = "__codelineno-11-4" href = "#__codelineno-11-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "na" > size< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > .< / span > < span class = "na" > length< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-5" name = "__codelineno-11-5" href = "#__codelineno-11-5" > < / a > < span class = "w" > < / span > < span class = "n" > res< / 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 = "n" > Integer< / span > < span class = "o" > > < / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ));< / span >
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< a id = "__codelineno-11-6" name = "__codelineno-11-6" href = "#__codelineno-11-6" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-11-7" name = "__codelineno-11-7" href = "#__codelineno-11-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-8" name = "__codelineno-11-8" href = "#__codelineno-11-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
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< a id = "__codelineno-11-9" name = "__codelineno-11-9" href = "#__codelineno-11-9" > < / a > < span class = "w" > < / span > < span class = "n" > Set< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > duplicated< / 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" > HashSet< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / span > < span class = "o" > > < / span > < span class = "p" > ();< / span >
< a id = "__codelineno-11-10" name = "__codelineno-11-10" href = "#__codelineno-11-10" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > .< / span > < span class = "na" > length< / 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-11-11" name = "__codelineno-11-11" href = "#__codelineno-11-11" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "o" > [< / span > < span class = "n" > i< / span > < span class = "o" > ]< / span > < span class = "p" > ;< / span >
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< a id = "__codelineno-11-12" name = "__codelineno-11-12" href = "#__codelineno-11-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：不允许重复选择元素 且 不允许重复选择相等元素< / span >
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< a id = "__codelineno-11-13" name = "__codelineno-11-13" href = "#__codelineno-11-13" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > !< / span > < span class = "n" > selected< / span > < span class = "o" > [< / span > < span class = "n" > i< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "o" > !< / span > < span class = "n" > duplicated< / span > < span class = "p" > .< / span > < span class = "na" > contains< / span > < span class = "p" > (< / span > < span class = "n" > choice< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
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< a id = "__codelineno-11-14" name = "__codelineno-11-14" href = "#__codelineno-11-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新状态< / span >
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< a id = "__codelineno-11-15" name = "__codelineno-11-15" href = "#__codelineno-11-15" > < / a > < span class = "w" > < / span > < span class = "n" > duplicated< / span > < span class = "p" > .< / span > < span class = "na" > add< / span > < span class = "p" > (< / span > < span class = "n" > choice< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 记录选择过的元素值< / span >
< a id = "__codelineno-11-16" name = "__codelineno-11-16" href = "#__codelineno-11-16" > < / a > < span class = "w" > < / span > < span class = "n" > selected< / span > < span class = "o" > [< / span > < span class = "n" > i< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "kc" > true< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-11-17" name = "__codelineno-11-17" href = "#__codelineno-11-17" > < / 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" > choice< / span > < span class = "p" > );< / span >
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< a id = "__codelineno-11-18" name = "__codelineno-11-18" href = "#__codelineno-11-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-11-19" name = "__codelineno-11-19" href = "#__codelineno-11-19" > < / a > < span class = "w" > < / span > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > selected< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-11-20" name = "__codelineno-11-20" href = "#__codelineno-11-20" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退：撤销选择，恢复到之前的状态< / span >
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< a id = "__codelineno-11-21" name = "__codelineno-11-21" href = "#__codelineno-11-21" > < / a > < span class = "w" > < / span > < span class = "n" > selected< / span > < span class = "o" > [< / span > < span class = "n" > i< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "kc" > false< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-11-22" name = "__codelineno-11-22" href = "#__codelineno-11-22" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "na" > remove< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "na" > size< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > );< / span >
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< a id = "__codelineno-11-23" name = "__codelineno-11-23" href = "#__codelineno-11-23" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-24" name = "__codelineno-11-24" href = "#__codelineno-11-24" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-25" name = "__codelineno-11-25" href = "#__codelineno-11-25" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-11-26" name = "__codelineno-11-26" href = "#__codelineno-11-26" > < / a >
< a id = "__codelineno-11-27" name = "__codelineno-11-27" href = "#__codelineno-11-27" > < / a > < span class = "cm" > /* 全排列 II */< / span >
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< a id = "__codelineno-11-28" name = "__codelineno-11-28" href = "#__codelineno-11-28" > < / a > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "nf" > permutationsII< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "o" > []< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-29" name = "__codelineno-11-29" href = "#__codelineno-11-29" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "n" > 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 = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / span > < span class = "o" > > > < / span > < span class = "p" > ();< / span >
< a id = "__codelineno-11-30" name = "__codelineno-11-30" href = "#__codelineno-11-30" > < / a > < span class = "w" > < / span > < span class = "n" > backtrack< / 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 = "n" > Integer< / span > < span class = "o" > > < / span > < span class = "p" > (),< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > ,< / 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" > nums< / span > < span class = "p" > .< / span > < span class = "na" > length< / span > < span class = "o" > ]< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-11-31" name = "__codelineno-11-31" href = "#__codelineno-11-31" > < / 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-11-32" name = "__codelineno-11-32" href = "#__codelineno-11-32" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > permutations_ii.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-12-1" name = "__codelineno-12-1" href = "#__codelineno-12-1" > < / a > < span class = "cm" > /* 回溯算法：全排列 II */< / span >
< a id = "__codelineno-12-2" name = "__codelineno-12-2" href = "#__codelineno-12-2" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "k" > const< / span > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > choices< / 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" > selected< / 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 = "kt" > int< / 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 = "p" > {< / span >
