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13.3 子集和问题
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第 0 章 前言
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第 0 章 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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第 1 章 初识算法
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第 1 章 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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第 2 章 复杂度分析
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第 2 章 复杂度分析
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2.1 算法效率评估
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2.2 迭代与递归
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2.3 时间复杂度
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2.4 空间复杂度
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2.5 小结
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第 3 章 数据结构
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第 3 章 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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第 4 章 数组与链表
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第 4 章 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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第 5 章 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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第 6 章 哈希表
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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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第 7 章 树
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第 7 章 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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第 8 章 堆
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第 8 章 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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< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z" / > < / svg >
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第 9 章 图
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第 9 章 图
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< a href = "../../chapter_graph/graph/" class = "md-nav__link" >
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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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< div class = "md-nav__link md-nav__container" >
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< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z" / > < / svg >
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第 10 章 搜索
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第 10 章 搜索
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< / label >
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< li class = "md-nav__item" >
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10.1 二分查找
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< li class = "md-nav__item" >
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10.2 二分查找插入点
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10.3 二分查找边界
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< li class = "md-nav__item" >
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10.4 哈希优化策略
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< li class = "md-nav__item" >
< a href = "../../chapter_searching/searching_algorithm_revisited/" class = "md-nav__link" >
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10.5 重识搜索算法
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< li class = "md-nav__item" >
< a href = "../../chapter_searching/summary/" class = "md-nav__link" >
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10.6 小结
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< li class = "md-nav__item md-nav__item--nested" >
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< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_sorting/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z" / > < / svg >
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第 11 章 排序
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第 11 章 排序
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< / label >
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< li class = "md-nav__item" >
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11.1 排序算法
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11.2 选择排序
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< li class = "md-nav__item" >
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11.3 冒泡排序
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11.4 插入排序
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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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第 12 章 分治
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第 12 章 分治
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12.1 分治算法
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12.3 构建树问题
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12.4 汉诺塔问题
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12.5 小结
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第 13 章 回溯
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第 13 章 回溯
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13.1 回溯算法
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13.2 全排列问题
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13.3 子集和问题
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13.3 子集和问题
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13.3.1 无重复元素的情况
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1. 参考全排列解法
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1. 相等元素剪枝
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13.4 N 皇后问题
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13.5 小结
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14.3 DP 解题思路
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14.4 0-1 背包问题
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14.6 编辑距离问题
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15.1 贪心算法
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15.5 小结
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第 16 章 附录
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16.2 一起参与创作
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13.3.1 无重复元素的情况
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1. 参考全排列解法
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13.3.2 考虑重复元素的情况
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< h1 id = "133" > 13.3 子集和问题< a class = "headerlink" href = "#133" title = "Permanent link" > ¶ < / a > < / h1 >
< h2 id = "1331" > 13.3.1 无重复元素的情况< a class = "headerlink" href = "#1331" title = "Permanent link" > ¶ < / a > < / h2 >
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< p class = "admonition-title" > Question< / p >
< p > 给定一个正整数数组 < code > nums< / code > 和一个目标正整数 < code > target< / code > ，请找出所有可能的组合，使得组合中的元素和等于 < code > target< / code > 。给定数组无重复元素，每个元素可以被选取多次。请以列表形式返回这些组合，列表中不应包含重复组合。< / p >
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< p > 例如，输入集合 < span class = "arithmatex" > \(\{3, 4, 5\}\)< / span > 和目标整数 < span class = "arithmatex" > \(9\)< / span > ，解为 < span class = "arithmatex" > \(\{3, 3, 3\}, \{4, 5\}\)< / span > 。需要注意以下两点。< / p >
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< ul >
< li > 输入集合中的元素可以被无限次重复选取。< / li >
< li > 子集是不区分元素顺序的，比如 < span class = "arithmatex" > \(\{4, 5\}\)< / span > 和 < span class = "arithmatex" > \(\{5, 4\}\)< / span > 是同一个子集。< / li >
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< h3 id = "1" > 1. 参考全排列解法< a class = "headerlink" href = "#1" title = "Permanent link" > ¶ < / a > < / h3 >
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< p > 类似于全排列问题，我们可以把子集的生成过程想象成一系列选择的结果，并在选择过程中实时更新“元素和”，当元素和等于 < code > target< / code > 时，就将子集记录至结果列表。< / p >
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< p > 而与全排列问题不同的是，< strong > 本题集合中的元素可以被无限次选取< / strong > ，因此无须借助 < code > selected< / code > 布尔列表来记录元素是否已被选择。我们可以对全排列代码进行小幅修改，初步得到解题代码。< / p >
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< div class = "tabbed-set tabbed-alternate" data-tabs = "1:12" > < input checked = "checked" id = "__tabbed_1_1" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_2" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_3" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_4" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_5" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_6" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_7" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_8" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_9" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_10" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_11" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_12" name = "__tabbed_1" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_1_1" > Python< / label > < label for = "__tabbed_1_2" > C++< / label > < label for = "__tabbed_1_3" > Java< / label > < label for = "__tabbed_1_4" > C#< / label > < label for = "__tabbed_1_5" > Go< / label > < label for = "__tabbed_1_6" > Swift< / label > < label for = "__tabbed_1_7" > JS< / label > < label for = "__tabbed_1_8" > TS< / label > < label for = "__tabbed_1_9" > Dart< / label > < label for = "__tabbed_1_10" > Rust< / label > < label for = "__tabbed_1_11" > C< / label > < label for = "__tabbed_1_12" > Zig< / label > < / div >
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< div class = "tabbed-content" >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > subset_sum_i_naive.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-0-1" name = "__codelineno-0-1" href = "#__codelineno-0-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > backtrack< / span > < span class = "p" > (< / span >
< a id = "__codelineno-0-2" name = "__codelineno-0-2" href = "#__codelineno-0-2" > < / 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 >
< a id = "__codelineno-0-3" name = "__codelineno-0-3" href = "#__codelineno-0-3" > < / a > < span class = "n" > target< / span > < span class = "p" > :< / span > < span class = "nb" > int< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-0-4" name = "__codelineno-0-4" href = "#__codelineno-0-4" > < / a > < span class = "n" > total< / span > < span class = "p" > :< / span > < span class = "nb" > int< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-0-5" name = "__codelineno-0-5" href = "#__codelineno-0-5" > < / a > < 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 >
< a id = "__codelineno-0-6" name = "__codelineno-0-6" href = "#__codelineno-0-6" > < / a > < span class = "n" > res< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > int< / span > < span class = "p" > ]],< / span >
< a id = "__codelineno-0-7" name = "__codelineno-0-7" href = "#__codelineno-0-7" > < / a > < span class = "p" > ):< / span >
< a id = "__codelineno-0-8" name = "__codelineno-0-8" href = "#__codelineno-0-8" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 回溯算法：子集和 I" " " < / span >
< a id = "__codelineno-0-9" name = "__codelineno-0-9" href = "#__codelineno-0-9" > < / a > < span class = "c1" > # 子集和等于 target 时，记录解< / span >
< a id = "__codelineno-0-10" name = "__codelineno-0-10" href = "#__codelineno-0-10" > < / a > < span class = "k" > if< / span > < span class = "n" > total< / span > < span class = "o" > ==< / span > < span class = "n" > target< / span > < span class = "p" > :< / span >
< a id = "__codelineno-0-11" name = "__codelineno-0-11" href = "#__codelineno-0-11" > < / 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-0-12" name = "__codelineno-0-12" href = "#__codelineno-0-12" > < / a > < span class = "k" > return< / span >
< a id = "__codelineno-0-13" name = "__codelineno-0-13" href = "#__codelineno-0-13" > < / a > < span class = "c1" > # 遍历所有选择< / span >
< a id = "__codelineno-0-14" name = "__codelineno-0-14" href = "#__codelineno-0-14" > < / a > < span class = "k" > for< / span > < span class = "n" > i< / span > < span class = "ow" > in< / span > < span class = "nb" > range< / span > < span class = "p" > (< / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "n" > choices< / span > < span class = "p" > )):< / span >
< a id = "__codelineno-0-15" name = "__codelineno-0-15" href = "#__codelineno-0-15" > < / a > < span class = "c1" > # 剪枝：若子集和超过 target ，则跳过该选择< / span >
< a id = "__codelineno-0-16" name = "__codelineno-0-16" href = "#__codelineno-0-16" > < / a > < span class = "k" > if< / span > < span class = "n" > total< / span > < span class = "o" > +< / span > < span class = "n" > choices< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "o" > > < / span > < span class = "n" > target< / span > < span class = "p" > :< / span >
< a id = "__codelineno-0-17" name = "__codelineno-0-17" href = "#__codelineno-0-17" > < / a > < span class = "k" > continue< / span >
< a id = "__codelineno-0-18" name = "__codelineno-0-18" href = "#__codelineno-0-18" > < / a > < span class = "c1" > # 尝试：做出选择，更新元素和 total< / span >
< a id = "__codelineno-0-19" name = "__codelineno-0-19" href = "#__codelineno-0-19" > < / a > < span class = "n" > state< / span > < span class = "o" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > choices< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ])< / span >
< a id = "__codelineno-0-20" name = "__codelineno-0-20" href = "#__codelineno-0-20" > < / a > < span class = "c1" > # 进行下一轮选择< / span >
< a id = "__codelineno-0-21" name = "__codelineno-0-21" href = "#__codelineno-0-21" > < / a > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "n" > target< / span > < span class = "p" > ,< / span > < span class = "n" > total< / span > < span class = "o" > +< / span > < span class = "n" > choices< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ],< / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span > < span class = "n" > res< / span > < span class = "p" > )< / span >
< a id = "__codelineno-0-22" name = "__codelineno-0-22" href = "#__codelineno-0-22" > < / a > < span class = "c1" > # 回退：撤销选择，恢复到之前的状态< / span >
< a id = "__codelineno-0-23" name = "__codelineno-0-23" href = "#__codelineno-0-23" > < / a > < span class = "n" > state< / span > < span class = "o" > .< / span > < span class = "n" > pop< / span > < 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 = "k" > def< / span > < span class = "nf" > subset_sum_i_naive< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > int< / span > < span class = "p" > ],< / span > < span class = "n" > target< / 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-0-26" name = "__codelineno-0-26" href = "#__codelineno-0-26" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 求解子集和 I（ ） " " " < / span >
< a id = "__codelineno-0-27" name = "__codelineno-0-27" href = "#__codelineno-0-27" > < / a > < span class = "n" > state< / span > < span class = "o" > =< / span > < span class = "p" > []< / span > < span class = "c1" > # 状态（子集）< / span >
< a id = "__codelineno-0-28" name = "__codelineno-0-28" href = "#__codelineno-0-28" > < / a > < span class = "n" > total< / span > < span class = "o" > =< / span > < span class = "mi" > 0< / span > < span class = "c1" > # 子集和< / span >
< a id = "__codelineno-0-29" name = "__codelineno-0-29" href = "#__codelineno-0-29" > < / a > < span class = "n" > res< / span > < span class = "o" > =< / span > < span class = "p" > []< / span > < span class = "c1" > # 结果列表（子集列表）< / span >
< a id = "__codelineno-0-30" name = "__codelineno-0-30" href = "#__codelineno-0-30" > < / a > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "n" > target< / span > < span class = "p" > ,< / span > < span class = "n" > total< / span > < span class = "p" > ,< / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "n" > res< / span > < span class = "p" > )< / span >
< a id = "__codelineno-0-31" name = "__codelineno-0-31" href = "#__codelineno-0-31" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > subset_sum_i_naive.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：子集和 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 = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > target< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > total< / span > < span class = "p" > ,< / 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 = "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" > // 子集和等于 target 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" > total< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "n" > target< / 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" > size_t< / 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 = "c1" > // 剪枝：若子集和超过 target ，则跳过该选择< / span >
< a id = "__codelineno-1-11" name = "__codelineno-1-11" href = "#__codelineno-1-11" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > total< / 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 > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > target< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-12" name = "__codelineno-1-12" href = "#__codelineno-1-12" > < / a > < span class = "w" > < / span > < span class = "k" > continue< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-13" name = "__codelineno-1-13" href = "#__codelineno-1-13" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-1-14" name = "__codelineno-1-14" href = "#__codelineno-1-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新元素和 total< / 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" > choices< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]);< / span >
< a id = "__codelineno-1-16" name = "__codelineno-1-16" href = "#__codelineno-1-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 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" > target< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > total< / 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 > < span class = "w" > < / span > < span class = "n" > choices< / 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" > state< / span > < span class = "p" > .< / span > < span class = "n" > pop_back< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-1-20" name = "__codelineno-1-20" href = "#__codelineno-1-20" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-1-21" name = "__codelineno-1-21" href = "#__codelineno-1-21" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-1-22" name = "__codelineno-1-22" href = "#__codelineno-1-22" > < / a >
< a id = "__codelineno-1-23" name = "__codelineno-1-23" href = "#__codelineno-1-23" > < / a > < span class = "cm" > /* 求解子集和 I（ ） < / span >
< a id = "__codelineno-1-24" name = "__codelineno-1-24" href = "#__codelineno-1-24" > < / 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" > subsetSumINaive< / span > < span class = "p" > (< / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > target< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-25" name = "__codelineno-1-25" href = "#__codelineno-1-25" > < / a > < span class = "w" > < / span > < span class = "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 > < span class = "w" > < / span > < span class = "c1" > // 状态（子集）< / span >
< a id = "__codelineno-1-26" name = "__codelineno-1-26" href = "#__codelineno-1-26" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > total< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 子集和< / 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 = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 结果列表（子集列表）< / span >
< a id = "__codelineno-1-28" name = "__codelineno-1-28" href = "#__codelineno-1-28" > < / 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" > target< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > total< / 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" > res< / 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 = "k" > return< / 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 = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > subset_sum_i_naive.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-2-1" name = "__codelineno-2-1" href = "#__codelineno-2-1" > < / a > < span class = "cm" > /* 回溯算法：子集和 I */< / span >
< a id = "__codelineno-2-2" name = "__codelineno-2-2" href = "#__codelineno-2-2" > < / 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 = "w" > < / span > < span class = "n" > target< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > total< / 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 = "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-2-3" name = "__codelineno-2-3" href = "#__codelineno-2-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子集和等于 target 时，记录解< / span >
< a id = "__codelineno-2-4" name = "__codelineno-2-4" href = "#__codelineno-2-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > total< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "n" > target< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-2-5" name = "__codelineno-2-5" href = "#__codelineno-2-5" > < / 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 = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-2-6" name = "__codelineno-2-6" href = "#__codelineno-2-6" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-2-7" name = "__codelineno-2-7" href = "#__codelineno-2-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-2-8" name = "__codelineno-2-8" href = "#__codelineno-2-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-2-9" name = "__codelineno-2-9" href = "#__codelineno-2-9" > < / 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-2-10" name = "__codelineno-2-10" href = "#__codelineno-2-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：若子集和超过 target ，则跳过该选择< / span >
< a id = "__codelineno-2-11" name = "__codelineno-2-11" href = "#__codelineno-2-11" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > total< / 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 = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > target< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-2-12" name = "__codelineno-2-12" href = "#__codelineno-2-12" > < / a > < span class = "w" > < / span > < span class = "k" > continue< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-2-13" name = "__codelineno-2-13" href = "#__codelineno-2-13" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-2-14" name = "__codelineno-2-14" href = "#__codelineno-2-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新元素和 total< / span >
< a id = "__codelineno-2-15" name = "__codelineno-2-15" href = "#__codelineno-2-15" > < / 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" > choices< / span > < span class = "o" > [< / span > < span class = "n" > i< / span > < span class = "o" > ]< / span > < span class = "p" > );< / span >
< a id = "__codelineno-2-16" name = "__codelineno-2-16" href = "#__codelineno-2-16" > < / a > < span class = "w" > < / span > < 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 = "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" > target< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > total< / 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 > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / 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 = "w" > < / span > < 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 = "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-2-20" name = "__codelineno-2-20" href = "#__codelineno-2-20" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-2-21" name = "__codelineno-2-21" href = "#__codelineno-2-21" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-2-22" name = "__codelineno-2-22" href = "#__codelineno-2-22" > < / a >
< a id = "__codelineno-2-23" name = "__codelineno-2-23" href = "#__codelineno-2-23" > < / a > < span class = "cm" > /* 求解子集和 I（ ） < / span >
< a id = "__codelineno-2-24" name = "__codelineno-2-24" href = "#__codelineno-2-24" > < / 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" > subsetSumINaive< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "o" > []< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > target< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-2-25" name = "__codelineno-2-25" href = "#__codelineno-2-25" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > ArrayList< / span > < span class = "o" > < > < / span > < span class = "p" > ();< / span > < span class = "w" > < / span > < span class = "c1" > // 状态（子集）< / span >
< a id = "__codelineno-2-26" name = "__codelineno-2-26" href = "#__codelineno-2-26" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > total< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 子集和< / span >
< a id = "__codelineno-2-27" name = "__codelineno-2-27" href = "#__codelineno-2-27" > < / 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 = "p" > ();< / span > < span class = "w" > < / span > < span class = "c1" > // 结果列表（子集列表）< / span >
< a id = "__codelineno-2-28" name = "__codelineno-2-28" href = "#__codelineno-2-28" > < / 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" > target< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > total< / 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" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-2-29" name = "__codelineno-2-29" href = "#__codelineno-2-29" > < / 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-2-30" name = "__codelineno-2-30" href = "#__codelineno-2-30" > < / 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" > subset_sum_i_naive.cs< / 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：子集和 I */< / span >
< a id = "__codelineno-3-2" name = "__codelineno-3-2" href = "#__codelineno-3-2" > < / 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 = "w" > < / span > < span class = "n" > target< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > total< / 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 = "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 >
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< a id = "__codelineno-3-3" name = "__codelineno-3-3" href = "#__codelineno-3-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子集和等于 target 时，记录解< / span >
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< 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 = "p" > (< / span > < span class = "n" > total< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "n" > target< / 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 = "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-3-6" name = "__codelineno-3-6" href = "#__codelineno-3-6" > < / a > < span class = "w" > < / span > < span class = "k" > return< / 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 = "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-3-10" name = "__codelineno-3-10" href = "#__codelineno-3-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：若子集和超过 target ，则跳过该选择< / span >
< a id = "__codelineno-3-11" name = "__codelineno-3-11" href = "#__codelineno-3-11" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > total< / 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 > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > target< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-12" name = "__codelineno-3-12" href = "#__codelineno-3-12" > < / a > < span class = "w" > < / span > < span class = "k" > continue< / 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 = "p" > }< / span >
< a id = "__codelineno-3-14" name = "__codelineno-3-14" href = "#__codelineno-3-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新元素和 total< / span >
< a id = "__codelineno-3-15" name = "__codelineno-3-15" href = "#__codelineno-3-15" > < / 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" > choices< / span > < span class = "p" > [< / span > < span class = "n" > i< / 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 = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > target< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > total< / 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 > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > 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 = "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-3-20" name = "__codelineno-3-20" href = "#__codelineno-3-20" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-21" name = "__codelineno-3-21" href = "#__codelineno-3-21" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-3-22" name = "__codelineno-3-22" href = "#__codelineno-3-22" > < / a >
< a id = "__codelineno-3-23" name = "__codelineno-3-23" href = "#__codelineno-3-23" > < / a > < span class = "cm" > /* 求解子集和 I（ ） < / span >
< a id = "__codelineno-3-24" name = "__codelineno-3-24" href = "#__codelineno-3-24" > < / 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" > subsetSumINaive< / 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 = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > target< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-25" name = "__codelineno-3-25" href = "#__codelineno-3-25" > < / a > < span class = "w" > < / span > < span class = "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 = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "p" > ();< / span > < span class = "w" > < / span > < span class = "c1" > // 状态（子集）< / span >
< a id = "__codelineno-3-26" name = "__codelineno-3-26" href = "#__codelineno-3-26" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > total< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 子集和< / span >
< a id = "__codelineno-3-27" name = "__codelineno-3-27" href = "#__codelineno-3-27" > < / 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 > < span class = "w" > < / span > < span class = "c1" > // 结果列表（子集列表）< / span >
< a id = "__codelineno-3-28" name = "__codelineno-3-28" href = "#__codelineno-3-28" > < / 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" > target< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > total< / 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" > res< / 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 = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-3-30" name = "__codelineno-3-30" href = "#__codelineno-3-30" > < / a > < span class = "p" > }< / span >
2023-06-21 02:55:52 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-09-04 03:17:06 +08:00
< div class = "highlight" > < span class = "filename" > subset_sum_i_naive.go< / 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：子集和 I */< / span >
< a id = "__codelineno-4-2" name = "__codelineno-4-2" href = "#__codelineno-4-2" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > backtrackSubsetSumINaive< / span > < span class = "p" > (< / span > < span class = "nx" > total< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > target< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "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" > 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 >
2023-08-04 05:25:00 +08:00
< a id = "__codelineno-4-3" name = "__codelineno-4-3" href = "#__codelineno-4-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子集和等于 target 时，记录解< / span >
2023-09-04 03:17:06 +08:00
< 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 = "nx" > target< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "nx" > total< / 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" > 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-4-6" name = "__codelineno-4-6" href = "#__codelineno-4-6" > < / 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-4-7" name = "__codelineno-4-7" href = "#__codelineno-4-7" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span >
< a id = "__codelineno-4-8" name = "__codelineno-4-8" href = "#__codelineno-4-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-9" name = "__codelineno-4-9" href = "#__codelineno-4-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-4-10" name = "__codelineno-4-10" href = "#__codelineno-4-10" > < / 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-4-11" name = "__codelineno-4-11" href = "#__codelineno-4-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：若子集和超过 target ，则跳过该选择< / span >
< a id = "__codelineno-4-12" name = "__codelineno-4-12" href = "#__codelineno-4-12" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > total< / span > < span class = "o" > +< / 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 > < span class = "w" > < / span > < span class = "p" > > < / span > < span class = "w" > < / span > < span class = "nx" > target< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-13" name = "__codelineno-4-13" href = "#__codelineno-4-13" > < / a > < span class = "w" > < / span > < span class = "k" > continue< / span >
< a id = "__codelineno-4-14" name = "__codelineno-4-14" href = "#__codelineno-4-14" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-15" name = "__codelineno-4-15" href = "#__codelineno-4-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新元素和 total< / span >
< a id = "__codelineno-4-16" name = "__codelineno-4-16" href = "#__codelineno-4-16" > < / 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 = "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-4-17" name = "__codelineno-4-17" href = "#__codelineno-4-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-4-18" name = "__codelineno-4-18" href = "#__codelineno-4-18" > < / a > < span class = "w" > < / span > < span class = "nx" > backtrackSubsetSumINaive< / span > < span class = "p" > (< / span > < span class = "nx" > total< / span > < span class = "o" > +< / 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 > < span class = "w" > < / span > < span class = "nx" > target< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / 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 = "c1" > // 回退：撤销选择，恢复到之前的状态< / span >
< a id = "__codelineno-4-20" name = "__codelineno-4-20" href = "#__codelineno-4-20" > < / 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-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" > /* 求解子集和 I（ ） < / span >
< a id = "__codelineno-4-25" name = "__codelineno-4-25" href = "#__codelineno-4-25" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > subsetSumINaive< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "w" > < / span > < span class = "p" > []< / span > < span class = "kt" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > target< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > [][]< / span > < span class = "kt" > int< / 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 = "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 > < span class = "w" > < / span > < span class = "c1" > // 状态（子集）< / span >
< a id = "__codelineno-4-27" name = "__codelineno-4-27" href = "#__codelineno-4-27" > < / a > < span class = "w" > < / span > < span class = "nx" > total< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "w" > < / span > < span class = "c1" > // 子集和< / span >
< a id = "__codelineno-4-28" name = "__codelineno-4-28" href = "#__codelineno-4-28" > < / 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 > < span class = "w" > < / span > < span class = "c1" > // 结果列表（子集列表）< / span >
< a id = "__codelineno-4-29" name = "__codelineno-4-29" href = "#__codelineno-4-29" > < / a > < span class = "w" > < / span > < span class = "nx" > backtrackSubsetSumINaive< / span > < span class = "p" > (< / span > < span class = "nx" > total< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > target< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "nx" > nums< / 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-4-30" name = "__codelineno-4-30" href = "#__codelineno-4-30" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span >
< a id = "__codelineno-4-31" name = "__codelineno-4-31" href = "#__codelineno-4-31" > < / 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" > subset_sum_i_naive.swift< / 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：子集和 I */< / span >
< a id = "__codelineno-5-2" name = "__codelineno-5-2" href = "#__codelineno-5-2" > < / 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" > target< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / span > < span class = "p" > ,< / span > < span class = "n" > total< / 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" > 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-5-3" name = "__codelineno-5-3" href = "#__codelineno-5-3" > < / a > < span class = "c1" > // 子集和等于 target 时，记录解< / span >
< a id = "__codelineno-5-4" name = "__codelineno-5-4" href = "#__codelineno-5-4" > < / a > < span class = "k" > if< / span > < span class = "n" > total< / span > < span class = "p" > ==< / span > < span class = "n" > target< / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-5" name = "__codelineno-5-5" href = "#__codelineno-5-5" > < / 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-5-6" name = "__codelineno-5-6" href = "#__codelineno-5-6" > < / a > < span class = "k" > return< / span >
< a id = "__codelineno-5-7" name = "__codelineno-5-7" href = "#__codelineno-5-7" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-5-8" name = "__codelineno-5-8" href = "#__codelineno-5-8" > < / a > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-5-9" name = "__codelineno-5-9" href = "#__codelineno-5-9" > < / a > < span class = "k" > for< / span > < span class = "n" > i< / span > < span class = "k" > in< / span > < span class = "bp" > stride< / span > < span class = "p" > (< / span > < span class = "n" > from< / span > < span class = "p" > :< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "n" > to< / span > < span class = "p" > :< / span > < span class = "n" > choices< / span > < span class = "p" > .< / span > < span class = "bp" > count< / span > < span class = "p" > ,< / span > < span class = "n" > by< / span > < span class = "p" > :< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-10" name = "__codelineno-5-10" href = "#__codelineno-5-10" > < / a > < span class = "c1" > // 剪枝：若子集和超过 target ，则跳过该选择< / span >
< a id = "__codelineno-5-11" name = "__codelineno-5-11" href = "#__codelineno-5-11" > < / a > < span class = "k" > if< / span > < span class = "n" > total< / span > < span class = "o" > +< / span > < span class = "n" > choices< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "o" > > < / span > < span class = "n" > target< / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-12" name = "__codelineno-5-12" href = "#__codelineno-5-12" > < / a > < span class = "k" > continue< / span >
< a id = "__codelineno-5-13" name = "__codelineno-5-13" href = "#__codelineno-5-13" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-5-14" name = "__codelineno-5-14" href = "#__codelineno-5-14" > < / a > < span class = "c1" > // 尝试：做出选择，更新元素和 total< / span >
< a id = "__codelineno-5-15" name = "__codelineno-5-15" href = "#__codelineno-5-15" > < / a > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > choices< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ])< / span >
< a id = "__codelineno-5-16" name = "__codelineno-5-16" href = "#__codelineno-5-16" > < / a > < span class = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-5-17" name = "__codelineno-5-17" href = "#__codelineno-5-17" > < / 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" > target< / span > < span class = "p" > :< / span > < span class = "n" > target< / span > < span class = "p" > ,< / span > < span class = "n" > total< / span > < span class = "p" > :< / span > < span class = "n" > total< / span > < span class = "o" > +< / span > < span class = "n" > choices< / span > < span class = "p" > [< / span > < span class = "n" > i< / 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" > res< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > res< / span > < span class = "p" > )< / span >
< a id = "__codelineno-5-18" name = "__codelineno-5-18" href = "#__codelineno-5-18" > < / a > < span class = "c1" > // 回退：撤销选择，恢复到之前的状态< / span >
< a id = "__codelineno-5-19" name = "__codelineno-5-19" href = "#__codelineno-5-19" > < / a > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "bp" > removeLast< / span > < span class = "p" > ()< / span >
< a id = "__codelineno-5-20" name = "__codelineno-5-20" href = "#__codelineno-5-20" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-5-21" name = "__codelineno-5-21" href = "#__codelineno-5-21" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-5-22" name = "__codelineno-5-22" href = "#__codelineno-5-22" > < / a >
< a id = "__codelineno-5-23" name = "__codelineno-5-23" href = "#__codelineno-5-23" > < / a > < span class = "cm" > /* 求解子集和 I（ ） < / span >
< a id = "__codelineno-5-24" name = "__codelineno-5-24" href = "#__codelineno-5-24" > < / a > < span class = "kd" > func< / span > < span class = "nf" > subsetSumINaive< / 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 = "n" > target< / 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-5-25" name = "__codelineno-5-25" href = "#__codelineno-5-25" > < / 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 > < span class = "c1" > // 状态（子集）< / span >
< a id = "__codelineno-5-26" name = "__codelineno-5-26" href = "#__codelineno-5-26" > < / a > < span class = "kd" > let< / span > < span class = "nv" > total< / span > < span class = "p" > =< / span > < span class = "mi" > 0< / span > < span class = "c1" > // 子集和< / span >
< a id = "__codelineno-5-27" name = "__codelineno-5-27" href = "#__codelineno-5-27" > < / 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 > < span class = "c1" > // 结果列表（子集列表）< / span >
< a id = "__codelineno-5-28" name = "__codelineno-5-28" href = "#__codelineno-5-28" > < / 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" > target< / span > < span class = "p" > :< / span > < span class = "n" > target< / span > < span class = "p" > ,< / span > < span class = "n" > total< / span > < span class = "p" > :< / span > < span class = "n" > total< / 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" > res< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > res< / span > < span class = "p" > )< / span >
< a id = "__codelineno-5-29" name = "__codelineno-5-29" href = "#__codelineno-5-29" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
< a id = "__codelineno-5-30" name = "__codelineno-5-30" href = "#__codelineno-5-30" > < / 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" > subset_sum_i_naive.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-6-1" name = "__codelineno-6-1" href = "#__codelineno-6-1" > < / a > < span class = "cm" > /* 回溯算法：子集和 I */< / span >
< a id = "__codelineno-6-2" name = "__codelineno-6-2" href = "#__codelineno-6-2" > < / 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" > target< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > total< / 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" > res< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
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< a id = "__codelineno-6-3" name = "__codelineno-6-3" href = "#__codelineno-6-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子集和等于 target 时，记录解< / span >
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< a id = "__codelineno-6-4" name = "__codelineno-6-4" href = "#__codelineno-6-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > total< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "nx" > target< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-6-5" name = "__codelineno-6-5" href = "#__codelineno-6-5" > < / 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-6-6" name = "__codelineno-6-6" href = "#__codelineno-6-6" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-6-7" name = "__codelineno-6-7" href = "#__codelineno-6-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-6-8" name = "__codelineno-6-8" href = "#__codelineno-6-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-6-9" name = "__codelineno-6-9" href = "#__codelineno-6-9" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "nx" > choices< / span > < span class = "p" > .< / span > < span class = "nx" > length< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-6-10" name = "__codelineno-6-10" href = "#__codelineno-6-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：若子集和超过 target ，则跳过该选择< / span >
< a id = "__codelineno-6-11" name = "__codelineno-6-11" href = "#__codelineno-6-11" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > total< / 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" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "nx" > target< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-6-12" name = "__codelineno-6-12" href = "#__codelineno-6-12" > < / a > < span class = "w" > < / span > < span class = "k" > continue< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-6-13" name = "__codelineno-6-13" href = "#__codelineno-6-13" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-6-14" name = "__codelineno-6-14" href = "#__codelineno-6-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新元素和 total< / span >
< a id = "__codelineno-6-15" name = "__codelineno-6-15" href = "#__codelineno-6-15" > < / 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" > choices< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ]);< / span >
< a id = "__codelineno-6-16" name = "__codelineno-6-16" href = "#__codelineno-6-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-6-17" name = "__codelineno-6-17" href = "#__codelineno-6-17" > < / 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" > target< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > total< / 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" > i< / 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" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-6-18" name = "__codelineno-6-18" href = "#__codelineno-6-18" > < / 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-6-19" name = "__codelineno-6-19" href = "#__codelineno-6-19" > < / 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-6-20" name = "__codelineno-6-20" href = "#__codelineno-6-20" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-6-21" name = "__codelineno-6-21" href = "#__codelineno-6-21" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-6-22" name = "__codelineno-6-22" href = "#__codelineno-6-22" > < / a >
< a id = "__codelineno-6-23" name = "__codelineno-6-23" href = "#__codelineno-6-23" > < / a > < span class = "cm" > /* 求解子集和 I（ ） < / span >
< a id = "__codelineno-6-24" name = "__codelineno-6-24" href = "#__codelineno-6-24" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > subsetSumINaive< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > target< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-6-25" name = "__codelineno-6-25" href = "#__codelineno-6-25" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [];< / span > < span class = "w" > < / span > < span class = "c1" > // 状态（子集）< / span >
< a id = "__codelineno-6-26" name = "__codelineno-6-26" href = "#__codelineno-6-26" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > total< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 子集和< / span >
< a id = "__codelineno-6-27" name = "__codelineno-6-27" href = "#__codelineno-6-27" > < / 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 > < span class = "w" > < / span > < span class = "c1" > // 结果列表（子集列表）< / span >
< a id = "__codelineno-6-28" name = "__codelineno-6-28" href = "#__codelineno-6-28" > < / 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" > target< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > total< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-6-29" name = "__codelineno-6-29" href = "#__codelineno-6-29" > < / 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-6-30" name = "__codelineno-6-30" href = "#__codelineno-6-30" > < / 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" > subset_sum_i_naive.ts< / 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：子集和 I */< / span >
< a id = "__codelineno-7-2" name = "__codelineno-7-2" href = "#__codelineno-7-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > backtrack< / 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 = "nx" > state< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > [],< / span >
< a id = "__codelineno-7-4" name = "__codelineno-7-4" href = "#__codelineno-7-4" > < / a > < span class = "w" > < / span > < span class = "nx" > target< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / 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 = "nx" > total< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / 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 = "nx" > choices< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / 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 = "nx" > res< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > [][]< / span >
< a id = "__codelineno-7-8" name = "__codelineno-7-8" href = "#__codelineno-7-8" > < / 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-7-9" name = "__codelineno-7-9" href = "#__codelineno-7-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子集和等于 target 时，记录解< / span >
< a id = "__codelineno-7-10" name = "__codelineno-7-10" href = "#__codelineno-7-10" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > total< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "nx" > target< / span > < span class = "p" > )< / span > < span class = "w" > < / 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 = "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-7-12" name = "__codelineno-7-12" href = "#__codelineno-7-12" > < / a > < span class = "w" > < / span > < span class = "k" > return< / 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 = "p" > }< / span >
< a id = "__codelineno-7-14" name = "__codelineno-7-14" href = "#__codelineno-7-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-7-15" name = "__codelineno-7-15" href = "#__codelineno-7-15" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "nx" > choices< / span > < span class = "p" > .< / span > < span class = "nx" > length< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-16" name = "__codelineno-7-16" href = "#__codelineno-7-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：若子集和超过 target ，则跳过该选择< / span >
< a id = "__codelineno-7-17" name = "__codelineno-7-17" href = "#__codelineno-7-17" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > total< / 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" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "nx" > target< / span > < span class = "p" > )< / span > < span class = "w" > < / 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 = "k" > continue< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-19" name = "__codelineno-7-19" href = "#__codelineno-7-19" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-7-20" name = "__codelineno-7-20" href = "#__codelineno-7-20" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新元素和 total< / span >
< a id = "__codelineno-7-21" name = "__codelineno-7-21" href = "#__codelineno-7-21" > < / 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" > choices< / span > < span class = "p" > [< / span > < span class = "nx" > i< / 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 = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-7-23" name = "__codelineno-7-23" href = "#__codelineno-7-23" > < / 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" > target< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > total< / 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" > i< / 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" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-7-24" name = "__codelineno-7-24" href = "#__codelineno-7-24" > < / 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-7-25" name = "__codelineno-7-25" href = "#__codelineno-7-25" > < / 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-7-26" name = "__codelineno-7-26" href = "#__codelineno-7-26" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-7-27" name = "__codelineno-7-27" href = "#__codelineno-7-27" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-7-28" name = "__codelineno-7-28" href = "#__codelineno-7-28" > < / a >
< a id = "__codelineno-7-29" name = "__codelineno-7-29" href = "#__codelineno-7-29" > < / a > < span class = "cm" > /* 求解子集和 I（ ） < / span >
< a id = "__codelineno-7-30" name = "__codelineno-7-30" href = "#__codelineno-7-30" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > subsetSumINaive< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > [],< / span > < span class = "w" > < / span > < span class = "nx" > target< / 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-7-31" name = "__codelineno-7-31" href = "#__codelineno-7-31" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [];< / span > < span class = "w" > < / span > < span class = "c1" > // 状态（子集）< / span >
< a id = "__codelineno-7-32" name = "__codelineno-7-32" href = "#__codelineno-7-32" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > total< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 子集和< / span >
< a id = "__codelineno-7-33" name = "__codelineno-7-33" href = "#__codelineno-7-33" > < / 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 > < span class = "w" > < / span > < span class = "c1" > // 结果列表（子集列表）< / span >
< a id = "__codelineno-7-34" name = "__codelineno-7-34" href = "#__codelineno-7-34" > < / 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" > target< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > total< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-7-35" name = "__codelineno-7-35" href = "#__codelineno-7-35" > < / 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-7-36" name = "__codelineno-7-36" href = "#__codelineno-7-36" > < / 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" > subset_sum_i_naive.dart< / 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：子集和 I */< / span >