< a id = "__codelineno-12-3" name = "__codelineno-12-3" href = "#__codelineno-12-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 当状态长度等于元素数量时，记录解< / span >
< a id = "__codelineno-12-4" name = "__codelineno-12-4" href = "#__codelineno-12-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > size< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > .< / span > < span class = "n" > size< / span > < span class = "p" > ())< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-12-5" name = "__codelineno-12-5" href = "#__codelineno-12-5" > < / 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-12-6" name = "__codelineno-12-6" href = "#__codelineno-12-6" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-12-7" name = "__codelineno-12-7" href = "#__codelineno-12-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-12-8" name = "__codelineno-12-8" href = "#__codelineno-12-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-12-9" name = "__codelineno-12-9" href = "#__codelineno-12-9" > < / a > < span class = "w" > < / span > < span class = "n" > unordered_set< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > duplicated< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-12-10" name = "__codelineno-12-10" href = "#__codelineno-12-10" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > .< / span > < span class = "n" > size< / 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-12-11" name = "__codelineno-12-11" href = "#__codelineno-12-11" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-12-12" name = "__codelineno-12-12" href = "#__codelineno-12-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：不允许重复选择元素 且 不允许重复选择相等元素< / span >
< a id = "__codelineno-12-13" name = "__codelineno-12-13" href = "#__codelineno-12-13" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > !< / span > < span class = "n" > selected< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "n" > duplicated< / span > < span class = "p" > .< / span > < span class = "n" > find< / span > < span class = "p" > (< / span > < span class = "n" > choice< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "n" > duplicated< / span > < span class = "p" > .< / span > < span class = "n" > end< / span > < span class = "p" > ())< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-12-14" name = "__codelineno-12-14" href = "#__codelineno-12-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新状态< / span >
< a id = "__codelineno-12-15" name = "__codelineno-12-15" href = "#__codelineno-12-15" > < / a > < span class = "w" > < / span > < span class = "n" > duplicated< / span > < span class = "p" > .< / span > < span class = "n" > emplace< / span > < span class = "p" > (< / span > < span class = "n" > choice< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 记录选择过的元素值< / span >
< a id = "__codelineno-12-16" name = "__codelineno-12-16" href = "#__codelineno-12-16" > < / a > < span class = "w" > < / span > < span class = "n" > selected< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > true< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-12-17" name = "__codelineno-12-17" href = "#__codelineno-12-17" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > push_back< / span > < span class = "p" > (< / span > < span class = "n" > choice< / span > < span class = "p" > );< / span >
< a id = "__codelineno-12-18" name = "__codelineno-12-18" href = "#__codelineno-12-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-12-19" name = "__codelineno-12-19" href = "#__codelineno-12-19" > < / a > < span class = "w" > < / span > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > selected< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-12-20" name = "__codelineno-12-20" href = "#__codelineno-12-20" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退：撤销选择，恢复到之前的状态< / span >
< a id = "__codelineno-12-21" name = "__codelineno-12-21" href = "#__codelineno-12-21" > < / a > < span class = "w" > < / span > < span class = "n" > selected< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > false< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-12-22" name = "__codelineno-12-22" href = "#__codelineno-12-22" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > pop_back< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-12-23" name = "__codelineno-12-23" href = "#__codelineno-12-23" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-12-24" name = "__codelineno-12-24" href = "#__codelineno-12-24" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-12-25" name = "__codelineno-12-25" href = "#__codelineno-12-25" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-12-26" name = "__codelineno-12-26" href = "#__codelineno-12-26" > < / a >
< a id = "__codelineno-12-27" name = "__codelineno-12-27" href = "#__codelineno-12-27" > < / a > < span class = "cm" > /* 全排列 II */< / span >
< a id = "__codelineno-12-28" name = "__codelineno-12-28" href = "#__codelineno-12-28" > < / a > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "n" > permutationsII< / span > < span class = "p" > (< / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-12-29" name = "__codelineno-12-29" href = "#__codelineno-12-29" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-12-30" name = "__codelineno-12-30" href = "#__codelineno-12-30" > < / 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" > selected< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > .< / span > < span class = "n" > size< / span > < span class = "p" > (),< / span > < span class = "w" > < / span > < span class = "nb" > false< / span > < span class = "p" > );< / span >
< a id = "__codelineno-12-31" name = "__codelineno-12-31" href = "#__codelineno-12-31" > < / 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 = "kt" > int< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-12-32" name = "__codelineno-12-32" href = "#__codelineno-12-32" > < / a > < span class = "w" > < / span > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > selected< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-12-33" name = "__codelineno-12-33" href = "#__codelineno-12-33" > < / 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-12-34" name = "__codelineno-12-34" href = "#__codelineno-12-34" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
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< div class = "highlight" > < span class = "filename" > permutations_ii.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-13-1" name = "__codelineno-13-1" href = "#__codelineno-13-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > backtrack< / span > < span class = "p" > (< / span >
< a id = "__codelineno-13-2" name = "__codelineno-13-2" href = "#__codelineno-13-2" > < / a > < span class = "n" > state< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > int< / span > < span class = "p" > ],< / span > < span class = "n" > choices< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > int< / span > < span class = "p" > ],< / span > < span class = "n" > selected< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > bool< / span > < span class = "p" > ],< / span > < 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" > int< / span > < span class = "p" > ]]< / span >
< a id = "__codelineno-13-3" name = "__codelineno-13-3" href = "#__codelineno-13-3" > < / a > < span class = "p" > ):< / span >
< a id = "__codelineno-13-4" name = "__codelineno-13-4" href = "#__codelineno-13-4" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 回溯算法：全排列 II" " " < / span >
< a id = "__codelineno-13-5" name = "__codelineno-13-5" href = "#__codelineno-13-5" > < / a > < span class = "c1" > # 当状态长度等于元素数量时，记录解< / span >
< a id = "__codelineno-13-6" name = "__codelineno-13-6" href = "#__codelineno-13-6" > < / a > < span class = "k" > if< / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > )< / span > < span class = "o" > ==< / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "n" > choices< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-13-7" name = "__codelineno-13-7" href = "#__codelineno-13-7" > < / 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" > state< / span > < span class = "p" > ))< / span >