< a id = "__codelineno-8-2" name = "__codelineno-8-2" href = "#__codelineno-8-2" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "n" > backtrack< / span > < span class = "p" > (< / span >
< a id = "__codelineno-8-3" name = "__codelineno-8-3" href = "#__codelineno-8-3" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-8-4" name = "__codelineno-8-4" href = "#__codelineno-8-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > target< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-8-5" name = "__codelineno-8-5" href = "#__codelineno-8-5" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > total< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-8-6" name = "__codelineno-8-6" href = "#__codelineno-8-6" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-8-7" name = "__codelineno-8-7" href = "#__codelineno-8-7" > < / 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 = "p" > ,< / span >
< a id = "__codelineno-8-8" name = "__codelineno-8-8" href = "#__codelineno-8-8" > < / a > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-9" name = "__codelineno-8-9" href = "#__codelineno-8-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子集和等于 target 时，记录解< / span >
< a id = "__codelineno-8-10" name = "__codelineno-8-10" href = "#__codelineno-8-10" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > total< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "n" > target< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-11" name = "__codelineno-8-11" href = "#__codelineno-8-11" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > add< / span > < span class = "p" > (< / span > < span class = "n" > List< / span > < span class = "p" > .< / span > < span class = "n" > from< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-8-12" name = "__codelineno-8-12" href = "#__codelineno-8-12" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-8-13" name = "__codelineno-8-13" href = "#__codelineno-8-13" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-8-14" name = "__codelineno-8-14" href = "#__codelineno-8-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-8-15" name = "__codelineno-8-15" href = "#__codelineno-8-15" > < / 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-8-16" name = "__codelineno-8-16" href = "#__codelineno-8-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：若子集和超过 target ，则跳过该选择< / span >
< a id = "__codelineno-8-17" name = "__codelineno-8-17" href = "#__codelineno-8-17" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > total< / 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 > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > target< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-18" name = "__codelineno-8-18" href = "#__codelineno-8-18" > < / a > < span class = "w" > < / span > < span class = "k" > continue< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-8-19" name = "__codelineno-8-19" href = "#__codelineno-8-19" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-8-20" name = "__codelineno-8-20" href = "#__codelineno-8-20" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新元素和 total< / span >
< a id = "__codelineno-8-21" name = "__codelineno-8-21" href = "#__codelineno-8-21" > < / 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" > choices< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]);< / span >
< a id = "__codelineno-8-22" name = "__codelineno-8-22" href = "#__codelineno-8-22" > < / a > < span class = "w" > < / span > < span class = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-8-23" name = "__codelineno-8-23" href = "#__codelineno-8-23" > < / 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" > target< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > total< / 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 > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-8-24" name = "__codelineno-8-24" href = "#__codelineno-8-24" > < / 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-8-25" name = "__codelineno-8-25" href = "#__codelineno-8-25" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > removeLast< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-8-26" name = "__codelineno-8-26" href = "#__codelineno-8-26" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-8-27" name = "__codelineno-8-27" href = "#__codelineno-8-27" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-28" name = "__codelineno-8-28" href = "#__codelineno-8-28" > < / a >
< a id = "__codelineno-8-29" name = "__codelineno-8-29" href = "#__codelineno-8-29" > < / a > < span class = "cm" > /* 求解子集和 I（ ） < / span >
< a id = "__codelineno-8-30" name = "__codelineno-8-30" href = "#__codelineno-8-30" > < / 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" > subsetSumINaive< / 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" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > target< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-31" name = "__codelineno-8-31" href = "#__codelineno-8-31" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [];< / span > < span class = "w" > < / span > < span class = "c1" > // 状态（子集）< / span >
< a id = "__codelineno-8-32" name = "__codelineno-8-32" href = "#__codelineno-8-32" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > total< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 元素和< / span >
< a id = "__codelineno-8-33" name = "__codelineno-8-33" href = "#__codelineno-8-33" > < / 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 = "p" > [];< / span > < span class = "w" > < / span > < span class = "c1" > // 结果列表（子集列表）< / span >
< a id = "__codelineno-8-34" name = "__codelineno-8-34" href = "#__codelineno-8-34" > < / 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" > target< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > total< / 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" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-8-35" name = "__codelineno-8-35" href = "#__codelineno-8-35" > < / 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-8-36" name = "__codelineno-8-36" href = "#__codelineno-8-36" > < / a > < span class = "p" > }< / span >
2023-06-21 02:55:52 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-09-04 03:17:06 +08:00
< div class = "highlight" > < span class = "filename" > subset_sum_i_naive.rs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-9-1" name = "__codelineno-9-1" href = "#__codelineno-9-1" > < / a > < span class = "cm" > /* 回溯算法：子集和 I */< / span >
< a id = "__codelineno-9-2" name = "__codelineno-9-2" href = "#__codelineno-9-2" > < / a > < span class = "k" > fn< / span > < span class = "nf" > backtrack< / span > < span class = "p" > (< / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > state< / span > : < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "kt" > i32< / span > < span class = "o" > > < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > target< / span > : < span class = "kt" > i32< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > total< / span > : < span class = "kt" > i32< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > choices< / span > : < span class = "kp" > & < / span > < span class = "p" > [< / span > < span class = "kt" > i32< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "n" > res< / span > : < span class = "kp" > & < / span > < span class = "nc" > mut< / span > < span class = "w" > < / span > < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "kt" > i32< / span > < span class = "o" > > > < / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-3" name = "__codelineno-9-3" href = "#__codelineno-9-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子集和等于 target 时，记录解< / span >
< a id = "__codelineno-9-4" name = "__codelineno-9-4" href = "#__codelineno-9-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "n" > total< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "n" > target< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-5" name = "__codelineno-9-5" href = "#__codelineno-9-5" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > push< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > );< / span >
< a id = "__codelineno-9-6" name = "__codelineno-9-6" href = "#__codelineno-9-6" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-9-7" name = "__codelineno-9-7" href = "#__codelineno-9-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-9-8" name = "__codelineno-9-8" href = "#__codelineno-9-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-9-9" name = "__codelineno-9-9" href = "#__codelineno-9-9" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "k" > in< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "o" > ..< / span > < span class = "n" > choices< / span > < span class = "p" > .< / span > < span class = "n" > len< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-10" name = "__codelineno-9-10" href = "#__codelineno-9-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：若子集和超过 target ，则跳过该选择< / span >
< a id = "__codelineno-9-11" name = "__codelineno-9-11" href = "#__codelineno-9-11" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "n" > total< / 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 > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > target< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-12" name = "__codelineno-9-12" href = "#__codelineno-9-12" > < / a > < span class = "w" > < / span > < span class = "k" > continue< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-9-13" name = "__codelineno-9-13" href = "#__codelineno-9-13" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-9-14" name = "__codelineno-9-14" href = "#__codelineno-9-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新元素和 total< / span >
< a id = "__codelineno-9-15" name = "__codelineno-9-15" href = "#__codelineno-9-15" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > push< / span > < span class = "p" > (< / span > < span class = "n" > choices< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]);< / span >
< a id = "__codelineno-9-16" name = "__codelineno-9-16" href = "#__codelineno-9-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-9-17" name = "__codelineno-9-17" href = "#__codelineno-9-17" > < / 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 = "n" > clone< / span > < span class = "p" > (),< / span > < span class = "w" > < / span > < span class = "n" > target< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > total< / 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 > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-9-18" name = "__codelineno-9-18" href = "#__codelineno-9-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退：撤销选择，恢复到之前的状态< / span >
< a id = "__codelineno-9-19" name = "__codelineno-9-19" href = "#__codelineno-9-19" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > pop< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-9-20" name = "__codelineno-9-20" href = "#__codelineno-9-20" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-9-21" name = "__codelineno-9-21" href = "#__codelineno-9-21" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-9-22" name = "__codelineno-9-22" href = "#__codelineno-9-22" > < / a >
< a id = "__codelineno-9-23" name = "__codelineno-9-23" href = "#__codelineno-9-23" > < / a > < span class = "cm" > /* 求解子集和 I（ ） < / span >
< a id = "__codelineno-9-24" name = "__codelineno-9-24" href = "#__codelineno-9-24" > < / a > < span class = "k" > fn< / span > < span class = "nf" > subset_sum_i_naive< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > : < span class = "kp" > & < / span > < span class = "p" > [< / span > < span class = "kt" > i32< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "n" > target< / span > : < span class = "kt" > i32< / span > < span class = "p" > )< / span > < span class = "w" > < / span > -> < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "kt" > i32< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-25" name = "__codelineno-9-25" href = "#__codelineno-9-25" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > Vec< / span > ::< span class = "n" > new< / span > < span class = "p" > ();< / span > < span class = "w" > < / span > < span class = "c1" > // 状态（子集）< / span >
< a id = "__codelineno-9-26" name = "__codelineno-9-26" href = "#__codelineno-9-26" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "n" > total< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 子集和< / span >
< a id = "__codelineno-9-27" name = "__codelineno-9-27" href = "#__codelineno-9-27" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > Vec< / span > ::< span class = "n" > new< / span > < span class = "p" > ();< / span > < span class = "w" > < / span > < span class = "c1" > // 结果列表（子集列表）< / span >
< a id = "__codelineno-9-28" name = "__codelineno-9-28" href = "#__codelineno-9-28" > < / 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" > target< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > total< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-9-29" name = "__codelineno-9-29" href = "#__codelineno-9-29" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span >
< a id = "__codelineno-9-30" name = "__codelineno-9-30" href = "#__codelineno-9-30" > < / 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" > subset_sum_i_naive.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-10-1" name = "__codelineno-10-1" href = "#__codelineno-10-1" > < / a > < span class = "cm" > /* 回溯算法：子集和 I */< / span >
< a id = "__codelineno-10-2" name = "__codelineno-10-2" href = "#__codelineno-10-2" > < / 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 = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > target< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > total< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > vector< / 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 = "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-10-3" name = "__codelineno-10-3" href = "#__codelineno-10-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子集和等于 target 时，记录解< / span >
< a id = "__codelineno-10-4" name = "__codelineno-10-4" href = "#__codelineno-10-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > total< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "n" > target< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-10-5" name = "__codelineno-10-5" href = "#__codelineno-10-5" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > tmpVector< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > newVector< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-10-6" name = "__codelineno-10-6" href = "#__codelineno-10-6" > < / 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" > state< / span > < span class = "o" > -> < / 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-10-7" name = "__codelineno-10-7" href = "#__codelineno-10-7" > < / a > < span class = "w" > < / span > < span class = "n" > vectorPushback< / span > < span class = "p" > (< / span > < span class = "n" > tmpVector< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "o" > -> < / span > < span class = "n" > data< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "k" > sizeof< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-10-8" name = "__codelineno-10-8" href = "#__codelineno-10-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-10-9" name = "__codelineno-10-9" href = "#__codelineno-10-9" > < / a > < span class = "w" > < / span > < span class = "n" > vectorPushback< / span > < span class = "p" > (< / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > tmpVector< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "k" > sizeof< / span > < span class = "p" > (< / span > < span class = "n" > vector< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-10-10" name = "__codelineno-10-10" href = "#__codelineno-10-10" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-11" name = "__codelineno-10-11" href = "#__codelineno-10-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-10-12" name = "__codelineno-10-12" href = "#__codelineno-10-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-10-13" name = "__codelineno-10-13" href = "#__codelineno-10-13" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > size_t< / 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 = "o" > -> < / 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-10-14" name = "__codelineno-10-14" href = "#__codelineno-10-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：若子集和超过 target ，则跳过该选择< / span >
< a id = "__codelineno-10-15" name = "__codelineno-10-15" href = "#__codelineno-10-15" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > total< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > )(< / span > < span class = "n" > choices< / span > < span class = "o" > -> < / span > < span class = "n" > data< / 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" > target< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-10-16" name = "__codelineno-10-16" href = "#__codelineno-10-16" > < / a > < span class = "w" > < / span > < span class = "k" > continue< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-17" name = "__codelineno-10-17" href = "#__codelineno-10-17" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-10-18" name = "__codelineno-10-18" href = "#__codelineno-10-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新元素和 total< / span >
< a id = "__codelineno-10-19" name = "__codelineno-10-19" href = "#__codelineno-10-19" > < / a > < span class = "w" > < / span > < span class = "n" > vectorPushback< / 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 = "o" > -> < / span > < span class = "n" > data< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "k" > sizeof< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-10-20" name = "__codelineno-10-20" href = "#__codelineno-10-20" > < / a > < span class = "w" > < / span > < span class = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-10-21" name = "__codelineno-10-21" href = "#__codelineno-10-21" > < / 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" > target< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > total< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > )(< / span > < span class = "n" > choices< / span > < span class = "o" > -> < / span > < span class = "n" > data< / span > < span class = "p" > [< / span > < span class = "n" > i< / 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" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-10-22" name = "__codelineno-10-22" href = "#__codelineno-10-22" > < / 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-10-23" name = "__codelineno-10-23" href = "#__codelineno-10-23" > < / a > < span class = "w" > < / span > < span class = "n" > vectorPopback< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > );< / span >
< a id = "__codelineno-10-24" name = "__codelineno-10-24" href = "#__codelineno-10-24" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-10-25" name = "__codelineno-10-25" href = "#__codelineno-10-25" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-10-26" name = "__codelineno-10-26" href = "#__codelineno-10-26" > < / a >
< a id = "__codelineno-10-27" name = "__codelineno-10-27" href = "#__codelineno-10-27" > < / a > < span class = "cm" > /* 求解子集和 I（ ） < / span >
< a id = "__codelineno-10-28" name = "__codelineno-10-28" href = "#__codelineno-10-28" > < / a > < span class = "n" > vector< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nf" > subsetSumINaive< / span > < span class = "p" > (< / span > < span class = "n" > vector< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > target< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-10-29" name = "__codelineno-10-29" href = "#__codelineno-10-29" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > state< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > newVector< / span > < span class = "p" > ();< / span > < span class = "w" > < / span > < span class = "c1" > // 状态（子集）< / span >
< a id = "__codelineno-10-30" name = "__codelineno-10-30" href = "#__codelineno-10-30" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > total< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 子集和< / span >
< a id = "__codelineno-10-31" name = "__codelineno-10-31" href = "#__codelineno-10-31" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > newVector< / span > < span class = "p" > ();< / span > < span class = "w" > < / span > < span class = "c1" > // 结果列表（子集列表）< / span >
< a id = "__codelineno-10-32" name = "__codelineno-10-32" href = "#__codelineno-10-32" > < / 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" > target< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > total< / 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" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-10-33" name = "__codelineno-10-33" href = "#__codelineno-10-33" > < / 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-10-34" name = "__codelineno-10-34" href = "#__codelineno-10-34" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
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< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > subset_sum_i_naive.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-11-1" name = "__codelineno-11-1" href = "#__codelineno-11-1" > < / 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-11-2" name = "__codelineno-11-2" href = "#__codelineno-11-2" > < / a >
< a id = "__codelineno-11-3" name = "__codelineno-11-3" href = "#__codelineno-11-3" > < / 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" > subsetSumINaive< / span > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
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< / div >
< / div >
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< p > 向以上代码输入数组 < span class = "arithmatex" > \([3, 4, 5]\)< / span > 和目标元素 < span class = "arithmatex" > \(9\)< / span > ，输出结果为 < span class = "arithmatex" > \([3, 3, 3], [4, 5], [5, 4]\)< / span > 。< strong > 虽然成功找出了所有和为 < span class = "arithmatex" > \(9\)< / span > 的子集，但其中存在重复的子集 < span class = "arithmatex" > \([4, 5]\)< / span > 和 < span class = "arithmatex" > \([5, 4]\)< / span > < / strong > 。< / p >
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< p > 这是因为搜索过程是区分选择顺序的，然而子集不区分选择顺序。如图 13-10 所示，先选 < span class = "arithmatex" > \(4\)< / span > 后选 < span class = "arithmatex" > \(5\)< / span > 与先选 < span class = "arithmatex" > \(5\)< / span > 后选 < span class = "arithmatex" > \(4\)< / span > 是两个不同的分支，但两者对应同一个子集。< / p >
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< p > < a class = "glightbox" href = "../subset_sum_problem.assets/subset_sum_i_naive.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "子集搜索与越界剪枝" src = "../subset_sum_problem.assets/subset_sum_i_naive.png" / > < / a > < / p >
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< p align = "center" > 图 13-10 子集搜索与越界剪枝 < / p >
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< p > 为了去除重复子集，< strong > 一种直接的思路是对结果列表进行去重< / strong > 。但这个方法效率很低，有两方面原因。< / p >
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< ul >
< li > 当数组元素较多，尤其是当 < code > target< / code > 较大时，搜索过程会产生大量的重复子集。< / li >
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< li > 比较子集（数组）的异同非常耗时，需要先排序数组，再比较数组中每个元素的异同。< / li >
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< / ul >
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< h3 id = "2" > 2. 重复子集剪枝< a class = "headerlink" href = "#2" title = "Permanent link" > ¶ < / a > < / h3 >
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< p > < strong > 我们考虑在搜索过程中通过剪枝进行去重< / strong > 。观察图 13-11 ，重复子集是在以不同顺序选择数组元素时产生的，例如以下情况。< / p >
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< ol >
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< li > 当第一轮和第二轮分别选择 < span class = "arithmatex" > \(3\)< / span > 和 < span class = "arithmatex" > \(4\)< / span > 时，会生成包含这两个元素的所有子集，记为 < span class = "arithmatex" > \([3, 4, \dots]\)< / span > 。< / li >
< li > 之后，当第一轮选择 < span class = "arithmatex" > \(4\)< / span > 时，< strong > 则第二轮应该跳过 < span class = "arithmatex" > \(3\)< / span > < / strong > ，因为该选择产生的子集 < span class = "arithmatex" > \([4, 3, \dots]\)< / span > 和 < code > 1.< / code > 中生成的子集完全重复。< / li >
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< / ol >
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< p > 在搜索中，每一层的选择都是从左到右被逐个尝试的，因此越靠右的分支被剪掉的越多。< / p >
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< ol >
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< li > 前两轮选择 < span class = "arithmatex" > \(3\)< / span > 和 < span class = "arithmatex" > \(5\)< / span > ，生成子集 < span class = "arithmatex" > \([3, 5, \dots]\)< / span > 。< / li >
< li > 前两轮选择 < span class = "arithmatex" > \(4\)< / span > 和 < span class = "arithmatex" > \(5\)< / span > ，生成子集 < span class = "arithmatex" > \([4, 5, \dots]\)< / span > 。< / li >
< li > 若第一轮选择 < span class = "arithmatex" > \(5\)< / span > ， < strong > 则第二轮应该跳过 < span class = "arithmatex" > \(3\)< / span > 和 < span class = "arithmatex" > \(4\)< / span > < / strong > ，因为子集 < span class = "arithmatex" > \([5, 3, \dots]\)< / span > 和 < span class = "arithmatex" > \([5, 4, \dots]\)< / span > 与第 < code > 1.< / code > 和 < code > 2.< / code > 步中描述的子集完全重复。< / li >
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< / ol >
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< p > < a class = "glightbox" href = "../subset_sum_problem.assets/subset_sum_i_pruning.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "不同选择顺序导致的重复子集" src = "../subset_sum_problem.assets/subset_sum_i_pruning.png" / > < / a > < / p >
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< p align = "center" > 图 13-11 不同选择顺序导致的重复子集 < / p >
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< p > 总结来看，给定输入数组 < span class = "arithmatex" > \([x_1, x_2, \dots, x_n]\)< / span > ，设搜索过程中的选择序列为 < span class = "arithmatex" > \([x_{i_1}, x_{i_2}, \dots, x_{i_m}]\)< / span > ，则该选择序列需要满足 < span class = "arithmatex" > \(i_1 \leq i_2 \leq \dots \leq i_m\)< / span > ， < strong > 不满足该条件的选择序列都会造成重复，应当剪枝< / strong > 。< / p >
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< h3 id = "3" > 3. 代码实现< a class = "headerlink" href = "#3" title = "Permanent link" > ¶ < / a > < / h3 >
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< p > 为实现该剪枝，我们初始化变量 < code > start< / code > ，用于指示遍历起点。< strong > 当做出选择 < span class = "arithmatex" > \(x_{i}\)< / span > 后，设定下一轮从索引 < span class = "arithmatex" > \(i\)< / span > 开始遍历< / strong > 。这样做就可以让选择序列满足 < span class = "arithmatex" > \(i_1 \leq i_2 \leq \dots \leq i_m\)< / span > ，从而保证子集唯一。< / p >
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< p > 除此之外，我们还对代码进行了以下两项优化。< / p >
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< ul >
< li > 在开启搜索前，先将数组 < code > nums< / code > 排序。在遍历所有选择时，< strong > 当子集和超过 < code > target< / code > 时直接结束循环< / strong > ，因为后边的元素更大，其子集和都一定会超过 < code > target< / code > 。< / li >
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< li > 省去元素和变量 < code > total< / code > ， < strong > 通过在 < code > target< / code > 上执行减法来统计元素和< / strong > ，当 < code > target< / code > 等于 < span class = "arithmatex" > \(0\)< / span > 时记录解。< / li >
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< / ul >
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< div class = "tabbed-set tabbed-alternate" data-tabs = "2:12" > < 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" / > < input id = "__tabbed_2_12" name = "__tabbed_2" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_2_1" > Python< / label > < label for = "__tabbed_2_2" > C++< / label > < label for = "__tabbed_2_3" > Java< / label > < label for = "__tabbed_2_4" > C#< / label > < label for = "__tabbed_2_5" > Go< / label > < label for = "__tabbed_2_6" > Swift< / label > < label for = "__tabbed_2_7" > JS< / label > < label for = "__tabbed_2_8" > TS< / label > < label for = "__tabbed_2_9" > Dart< / label > < label for = "__tabbed_2_10" > Rust< / label > < label for = "__tabbed_2_11" > C< / label > < label for = "__tabbed_2_12" > Zig< / label > < / div >
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< div class = "tabbed-content" >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > subset_sum_i.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-12-1" name = "__codelineno-12-1" href = "#__codelineno-12-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > backtrack< / span > < span class = "p" > (< / span >
< a id = "__codelineno-12-2" name = "__codelineno-12-2" href = "#__codelineno-12-2" > < / 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" > target< / 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" > start< / span > < span class = "p" > :< / span > < span class = "nb" > int< / 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-12-3" name = "__codelineno-12-3" href = "#__codelineno-12-3" > < / a > < span class = "p" > ):< / span >
< a id = "__codelineno-12-4" name = "__codelineno-12-4" href = "#__codelineno-12-4" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 回溯算法：子集和 I" " " < / span >
< a id = "__codelineno-12-5" name = "__codelineno-12-5" href = "#__codelineno-12-5" > < / a > < span class = "c1" > # 子集和等于 target 时，记录解< / span >
< a id = "__codelineno-12-6" name = "__codelineno-12-6" href = "#__codelineno-12-6" > < / a > < span class = "k" > if< / span > < span class = "n" > target< / span > < span class = "o" > ==< / span > < span class = "mi" > 0< / span > < span class = "p" > :< / span >
< a id = "__codelineno-12-7" name = "__codelineno-12-7" href = "#__codelineno-12-7" > < / 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-12-8" name = "__codelineno-12-8" href = "#__codelineno-12-8" > < / a > < span class = "k" > return< / span >
< a id = "__codelineno-12-9" name = "__codelineno-12-9" href = "#__codelineno-12-9" > < / a > < span class = "c1" > # 遍历所有选择< / span >
< a id = "__codelineno-12-10" name = "__codelineno-12-10" href = "#__codelineno-12-10" > < / a > < span class = "c1" > # 剪枝二：从 start 开始遍历，避免生成重复子集< / span >
< a id = "__codelineno-12-11" name = "__codelineno-12-11" href = "#__codelineno-12-11" > < / a > < span class = "k" > for< / span > < span class = "n" > i< / span > < span class = "ow" > in< / span > < span class = "nb" > range< / span > < span class = "p" > (< / span > < span class = "n" > start< / span > < span class = "p" > ,< / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "n" > choices< / span > < span class = "p" > )):< / span >
< a id = "__codelineno-12-12" name = "__codelineno-12-12" href = "#__codelineno-12-12" > < / a > < span class = "c1" > # 剪枝一：若子集和超过 target ，则直接结束循环< / span >
< a id = "__codelineno-12-13" name = "__codelineno-12-13" href = "#__codelineno-12-13" > < / a > < span class = "c1" > # 这是因为数组已排序，后边元素更大，子集和一定超过 target< / span >
< a id = "__codelineno-12-14" name = "__codelineno-12-14" href = "#__codelineno-12-14" > < / a > < span class = "k" > if< / span > < span class = "n" > target< / span > < span class = "o" > -< / span > < span class = "n" > choices< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "o" > < < / span > < span class = "mi" > 0< / span > < span class = "p" > :< / span >
< a id = "__codelineno-12-15" name = "__codelineno-12-15" href = "#__codelineno-12-15" > < / a > < span class = "k" > break< / span >
< a id = "__codelineno-12-16" name = "__codelineno-12-16" href = "#__codelineno-12-16" > < / a > < span class = "c1" > # 尝试：做出选择，更新 target, start< / span >
< a id = "__codelineno-12-17" name = "__codelineno-12-17" href = "#__codelineno-12-17" > < / a > < span class = "n" > state< / span > < span class = "o" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > choices< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ])< / span >
< a id = "__codelineno-12-18" name = "__codelineno-12-18" href = "#__codelineno-12-18" > < / a > < 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 = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "n" > target< / span > < span class = "o" > -< / span > < span class = "n" > choices< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ],< / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span > < span class = "n" > i< / span > < span class = "p" > ,< / 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 = "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 = "n" > state< / span > < span class = "o" > .< / span > < span class = "n" > pop< / span > < span class = "p" > ()< / span >
< a id = "__codelineno-12-22" name = "__codelineno-12-22" href = "#__codelineno-12-22" > < / a >
< a id = "__codelineno-12-23" name = "__codelineno-12-23" href = "#__codelineno-12-23" > < / a > < span class = "k" > def< / span > < span class = "nf" > subset_sum_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 = "n" > target< / 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-12-24" name = "__codelineno-12-24" href = "#__codelineno-12-24" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 求解子集和 I" " " < / span >
< a id = "__codelineno-12-25" name = "__codelineno-12-25" href = "#__codelineno-12-25" > < / a > < span class = "n" > state< / span > < span class = "o" > =< / span > < span class = "p" > []< / span > < span class = "c1" > # 状态（子集）< / span >
< a id = "__codelineno-12-26" name = "__codelineno-12-26" href = "#__codelineno-12-26" > < / a > < span class = "n" > nums< / span > < span class = "o" > .< / span > < span class = "n" > sort< / span > < span class = "p" > ()< / span > < span class = "c1" > # 对 nums 进行排序< / span >
< a id = "__codelineno-12-27" name = "__codelineno-12-27" href = "#__codelineno-12-27" > < / a > < span class = "n" > start< / span > < span class = "o" > =< / span > < span class = "mi" > 0< / span > < span class = "c1" > # 遍历起始点< / span >
< a id = "__codelineno-12-28" name = "__codelineno-12-28" href = "#__codelineno-12-28" > < / a > < span class = "n" > res< / span > < span class = "o" > =< / span > < span class = "p" > []< / span > < span class = "c1" > # 结果列表（子集列表）< / span >
< a id = "__codelineno-12-29" name = "__codelineno-12-29" href = "#__codelineno-12-29" > < / a > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "n" > target< / span > < span class = "p" > ,< / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "n" > start< / span > < span class = "p" > ,< / span > < span class = "n" > res< / span > < span class = "p" > )< / span >
< a id = "__codelineno-12-30" name = "__codelineno-12-30" href = "#__codelineno-12-30" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > subset_sum_i.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-13-1" name = "__codelineno-13-1" href = "#__codelineno-13-1" > < / a > < span class = "cm" > /* 回溯算法：子集和 I */< / span >
< a id = "__codelineno-13-2" name = "__codelineno-13-2" href = "#__codelineno-13-2" > < / 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 = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > target< / span > < span class = "p" > ,< / 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 = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > start< / 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-13-3" name = "__codelineno-13-3" href = "#__codelineno-13-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子集和等于 target 时，记录解< / span >
< a id = "__codelineno-13-4" name = "__codelineno-13-4" href = "#__codelineno-13-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > target< / 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 = "p" > {< / span >
< a id = "__codelineno-13-5" name = "__codelineno-13-5" href = "#__codelineno-13-5" > < / 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-13-6" name = "__codelineno-13-6" href = "#__codelineno-13-6" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-13-7" name = "__codelineno-13-7" href = "#__codelineno-13-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-13-8" name = "__codelineno-13-8" href = "#__codelineno-13-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-13-9" name = "__codelineno-13-9" href = "#__codelineno-13-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝二：从 start 开始遍历，避免生成重复子集< / span >
< a id = "__codelineno-13-10" name = "__codelineno-13-10" href = "#__codelineno-13-10" > < / 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 = "n" > start< / 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-13-11" name = "__codelineno-13-11" href = "#__codelineno-13-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝一：若子集和超过 target ，则直接结束循环< / span >
< a id = "__codelineno-13-12" name = "__codelineno-13-12" href = "#__codelineno-13-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 这是因为数组已排序，后边元素更大，子集和一定超过 target< / span >
< a id = "__codelineno-13-13" name = "__codelineno-13-13" href = "#__codelineno-13-13" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > target< / 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 > < 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 = "p" > {< / span >
< a id = "__codelineno-13-14" name = "__codelineno-13-14" href = "#__codelineno-13-14" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-13-15" name = "__codelineno-13-15" href = "#__codelineno-13-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-13-16" name = "__codelineno-13-16" href = "#__codelineno-13-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新 target, start< / span >
< a id = "__codelineno-13-17" name = "__codelineno-13-17" href = "#__codelineno-13-17" > < / 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" > choices< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]);< / span >
< a id = "__codelineno-13-18" name = "__codelineno-13-18" href = "#__codelineno-13-18" > < / a > < span class = "w" > < / span > < 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 = "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" > target< / 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 > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / 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 = "w" > < / span > < 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 = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > pop_back< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-13-22" name = "__codelineno-13-22" href = "#__codelineno-13-22" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-13-23" name = "__codelineno-13-23" href = "#__codelineno-13-23" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-13-24" name = "__codelineno-13-24" href = "#__codelineno-13-24" > < / a >
< a id = "__codelineno-13-25" name = "__codelineno-13-25" href = "#__codelineno-13-25" > < / a > < span class = "cm" > /* 求解子集和 I */< / span >
< a id = "__codelineno-13-26" name = "__codelineno-13-26" href = "#__codelineno-13-26" > < / 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" > subsetSumI< / span > < span class = "p" > (< / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > target< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-13-27" name = "__codelineno-13-27" href = "#__codelineno-13-27" > < / 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 > < span class = "w" > < / span > < span class = "c1" > // 状态（子集）< / span >
< a id = "__codelineno-13-28" name = "__codelineno-13-28" href = "#__codelineno-13-28" > < / a > < span class = "w" > < / span > < span class = "n" > sort< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > .< / span > < span class = "n" > begin< / span > < span class = "p" > (),< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > .< / span > < span class = "n" > end< / span > < span class = "p" > ());< / span > < span class = "w" > < / span > < span class = "c1" > // 对 nums 进行排序< / span >
< a id = "__codelineno-13-29" name = "__codelineno-13-29" href = "#__codelineno-13-29" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > start< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 遍历起始点< / span >
< a id = "__codelineno-13-30" name = "__codelineno-13-30" href = "#__codelineno-13-30" > < / 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 > < span class = "w" > < / span > < span class = "c1" > // 结果列表（子集列表）< / span >
< a id = "__codelineno-13-31" name = "__codelineno-13-31" href = "#__codelineno-13-31" > < / 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" > target< / 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" > start< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-13-32" name = "__codelineno-13-32" href = "#__codelineno-13-32" > < / 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-13-33" name = "__codelineno-13-33" href = "#__codelineno-13-33" > < / a > < span class = "p" > }< / span >
2023-06-21 02:55:52 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-09-04 03:17:06 +08:00
< div class = "highlight" > < span class = "filename" > subset_sum_i.java< / 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：子集和 I */< / span >
< a id = "__codelineno-14-2" name = "__codelineno-14-2" href = "#__codelineno-14-2" > < / 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 = "w" > < / span > < span class = "n" > target< / 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" > int< / span > < span class = "w" > < / span > < span class = "n" > start< / 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-14-3" name = "__codelineno-14-3" href = "#__codelineno-14-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子集和等于 target 时，记录解< / span >
< a id = "__codelineno-14-4" name = "__codelineno-14-4" href = "#__codelineno-14-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > target< / 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 = "p" > {< / span >
< a id = "__codelineno-14-5" name = "__codelineno-14-5" href = "#__codelineno-14-5" > < / 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 = "p" > (< / span > < span class = "n" > state< / 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 = "k" > return< / span > < span class = "p" > ;< / span >
< 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 >
< a id = "__codelineno-14-9" name = "__codelineno-14-9" href = "#__codelineno-14-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝二：从 start 开始遍历，避免生成重复子集< / 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 = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > start< / 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-14-11" name = "__codelineno-14-11" href = "#__codelineno-14-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝一：若子集和超过 target ，则直接结束循环< / span >
< a id = "__codelineno-14-12" name = "__codelineno-14-12" href = "#__codelineno-14-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 这是因为数组已排序，后边元素更大，子集和一定超过 target< / 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 = "p" > (< / span > < span class = "n" > target< / 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 = "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 = "p" > {< / span >
< a id = "__codelineno-14-14" name = "__codelineno-14-14" href = "#__codelineno-14-14" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-14-15" name = "__codelineno-14-15" href = "#__codelineno-14-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-14-16" name = "__codelineno-14-16" href = "#__codelineno-14-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新 target, start< / span >
< a id = "__codelineno-14-17" name = "__codelineno-14-17" href = "#__codelineno-14-17" > < / 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" > choices< / span > < span class = "o" > [< / span > < span class = "n" > i< / span > < span class = "o" > ]< / span > < span class = "p" > );< / span >
< a id = "__codelineno-14-18" name = "__codelineno-14-18" href = "#__codelineno-14-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-14-19" name = "__codelineno-14-19" href = "#__codelineno-14-19" > < / 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" > target< / 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 > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-14-20" name = "__codelineno-14-20" href = "#__codelineno-14-20" > < / 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-14-21" name = "__codelineno-14-21" href = "#__codelineno-14-21" > < / 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-14-22" name = "__codelineno-14-22" href = "#__codelineno-14-22" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-14-23" name = "__codelineno-14-23" href = "#__codelineno-14-23" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-14-24" name = "__codelineno-14-24" href = "#__codelineno-14-24" > < / a >
< a id = "__codelineno-14-25" name = "__codelineno-14-25" href = "#__codelineno-14-25" > < / a > < span class = "cm" > /* 求解子集和 I */< / span >
< a id = "__codelineno-14-26" name = "__codelineno-14-26" href = "#__codelineno-14-26" > < / 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" > subsetSumI< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "o" > []< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > target< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-14-27" name = "__codelineno-14-27" href = "#__codelineno-14-27" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > ArrayList< / span > < span class = "o" > < > < / span > < span class = "p" > ();< / span > < span class = "w" > < / span > < span class = "c1" > // 状态（子集）< / span >
< a id = "__codelineno-14-28" name = "__codelineno-14-28" href = "#__codelineno-14-28" > < / a > < span class = "w" > < / span > < span class = "n" > Arrays< / span > < span class = "p" > .< / span > < span class = "na" > sort< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 对 nums 进行排序< / span >
< a id = "__codelineno-14-29" name = "__codelineno-14-29" href = "#__codelineno-14-29" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > start< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 遍历起始点< / span >
< a id = "__codelineno-14-30" name = "__codelineno-14-30" href = "#__codelineno-14-30" > < / 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 = "p" > ();< / span > < span class = "w" > < / span > < span class = "c1" > // 结果列表（子集列表）< / span >
< a id = "__codelineno-14-31" name = "__codelineno-14-31" href = "#__codelineno-14-31" > < / 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" > target< / 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" > start< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / 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 = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-14-33" name = "__codelineno-14-33" href = "#__codelineno-14-33" > < / a > < span class = "p" > }< / span >
2023-06-21 02:55:52 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-09-04 03:17:06 +08:00
< div class = "highlight" > < span class = "filename" > subset_sum_i.cs< / 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：子集和 I */< / span >
< a id = "__codelineno-15-2" name = "__codelineno-15-2" href = "#__codelineno-15-2" > < / 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 = "w" > < / span > < span class = "n" > target< / 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" > int< / span > < span class = "w" > < / span > < span class = "n" > start< / 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 >
2023-07-26 10:57:52 +08:00
< a id = "__codelineno-15-3" name = "__codelineno-15-3" href = "#__codelineno-15-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子集和等于 target 时，记录解< / span >
2023-09-04 03:17:06 +08:00
< 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 = "n" > target< / 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 = "p" > {< / span >
< a id = "__codelineno-15-5" name = "__codelineno-15-5" href = "#__codelineno-15-5" > < / 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-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 = "c1" > // 剪枝二：从 start 开始遍历，避免生成重复子集< / span >
< a id = "__codelineno-15-10" name = "__codelineno-15-10" href = "#__codelineno-15-10" > < / 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 = "n" > start< / 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-15-11" name = "__codelineno-15-11" href = "#__codelineno-15-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝一：若子集和超过 target ，则直接结束循环< / span >
< a id = "__codelineno-15-12" name = "__codelineno-15-12" href = "#__codelineno-15-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 这是因为数组已排序，后边元素更大，子集和一定超过 target< / span >
< a id = "__codelineno-15-13" name = "__codelineno-15-13" href = "#__codelineno-15-13" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > target< / 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 > < 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 = "p" > {< / span >
< a id = "__codelineno-15-14" name = "__codelineno-15-14" href = "#__codelineno-15-14" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-15-15" name = "__codelineno-15-15" href = "#__codelineno-15-15" > < / a > < span class = "w" > < / 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 = "c1" > // 尝试：做出选择，更新 target, start< / span >
< a id = "__codelineno-15-17" name = "__codelineno-15-17" href = "#__codelineno-15-17" > < / 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" > choices< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]);< / span >
< a id = "__codelineno-15-18" name = "__codelineno-15-18" href = "#__codelineno-15-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-15-19" name = "__codelineno-15-19" href = "#__codelineno-15-19" > < / 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" > target< / 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 > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-15-20" name = "__codelineno-15-20" href = "#__codelineno-15-20" > < / 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-15-21" name = "__codelineno-15-21" href = "#__codelineno-15-21" > < / 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-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 = "p" > }< / span >
< a id = "__codelineno-15-24" name = "__codelineno-15-24" href = "#__codelineno-15-24" > < / a >
< a id = "__codelineno-15-25" name = "__codelineno-15-25" href = "#__codelineno-15-25" > < / a > < span class = "cm" > /* 求解子集和 I */< / span >
< a id = "__codelineno-15-26" name = "__codelineno-15-26" href = "#__codelineno-15-26" > < / 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" > subsetSumI< / 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 = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > target< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-15-27" name = "__codelineno-15-27" href = "#__codelineno-15-27" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "p" > ();< / span > < span class = "w" > < / span > < span class = "c1" > // 状态（子集）< / span >
< a id = "__codelineno-15-28" name = "__codelineno-15-28" href = "#__codelineno-15-28" > < / a > < span class = "w" > < / span > < span class = "n" > Array< / span > < span class = "p" > .< / span > < span class = "n" > Sort< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 对 nums 进行排序< / span >
< a id = "__codelineno-15-29" name = "__codelineno-15-29" href = "#__codelineno-15-29" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > start< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 遍历起始点< / span >
< a id = "__codelineno-15-30" name = "__codelineno-15-30" href = "#__codelineno-15-30" > < / 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 > < span class = "w" > < / span > < span class = "c1" > // 结果列表（子集列表）< / span >
< a id = "__codelineno-15-31" name = "__codelineno-15-31" href = "#__codelineno-15-31" > < / 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" > target< / 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" > start< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-15-32" name = "__codelineno-15-32" href = "#__codelineno-15-32" > < / 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-15-33" name = "__codelineno-15-33" href = "#__codelineno-15-33" > < / 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" > subset_sum_i.go< / 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：子集和 I */< / span >
< a id = "__codelineno-16-2" name = "__codelineno-16-2" href = "#__codelineno-16-2" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > backtrackSubsetSumI< / span > < span class = "p" > (< / span > < span class = "nx" > start< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > target< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "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" > 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-16-3" name = "__codelineno-16-3" href = "#__codelineno-16-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子集和等于 target 时，记录解< / span >
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< a id = "__codelineno-16-4" name = "__codelineno-16-4" href = "#__codelineno-16-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > target< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-16-5" name = "__codelineno-16-5" href = "#__codelineno-16-5" > < / 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-16-6" name = "__codelineno-16-6" href = "#__codelineno-16-6" > < / 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-16-7" name = "__codelineno-16-7" href = "#__codelineno-16-7" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span >
< a id = "__codelineno-16-8" name = "__codelineno-16-8" href = "#__codelineno-16-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-16-9" name = "__codelineno-16-9" href = "#__codelineno-16-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-16-10" name = "__codelineno-16-10" href = "#__codelineno-16-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝二：从 start 开始遍历，避免生成重复子集< / span >
< a id = "__codelineno-16-11" name = "__codelineno-16-11" href = "#__codelineno-16-11" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > start< / 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-16-12" name = "__codelineno-16-12" href = "#__codelineno-16-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝一：若子集和超过 target ，则直接结束循环< / span >