< a id = "__codelineno-13-8" name = "__codelineno-13-8" href = "#__codelineno-13-8" > < / a > < span class = "k" > return< / span >
< a id = "__codelineno-13-9" name = "__codelineno-13-9" href = "#__codelineno-13-9" > < / a > < span class = "c1" > # 遍历所有选择< / span >
< a id = "__codelineno-13-10" name = "__codelineno-13-10" href = "#__codelineno-13-10" > < / a > < span class = "n" > duplicated< / span > < span class = "o" > =< / span > < span class = "nb" > set< / span > < span class = "p" > [< / span > < span class = "nb" > int< / span > < span class = "p" > ]()< / span >
< a id = "__codelineno-13-11" name = "__codelineno-13-11" href = "#__codelineno-13-11" > < / a > < span class = "k" > for< / span > < span class = "n" > i< / span > < span class = "p" > ,< / span > < span class = "n" > choice< / span > < span class = "ow" > in< / span > < span class = "nb" > enumerate< / span > < span class = "p" > (< / span > < span class = "n" > choices< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-13-12" name = "__codelineno-13-12" href = "#__codelineno-13-12" > < / a > < span class = "c1" > # 剪枝：不允许重复选择元素 且 不允许重复选择相等元素< / span >
< a id = "__codelineno-13-13" name = "__codelineno-13-13" href = "#__codelineno-13-13" > < / a > < span class = "k" > if< / span > < span class = "ow" > not< / span > < span class = "n" > selected< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "ow" > and< / span > < span class = "n" > choice< / span > < span class = "ow" > not< / span > < span class = "ow" > in< / span > < span class = "n" > duplicated< / span > < span class = "p" > :< / span >
< a id = "__codelineno-13-14" name = "__codelineno-13-14" href = "#__codelineno-13-14" > < / a > < span class = "c1" > # 尝试：做出选择，更新状态< / span >
< a id = "__codelineno-13-15" name = "__codelineno-13-15" href = "#__codelineno-13-15" > < / a > < span class = "n" > duplicated< / span > < span class = "o" > .< / span > < span class = "n" > add< / span > < span class = "p" > (< / span > < span class = "n" > choice< / span > < span class = "p" > )< / span > < span class = "c1" > # 记录选择过的元素值< / span >
< a id = "__codelineno-13-16" name = "__codelineno-13-16" href = "#__codelineno-13-16" > < / a > < span class = "n" > selected< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "kc" > True< / span >
< a id = "__codelineno-13-17" name = "__codelineno-13-17" href = "#__codelineno-13-17" > < / a > < span class = "n" > state< / span > < span class = "o" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > choice< / span > < span class = "p" > )< / span >
< a id = "__codelineno-13-18" name = "__codelineno-13-18" href = "#__codelineno-13-18" > < / a > < span class = "c1" > # 进行下一轮选择< / span >
< a id = "__codelineno-13-19" name = "__codelineno-13-19" href = "#__codelineno-13-19" > < / a > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span > < span class = "n" > selected< / span > < span class = "p" > ,< / span > < span class = "n" > res< / span > < span class = "p" > )< / span >
< a id = "__codelineno-13-20" name = "__codelineno-13-20" href = "#__codelineno-13-20" > < / a > < span class = "c1" > # 回退：撤销选择，恢复到之前的状态< / span >
< a id = "__codelineno-13-21" name = "__codelineno-13-21" href = "#__codelineno-13-21" > < / a > < span class = "n" > selected< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "kc" > False< / span >
< a id = "__codelineno-13-22" name = "__codelineno-13-22" href = "#__codelineno-13-22" > < / a > < span class = "n" > state< / span > < span class = "o" > .< / span > < span class = "n" > pop< / span > < span class = "p" > ()< / span >
< a id = "__codelineno-13-23" name = "__codelineno-13-23" href = "#__codelineno-13-23" > < / a >
< a id = "__codelineno-13-24" name = "__codelineno-13-24" href = "#__codelineno-13-24" > < / a > < span class = "k" > def< / span > < span class = "nf" > permutations_ii< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > int< / span > < span class = "p" > ])< / span > < span class = "o" > -> < / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > int< / span > < span class = "p" > ]]:< / span >
< a id = "__codelineno-13-25" name = "__codelineno-13-25" href = "#__codelineno-13-25" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 全排列 II" " " < / span >
< a id = "__codelineno-13-26" name = "__codelineno-13-26" href = "#__codelineno-13-26" > < / a > < span class = "n" > res< / span > < span class = "o" > =< / span > < span class = "p" > []< / span >
< a id = "__codelineno-13-27" name = "__codelineno-13-27" href = "#__codelineno-13-27" > < / a > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "o" > =< / span > < span class = "p" > [],< / span > < span class = "n" > choices< / span > < span class = "o" > =< / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "n" > selected< / span > < span class = "o" > =< / span > < span class = "p" > [< / span > < span class = "kc" > False< / span > < span class = "p" > ]< / span > < span class = "o" > *< / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > ),< / span > < span class = "n" > res< / span > < span class = "o" > =< / span > < span class = "n" > res< / span > < span class = "p" > )< / span >
< a id = "__codelineno-13-28" name = "__codelineno-13-28" href = "#__codelineno-13-28" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
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< / code > < / pre > < / div >
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< div class = "highlight" > < span class = "filename" > permutations_ii.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-14-1" name = "__codelineno-14-1" href = "#__codelineno-14-1" > < / a > < span class = "cm" > /* 回溯算法：全排列 II */< / span >
< a id = "__codelineno-14-2" name = "__codelineno-14-2" href = "#__codelineno-14-2" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > backtrackII< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > []< / span > < span class = "kt" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choices< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > []< / span > < span class = "kt" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > selected< / 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 = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > [][]< / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
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< a id = "__codelineno-14-3" name = "__codelineno-14-3" href = "#__codelineno-14-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 当状态长度等于元素数量时，记录解< / span >
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< a id = "__codelineno-14-4" name = "__codelineno-14-4" href = "#__codelineno-14-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > state< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > choices< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-14-5" name = "__codelineno-14-5" href = "#__codelineno-14-5" > < / a > < span class = "w" > < / span > < span class = "nx" > newState< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nb" > append< / span > < span class = "p" > ([]< / span > < span class = "kt" > int< / span > < span class = "p" > {},< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > state< / span > < span class = "o" > ...< / span > < span class = "p" > )< / span >
< a id = "__codelineno-14-6" name = "__codelineno-14-6" href = "#__codelineno-14-6" > < / 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 >
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< a id = "__codelineno-14-7" name = "__codelineno-14-7" href = "#__codelineno-14-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-14-8" name = "__codelineno-14-8" href = "#__codelineno-14-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