< a id = "__codelineno-16-13" name = "__codelineno-16-13" href = "#__codelineno-16-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 这是因为数组已排序，后边元素更大，子集和一定超过 target< / span >
< a id = "__codelineno-16-14" name = "__codelineno-16-14" href = "#__codelineno-16-14" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > target< / span > < span class = "o" > -< / 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 > < span class = "w" > < / span > < span class = "p" > < < / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "w" > < / 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 = "k" > break< / span >
< a id = "__codelineno-16-16" name = "__codelineno-16-16" href = "#__codelineno-16-16" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-16-17" name = "__codelineno-16-17" href = "#__codelineno-16-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新 target, start< / span >
< a id = "__codelineno-16-18" name = "__codelineno-16-18" href = "#__codelineno-16-18" > < / 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 = "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-16-19" name = "__codelineno-16-19" href = "#__codelineno-16-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-16-20" name = "__codelineno-16-20" href = "#__codelineno-16-20" > < / a > < span class = "w" > < / span > < span class = "nx" > backtrackSubsetSumI< / span > < span class = "p" > (< / span > < span class = "nx" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > target< / span > < span class = "o" > -< / 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 > < span class = "w" > < / 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" > res< / 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 = "c1" > // 回退：撤销选择，恢复到之前的状态< / span >
< a id = "__codelineno-16-22" name = "__codelineno-16-22" href = "#__codelineno-16-22" > < / 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-16-23" name = "__codelineno-16-23" href = "#__codelineno-16-23" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-16-24" name = "__codelineno-16-24" href = "#__codelineno-16-24" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-16-25" name = "__codelineno-16-25" href = "#__codelineno-16-25" > < / a >
< a id = "__codelineno-16-26" name = "__codelineno-16-26" href = "#__codelineno-16-26" > < / a > < span class = "cm" > /* 求解子集和 I */< / span >
< a id = "__codelineno-16-27" name = "__codelineno-16-27" href = "#__codelineno-16-27" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > subsetSumI< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "w" > < / span > < span class = "p" > []< / span > < span class = "kt" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > target< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > [][]< / span > < span class = "kt" > int< / span > < 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 = "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 > < span class = "w" > < / span > < span class = "c1" > // 状态（子集）< / span >
< a id = "__codelineno-16-29" name = "__codelineno-16-29" href = "#__codelineno-16-29" > < / a > < span class = "w" > < / span > < span class = "nx" > sort< / span > < span class = "p" > .< / span > < span class = "nx" > Ints< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "c1" > // 对 nums 进行排序< / span >
< a id = "__codelineno-16-30" name = "__codelineno-16-30" href = "#__codelineno-16-30" > < / a > < span class = "w" > < / span > < span class = "nx" > start< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "w" > < / span > < span class = "c1" > // 遍历起始点< / span >
< a id = "__codelineno-16-31" name = "__codelineno-16-31" href = "#__codelineno-16-31" > < / 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 > < span class = "w" > < / span > < span class = "c1" > // 结果列表（子集列表）< / span >
< a id = "__codelineno-16-32" name = "__codelineno-16-32" href = "#__codelineno-16-32" > < / a > < span class = "w" > < / span > < span class = "nx" > backtrackSubsetSumI< / span > < span class = "p" > (< / span > < span class = "nx" > start< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > target< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "nx" > nums< / 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-16-33" name = "__codelineno-16-33" href = "#__codelineno-16-33" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span >
< a id = "__codelineno-16-34" name = "__codelineno-16-34" href = "#__codelineno-16-34" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-09-04 03:17:06 +08:00
< div class = "highlight" > < span class = "filename" > subset_sum_i.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-17-1" name = "__codelineno-17-1" href = "#__codelineno-17-1" > < / a > < span class = "cm" > /* 回溯算法：子集和 I */< / span >
< a id = "__codelineno-17-2" name = "__codelineno-17-2" href = "#__codelineno-17-2" > < / 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" > target< / 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" > start< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / 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-17-3" name = "__codelineno-17-3" href = "#__codelineno-17-3" > < / a > < span class = "c1" > // 子集和等于 target 时，记录解< / span >
< a id = "__codelineno-17-4" name = "__codelineno-17-4" href = "#__codelineno-17-4" > < / a > < span class = "k" > if< / span > < span class = "n" > target< / span > < span class = "p" > ==< / span > < span class = "mi" > 0< / span > < span class = "p" > {< / span >
< a id = "__codelineno-17-5" name = "__codelineno-17-5" href = "#__codelineno-17-5" > < / 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-17-6" name = "__codelineno-17-6" href = "#__codelineno-17-6" > < / a > < span class = "k" > return< / span >
< a id = "__codelineno-17-7" name = "__codelineno-17-7" href = "#__codelineno-17-7" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-17-8" name = "__codelineno-17-8" href = "#__codelineno-17-8" > < / a > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-17-9" name = "__codelineno-17-9" href = "#__codelineno-17-9" > < / a > < span class = "c1" > // 剪枝二：从 start 开始遍历，避免生成重复子集< / span >
< a id = "__codelineno-17-10" name = "__codelineno-17-10" href = "#__codelineno-17-10" > < / a > < span class = "k" > for< / span > < span class = "n" > i< / span > < span class = "k" > in< / span > < span class = "bp" > stride< / span > < span class = "p" > (< / span > < span class = "n" > from< / span > < span class = "p" > :< / span > < span class = "n" > start< / span > < span class = "p" > ,< / span > < span class = "n" > to< / span > < span class = "p" > :< / span > < span class = "n" > choices< / span > < span class = "p" > .< / span > < span class = "bp" > count< / span > < span class = "p" > ,< / span > < span class = "n" > by< / span > < span class = "p" > :< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "p" > {< / span >
< a id = "__codelineno-17-11" name = "__codelineno-17-11" href = "#__codelineno-17-11" > < / a > < span class = "c1" > // 剪枝一：若子集和超过 target ，则直接结束循环< / span >
< a id = "__codelineno-17-12" name = "__codelineno-17-12" href = "#__codelineno-17-12" > < / a > < span class = "c1" > // 这是因为数组已排序，后边元素更大，子集和一定超过 target< / span >
< a id = "__codelineno-17-13" name = "__codelineno-17-13" href = "#__codelineno-17-13" > < / a > < span class = "k" > if< / span > < span class = "n" > target< / span > < span class = "o" > -< / span > < span class = "n" > choices< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "o" > < < / span > < span class = "mi" > 0< / span > < span class = "p" > {< / span >
< a id = "__codelineno-17-14" name = "__codelineno-17-14" href = "#__codelineno-17-14" > < / a > < span class = "k" > break< / span >
< a id = "__codelineno-17-15" name = "__codelineno-17-15" href = "#__codelineno-17-15" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-17-16" name = "__codelineno-17-16" href = "#__codelineno-17-16" > < / a > < span class = "c1" > // 尝试：做出选择，更新 target, start< / span >
< a id = "__codelineno-17-17" name = "__codelineno-17-17" href = "#__codelineno-17-17" > < / a > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > choices< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ])< / span >
< a id = "__codelineno-17-18" name = "__codelineno-17-18" href = "#__codelineno-17-18" > < / a > < span class = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-17-19" name = "__codelineno-17-19" href = "#__codelineno-17-19" > < / 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" > target< / span > < span class = "p" > :< / span > < span class = "n" > target< / span > < span class = "o" > -< / span > < span class = "n" > choices< / span > < span class = "p" > [< / span > < span class = "n" > i< / 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" > start< / span > < span class = "p" > :< / span > < span class = "n" > i< / 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-17-20" name = "__codelineno-17-20" href = "#__codelineno-17-20" > < / a > < span class = "c1" > // 回退：撤销选择，恢复到之前的状态< / span >
< a id = "__codelineno-17-21" name = "__codelineno-17-21" href = "#__codelineno-17-21" > < / a > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "bp" > removeLast< / span > < span class = "p" > ()< / span >
< a id = "__codelineno-17-22" name = "__codelineno-17-22" href = "#__codelineno-17-22" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-17-23" name = "__codelineno-17-23" href = "#__codelineno-17-23" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-17-24" name = "__codelineno-17-24" href = "#__codelineno-17-24" > < / a >
< a id = "__codelineno-17-25" name = "__codelineno-17-25" href = "#__codelineno-17-25" > < / a > < span class = "cm" > /* 求解子集和 I */< / span >
< a id = "__codelineno-17-26" name = "__codelineno-17-26" href = "#__codelineno-17-26" > < / a > < span class = "kd" > func< / span > < span class = "nf" > subsetSumI< / 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 = "n" > target< / 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-17-27" name = "__codelineno-17-27" href = "#__codelineno-17-27" > < / 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 > < span class = "c1" > // 状态（子集）< / span >
< a id = "__codelineno-17-28" name = "__codelineno-17-28" href = "#__codelineno-17-28" > < / a > < span class = "kd" > let< / span > < span class = "nv" > nums< / span > < span class = "p" > =< / span > < span class = "n" > nums< / span > < span class = "p" > .< / span > < span class = "bp" > sorted< / span > < span class = "p" > ()< / span > < span class = "c1" > // 对 nums 进行排序< / span >
< a id = "__codelineno-17-29" name = "__codelineno-17-29" href = "#__codelineno-17-29" > < / a > < span class = "kd" > let< / span > < span class = "nv" > start< / span > < span class = "p" > =< / span > < span class = "mi" > 0< / span > < span class = "c1" > // 遍历起始点< / span >
< a id = "__codelineno-17-30" name = "__codelineno-17-30" href = "#__codelineno-17-30" > < / 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 > < span class = "c1" > // 结果列表（子集列表）< / span >
< a id = "__codelineno-17-31" name = "__codelineno-17-31" href = "#__codelineno-17-31" > < / 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" > target< / span > < span class = "p" > :< / span > < span class = "n" > target< / 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" > start< / span > < span class = "p" > :< / span > < span class = "n" > start< / 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-17-32" name = "__codelineno-17-32" href = "#__codelineno-17-32" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
< a id = "__codelineno-17-33" name = "__codelineno-17-33" href = "#__codelineno-17-33" > < / a > < span class = "p" > }< / span >
2023-06-21 02:55:52 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-09-04 03:17:06 +08:00
< div class = "highlight" > < span class = "filename" > subset_sum_i.js< / 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：子集和 I */< / span >
< a id = "__codelineno-18-2" name = "__codelineno-18-2" href = "#__codelineno-18-2" > < / 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" > target< / 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" > start< / 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 >
2023-07-31 03:27:17 +08:00
< a id = "__codelineno-18-3" name = "__codelineno-18-3" href = "#__codelineno-18-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子集和等于 target 时，记录解< / span >
2023-09-04 03:17:06 +08:00
< 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 = "nx" > target< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-18-5" name = "__codelineno-18-5" href = "#__codelineno-18-5" > < / 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-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 = "c1" > // 剪枝二：从 start 开始遍历，避免生成重复子集< / 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 = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > start< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "nx" > choices< / span > < span class = "p" > .< / span > < span class = "nx" > length< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-18-11" name = "__codelineno-18-11" href = "#__codelineno-18-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝一：若子集和超过 target ，则直接结束循环< / span >
< a id = "__codelineno-18-12" name = "__codelineno-18-12" href = "#__codelineno-18-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 这是因为数组已排序，后边元素更大，子集和一定超过 target< / 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 = "nx" > target< / 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" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-18-14" name = "__codelineno-18-14" href = "#__codelineno-18-14" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-18-15" name = "__codelineno-18-15" href = "#__codelineno-18-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-18-16" name = "__codelineno-18-16" href = "#__codelineno-18-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新 target, start< / span >
< a id = "__codelineno-18-17" name = "__codelineno-18-17" href = "#__codelineno-18-17" > < / 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" > choices< / span > < span class = "p" > [< / span > < span class = "nx" > i< / 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 = "nx" > backtrack< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > target< / 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" > i< / 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" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > 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 = "nx" > state< / span > < span class = "p" > .< / span > < span class = "nx" > pop< / 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 = "p" > }< / span >
< a id = "__codelineno-18-23" name = "__codelineno-18-23" href = "#__codelineno-18-23" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-18-24" name = "__codelineno-18-24" href = "#__codelineno-18-24" > < / a >
< a id = "__codelineno-18-25" name = "__codelineno-18-25" href = "#__codelineno-18-25" > < / a > < span class = "cm" > /* 求解子集和 I */< / span >
< a id = "__codelineno-18-26" name = "__codelineno-18-26" href = "#__codelineno-18-26" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > subsetSumI< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > target< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-18-27" name = "__codelineno-18-27" href = "#__codelineno-18-27" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [];< / span > < span class = "w" > < / span > < span class = "c1" > // 状态（子集）< / span >
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< a id = "__codelineno-18-28" name = "__codelineno-18-28" href = "#__codelineno-18-28" > < / a > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "p" > .< / span > < span class = "nx" > sort< / span > < span class = "p" > ((< / span > < span class = "nx" > a< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > b< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > => < / span > < span class = "w" > < / span > < span class = "nx" > a< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "nx" > b< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 对 nums 进行排序< / span >
2023-09-04 03:17:06 +08:00
< a id = "__codelineno-18-29" name = "__codelineno-18-29" href = "#__codelineno-18-29" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > start< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 遍历起始点< / span >
< a id = "__codelineno-18-30" name = "__codelineno-18-30" href = "#__codelineno-18-30" > < / 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 > < span class = "w" > < / span > < span class = "c1" > // 结果列表（子集列表）< / span >
< a id = "__codelineno-18-31" name = "__codelineno-18-31" href = "#__codelineno-18-31" > < / 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" > target< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > start< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-18-32" name = "__codelineno-18-32" href = "#__codelineno-18-32" > < / 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-18-33" name = "__codelineno-18-33" href = "#__codelineno-18-33" > < / 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" > subset_sum_i.ts< / 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：子集和 I */< / span >
< a id = "__codelineno-19-2" name = "__codelineno-19-2" href = "#__codelineno-19-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > (< / span >
< a id = "__codelineno-19-3" name = "__codelineno-19-3" href = "#__codelineno-19-3" > < / 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-19-4" name = "__codelineno-19-4" href = "#__codelineno-19-4" > < / a > < span class = "w" > < / span > < span class = "nx" > target< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-19-5" name = "__codelineno-19-5" href = "#__codelineno-19-5" > < / 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-19-6" name = "__codelineno-19-6" href = "#__codelineno-19-6" > < / a > < span class = "w" > < / span > < span class = "nx" > start< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-19-7" name = "__codelineno-19-7" href = "#__codelineno-19-7" > < / 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-19-8" name = "__codelineno-19-8" href = "#__codelineno-19-8" > < / 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-19-9" name = "__codelineno-19-9" href = "#__codelineno-19-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子集和等于 target 时，记录解< / span >
< a id = "__codelineno-19-10" name = "__codelineno-19-10" href = "#__codelineno-19-10" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > target< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-19-11" name = "__codelineno-19-11" href = "#__codelineno-19-11" > < / 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-19-12" name = "__codelineno-19-12" href = "#__codelineno-19-12" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-19-13" name = "__codelineno-19-13" href = "#__codelineno-19-13" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-19-14" name = "__codelineno-19-14" href = "#__codelineno-19-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-19-15" name = "__codelineno-19-15" href = "#__codelineno-19-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝二：从 start 开始遍历，避免生成重复子集< / span >
< a id = "__codelineno-19-16" name = "__codelineno-19-16" href = "#__codelineno-19-16" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > start< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "nx" > choices< / span > < span class = "p" > .< / span > < span class = "nx" > length< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-19-17" name = "__codelineno-19-17" href = "#__codelineno-19-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝一：若子集和超过 target ，则直接结束循环< / span >
< a id = "__codelineno-19-18" name = "__codelineno-19-18" href = "#__codelineno-19-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 这是因为数组已排序，后边元素更大，子集和一定超过 target< / span >
< a id = "__codelineno-19-19" name = "__codelineno-19-19" href = "#__codelineno-19-19" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > target< / 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" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-19-20" name = "__codelineno-19-20" href = "#__codelineno-19-20" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-19-21" name = "__codelineno-19-21" href = "#__codelineno-19-21" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-19-22" name = "__codelineno-19-22" href = "#__codelineno-19-22" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新 target, start< / span >
< a id = "__codelineno-19-23" name = "__codelineno-19-23" href = "#__codelineno-19-23" > < / 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" > choices< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ]);< / span >
< a id = "__codelineno-19-24" name = "__codelineno-19-24" href = "#__codelineno-19-24" > < / a > < span class = "w" > < / span > < span class = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-19-25" name = "__codelineno-19-25" href = "#__codelineno-19-25" > < / 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" > target< / 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" > i< / 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" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-19-26" name = "__codelineno-19-26" href = "#__codelineno-19-26" > < / 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-19-27" name = "__codelineno-19-27" href = "#__codelineno-19-27" > < / 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-19-28" name = "__codelineno-19-28" href = "#__codelineno-19-28" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-19-29" name = "__codelineno-19-29" href = "#__codelineno-19-29" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-19-30" name = "__codelineno-19-30" href = "#__codelineno-19-30" > < / a >
< a id = "__codelineno-19-31" name = "__codelineno-19-31" href = "#__codelineno-19-31" > < / a > < span class = "cm" > /* 求解子集和 I */< / span >
< a id = "__codelineno-19-32" name = "__codelineno-19-32" href = "#__codelineno-19-32" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > subsetSumI< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > [],< / span > < span class = "w" > < / span > < span class = "nx" > target< / 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-19-33" name = "__codelineno-19-33" href = "#__codelineno-19-33" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [];< / span > < span class = "w" > < / span > < span class = "c1" > // 状态（子集）< / span >
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< a id = "__codelineno-19-34" name = "__codelineno-19-34" href = "#__codelineno-19-34" > < / a > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "p" > .< / span > < span class = "nx" > sort< / span > < span class = "p" > ((< / span > < span class = "nx" > a< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > b< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > => < / span > < span class = "w" > < / span > < span class = "nx" > a< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "nx" > b< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 对 nums 进行排序< / span >
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< a id = "__codelineno-19-35" name = "__codelineno-19-35" href = "#__codelineno-19-35" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > start< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 遍历起始点< / span >
< a id = "__codelineno-19-36" name = "__codelineno-19-36" href = "#__codelineno-19-36" > < / 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 > < span class = "w" > < / span > < span class = "c1" > // 结果列表（子集列表）< / span >
< a id = "__codelineno-19-37" name = "__codelineno-19-37" href = "#__codelineno-19-37" > < / 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" > target< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > start< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-19-38" name = "__codelineno-19-38" href = "#__codelineno-19-38" > < / 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-19-39" name = "__codelineno-19-39" href = "#__codelineno-19-39" > < / 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" > subset_sum_i.dart< / span > < pre > < span > < / span > < code > < a id = "__codelineno-20-1" name = "__codelineno-20-1" href = "#__codelineno-20-1" > < / a > < span class = "cm" > /* 回溯算法：子集和 I */< / span >
< a id = "__codelineno-20-2" name = "__codelineno-20-2" href = "#__codelineno-20-2" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "n" > backtrack< / span > < span class = "p" > (< / span >
< a id = "__codelineno-20-3" name = "__codelineno-20-3" href = "#__codelineno-20-3" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-20-4" name = "__codelineno-20-4" href = "#__codelineno-20-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > target< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-20-5" name = "__codelineno-20-5" href = "#__codelineno-20-5" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-20-6" name = "__codelineno-20-6" href = "#__codelineno-20-6" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > start< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-20-7" name = "__codelineno-20-7" href = "#__codelineno-20-7" > < / a > < span class = "w" > < / span > < span class = "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 >
< a id = "__codelineno-20-8" name = "__codelineno-20-8" href = "#__codelineno-20-8" > < / a > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-20-9" name = "__codelineno-20-9" href = "#__codelineno-20-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子集和等于 target 时，记录解< / span >
< a id = "__codelineno-20-10" name = "__codelineno-20-10" href = "#__codelineno-20-10" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > target< / 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 = "p" > {< / span >
< a id = "__codelineno-20-11" name = "__codelineno-20-11" href = "#__codelineno-20-11" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > add< / span > < span class = "p" > (< / span > < span class = "n" > List< / span > < span class = "p" > .< / span > < span class = "n" > from< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-20-12" name = "__codelineno-20-12" href = "#__codelineno-20-12" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-20-13" name = "__codelineno-20-13" href = "#__codelineno-20-13" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-20-14" name = "__codelineno-20-14" href = "#__codelineno-20-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-20-15" name = "__codelineno-20-15" href = "#__codelineno-20-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝二：从 start 开始遍历，避免生成重复子集< / span >