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< a id = "__codelineno-14-9" name = "__codelineno-14-9" href = "#__codelineno-14-9" > < / a > < span class = "w" > < / span > < span class = "nx" > duplicated< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nb" > make< / span > < span class = "p" > (< / span > < span class = "kd" > map< / span > < span class = "p" > [< / span > < span class = "kt" > int< / span > < span class = "p" > ]< / span > < span class = "kd" > struct< / span > < span class = "p" > {},< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span >
< a id = "__codelineno-14-10" name = "__codelineno-14-10" href = "#__codelineno-14-10" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "p" > < < / span > < span class = "w" > < / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > choices< / 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-14-11" name = "__codelineno-14-11" href = "#__codelineno-14-11" > < / a > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > choices< / span > < span class = "p" > )[< / span > < span class = "nx" > i< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-14-12" name = "__codelineno-14-12" href = "#__codelineno-14-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：不允许重复选择元素 且 不允许重复选择相等元素< / span >
< a id = "__codelineno-14-13" name = "__codelineno-14-13" href = "#__codelineno-14-13" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > _< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > ok< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > duplicated< / span > < span class = "p" > [< / span > < span class = "nx" > choice< / span > < span class = "p" > ];< / span > < span class = "w" > < / span > < span class = "p" > !< / span > < span class = "nx" > ok< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "p" > !(< / span > < span class = "o" > *< / span > < span class = "nx" > selected< / span > < span class = "p" > )[< / span > < span class = "nx" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-14-14" name = "__codelineno-14-14" href = "#__codelineno-14-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新状态< / span >
< a id = "__codelineno-14-15" name = "__codelineno-14-15" href = "#__codelineno-14-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 记录选择过的元素值< / span >
< a id = "__codelineno-14-16" name = "__codelineno-14-16" href = "#__codelineno-14-16" > < / a > < span class = "w" > < / span > < span class = "nx" > duplicated< / span > < span class = "p" > [< / span > < span class = "nx" > choice< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "kd" > struct< / span > < span class = "p" > {}{}< / span >
< a id = "__codelineno-14-17" name = "__codelineno-14-17" href = "#__codelineno-14-17" > < / a > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > selected< / 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 = "kc" > true< / span >
< a id = "__codelineno-14-18" name = "__codelineno-14-18" href = "#__codelineno-14-18" > < / a > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > state< / 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" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "p" > )< / span >
< a id = "__codelineno-14-19" name = "__codelineno-14-19" href = "#__codelineno-14-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-14-20" name = "__codelineno-14-20" href = "#__codelineno-14-20" > < / a > < span class = "w" > < / span > < span class = "nx" > backtrackI< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > selected< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > )< / span >
< a id = "__codelineno-14-21" name = "__codelineno-14-21" href = "#__codelineno-14-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退：撤销选择，恢复到之前的状态< / span >
< a id = "__codelineno-14-22" name = "__codelineno-14-22" href = "#__codelineno-14-22" > < / a > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > selected< / 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 = "kc" > false< / span >
< a id = "__codelineno-14-23" name = "__codelineno-14-23" href = "#__codelineno-14-23" > < / a > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > state< / span > < span class = "w" > < / 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 = "nb" > len< / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > state< / span > < span class = "p" > )< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-14-24" name = "__codelineno-14-24" href = "#__codelineno-14-24" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-14-25" name = "__codelineno-14-25" href = "#__codelineno-14-25" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-14-26" name = "__codelineno-14-26" href = "#__codelineno-14-26" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-14-27" name = "__codelineno-14-27" href = "#__codelineno-14-27" > < / a >
< a id = "__codelineno-14-28" name = "__codelineno-14-28" href = "#__codelineno-14-28" > < / a > < span class = "cm" > /* 全排列 II */< / span >
< a id = "__codelineno-14-29" name = "__codelineno-14-29" href = "#__codelineno-14-29" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > permutationsII< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "w" > < / span > < span class = "p" > []< / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > [][]< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-14-30" name = "__codelineno-14-30" href = "#__codelineno-14-30" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nb" > make< / span > < span class = "p" > ([][]< / span > < span class = "kt" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span >
< a id = "__codelineno-14-31" name = "__codelineno-14-31" href = "#__codelineno-14-31" > < / 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" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span >
< a id = "__codelineno-14-32" name = "__codelineno-14-32" href = "#__codelineno-14-32" > < / a > < span class = "w" > < / span > < span class = "nx" > selected< / 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 = "nb" > len< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "p" > ))< / span >
< a id = "__codelineno-14-33" name = "__codelineno-14-33" href = "#__codelineno-14-33" > < / a > < span class = "w" > < / span > < span class = "nx" > backtrackII< / span > < span class = "p" > (< / 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" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "nx" > selected< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "nx" > res< / span > < span class = "p" > )< / span >
< a id = "__codelineno-14-34" name = "__codelineno-14-34" href = "#__codelineno-14-34" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span >
< a id = "__codelineno-14-35" name = "__codelineno-14-35" href = "#__codelineno-14-35" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > permutations_ii.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-15-1" name = "__codelineno-15-1" href = "#__codelineno-15-1" > < / a > < span class = "cm" > /* 回溯算法：全排列 II */< / span >
< a id = "__codelineno-15-2" name = "__codelineno-15-2" href = "#__codelineno-15-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > selected< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-15-3" name = "__codelineno-15-3" href = "#__codelineno-15-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 当状态长度等于元素数量时，记录解< / span >
< a id = "__codelineno-15-4" name = "__codelineno-15-4" href = "#__codelineno-15-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > .< / span > < span class = "nx" > length< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "nx" > choices< / span > < span class = "p" > .< / span > < span class = "nx" > length< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-15-5" name = "__codelineno-15-5" href = "#__codelineno-15-5" > < / a > < span class = "w" > < / span > < span class = "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 >
< a id = "__codelineno-15-6" name = "__codelineno-15-6" href = "#__codelineno-15-6" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-15-7" name = "__codelineno-15-7" href = "#__codelineno-15-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-15-8" name = "__codelineno-15-8" href = "#__codelineno-15-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-15-9" name = "__codelineno-15-9" href = "#__codelineno-15-9" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > duplicated< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "ow" > new< / span > < span class = "w" > < / span > < span class = "nb" > Set< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-15-10" name = "__codelineno-15-10" href = "#__codelineno-15-10" > < / a > < span class = "w" > < / span > < span class = "nx" > choices< / span > < span class = "p" > .< / span > < span class = "nx" > forEach< / span > < span class = "p" > ((< / span > < span class = "nx" > choice< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > => < / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-15-11" name = "__codelineno-15-11" href = "#__codelineno-15-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：不允许重复选择元素 且 不允许重复选择相等元素< / span >
< a id = "__codelineno-15-12" name = "__codelineno-15-12" href = "#__codelineno-15-12" > < / 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" > selected< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "o" > !< / span > < span class = "nx" > duplicated< / span > < span class = "p" > .< / span > < span class = "nx" > has< / span > < span class = "p" > (< / span > < span class = "nx" > choice< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-15-13" name = "__codelineno-15-13" href = "#__codelineno-15-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新状态< / span >
< a id = "__codelineno-15-14" name = "__codelineno-15-14" href = "#__codelineno-15-14" > < / a > < span class = "w" > < / span > < span class = "nx" > duplicated< / span > < span class = "p" > .< / span > < span class = "nx" > add< / span > < span class = "p" > (< / span > < span class = "nx" > choice< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 记录选择过的元素值< / span >
< a id = "__codelineno-15-15" name = "__codelineno-15-15" href = "#__codelineno-15-15" > < / a > < span class = "w" > < / span > < span class = "nx" > selected< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "kc" > true< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-15-16" name = "__codelineno-15-16" href = "#__codelineno-15-16" > < / a > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > (< / span > < span class = "nx" > choice< / span > < span class = "p" > );< / span >
< a id = "__codelineno-15-17" name = "__codelineno-15-17" href = "#__codelineno-15-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-15-18" name = "__codelineno-15-18" href = "#__codelineno-15-18" > < / a > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > selected< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-15-19" name = "__codelineno-15-19" href = "#__codelineno-15-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退：撤销选择，恢复到之前的状态< / span >
< a id = "__codelineno-15-20" name = "__codelineno-15-20" href = "#__codelineno-15-20" > < / a > < span class = "w" > < / span > < span class = "nx" > selected< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "kc" > false< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-15-21" name = "__codelineno-15-21" href = "#__codelineno-15-21" > < / a > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "p" > .< / span > < span class = "nx" > pop< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-15-22" name = "__codelineno-15-22" href = "#__codelineno-15-22" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-15-23" name = "__codelineno-15-23" href = "#__codelineno-15-23" > < / a > < span class = "w" > < / span > < span class = "p" > });< / span >
< a id = "__codelineno-15-24" name = "__codelineno-15-24" href = "#__codelineno-15-24" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-15-25" name = "__codelineno-15-25" href = "#__codelineno-15-25" > < / a >
< a id = "__codelineno-15-26" name = "__codelineno-15-26" href = "#__codelineno-15-26" > < / a > < span class = "cm" > /* 全排列 II */< / span >
< a id = "__codelineno-15-27" name = "__codelineno-15-27" href = "#__codelineno-15-27" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > permutationsII< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-15-28" name = "__codelineno-15-28" href = "#__codelineno-15-28" > < / 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-15-29" name = "__codelineno-15-29" href = "#__codelineno-15-29" > < / a > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > ([],< / span > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nb" > Array< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "p" > .< / span > < span class = "nx" > length< / 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 = "nx" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-15-30" name = "__codelineno-15-30" href = "#__codelineno-15-30" > < / 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-15-31" name = "__codelineno-15-31" href = "#__codelineno-15-31" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > permutations_ii.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-16-1" name = "__codelineno-16-1" href = "#__codelineno-16-1" > < / a > < span class = "cm" > /* 回溯算法：全排列 II */< / span >
< a id = "__codelineno-16-2" name = "__codelineno-16-2" href = "#__codelineno-16-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > (< / span >
< a id = "__codelineno-16-3" name = "__codelineno-16-3" href = "#__codelineno-16-3" > < / a > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > [],< / span >
< a id = "__codelineno-16-4" name = "__codelineno-16-4" href = "#__codelineno-16-4" > < / a > < span class = "w" > < / span > < span class = "nx" > choices< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > [],< / span >
< a id = "__codelineno-16-5" name = "__codelineno-16-5" href = "#__codelineno-16-5" > < / a > < span class = "w" > < / span > < span class = "nx" > selected< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > boolean< / span > < span class = "p" > [],< / span >
< a id = "__codelineno-16-6" name = "__codelineno-16-6" href = "#__codelineno-16-6" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > [][]< / span >
< a id = "__codelineno-16-7" name = "__codelineno-16-7" href = "#__codelineno-16-7" > < / 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-16-8" name = "__codelineno-16-8" href = "#__codelineno-16-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 当状态长度等于元素数量时，记录解< / span >
< a id = "__codelineno-16-9" name = "__codelineno-16-9" href = "#__codelineno-16-9" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > .< / span > < span class = "nx" > length< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "nx" > choices< / span > < span class = "p" > .< / span > < span class = "nx" > length< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-16-10" name = "__codelineno-16-10" href = "#__codelineno-16-10" > < / 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 >
< a id = "__codelineno-16-11" name = "__codelineno-16-11" href = "#__codelineno-16-11" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-16-12" name = "__codelineno-16-12" href = "#__codelineno-16-12" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-16-13" name = "__codelineno-16-13" href = "#__codelineno-16-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-16-14" name = "__codelineno-16-14" href = "#__codelineno-16-14" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > duplicated< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "ow" > new< / span > < span class = "w" > < / span > < span class = "nb" > Set< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-16-15" name = "__codelineno-16-15" href = "#__codelineno-16-15" > < / a > < span class = "w" > < / span > < span class = "nx" > choices< / span > < span class = "p" > .< / span > < span class = "nx" > forEach< / span > < span class = "p" > ((< / span > < span class = "nx" > choice< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > => < / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-16-16" name = "__codelineno-16-16" href = "#__codelineno-16-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：不允许重复选择元素 且 不允许重复选择相等元素< / span >