< a id = "__codelineno-20-16" name = "__codelineno-20-16" href = "#__codelineno-20-16" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > start< / 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-20-17" name = "__codelineno-20-17" href = "#__codelineno-20-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝一：若子集和超过 target ，则直接结束循环< / span >
< a id = "__codelineno-20-18" name = "__codelineno-20-18" href = "#__codelineno-20-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 这是因为数组已排序，后边元素更大，子集和一定超过 target< / span >
< a id = "__codelineno-20-19" name = "__codelineno-20-19" href = "#__codelineno-20-19" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > target< / 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 > < 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 = "p" > {< / span >
< a id = "__codelineno-20-20" name = "__codelineno-20-20" href = "#__codelineno-20-20" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-20-21" name = "__codelineno-20-21" href = "#__codelineno-20-21" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-20-22" name = "__codelineno-20-22" href = "#__codelineno-20-22" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新 target, start< / span >
< a id = "__codelineno-20-23" name = "__codelineno-20-23" href = "#__codelineno-20-23" > < / 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" > choices< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]);< / span >
< a id = "__codelineno-20-24" name = "__codelineno-20-24" href = "#__codelineno-20-24" > < / a > < span class = "w" > < / span > < span class = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-20-25" name = "__codelineno-20-25" href = "#__codelineno-20-25" > < / 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" > target< / 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 > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-20-26" name = "__codelineno-20-26" href = "#__codelineno-20-26" > < / 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-20-27" name = "__codelineno-20-27" href = "#__codelineno-20-27" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > removeLast< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-20-28" name = "__codelineno-20-28" href = "#__codelineno-20-28" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-20-29" name = "__codelineno-20-29" href = "#__codelineno-20-29" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-20-30" name = "__codelineno-20-30" href = "#__codelineno-20-30" > < / a >
< a id = "__codelineno-20-31" name = "__codelineno-20-31" href = "#__codelineno-20-31" > < / a > < span class = "cm" > /* 求解子集和 I */< / span >
< a id = "__codelineno-20-32" name = "__codelineno-20-32" href = "#__codelineno-20-32" > < / 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" > subsetSumI< / 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" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > target< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-20-33" name = "__codelineno-20-33" href = "#__codelineno-20-33" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [];< / span > < span class = "w" > < / span > < span class = "c1" > // 状态（子集）< / span >
< a id = "__codelineno-20-34" name = "__codelineno-20-34" href = "#__codelineno-20-34" > < / a > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > .< / span > < span class = "n" > sort< / span > < span class = "p" > ();< / span > < span class = "w" > < / span > < span class = "c1" > // 对 nums 进行排序< / span >
< a id = "__codelineno-20-35" name = "__codelineno-20-35" href = "#__codelineno-20-35" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > start< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 遍历起始点< / span >
< a id = "__codelineno-20-36" name = "__codelineno-20-36" href = "#__codelineno-20-36" > < / 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 = "p" > [];< / span > < span class = "w" > < / span > < span class = "c1" > // 结果列表（子集列表）< / span >
< a id = "__codelineno-20-37" name = "__codelineno-20-37" href = "#__codelineno-20-37" > < / 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" > target< / 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" > start< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-20-38" name = "__codelineno-20-38" href = "#__codelineno-20-38" > < / 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-20-39" name = "__codelineno-20-39" href = "#__codelineno-20-39" > < / a > < span class = "p" > }< / span >
2023-06-21 02:55:52 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-09-04 03:17:06 +08:00
< div class = "highlight" > < span class = "filename" > subset_sum_i.rs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-21-1" name = "__codelineno-21-1" href = "#__codelineno-21-1" > < / a > < span class = "cm" > /* 回溯算法：子集和 I */< / span >
< a id = "__codelineno-21-2" name = "__codelineno-21-2" href = "#__codelineno-21-2" > < / a > < span class = "k" > fn< / span > < span class = "nf" > backtrack< / span > < span class = "p" > (< / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > state< / span > : < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "kt" > i32< / span > < span class = "o" > > < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > target< / span > : < span class = "kt" > i32< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > choices< / span > : < span class = "kp" > & < / span > < span class = "p" > [< / span > < span class = "kt" > i32< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "n" > start< / span > : < span class = "kt" > usize< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > : < span class = "kp" > & < / span > < span class = "nc" > mut< / span > < span class = "w" > < / span > < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "kt" > i32< / span > < span class = "o" > > > < / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-21-3" name = "__codelineno-21-3" href = "#__codelineno-21-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子集和等于 target 时，记录解< / span >
< a id = "__codelineno-21-4" name = "__codelineno-21-4" href = "#__codelineno-21-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "n" > target< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-21-5" name = "__codelineno-21-5" href = "#__codelineno-21-5" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > push< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > );< / span >
< a id = "__codelineno-21-6" name = "__codelineno-21-6" href = "#__codelineno-21-6" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-21-7" name = "__codelineno-21-7" href = "#__codelineno-21-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-21-8" name = "__codelineno-21-8" href = "#__codelineno-21-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-21-9" name = "__codelineno-21-9" href = "#__codelineno-21-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝二：从 start 开始遍历，避免生成重复子集< / span >
< a id = "__codelineno-21-10" name = "__codelineno-21-10" href = "#__codelineno-21-10" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "k" > in< / span > < span class = "w" > < / span > < span class = "n" > start< / span > < span class = "o" > ..< / span > < span class = "n" > choices< / span > < span class = "p" > .< / span > < span class = "n" > len< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-21-11" name = "__codelineno-21-11" href = "#__codelineno-21-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝一：若子集和超过 target ，则直接结束循环< / span >
< a id = "__codelineno-21-12" name = "__codelineno-21-12" href = "#__codelineno-21-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 这是因为数组已排序，后边元素更大，子集和一定超过 target< / span >
< a id = "__codelineno-21-13" name = "__codelineno-21-13" href = "#__codelineno-21-13" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "n" > target< / 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 > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-21-14" name = "__codelineno-21-14" href = "#__codelineno-21-14" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-21-15" name = "__codelineno-21-15" href = "#__codelineno-21-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-21-16" name = "__codelineno-21-16" href = "#__codelineno-21-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新 target, start< / span >
< a id = "__codelineno-21-17" name = "__codelineno-21-17" href = "#__codelineno-21-17" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > push< / span > < span class = "p" > (< / span > < span class = "n" > choices< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]);< / span >
< a id = "__codelineno-21-18" name = "__codelineno-21-18" href = "#__codelineno-21-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-21-19" name = "__codelineno-21-19" href = "#__codelineno-21-19" > < / 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 = "n" > clone< / span > < span class = "p" > (),< / span > < span class = "w" > < / span > < span class = "n" > target< / 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 > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-21-20" name = "__codelineno-21-20" href = "#__codelineno-21-20" > < / 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-21-21" name = "__codelineno-21-21" href = "#__codelineno-21-21" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > pop< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-21-22" name = "__codelineno-21-22" href = "#__codelineno-21-22" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-21-23" name = "__codelineno-21-23" href = "#__codelineno-21-23" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-21-24" name = "__codelineno-21-24" href = "#__codelineno-21-24" > < / a >
< a id = "__codelineno-21-25" name = "__codelineno-21-25" href = "#__codelineno-21-25" > < / a > < span class = "cm" > /* 求解子集和 I */< / span >
< a id = "__codelineno-21-26" name = "__codelineno-21-26" href = "#__codelineno-21-26" > < / a > < span class = "k" > fn< / span > < span class = "nf" > subset_sum_i< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > : < span class = "kp" > & < / span > < span class = "nc" > mut< / span > < span class = "w" > < / span > < span class = "p" > [< / span > < span class = "kt" > i32< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "n" > target< / span > : < span class = "kt" > i32< / span > < span class = "p" > )< / span > < span class = "w" > < / span > -> < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "kt" > i32< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-21-27" name = "__codelineno-21-27" href = "#__codelineno-21-27" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > Vec< / span > ::< span class = "n" > new< / span > < span class = "p" > ();< / span > < span class = "w" > < / span > < span class = "c1" > // 状态（子集）< / span >
< a id = "__codelineno-21-28" name = "__codelineno-21-28" href = "#__codelineno-21-28" > < / a > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > .< / span > < span class = "n" > sort< / span > < span class = "p" > ();< / span > < span class = "w" > < / span > < span class = "c1" > // 对 nums 进行排序< / span >
< a id = "__codelineno-21-29" name = "__codelineno-21-29" href = "#__codelineno-21-29" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "n" > start< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 遍历起始点< / span >
< a id = "__codelineno-21-30" name = "__codelineno-21-30" href = "#__codelineno-21-30" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > Vec< / span > ::< span class = "n" > new< / span > < span class = "p" > ();< / span > < span class = "w" > < / span > < span class = "c1" > // 结果列表（子集列表）< / span >
< a id = "__codelineno-21-31" name = "__codelineno-21-31" href = "#__codelineno-21-31" > < / 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" > target< / 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" > start< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-21-32" name = "__codelineno-21-32" href = "#__codelineno-21-32" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span >
< a id = "__codelineno-21-33" name = "__codelineno-21-33" href = "#__codelineno-21-33" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
2023-07-26 10:57:52 +08:00
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > subset_sum_i.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-22-1" name = "__codelineno-22-1" href = "#__codelineno-22-1" > < / a > < span class = "cm" > /* 回溯算法：子集和 I */< / span >
< a id = "__codelineno-22-2" name = "__codelineno-22-2" href = "#__codelineno-22-2" > < / 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 = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > target< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > start< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > vector< / 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-22-3" name = "__codelineno-22-3" href = "#__codelineno-22-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子集和等于 target 时，记录解< / span >
< a id = "__codelineno-22-4" name = "__codelineno-22-4" href = "#__codelineno-22-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > target< / 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 = "p" > {< / span >
< a id = "__codelineno-22-5" name = "__codelineno-22-5" href = "#__codelineno-22-5" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > tmpVector< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > newVector< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-22-6" name = "__codelineno-22-6" href = "#__codelineno-22-6" > < / a > < span class = "w" > < / span > < span class = "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" > state< / span > < span class = "o" > -> < / 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-22-7" name = "__codelineno-22-7" href = "#__codelineno-22-7" > < / a > < span class = "w" > < / span > < span class = "n" > vectorPushback< / span > < span class = "p" > (< / span > < span class = "n" > tmpVector< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "o" > -> < / span > < span class = "n" > data< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "k" > sizeof< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-22-8" name = "__codelineno-22-8" href = "#__codelineno-22-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-22-9" name = "__codelineno-22-9" href = "#__codelineno-22-9" > < / a > < span class = "w" > < / span > < span class = "n" > vectorPushback< / span > < span class = "p" > (< / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > tmpVector< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "k" > sizeof< / span > < span class = "p" > (< / span > < span class = "n" > vector< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-22-10" name = "__codelineno-22-10" href = "#__codelineno-22-10" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-22-11" name = "__codelineno-22-11" href = "#__codelineno-22-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-22-12" name = "__codelineno-22-12" href = "#__codelineno-22-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-22-13" name = "__codelineno-22-13" href = "#__codelineno-22-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝二：从 start 开始遍历，避免生成重复子集< / span >
< a id = "__codelineno-22-14" name = "__codelineno-22-14" href = "#__codelineno-22-14" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > start< / 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 = "o" > -> < / 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-22-15" name = "__codelineno-22-15" href = "#__codelineno-22-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：若子集和超过 target ，则跳过该选择< / span >
< a id = "__codelineno-22-16" name = "__codelineno-22-16" href = "#__codelineno-22-16" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > target< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > )(< / span > < span class = "n" > choices< / span > < span class = "o" > -> < / span > < span class = "n" > data< / 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 = "mi" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-22-17" name = "__codelineno-22-17" href = "#__codelineno-22-17" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-22-18" name = "__codelineno-22-18" href = "#__codelineno-22-18" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-22-19" name = "__codelineno-22-19" href = "#__codelineno-22-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新 target, start< / span >
< a id = "__codelineno-22-20" name = "__codelineno-22-20" href = "#__codelineno-22-20" > < / a > < span class = "w" > < / span > < span class = "n" > vectorPushback< / 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 = "o" > -> < / span > < span class = "n" > data< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "k" > sizeof< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-22-21" name = "__codelineno-22-21" href = "#__codelineno-22-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-22-22" name = "__codelineno-22-22" href = "#__codelineno-22-22" > < / 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" > target< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > )(< / span > < span class = "n" > choices< / span > < span class = "o" > -> < / span > < span class = "n" > data< / span > < span class = "p" > [< / span > < span class = "n" > i< / 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" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-22-23" name = "__codelineno-22-23" href = "#__codelineno-22-23" > < / 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-22-24" name = "__codelineno-22-24" href = "#__codelineno-22-24" > < / a > < span class = "w" > < / span > < span class = "n" > vectorPopback< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > );< / span >
< a id = "__codelineno-22-25" name = "__codelineno-22-25" href = "#__codelineno-22-25" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-22-26" name = "__codelineno-22-26" href = "#__codelineno-22-26" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-22-27" name = "__codelineno-22-27" href = "#__codelineno-22-27" > < / a >
< a id = "__codelineno-22-28" name = "__codelineno-22-28" href = "#__codelineno-22-28" > < / a > < span class = "cm" > /* 求解子集和 I */< / span >
< a id = "__codelineno-22-29" name = "__codelineno-22-29" href = "#__codelineno-22-29" > < / a > < span class = "n" > vector< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nf" > subsetSumI< / span > < span class = "p" > (< / span > < span class = "n" > vector< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > target< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-22-30" name = "__codelineno-22-30" href = "#__codelineno-22-30" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > state< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > newVector< / span > < span class = "p" > ();< / span > < span class = "w" > < / span > < span class = "c1" > // 状态（子集）< / span >
< a id = "__codelineno-22-31" name = "__codelineno-22-31" href = "#__codelineno-22-31" > < / a > < span class = "w" > < / span > < span class = "n" > qsort< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "o" > -> < / span > < span class = "n" > data< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "o" > -> < / span > < span class = "n" > size< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "k" > sizeof< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > ),< / span > < span class = "w" > < / span > < span class = "n" > comp< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 对 nums 进行排序< / span >
< a id = "__codelineno-22-32" name = "__codelineno-22-32" href = "#__codelineno-22-32" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > start< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 子集和< / span >
< a id = "__codelineno-22-33" name = "__codelineno-22-33" href = "#__codelineno-22-33" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > newVector< / span > < span class = "p" > ();< / span > < span class = "w" > < / span > < span class = "c1" > // 结果列表（子集列表）< / span >
< a id = "__codelineno-22-34" name = "__codelineno-22-34" href = "#__codelineno-22-34" > < / 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" > target< / 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" > start< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-22-35" name = "__codelineno-22-35" href = "#__codelineno-22-35" > < / 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-22-36" name = "__codelineno-22-36" href = "#__codelineno-22-36" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
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< div class = "highlight" > < span class = "filename" > subset_sum_i.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-23-1" name = "__codelineno-23-1" href = "#__codelineno-23-1" > < / 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-23-2" name = "__codelineno-23-2" href = "#__codelineno-23-2" > < / a >
< a id = "__codelineno-23-3" name = "__codelineno-23-3" href = "#__codelineno-23-3" > < / 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" > subsetSumI< / span > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
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< p > 如图 13-12 所示，为将数组 < span class = "arithmatex" > \([3, 4, 5]\)< / span > 和目标元素 < span class = "arithmatex" > \(9\)< / span > 输入到以上代码后的整体回溯过程。< / p >
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< p > < a class = "glightbox" href = "../subset_sum_problem.assets/subset_sum_i.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "子集和 I 回溯过程" src = "../subset_sum_problem.assets/subset_sum_i.png" / > < / a > < / p >
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< p align = "center" > 图 13-12 子集和 I 回溯过程 < / p >
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< h2 id = "1332" > 13.3.2 考虑重复元素的情况< a class = "headerlink" href = "#1332" title = "Permanent link" > ¶ < / a > < / h2 >
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< div class = "admonition question" >
< p class = "admonition-title" > Question< / p >
< p > 给定一个正整数数组 < code > nums< / code > 和一个目标正整数 < code > target< / code > ，请找出所有可能的组合，使得组合中的元素和等于 < code > target< / code > 。< strong > 给定数组可能包含重复元素，每个元素只可被选择一次< / strong > 。请以列表形式返回这些组合，列表中不应包含重复组合。< / p >
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< p > 相比于上题，< strong > 本题的输入数组可能包含重复元素< / strong > ，这引入了新的问题。例如，给定数组 < span class = "arithmatex" > \([4, \hat{4}, 5]\)< / span > 和目标元素 < span class = "arithmatex" > \(9\)< / span > ，则现有代码的输出结果为 < span class = "arithmatex" > \([4, 5], [\hat{4}, 5]\)< / span > ，出现了重复子集。< / p >
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< p > < strong > 造成这种重复的原因是相等元素在某轮中被多次选择< / strong > 。在图 13-13 中，第一轮共有三个选择，其中两个都为 < span class = "arithmatex" > \(4\)< / span > ，会产生两个重复的搜索分支，从而输出重复子集；同理，第二轮的两个 < span class = "arithmatex" > \(4\)< / span > 也会产生重复子集。< / p >
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< p > < a class = "glightbox" href = "../subset_sum_problem.assets/subset_sum_ii_repeat.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "相等元素导致的重复子集" src = "../subset_sum_problem.assets/subset_sum_ii_repeat.png" / > < / a > < / p >
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< p align = "center" > 图 13-13 相等元素导致的重复子集 < / p >
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< h3 id = "1_1" > 1. 相等元素剪枝< a class = "headerlink" href = "#1_1" title = "Permanent link" > ¶ < / a > < / h3 >
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< p > 为解决此问题，< strong > 我们需要限制相等元素在每一轮中只被选择一次< / strong > 。实现方式比较巧妙：由于数组是已排序的，因此相等元素都是相邻的。这意味着在某轮选择中，若当前元素与其左边元素相等，则说明它已经被选择过，因此直接跳过当前元素。< / p >
< p > 与此同时，< strong > 本题规定中的每个数组元素只能被选择一次< / strong > 。幸运的是，我们也可以利用变量 < code > start< / code > 来满足该约束：当做出选择 < span class = "arithmatex" > \(x_{i}\)< / span > 后，设定下一轮从索引 < span class = "arithmatex" > \(i + 1\)< / span > 开始向后遍历。这样即能去除重复子集，也能避免重复选择元素。< / p >
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< h3 id = "2_1" > 2. 代码实现< a class = "headerlink" href = "#2_1" title = "Permanent link" > ¶ < / a > < / h3 >
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< div class = "tabbed-set tabbed-alternate" data-tabs = "3:12" > < input checked = "checked" id = "__tabbed_3_1" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_2" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_3" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_4" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_5" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_6" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_7" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_8" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_9" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_10" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_11" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_12" name = "__tabbed_3" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_3_1" > Python< / label > < label for = "__tabbed_3_2" > C++< / label > < label for = "__tabbed_3_3" > Java< / label > < label for = "__tabbed_3_4" > C#< / label > < label for = "__tabbed_3_5" > Go< / label > < label for = "__tabbed_3_6" > Swift< / label > < label for = "__tabbed_3_7" > JS< / label > < label for = "__tabbed_3_8" > TS< / label > < label for = "__tabbed_3_9" > Dart< / label > < label for = "__tabbed_3_10" > Rust< / label > < label for = "__tabbed_3_11" > C< / label > < label for = "__tabbed_3_12" > Zig< / label > < / div >
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< div class = "highlight" > < span class = "filename" > subset_sum_ii.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-24-1" name = "__codelineno-24-1" href = "#__codelineno-24-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > backtrack< / span > < span class = "p" > (< / span >
< a id = "__codelineno-24-2" name = "__codelineno-24-2" href = "#__codelineno-24-2" > < / 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" > target< / 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" > start< / span > < span class = "p" > :< / span > < span class = "nb" > int< / 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-24-3" name = "__codelineno-24-3" href = "#__codelineno-24-3" > < / a > < span class = "p" > ):< / span >
< a id = "__codelineno-24-4" name = "__codelineno-24-4" href = "#__codelineno-24-4" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 回溯算法：子集和 II" " " < / span >
< a id = "__codelineno-24-5" name = "__codelineno-24-5" href = "#__codelineno-24-5" > < / a > < span class = "c1" > # 子集和等于 target 时，记录解< / span >
< a id = "__codelineno-24-6" name = "__codelineno-24-6" href = "#__codelineno-24-6" > < / a > < span class = "k" > if< / span > < span class = "n" > target< / span > < span class = "o" > ==< / span > < span class = "mi" > 0< / span > < span class = "p" > :< / span >