< a id = "__codelineno-16-17" name = "__codelineno-16-17" href = "#__codelineno-16-17" > < / 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" > selected< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "o" > !< / span > < span class = "nx" > duplicated< / span > < span class = "p" > .< / span > < span class = "nx" > has< / span > < span class = "p" > (< / span > < span class = "nx" > choice< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-16-18" name = "__codelineno-16-18" href = "#__codelineno-16-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新状态< / span >
< a id = "__codelineno-16-19" name = "__codelineno-16-19" href = "#__codelineno-16-19" > < / a > < span class = "w" > < / span > < span class = "nx" > duplicated< / span > < span class = "p" > .< / span > < span class = "nx" > add< / span > < span class = "p" > (< / span > < span class = "nx" > choice< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 记录选择过的元素值< / span >
< a id = "__codelineno-16-20" name = "__codelineno-16-20" href = "#__codelineno-16-20" > < / a > < span class = "w" > < / span > < span class = "nx" > selected< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "kc" > true< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-16-21" name = "__codelineno-16-21" href = "#__codelineno-16-21" > < / a > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > (< / span > < span class = "nx" > choice< / span > < span class = "p" > );< / span >
< a id = "__codelineno-16-22" name = "__codelineno-16-22" href = "#__codelineno-16-22" > < / a > < span class = "w" > < / span > < span class = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-16-23" name = "__codelineno-16-23" href = "#__codelineno-16-23" > < / a > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > selected< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-16-24" name = "__codelineno-16-24" href = "#__codelineno-16-24" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退：撤销选择，恢复到之前的状态< / span >
< a id = "__codelineno-16-25" name = "__codelineno-16-25" href = "#__codelineno-16-25" > < / a > < span class = "w" > < / span > < span class = "nx" > selected< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "kc" > false< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-16-26" name = "__codelineno-16-26" href = "#__codelineno-16-26" > < / a > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "p" > .< / span > < span class = "nx" > pop< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-16-27" name = "__codelineno-16-27" href = "#__codelineno-16-27" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-16-28" name = "__codelineno-16-28" href = "#__codelineno-16-28" > < / a > < span class = "w" > < / span > < span class = "p" > });< / span >
< a id = "__codelineno-16-29" name = "__codelineno-16-29" href = "#__codelineno-16-29" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-16-30" name = "__codelineno-16-30" href = "#__codelineno-16-30" > < / a >
< a id = "__codelineno-16-31" name = "__codelineno-16-31" href = "#__codelineno-16-31" > < / a > < span class = "cm" > /* 全排列 II */< / span >
< a id = "__codelineno-16-32" name = "__codelineno-16-32" href = "#__codelineno-16-32" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > permutationsII< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > [])< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > [][]< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-16-33" name = "__codelineno-16-33" href = "#__codelineno-16-33" > < / 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" > number< / span > < span class = "p" > [][]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [];< / span >
< a id = "__codelineno-16-34" name = "__codelineno-16-34" href = "#__codelineno-16-34" > < / a > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > ([],< / span > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nb" > Array< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "p" > .< / span > < span class = "nx" > length< / 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 = "nx" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-16-35" name = "__codelineno-16-35" href = "#__codelineno-16-35" > < / 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-16-36" name = "__codelineno-16-36" href = "#__codelineno-16-36" > < / a > < span class = "p" > }< / span >
2023-04-24 03:30:35 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > permutations_ii.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-17-1" name = "__codelineno-17-1" href = "#__codelineno-17-1" > < / 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-17-2" name = "__codelineno-17-2" href = "#__codelineno-17-2" > < / a >
< a id = "__codelineno-17-3" name = "__codelineno-17-3" href = "#__codelineno-17-3" > < / 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" > permutationsII< / span > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
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< div class = "highlight" > < span class = "filename" > permutations_ii.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-18-1" name = "__codelineno-18-1" href = "#__codelineno-18-1" > < / a > < span class = "cm" > /* 回溯算法：全排列 II */< / span >
< a id = "__codelineno-18-2" name = "__codelineno-18-2" href = "#__codelineno-18-2" > < / a > < span class = "k" > void< / span > < span class = "w" > < / span > < span class = "nf" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "n" > choices< / 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" > selected< / 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" > int< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-18-3" name = "__codelineno-18-3" href = "#__codelineno-18-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 当状态长度等于元素数量时，记录解< / span >
< a id = "__codelineno-18-4" name = "__codelineno-18-4" href = "#__codelineno-18-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > Count< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > .< / span > < span class = "n" > Length< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-18-5" name = "__codelineno-18-5" href = "#__codelineno-18-5" > < / 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 = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-18-6" name = "__codelineno-18-6" href = "#__codelineno-18-6" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-18-7" name = "__codelineno-18-7" href = "#__codelineno-18-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-18-8" name = "__codelineno-18-8" href = "#__codelineno-18-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-18-9" name = "__codelineno-18-9" href = "#__codelineno-18-9" > < / a > < span class = "w" > < / span > < span class = "n" > ISet< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > duplicated< / 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" > HashSet< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "p" > ();< / span >
< a id = "__codelineno-18-10" name = "__codelineno-18-10" href = "#__codelineno-18-10" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "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" > choices< / span > < span class = "p" > .< / span > < span class = "n" > Length< / 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-18-11" name = "__codelineno-18-11" href = "#__codelineno-18-11" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-18-12" name = "__codelineno-18-12" href = "#__codelineno-18-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：不允许重复选择元素 且 不允许重复选择相等元素< / span >
< a id = "__codelineno-18-13" name = "__codelineno-18-13" href = "#__codelineno-18-13" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > !< / span > < span class = "n" > selected< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "o" > !< / span > < span class = "n" > duplicated< / span > < span class = "p" > .< / span > < span class = "n" > Contains< / span > < span class = "p" > (< / span > < span class = "n" > choice< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-18-14" name = "__codelineno-18-14" href = "#__codelineno-18-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新状态< / span >
< a id = "__codelineno-18-15" name = "__codelineno-18-15" href = "#__codelineno-18-15" > < / a > < span class = "w" > < / span > < span class = "n" > duplicated< / span > < span class = "p" > .< / span > < span class = "n" > Add< / span > < span class = "p" > (< / span > < span class = "n" > choice< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 记录选择过的元素值< / span >
< a id = "__codelineno-18-16" name = "__codelineno-18-16" href = "#__codelineno-18-16" > < / a > < span class = "w" > < / span > < span class = "n" > selected< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > true< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-18-17" name = "__codelineno-18-17" href = "#__codelineno-18-17" > < / 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" > choice< / span > < span class = "p" > );< / span >
< a id = "__codelineno-18-18" name = "__codelineno-18-18" href = "#__codelineno-18-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-18-19" name = "__codelineno-18-19" href = "#__codelineno-18-19" > < / a > < span class = "w" > < / span > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > selected< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-18-20" name = "__codelineno-18-20" href = "#__codelineno-18-20" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退：撤销选择，恢复到之前的状态< / span >
< a id = "__codelineno-18-21" name = "__codelineno-18-21" href = "#__codelineno-18-21" > < / a > < span class = "w" > < / span > < span class = "n" > selected< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > false< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-18-22" name = "__codelineno-18-22" href = "#__codelineno-18-22" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > RemoveAt< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > Count< / 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-18-23" name = "__codelineno-18-23" href = "#__codelineno-18-23" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-18-24" name = "__codelineno-18-24" href = "#__codelineno-18-24" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-18-25" name = "__codelineno-18-25" href = "#__codelineno-18-25" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-18-26" name = "__codelineno-18-26" href = "#__codelineno-18-26" > < / a >
< a id = "__codelineno-18-27" name = "__codelineno-18-27" href = "#__codelineno-18-27" > < / a > < span class = "cm" > /* 全排列 II */< / span >
< a id = "__codelineno-18-28" name = "__codelineno-18-28" href = "#__codelineno-18-28" > < / a > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "n" > permutationsII< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-18-29" name = "__codelineno-18-29" href = "#__codelineno-18-29" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "n" > 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 = "kt" > int< / span > < span class = "o" > > > < / span > < span class = "p" > ();< / span >
< a id = "__codelineno-18-30" name = "__codelineno-18-30" href = "#__codelineno-18-30" > < / a > < span class = "w" > < / span > < span class = "n" > backtrack< / 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" > int< / span > < span class = "o" > > < / span > < span class = "p" > (),< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > ,< / 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" > nums< / span > < span class = "p" > .< / span > < span class = "n" > Length< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-18-31" name = "__codelineno-18-31" href = "#__codelineno-18-31" > < / 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-18-32" name = "__codelineno-18-32" href = "#__codelineno-18-32" > < / a > < span class = "p" > }< / span >
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< div class = "highlight" > < span class = "filename" > permutations_ii.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-19-1" name = "__codelineno-19-1" href = "#__codelineno-19-1" > < / a > < span class = "cm" > /* 回溯算法：全排列 II */< / span >
< a id = "__codelineno-19-2" name = "__codelineno-19-2" href = "#__codelineno-19-2" > < / a > < span class = "kd" > func< / span > < span class = "nf" > backtrack< / 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" > Int< / span > < span class = "p" > ],< / span > < span class = "n" > choices< / span > < span class = "p" > :< / span > < span class = "p" > [< / span > < span class = "nb" > Int< / span > < span class = "p" > ],< / span > < span class = "n" > selected< / 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" > res< / span > < span class = "p" > :< / span > < span class = "kr" > inout< / span > < span class = "p" > [[< / span > < span class = "nb" > Int< / span > < span class = "p" > ]])< / span > < span class = "p" > {< / span >
< a id = "__codelineno-19-3" name = "__codelineno-19-3" href = "#__codelineno-19-3" > < / a > < span class = "c1" > // 当状态长度等于元素数量时，记录解< / span >
< a id = "__codelineno-19-4" name = "__codelineno-19-4" href = "#__codelineno-19-4" > < / a > < span class = "k" > if< / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "bp" > count< / span > < span class = "p" > ==< / span > < span class = "n" > choices< / span > < span class = "p" > .< / span > < span class = "bp" > count< / span > < span class = "p" > {< / span >
< a id = "__codelineno-19-5" name = "__codelineno-19-5" href = "#__codelineno-19-5" > < / 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-19-6" name = "__codelineno-19-6" href = "#__codelineno-19-6" > < / a > < span class = "k" > return< / span >
< a id = "__codelineno-19-7" name = "__codelineno-19-7" href = "#__codelineno-19-7" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-19-8" name = "__codelineno-19-8" href = "#__codelineno-19-8" > < / a > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-19-9" name = "__codelineno-19-9" href = "#__codelineno-19-9" > < / a > < span class = "kd" > var< / span > < span class = "nv" > duplicated< / span > < span class = "p" > :< / span > < span class = "n" > Set< / span > < span class = "p" > < < / span > < span class = "nb" > Int< / span > < span class = "p" > > < / span > < span class = "p" > =< / span > < span class = "p" > []< / span >
< a id = "__codelineno-19-10" name = "__codelineno-19-10" href = "#__codelineno-19-10" > < / a > < span class = "k" > for< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > ,< / span > < span class = "n" > choice< / span > < span class = "p" > )< / span > < span class = "k" > in< / span > < span class = "n" > choices< / span > < span class = "p" > .< / span > < span class = "n" > enumerated< / span > < span class = "p" > ()< / span > < span class = "p" > {< / span >
< a id = "__codelineno-19-11" name = "__codelineno-19-11" href = "#__codelineno-19-11" > < / a > < span class = "c1" > // 剪枝：不允许重复选择元素 且 不允许重复选择相等元素< / span >