< a id = "__codelineno-24-7" name = "__codelineno-24-7" href = "#__codelineno-24-7" > < / 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-24-8" name = "__codelineno-24-8" href = "#__codelineno-24-8" > < / a > < span class = "k" > return< / span >
< a id = "__codelineno-24-9" name = "__codelineno-24-9" href = "#__codelineno-24-9" > < / a > < span class = "c1" > # 遍历所有选择< / span >
< a id = "__codelineno-24-10" name = "__codelineno-24-10" href = "#__codelineno-24-10" > < / a > < span class = "c1" > # 剪枝二：从 start 开始遍历，避免生成重复子集< / span >
< a id = "__codelineno-24-11" name = "__codelineno-24-11" href = "#__codelineno-24-11" > < / a > < span class = "c1" > # 剪枝三：从 start 开始遍历，避免重复选择同一元素< / span >
< a id = "__codelineno-24-12" name = "__codelineno-24-12" href = "#__codelineno-24-12" > < / a > < span class = "k" > for< / span > < span class = "n" > i< / span > < span class = "ow" > in< / span > < span class = "nb" > range< / span > < span class = "p" > (< / span > < span class = "n" > start< / span > < span class = "p" > ,< / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "n" > choices< / span > < span class = "p" > )):< / span >
< a id = "__codelineno-24-13" name = "__codelineno-24-13" href = "#__codelineno-24-13" > < / a > < span class = "c1" > # 剪枝一：若子集和超过 target ，则直接结束循环< / span >
< a id = "__codelineno-24-14" name = "__codelineno-24-14" href = "#__codelineno-24-14" > < / a > < span class = "c1" > # 这是因为数组已排序，后边元素更大，子集和一定超过 target< / span >
< a id = "__codelineno-24-15" name = "__codelineno-24-15" href = "#__codelineno-24-15" > < / a > < span class = "k" > if< / span > < span class = "n" > target< / span > < span class = "o" > -< / span > < span class = "n" > choices< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "o" > < < / span > < span class = "mi" > 0< / span > < span class = "p" > :< / span >
< a id = "__codelineno-24-16" name = "__codelineno-24-16" href = "#__codelineno-24-16" > < / a > < span class = "k" > break< / span >
< a id = "__codelineno-24-17" name = "__codelineno-24-17" href = "#__codelineno-24-17" > < / a > < span class = "c1" > # 剪枝四：如果该元素与左边元素相等，说明该搜索分支重复，直接跳过< / span >
< a id = "__codelineno-24-18" name = "__codelineno-24-18" href = "#__codelineno-24-18" > < / a > < span class = "k" > if< / span > < span class = "n" > i< / span > < span class = "o" > > < / span > < span class = "n" > start< / span > < span class = "ow" > and< / span > < span class = "n" > choices< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "o" > ==< / span > < span class = "n" > choices< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ]:< / span >
< a id = "__codelineno-24-19" name = "__codelineno-24-19" href = "#__codelineno-24-19" > < / a > < span class = "k" > continue< / span >
< a id = "__codelineno-24-20" name = "__codelineno-24-20" href = "#__codelineno-24-20" > < / a > < span class = "c1" > # 尝试：做出选择，更新 target, start< / span >
< a id = "__codelineno-24-21" name = "__codelineno-24-21" href = "#__codelineno-24-21" > < / a > < span class = "n" > state< / span > < span class = "o" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > choices< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ])< / span >
< a id = "__codelineno-24-22" name = "__codelineno-24-22" href = "#__codelineno-24-22" > < / a > < span class = "c1" > # 进行下一轮选择< / span >
< a id = "__codelineno-24-23" name = "__codelineno-24-23" href = "#__codelineno-24-23" > < / a > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "n" > target< / span > < span class = "o" > -< / span > < span class = "n" > choices< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ],< / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span > < span class = "n" > i< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "n" > res< / span > < span class = "p" > )< / span >
< a id = "__codelineno-24-24" name = "__codelineno-24-24" href = "#__codelineno-24-24" > < / a > < span class = "c1" > # 回退：撤销选择，恢复到之前的状态< / span >
< a id = "__codelineno-24-25" name = "__codelineno-24-25" href = "#__codelineno-24-25" > < / a > < span class = "n" > state< / span > < span class = "o" > .< / span > < span class = "n" > pop< / span > < span class = "p" > ()< / span >
< a id = "__codelineno-24-26" name = "__codelineno-24-26" href = "#__codelineno-24-26" > < / a >
< a id = "__codelineno-24-27" name = "__codelineno-24-27" href = "#__codelineno-24-27" > < / a > < span class = "k" > def< / span > < span class = "nf" > subset_sum_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 = "n" > target< / 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-24-28" name = "__codelineno-24-28" href = "#__codelineno-24-28" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 求解子集和 II" " " < / span >
< a id = "__codelineno-24-29" name = "__codelineno-24-29" href = "#__codelineno-24-29" > < / a > < span class = "n" > state< / span > < span class = "o" > =< / span > < span class = "p" > []< / span > < span class = "c1" > # 状态（子集）< / span >
< a id = "__codelineno-24-30" name = "__codelineno-24-30" href = "#__codelineno-24-30" > < / a > < span class = "n" > nums< / span > < span class = "o" > .< / span > < span class = "n" > sort< / span > < span class = "p" > ()< / span > < span class = "c1" > # 对 nums 进行排序< / span >
< a id = "__codelineno-24-31" name = "__codelineno-24-31" href = "#__codelineno-24-31" > < / a > < span class = "n" > start< / span > < span class = "o" > =< / span > < span class = "mi" > 0< / span > < span class = "c1" > # 遍历起始点< / span >
< a id = "__codelineno-24-32" name = "__codelineno-24-32" href = "#__codelineno-24-32" > < / a > < span class = "n" > res< / span > < span class = "o" > =< / span > < span class = "p" > []< / span > < span class = "c1" > # 结果列表（子集列表）< / span >
< a id = "__codelineno-24-33" name = "__codelineno-24-33" href = "#__codelineno-24-33" > < / a > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "n" > target< / span > < span class = "p" > ,< / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "n" > start< / span > < span class = "p" > ,< / span > < span class = "n" > res< / span > < span class = "p" > )< / span >
< a id = "__codelineno-24-34" name = "__codelineno-24-34" href = "#__codelineno-24-34" > < / 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" > subset_sum_ii.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-25-1" name = "__codelineno-25-1" href = "#__codelineno-25-1" > < / a > < span class = "cm" > /* 回溯算法：子集和 II */< / span >
< a id = "__codelineno-25-2" name = "__codelineno-25-2" href = "#__codelineno-25-2" > < / 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 = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > target< / span > < span class = "p" > ,< / 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 = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > start< / 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-25-3" name = "__codelineno-25-3" href = "#__codelineno-25-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子集和等于 target 时，记录解< / span >
< a id = "__codelineno-25-4" name = "__codelineno-25-4" href = "#__codelineno-25-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > target< / 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 = "p" > {< / span >
< a id = "__codelineno-25-5" name = "__codelineno-25-5" href = "#__codelineno-25-5" > < / 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-25-6" name = "__codelineno-25-6" href = "#__codelineno-25-6" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-25-7" name = "__codelineno-25-7" href = "#__codelineno-25-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-25-8" name = "__codelineno-25-8" href = "#__codelineno-25-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-25-9" name = "__codelineno-25-9" href = "#__codelineno-25-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝二：从 start 开始遍历，避免生成重复子集< / span >
< a id = "__codelineno-25-10" name = "__codelineno-25-10" href = "#__codelineno-25-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝三：从 start 开始遍历，避免重复选择同一元素< / span >
< a id = "__codelineno-25-11" name = "__codelineno-25-11" href = "#__codelineno-25-11" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > start< / 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-25-12" name = "__codelineno-25-12" href = "#__codelineno-25-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝一：若子集和超过 target ，则直接结束循环< / span >
< a id = "__codelineno-25-13" name = "__codelineno-25-13" href = "#__codelineno-25-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 这是因为数组已排序，后边元素更大，子集和一定超过 target< / span >
< a id = "__codelineno-25-14" name = "__codelineno-25-14" href = "#__codelineno-25-14" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > target< / 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 > < 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 = "p" > {< / span >
< a id = "__codelineno-25-15" name = "__codelineno-25-15" href = "#__codelineno-25-15" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-25-16" name = "__codelineno-25-16" href = "#__codelineno-25-16" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-25-17" name = "__codelineno-25-17" href = "#__codelineno-25-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝四：如果该元素与左边元素相等，说明该搜索分支重复，直接跳过< / span >
< a id = "__codelineno-25-18" name = "__codelineno-25-18" href = "#__codelineno-25-18" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > start< / 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 > < 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 = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ])< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-25-19" name = "__codelineno-25-19" href = "#__codelineno-25-19" > < / a > < span class = "w" > < / span > < span class = "k" > continue< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-25-20" name = "__codelineno-25-20" href = "#__codelineno-25-20" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-25-21" name = "__codelineno-25-21" href = "#__codelineno-25-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新 target, start< / span >
< a id = "__codelineno-25-22" name = "__codelineno-25-22" href = "#__codelineno-25-22" > < / 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" > choices< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]);< / span >
< a id = "__codelineno-25-23" name = "__codelineno-25-23" href = "#__codelineno-25-23" > < / a > < span class = "w" > < / span > < span class = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-25-24" name = "__codelineno-25-24" href = "#__codelineno-25-24" > < / 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" > target< / 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 > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-25-25" name = "__codelineno-25-25" href = "#__codelineno-25-25" > < / 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-25-26" name = "__codelineno-25-26" href = "#__codelineno-25-26" > < / 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-25-27" name = "__codelineno-25-27" href = "#__codelineno-25-27" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-25-28" name = "__codelineno-25-28" href = "#__codelineno-25-28" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-25-29" name = "__codelineno-25-29" href = "#__codelineno-25-29" > < / a >
< a id = "__codelineno-25-30" name = "__codelineno-25-30" href = "#__codelineno-25-30" > < / a > < span class = "cm" > /* 求解子集和 II */< / span >
< a id = "__codelineno-25-31" name = "__codelineno-25-31" href = "#__codelineno-25-31" > < / 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" > subsetSumII< / span > < span class = "p" > (< / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > target< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-25-32" name = "__codelineno-25-32" href = "#__codelineno-25-32" > < / 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 > < span class = "w" > < / span > < span class = "c1" > // 状态（子集）< / span >
< a id = "__codelineno-25-33" name = "__codelineno-25-33" href = "#__codelineno-25-33" > < / a > < span class = "w" > < / span > < span class = "n" > sort< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > .< / span > < span class = "n" > begin< / span > < span class = "p" > (),< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > .< / span > < span class = "n" > end< / span > < span class = "p" > ());< / span > < span class = "w" > < / span > < span class = "c1" > // 对 nums 进行排序< / span >
< a id = "__codelineno-25-34" name = "__codelineno-25-34" href = "#__codelineno-25-34" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > start< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 遍历起始点< / span >
< a id = "__codelineno-25-35" name = "__codelineno-25-35" href = "#__codelineno-25-35" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "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 = "c1" > // 结果列表（子集列表）< / span >
< a id = "__codelineno-25-36" name = "__codelineno-25-36" href = "#__codelineno-25-36" > < / 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" > target< / 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" > start< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-25-37" name = "__codelineno-25-37" href = "#__codelineno-25-37" > < / 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-25-38" name = "__codelineno-25-38" href = "#__codelineno-25-38" > < / a > < span class = "p" > }< / span >
2023-06-21 02:55:52 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-09-04 03:17:06 +08:00
< div class = "highlight" > < span class = "filename" > subset_sum_ii.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-26-1" name = "__codelineno-26-1" href = "#__codelineno-26-1" > < / a > < span class = "cm" > /* 回溯算法：子集和 II */< / span >
< a id = "__codelineno-26-2" name = "__codelineno-26-2" href = "#__codelineno-26-2" > < / 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 = "w" > < / span > < span class = "n" > target< / 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" > int< / span > < span class = "w" > < / span > < span class = "n" > start< / 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-26-3" name = "__codelineno-26-3" href = "#__codelineno-26-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子集和等于 target 时，记录解< / span >
< a id = "__codelineno-26-4" name = "__codelineno-26-4" href = "#__codelineno-26-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > target< / 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 = "p" > {< / span >
< a id = "__codelineno-26-5" name = "__codelineno-26-5" href = "#__codelineno-26-5" > < / 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 = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-26-6" name = "__codelineno-26-6" href = "#__codelineno-26-6" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-26-7" name = "__codelineno-26-7" href = "#__codelineno-26-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-26-8" name = "__codelineno-26-8" href = "#__codelineno-26-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-26-9" name = "__codelineno-26-9" href = "#__codelineno-26-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝二：从 start 开始遍历，避免生成重复子集< / span >
< a id = "__codelineno-26-10" name = "__codelineno-26-10" href = "#__codelineno-26-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝三：从 start 开始遍历，避免重复选择同一元素< / span >
< a id = "__codelineno-26-11" name = "__codelineno-26-11" href = "#__codelineno-26-11" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > start< / 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-26-12" name = "__codelineno-26-12" href = "#__codelineno-26-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝一：若子集和超过 target ，则直接结束循环< / span >
< a id = "__codelineno-26-13" name = "__codelineno-26-13" href = "#__codelineno-26-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 这是因为数组已排序，后边元素更大，子集和一定超过 target< / span >
< a id = "__codelineno-26-14" name = "__codelineno-26-14" href = "#__codelineno-26-14" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > target< / 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 = "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 = "p" > {< / span >
< a id = "__codelineno-26-15" name = "__codelineno-26-15" href = "#__codelineno-26-15" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-26-16" name = "__codelineno-26-16" href = "#__codelineno-26-16" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-26-17" name = "__codelineno-26-17" href = "#__codelineno-26-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝四：如果该元素与左边元素相等，说明该搜索分支重复，直接跳过< / span >
< a id = "__codelineno-26-18" name = "__codelineno-26-18" href = "#__codelineno-26-18" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > start< / 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 = "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 = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "o" > ]< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-26-19" name = "__codelineno-26-19" href = "#__codelineno-26-19" > < / a > < span class = "w" > < / span > < span class = "k" > continue< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-26-20" name = "__codelineno-26-20" href = "#__codelineno-26-20" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-26-21" name = "__codelineno-26-21" href = "#__codelineno-26-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新 target, start< / span >
< a id = "__codelineno-26-22" name = "__codelineno-26-22" href = "#__codelineno-26-22" > < / 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" > choices< / span > < span class = "o" > [< / span > < span class = "n" > i< / span > < span class = "o" > ]< / span > < span class = "p" > );< / span >
< a id = "__codelineno-26-23" name = "__codelineno-26-23" href = "#__codelineno-26-23" > < / a > < span class = "w" > < / span > < span class = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-26-24" name = "__codelineno-26-24" href = "#__codelineno-26-24" > < / 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" > target< / 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 > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-26-25" name = "__codelineno-26-25" href = "#__codelineno-26-25" > < / 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-26-26" name = "__codelineno-26-26" href = "#__codelineno-26-26" > < / 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-26-27" name = "__codelineno-26-27" href = "#__codelineno-26-27" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-26-28" name = "__codelineno-26-28" href = "#__codelineno-26-28" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-26-29" name = "__codelineno-26-29" href = "#__codelineno-26-29" > < / a >
< a id = "__codelineno-26-30" name = "__codelineno-26-30" href = "#__codelineno-26-30" > < / a > < span class = "cm" > /* 求解子集和 II */< / span >
< a id = "__codelineno-26-31" name = "__codelineno-26-31" href = "#__codelineno-26-31" > < / 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" > subsetSumII< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "o" > []< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > target< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-26-32" name = "__codelineno-26-32" href = "#__codelineno-26-32" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > ArrayList< / span > < span class = "o" > < > < / span > < span class = "p" > ();< / span > < span class = "w" > < / span > < span class = "c1" > // 状态（子集）< / span >
< a id = "__codelineno-26-33" name = "__codelineno-26-33" href = "#__codelineno-26-33" > < / a > < span class = "w" > < / span > < span class = "n" > Arrays< / span > < span class = "p" > .< / span > < span class = "na" > sort< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 对 nums 进行排序< / span >
< a id = "__codelineno-26-34" name = "__codelineno-26-34" href = "#__codelineno-26-34" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > start< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 遍历起始点< / span >
< a id = "__codelineno-26-35" name = "__codelineno-26-35" href = "#__codelineno-26-35" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > 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 = "p" > ();< / span > < span class = "w" > < / span > < span class = "c1" > // 结果列表（子集列表）< / span >
< a id = "__codelineno-26-36" name = "__codelineno-26-36" href = "#__codelineno-26-36" > < / 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" > target< / 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" > start< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-26-37" name = "__codelineno-26-37" href = "#__codelineno-26-37" > < / 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-26-38" name = "__codelineno-26-38" href = "#__codelineno-26-38" > < / a > < span class = "p" > }< / span >
2023-06-21 02:55:52 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-09-04 03:17:06 +08:00
< div class = "highlight" > < span class = "filename" > subset_sum_ii.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-27-1" name = "__codelineno-27-1" href = "#__codelineno-27-1" > < / a > < span class = "cm" > /* 回溯算法：子集和 II */< / span >
< a id = "__codelineno-27-2" name = "__codelineno-27-2" href = "#__codelineno-27-2" > < / 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 = "w" > < / span > < span class = "n" > target< / 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" > int< / span > < span class = "w" > < / span > < span class = "n" > start< / 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 >
2023-07-26 10:57:52 +08:00
< a id = "__codelineno-27-3" name = "__codelineno-27-3" href = "#__codelineno-27-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子集和等于 target 时，记录解< / span >
2023-09-04 03:17:06 +08:00
< a id = "__codelineno-27-4" name = "__codelineno-27-4" href = "#__codelineno-27-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > target< / 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 = "p" > {< / span >
< a id = "__codelineno-27-5" name = "__codelineno-27-5" href = "#__codelineno-27-5" > < / 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-27-6" name = "__codelineno-27-6" href = "#__codelineno-27-6" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-27-7" name = "__codelineno-27-7" href = "#__codelineno-27-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-27-8" name = "__codelineno-27-8" href = "#__codelineno-27-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-27-9" name = "__codelineno-27-9" href = "#__codelineno-27-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝二：从 start 开始遍历，避免生成重复子集< / span >
< a id = "__codelineno-27-10" name = "__codelineno-27-10" href = "#__codelineno-27-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝三：从 start 开始遍历，避免重复选择同一元素< / span >
< a id = "__codelineno-27-11" name = "__codelineno-27-11" href = "#__codelineno-27-11" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > start< / 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-27-12" name = "__codelineno-27-12" href = "#__codelineno-27-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝一：若子集和超过 target ，则直接结束循环< / span >
< a id = "__codelineno-27-13" name = "__codelineno-27-13" href = "#__codelineno-27-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 这是因为数组已排序，后边元素更大，子集和一定超过 target< / span >
< a id = "__codelineno-27-14" name = "__codelineno-27-14" href = "#__codelineno-27-14" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > target< / 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 > < 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 = "p" > {< / span >
< a id = "__codelineno-27-15" name = "__codelineno-27-15" href = "#__codelineno-27-15" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-27-16" name = "__codelineno-27-16" href = "#__codelineno-27-16" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-27-17" name = "__codelineno-27-17" href = "#__codelineno-27-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝四：如果该元素与左边元素相等，说明该搜索分支重复，直接跳过< / span >
< a id = "__codelineno-27-18" name = "__codelineno-27-18" href = "#__codelineno-27-18" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > start< / 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 > < 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 = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ])< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-27-19" name = "__codelineno-27-19" href = "#__codelineno-27-19" > < / a > < span class = "w" > < / span > < span class = "k" > continue< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-27-20" name = "__codelineno-27-20" href = "#__codelineno-27-20" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-27-21" name = "__codelineno-27-21" href = "#__codelineno-27-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新 target, start< / span >
< a id = "__codelineno-27-22" name = "__codelineno-27-22" href = "#__codelineno-27-22" > < / 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" > choices< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]);< / span >
< a id = "__codelineno-27-23" name = "__codelineno-27-23" href = "#__codelineno-27-23" > < / a > < span class = "w" > < / span > < span class = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-27-24" name = "__codelineno-27-24" href = "#__codelineno-27-24" > < / 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" > target< / 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 > < span class = "w" > < / span > < span class = "n" > choices< / 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 = "m" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-27-25" name = "__codelineno-27-25" href = "#__codelineno-27-25" > < / 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-27-26" name = "__codelineno-27-26" href = "#__codelineno-27-26" > < / 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-27-27" name = "__codelineno-27-27" href = "#__codelineno-27-27" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-27-28" name = "__codelineno-27-28" href = "#__codelineno-27-28" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-27-29" name = "__codelineno-27-29" href = "#__codelineno-27-29" > < / a >
< a id = "__codelineno-27-30" name = "__codelineno-27-30" href = "#__codelineno-27-30" > < / a > < span class = "cm" > /* 求解子集和 II */< / span >
< a id = "__codelineno-27-31" name = "__codelineno-27-31" href = "#__codelineno-27-31" > < / 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" > subsetSumII< / 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 = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > target< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-27-32" name = "__codelineno-27-32" href = "#__codelineno-27-32" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "p" > ();< / span > < span class = "w" > < / span > < span class = "c1" > // 状态（子集）< / span >