< a id = "__codelineno-19-12" name = "__codelineno-19-12" href = "#__codelineno-19-12" > < / a > < span class = "k" > if< / span > < span class = "o" > !< / span > < span class = "n" > selected< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ],< / span > < span class = "o" > !< / span > < span class = "n" > duplicated< / span > < span class = "p" > .< / span > < span class = "bp" > contains< / span > < span class = "p" > (< / span > < span class = "n" > choice< / span > < span class = "p" > )< / span > < span class = "p" > {< / span >
< a id = "__codelineno-19-13" name = "__codelineno-19-13" href = "#__codelineno-19-13" > < / a > < span class = "c1" > // 尝试：做出选择，更新状态< / span >
< a id = "__codelineno-19-14" name = "__codelineno-19-14" href = "#__codelineno-19-14" > < / a > < span class = "n" > duplicated< / span > < span class = "p" > .< / span > < span class = "bp" > insert< / span > < span class = "p" > (< / span > < span class = "n" > choice< / span > < span class = "p" > )< / span > < span class = "c1" > // 记录选择过的元素值< / span >
< a id = "__codelineno-19-15" name = "__codelineno-19-15" href = "#__codelineno-19-15" > < / a > < span class = "n" > selected< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "kc" > true< / span >
< a id = "__codelineno-19-16" name = "__codelineno-19-16" href = "#__codelineno-19-16" > < / a > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > choice< / span > < span class = "p" > )< / span >
< a id = "__codelineno-19-17" name = "__codelineno-19-17" href = "#__codelineno-19-17" > < / a > < span class = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-19-18" name = "__codelineno-19-18" href = "#__codelineno-19-18" > < / a > < span class = "n" > backtrack< / 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" > choices< / span > < span class = "p" > :< / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span > < span class = "n" > selected< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > selected< / 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 >
< a id = "__codelineno-19-19" name = "__codelineno-19-19" href = "#__codelineno-19-19" > < / a > < span class = "c1" > // 回退：撤销选择，恢复到之前的状态< / span >
< a id = "__codelineno-19-20" name = "__codelineno-19-20" href = "#__codelineno-19-20" > < / a > < span class = "n" > selected< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "kc" > false< / span >
< a id = "__codelineno-19-21" name = "__codelineno-19-21" href = "#__codelineno-19-21" > < / a > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "bp" > removeLast< / span > < span class = "p" > ()< / span >
< a id = "__codelineno-19-22" name = "__codelineno-19-22" href = "#__codelineno-19-22" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-19-23" name = "__codelineno-19-23" href = "#__codelineno-19-23" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-19-24" name = "__codelineno-19-24" href = "#__codelineno-19-24" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-19-25" name = "__codelineno-19-25" href = "#__codelineno-19-25" > < / a >
< a id = "__codelineno-19-26" name = "__codelineno-19-26" href = "#__codelineno-19-26" > < / a > < span class = "cm" > /* 全排列 II */< / span >
< a id = "__codelineno-19-27" name = "__codelineno-19-27" href = "#__codelineno-19-27" > < / a > < span class = "kd" > func< / span > < span class = "nf" > permutationsII< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > :< / 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" > Int< / span > < span class = "p" > ]]< / span > < span class = "p" > {< / span >
< a id = "__codelineno-19-28" name = "__codelineno-19-28" href = "#__codelineno-19-28" > < / a > < span class = "kd" > var< / span > < span class = "nv" > state< / span > < span class = "p" > :< / span > < span class = "p" > [< / span > < span class = "nb" > Int< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "p" > []< / span >
< a id = "__codelineno-19-29" name = "__codelineno-19-29" href = "#__codelineno-19-29" > < / a > < span class = "kd" > var< / span > < span class = "nv" > selected< / 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" > nums< / span > < span class = "p" > .< / span > < span class = "bp" > count< / span > < span class = "p" > )< / span >
< a id = "__codelineno-19-30" name = "__codelineno-19-30" href = "#__codelineno-19-30" > < / a > < span class = "kd" > var< / span > < span class = "nv" > res< / span > < span class = "p" > :< / span > < span class = "p" > [[< / span > < span class = "nb" > Int< / span > < span class = "p" > ]]< / span > < span class = "p" > =< / span > < span class = "p" > []< / span >
< a id = "__codelineno-19-31" name = "__codelineno-19-31" href = "#__codelineno-19-31" > < / a > < span class = "n" > backtrack< / 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" > choices< / span > < span class = "p" > :< / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "n" > selected< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > selected< / 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 >
< a id = "__codelineno-19-32" name = "__codelineno-19-32" href = "#__codelineno-19-32" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
< a id = "__codelineno-19-33" name = "__codelineno-19-33" href = "#__codelineno-19-33" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > permutations_ii.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-20-1" name = "__codelineno-20-1" href = "#__codelineno-20-1" > < / 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-20-2" name = "__codelineno-20-2" href = "#__codelineno-20-2" > < / a >
< a id = "__codelineno-20-3" name = "__codelineno-20-3" href = "#__codelineno-20-3" > < / 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" > permutationsII< / span > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > permutations_ii.dart< / span > < pre > < span > < / span > < code > < a id = "__codelineno-21-1" name = "__codelineno-21-1" href = "#__codelineno-21-1" > < / 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-21-2" name = "__codelineno-21-2" href = "#__codelineno-21-2" > < / a >
< a id = "__codelineno-21-3" name = "__codelineno-21-3" href = "#__codelineno-21-3" > < / 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" > permutationsII< / span > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< p > 注意，虽然 < code > selected< / code > 和 < code > duplicated< / code > 都起到剪枝的作用，但他们剪掉的是不同的分支：< / p >
< ul >
< li > < strong > 剪枝条件一< / strong > ：整个搜索过程中只有一个 < code > selected< / code > 。它记录的是当前状态中包含哪些元素，作用是避免某个元素在 < code > state< / code > 中重复出现。< / li >
< li > < strong > 剪枝条件二< / strong > ：每轮选择（即每个开启的 < code > backtrack< / code > 函数）都包含一个 < code > duplicated< / code > 。它记录的是在遍历中哪些元素已被选择过，作用是保证相等元素只被选择一次，以避免产生重复的搜索分支。< / li >
< / ul >
< p > 下图展示了两个剪枝条件的生效范围。注意，树中的每个节点代表一个选择，从根节点到叶节点的路径上的各个节点构成一个排列。< / p >
< p > < img alt = "两种剪枝条件的作用范围" src = "../permutations_problem.assets/permutations_ii_pruning_summary.png" / > < / p >
< p align = "center" > Fig. 两种剪枝条件的作用范围 < / p >
2023-05-21 19:29:51 +08:00
< h2 id = "1223" > 12.2.3. 复杂度分析< a class = "headerlink" href = "#1223" title = "Permanent link" > ¶ < / a > < / h2 >
2023-05-04 05:22:36 +08:00
< p > 假设元素两两之间互不相同，则 < span class = "arithmatex" > \(n\)< / span > 个元素共有 < span class = "arithmatex" > \(n!\)< / span > 种排列（阶乘）；在记录结果时，需要复制长度为 < span class = "arithmatex" > \(n\)< / span > 的列表，使用 < span class = "arithmatex" > \(O(n)\)< / span > 时间。因此，< strong > 时间复杂度为 < span class = "arithmatex" > \(O(n!n)\)< / span > < / strong > 。< / p >
< p > 最大递归深度为 < span class = "arithmatex" > \(n\)< / span > ，使用 < span class = "arithmatex" > \(O(n)\)< / span > 栈帧空间。< code > selected< / code > 使用 < span class = "arithmatex" > \(O(n)\)< / span > 空间。同一时刻最多共有 < span class = "arithmatex" > \(n\)< / span > 个 < code > duplicated< / code > ，使用 < span class = "arithmatex" > \(O(n^2)\)< / span > 空间。因此，< strong > 全排列 I 的空间复杂度为 < span class = "arithmatex" > \(O(n)\)< / span > ，全排列 II 的空间复杂度为 < span class = "arithmatex" > \(O(n^2)\)< / span > < / strong > 。< / p >
2023-04-24 03:30:35 +08:00
< h2 id = "__comments" > 评论< / h2 >
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