< a id = "__codelineno-27-33" name = "__codelineno-27-33" href = "#__codelineno-27-33" > < / a > < span class = "w" > < / span > < span class = "n" > Array< / span > < span class = "p" > .< / span > < span class = "n" > Sort< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 对 nums 进行排序< / span >
< a id = "__codelineno-27-34" name = "__codelineno-27-34" href = "#__codelineno-27-34" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > start< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 遍历起始点< / span >
< a id = "__codelineno-27-35" name = "__codelineno-27-35" href = "#__codelineno-27-35" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > 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 > < span class = "w" > < / span > < span class = "c1" > // 结果列表（子集列表）< / span >
< a id = "__codelineno-27-36" name = "__codelineno-27-36" href = "#__codelineno-27-36" > < / 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" > target< / 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" > start< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-27-37" name = "__codelineno-27-37" href = "#__codelineno-27-37" > < / 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-27-38" name = "__codelineno-27-38" href = "#__codelineno-27-38" > < / a > < span class = "p" > }< / span >
2023-06-21 02:55:52 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-09-04 03:17:06 +08:00
< div class = "highlight" > < span class = "filename" > subset_sum_ii.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-28-1" name = "__codelineno-28-1" href = "#__codelineno-28-1" > < / a > < span class = "cm" > /* 回溯算法：子集和 II */< / span >
< a id = "__codelineno-28-2" name = "__codelineno-28-2" href = "#__codelineno-28-2" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > backtrackSubsetSumII< / span > < span class = "p" > (< / span > < span class = "nx" > start< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > target< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "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" > 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 >
2023-08-04 05:25:00 +08:00
< a id = "__codelineno-28-3" name = "__codelineno-28-3" href = "#__codelineno-28-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子集和等于 target 时，记录解< / span >
2023-09-04 03:17:06 +08:00
< a id = "__codelineno-28-4" name = "__codelineno-28-4" href = "#__codelineno-28-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > target< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-28-5" name = "__codelineno-28-5" href = "#__codelineno-28-5" > < / 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-28-6" name = "__codelineno-28-6" href = "#__codelineno-28-6" > < / 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-28-7" name = "__codelineno-28-7" href = "#__codelineno-28-7" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span >
< a id = "__codelineno-28-8" name = "__codelineno-28-8" href = "#__codelineno-28-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-28-9" name = "__codelineno-28-9" href = "#__codelineno-28-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-28-10" name = "__codelineno-28-10" href = "#__codelineno-28-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝二：从 start 开始遍历，避免生成重复子集< / span >
< a id = "__codelineno-28-11" name = "__codelineno-28-11" href = "#__codelineno-28-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝三：从 start 开始遍历，避免重复选择同一元素< / span >
< a id = "__codelineno-28-12" name = "__codelineno-28-12" href = "#__codelineno-28-12" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > start< / 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-28-13" name = "__codelineno-28-13" href = "#__codelineno-28-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝一：若子集和超过 target ，则直接结束循环< / span >
< a id = "__codelineno-28-14" name = "__codelineno-28-14" href = "#__codelineno-28-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 这是因为数组已排序，后边元素更大，子集和一定超过 target< / span >
< a id = "__codelineno-28-15" name = "__codelineno-28-15" href = "#__codelineno-28-15" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > target< / span > < span class = "o" > -< / 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 > < span class = "w" > < / span > < span class = "p" > < < / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-28-16" name = "__codelineno-28-16" href = "#__codelineno-28-16" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span >
< a id = "__codelineno-28-17" name = "__codelineno-28-17" href = "#__codelineno-28-17" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-28-18" name = "__codelineno-28-18" href = "#__codelineno-28-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝四：如果该元素与左边元素相等，说明该搜索分支重复，直接跳过< / span >
< a id = "__codelineno-28-19" name = "__codelineno-28-19" href = "#__codelineno-28-19" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "p" > > < / span > < span class = "w" > < / span > < span class = "nx" > start< / 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 > < 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 = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-28-20" name = "__codelineno-28-20" href = "#__codelineno-28-20" > < / a > < span class = "w" > < / span > < span class = "k" > continue< / span >
< a id = "__codelineno-28-21" name = "__codelineno-28-21" href = "#__codelineno-28-21" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-28-22" name = "__codelineno-28-22" href = "#__codelineno-28-22" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新 target, start< / span >
< a id = "__codelineno-28-23" name = "__codelineno-28-23" href = "#__codelineno-28-23" > < / 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 = "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 = "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-28-24" name = "__codelineno-28-24" href = "#__codelineno-28-24" > < / a > < span class = "w" > < / span > < span class = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-28-25" name = "__codelineno-28-25" href = "#__codelineno-28-25" > < / a > < span class = "w" > < / span > < span class = "nx" > backtrackSubsetSumII< / span > < span class = "p" > (< / span > < span class = "nx" > i< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > target< / span > < span class = "o" > -< / 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 > < span class = "w" > < / 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" > res< / span > < span class = "p" > )< / span >
< a id = "__codelineno-28-26" name = "__codelineno-28-26" href = "#__codelineno-28-26" > < / 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-28-27" name = "__codelineno-28-27" href = "#__codelineno-28-27" > < / 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-28-28" name = "__codelineno-28-28" href = "#__codelineno-28-28" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-28-29" name = "__codelineno-28-29" href = "#__codelineno-28-29" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-28-30" name = "__codelineno-28-30" href = "#__codelineno-28-30" > < / a >
< a id = "__codelineno-28-31" name = "__codelineno-28-31" href = "#__codelineno-28-31" > < / a > < span class = "cm" > /* 求解子集和 II */< / span >
< a id = "__codelineno-28-32" name = "__codelineno-28-32" href = "#__codelineno-28-32" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > subsetSumII< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "w" > < / span > < span class = "p" > []< / span > < span class = "kt" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > target< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > [][]< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-28-33" name = "__codelineno-28-33" href = "#__codelineno-28-33" > < / 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 > < span class = "w" > < / span > < span class = "c1" > // 状态（子集）< / span >
< a id = "__codelineno-28-34" name = "__codelineno-28-34" href = "#__codelineno-28-34" > < / a > < span class = "w" > < / span > < span class = "nx" > sort< / span > < span class = "p" > .< / span > < span class = "nx" > Ints< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "c1" > // 对 nums 进行排序< / span >
< a id = "__codelineno-28-35" name = "__codelineno-28-35" href = "#__codelineno-28-35" > < / a > < span class = "w" > < / span > < span class = "nx" > start< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "w" > < / span > < span class = "c1" > // 遍历起始点< / span >
< a id = "__codelineno-28-36" name = "__codelineno-28-36" href = "#__codelineno-28-36" > < / 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 > < span class = "w" > < / span > < span class = "c1" > // 结果列表（子集列表）< / span >
< a id = "__codelineno-28-37" name = "__codelineno-28-37" href = "#__codelineno-28-37" > < / a > < span class = "w" > < / span > < span class = "nx" > backtrackSubsetSumII< / span > < span class = "p" > (< / span > < span class = "nx" > start< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > target< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "nx" > nums< / 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-28-38" name = "__codelineno-28-38" href = "#__codelineno-28-38" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span >
< a id = "__codelineno-28-39" name = "__codelineno-28-39" href = "#__codelineno-28-39" > < / 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" > subset_sum_ii.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-29-1" name = "__codelineno-29-1" href = "#__codelineno-29-1" > < / a > < span class = "cm" > /* 回溯算法：子集和 II */< / span >
< a id = "__codelineno-29-2" name = "__codelineno-29-2" href = "#__codelineno-29-2" > < / 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" > target< / 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" > start< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / 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-29-3" name = "__codelineno-29-3" href = "#__codelineno-29-3" > < / a > < span class = "c1" > // 子集和等于 target 时，记录解< / span >
< a id = "__codelineno-29-4" name = "__codelineno-29-4" href = "#__codelineno-29-4" > < / a > < span class = "k" > if< / span > < span class = "n" > target< / span > < span class = "p" > ==< / span > < span class = "mi" > 0< / span > < span class = "p" > {< / span >
< a id = "__codelineno-29-5" name = "__codelineno-29-5" href = "#__codelineno-29-5" > < / 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-29-6" name = "__codelineno-29-6" href = "#__codelineno-29-6" > < / a > < span class = "k" > return< / span >
< a id = "__codelineno-29-7" name = "__codelineno-29-7" href = "#__codelineno-29-7" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-29-8" name = "__codelineno-29-8" href = "#__codelineno-29-8" > < / a > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-29-9" name = "__codelineno-29-9" href = "#__codelineno-29-9" > < / a > < span class = "c1" > // 剪枝二：从 start 开始遍历，避免生成重复子集< / span >
< a id = "__codelineno-29-10" name = "__codelineno-29-10" href = "#__codelineno-29-10" > < / a > < span class = "c1" > // 剪枝三：从 start 开始遍历，避免重复选择同一元素< / span >
< a id = "__codelineno-29-11" name = "__codelineno-29-11" href = "#__codelineno-29-11" > < / a > < span class = "k" > for< / span > < span class = "n" > i< / span > < span class = "k" > in< / span > < span class = "bp" > stride< / span > < span class = "p" > (< / span > < span class = "n" > from< / span > < span class = "p" > :< / span > < span class = "n" > start< / span > < span class = "p" > ,< / span > < span class = "n" > to< / span > < span class = "p" > :< / span > < span class = "n" > choices< / span > < span class = "p" > .< / span > < span class = "bp" > count< / span > < span class = "p" > ,< / span > < span class = "n" > by< / span > < span class = "p" > :< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "p" > {< / span >
< a id = "__codelineno-29-12" name = "__codelineno-29-12" href = "#__codelineno-29-12" > < / a > < span class = "c1" > // 剪枝一：若子集和超过 target ，则直接结束循环< / span >
< a id = "__codelineno-29-13" name = "__codelineno-29-13" href = "#__codelineno-29-13" > < / a > < span class = "c1" > // 这是因为数组已排序，后边元素更大，子集和一定超过 target< / span >
< a id = "__codelineno-29-14" name = "__codelineno-29-14" href = "#__codelineno-29-14" > < / a > < span class = "k" > if< / span > < span class = "n" > target< / span > < span class = "o" > -< / span > < span class = "n" > choices< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "o" > < < / span > < span class = "mi" > 0< / span > < span class = "p" > {< / span >
< a id = "__codelineno-29-15" name = "__codelineno-29-15" href = "#__codelineno-29-15" > < / a > < span class = "k" > break< / span >
< a id = "__codelineno-29-16" name = "__codelineno-29-16" href = "#__codelineno-29-16" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-29-17" name = "__codelineno-29-17" href = "#__codelineno-29-17" > < / a > < span class = "c1" > // 剪枝四：如果该元素与左边元素相等，说明该搜索分支重复，直接跳过< / span >
< a id = "__codelineno-29-18" name = "__codelineno-29-18" href = "#__codelineno-29-18" > < / a > < span class = "k" > if< / span > < span class = "n" > i< / span > < span class = "o" > > < / span > < span class = "n" > start< / span > < span class = "p" > ,< / span > < span class = "n" > choices< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "p" > ==< / span > < span class = "n" > choices< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ]< / span > < span class = "p" > {< / span >
< a id = "__codelineno-29-19" name = "__codelineno-29-19" href = "#__codelineno-29-19" > < / a > < span class = "k" > continue< / span >
< a id = "__codelineno-29-20" name = "__codelineno-29-20" href = "#__codelineno-29-20" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-29-21" name = "__codelineno-29-21" href = "#__codelineno-29-21" > < / a > < span class = "c1" > // 尝试：做出选择，更新 target, start< / span >
< a id = "__codelineno-29-22" name = "__codelineno-29-22" href = "#__codelineno-29-22" > < / a > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > choices< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ])< / span >
< a id = "__codelineno-29-23" name = "__codelineno-29-23" href = "#__codelineno-29-23" > < / a > < span class = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-29-24" name = "__codelineno-29-24" href = "#__codelineno-29-24" > < / 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" > target< / span > < span class = "p" > :< / span > < span class = "n" > target< / span > < span class = "o" > -< / span > < span class = "n" > choices< / span > < span class = "p" > [< / span > < span class = "n" > i< / 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" > start< / span > < span class = "p" > :< / span > < span class = "n" > i< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / 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-29-25" name = "__codelineno-29-25" href = "#__codelineno-29-25" > < / a > < span class = "c1" > // 回退：撤销选择，恢复到之前的状态< / span >
< a id = "__codelineno-29-26" name = "__codelineno-29-26" href = "#__codelineno-29-26" > < / a > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "bp" > removeLast< / span > < span class = "p" > ()< / span >
< a id = "__codelineno-29-27" name = "__codelineno-29-27" href = "#__codelineno-29-27" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-29-28" name = "__codelineno-29-28" href = "#__codelineno-29-28" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-29-29" name = "__codelineno-29-29" href = "#__codelineno-29-29" > < / a >
< a id = "__codelineno-29-30" name = "__codelineno-29-30" href = "#__codelineno-29-30" > < / a > < span class = "cm" > /* 求解子集和 II */< / span >
< a id = "__codelineno-29-31" name = "__codelineno-29-31" href = "#__codelineno-29-31" > < / a > < span class = "kd" > func< / span > < span class = "nf" > subsetSumII< / 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 = "n" > target< / 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-29-32" name = "__codelineno-29-32" href = "#__codelineno-29-32" > < / 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 > < span class = "c1" > // 状态（子集）< / span >
< a id = "__codelineno-29-33" name = "__codelineno-29-33" href = "#__codelineno-29-33" > < / a > < span class = "kd" > let< / span > < span class = "nv" > nums< / span > < span class = "p" > =< / span > < span class = "n" > nums< / span > < span class = "p" > .< / span > < span class = "bp" > sorted< / span > < span class = "p" > ()< / span > < span class = "c1" > // 对 nums 进行排序< / span >
< a id = "__codelineno-29-34" name = "__codelineno-29-34" href = "#__codelineno-29-34" > < / a > < span class = "kd" > let< / span > < span class = "nv" > start< / span > < span class = "p" > =< / span > < span class = "mi" > 0< / span > < span class = "c1" > // 遍历起始点< / span >
< a id = "__codelineno-29-35" name = "__codelineno-29-35" href = "#__codelineno-29-35" > < / 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 > < span class = "c1" > // 结果列表（子集列表）< / span >
< a id = "__codelineno-29-36" name = "__codelineno-29-36" href = "#__codelineno-29-36" > < / 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" > target< / span > < span class = "p" > :< / span > < span class = "n" > target< / 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" > start< / span > < span class = "p" > :< / span > < span class = "n" > start< / 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-29-37" name = "__codelineno-29-37" href = "#__codelineno-29-37" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
< a id = "__codelineno-29-38" name = "__codelineno-29-38" href = "#__codelineno-29-38" > < / 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" > subset_sum_ii.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-30-1" name = "__codelineno-30-1" href = "#__codelineno-30-1" > < / a > < span class = "cm" > /* 回溯算法：子集和 II */< / span >
< a id = "__codelineno-30-2" name = "__codelineno-30-2" href = "#__codelineno-30-2" > < / 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" > target< / 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" > start< / 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 >
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< a id = "__codelineno-30-3" name = "__codelineno-30-3" href = "#__codelineno-30-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子集和等于 target 时，记录解< / span >
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< a id = "__codelineno-30-4" name = "__codelineno-30-4" href = "#__codelineno-30-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > target< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-30-5" name = "__codelineno-30-5" href = "#__codelineno-30-5" > < / 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-30-6" name = "__codelineno-30-6" href = "#__codelineno-30-6" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-30-7" name = "__codelineno-30-7" href = "#__codelineno-30-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-30-8" name = "__codelineno-30-8" href = "#__codelineno-30-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-30-9" name = "__codelineno-30-9" href = "#__codelineno-30-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝二：从 start 开始遍历，避免生成重复子集< / span >
< a id = "__codelineno-30-10" name = "__codelineno-30-10" href = "#__codelineno-30-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝三：从 start 开始遍历，避免重复选择同一元素< / span >
< a id = "__codelineno-30-11" name = "__codelineno-30-11" href = "#__codelineno-30-11" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > start< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "nx" > choices< / span > < span class = "p" > .< / span > < span class = "nx" > length< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-30-12" name = "__codelineno-30-12" href = "#__codelineno-30-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝一：若子集和超过 target ，则直接结束循环< / span >
< a id = "__codelineno-30-13" name = "__codelineno-30-13" href = "#__codelineno-30-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 这是因为数组已排序，后边元素更大，子集和一定超过 target< / span >
< a id = "__codelineno-30-14" name = "__codelineno-30-14" href = "#__codelineno-30-14" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > target< / 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" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-30-15" name = "__codelineno-30-15" href = "#__codelineno-30-15" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-30-16" name = "__codelineno-30-16" href = "#__codelineno-30-16" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-30-17" name = "__codelineno-30-17" href = "#__codelineno-30-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝四：如果该元素与左边元素相等，说明该搜索分支重复，直接跳过< / span >
< a id = "__codelineno-30-18" name = "__codelineno-30-18" href = "#__codelineno-30-18" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "nx" > start< / 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" > i< / span > < span class = "p" > ]< / 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" > i< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ])< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
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< a id = "__codelineno-30-19" name = "__codelineno-30-19" href = "#__codelineno-30-19" > < / a > < span class = "w" > < / span > < span class = "k" > continue< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-30-20" name = "__codelineno-30-20" href = "#__codelineno-30-20" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
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< a id = "__codelineno-30-21" name = "__codelineno-30-21" href = "#__codelineno-30-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新 target, start< / span >
< a id = "__codelineno-30-22" name = "__codelineno-30-22" href = "#__codelineno-30-22" > < / 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" > choices< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ]);< / span >
< a id = "__codelineno-30-23" name = "__codelineno-30-23" href = "#__codelineno-30-23" > < / a > < span class = "w" > < / span > < span class = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-30-24" name = "__codelineno-30-24" href = "#__codelineno-30-24" > < / 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" > target< / 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" > i< / 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" > i< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-30-25" name = "__codelineno-30-25" href = "#__codelineno-30-25" > < / 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-30-26" name = "__codelineno-30-26" href = "#__codelineno-30-26" > < / 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-30-27" name = "__codelineno-30-27" href = "#__codelineno-30-27" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-30-28" name = "__codelineno-30-28" href = "#__codelineno-30-28" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-30-29" name = "__codelineno-30-29" href = "#__codelineno-30-29" > < / a >
< a id = "__codelineno-30-30" name = "__codelineno-30-30" href = "#__codelineno-30-30" > < / a > < span class = "cm" > /* 求解子集和 II */< / span >
< a id = "__codelineno-30-31" name = "__codelineno-30-31" href = "#__codelineno-30-31" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > subsetSumII< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > target< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-30-32" name = "__codelineno-30-32" href = "#__codelineno-30-32" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [];< / span > < span class = "w" > < / span > < span class = "c1" > // 状态（子集）< / span >
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< a id = "__codelineno-30-33" name = "__codelineno-30-33" href = "#__codelineno-30-33" > < / a > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "p" > .< / span > < span class = "nx" > sort< / span > < span class = "p" > ((< / span > < span class = "nx" > a< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > b< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > => < / span > < span class = "w" > < / span > < span class = "nx" > a< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "nx" > b< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 对 nums 进行排序< / span >
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< a id = "__codelineno-30-34" name = "__codelineno-30-34" href = "#__codelineno-30-34" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > start< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 遍历起始点< / span >
< a id = "__codelineno-30-35" name = "__codelineno-30-35" href = "#__codelineno-30-35" > < / 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 > < span class = "w" > < / span > < span class = "c1" > // 结果列表（子集列表）< / span >
< a id = "__codelineno-30-36" name = "__codelineno-30-36" href = "#__codelineno-30-36" > < / 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" > target< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > start< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-30-37" name = "__codelineno-30-37" href = "#__codelineno-30-37" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-30-38" name = "__codelineno-30-38" href = "#__codelineno-30-38" > < / 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" > subset_sum_ii.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-31-1" name = "__codelineno-31-1" href = "#__codelineno-31-1" > < / a > < span class = "cm" > /* 回溯算法：子集和 II */< / span >
< a id = "__codelineno-31-2" name = "__codelineno-31-2" href = "#__codelineno-31-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > (< / span >
< a id = "__codelineno-31-3" name = "__codelineno-31-3" href = "#__codelineno-31-3" > < / a > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > [],< / span >
< a id = "__codelineno-31-4" name = "__codelineno-31-4" href = "#__codelineno-31-4" > < / a > < span class = "w" > < / span > < span class = "nx" > target< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-31-5" name = "__codelineno-31-5" href = "#__codelineno-31-5" > < / a > < span class = "w" > < / span > < span class = "nx" > choices< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > [],< / span >
< a id = "__codelineno-31-6" name = "__codelineno-31-6" href = "#__codelineno-31-6" > < / a > < span class = "w" > < / span > < span class = "nx" > start< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-31-7" name = "__codelineno-31-7" href = "#__codelineno-31-7" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > [][]< / span >
< a id = "__codelineno-31-8" name = "__codelineno-31-8" href = "#__codelineno-31-8" > < / 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-31-9" name = "__codelineno-31-9" href = "#__codelineno-31-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子集和等于 target 时，记录解< / span >
< a id = "__codelineno-31-10" name = "__codelineno-31-10" href = "#__codelineno-31-10" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > target< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-31-11" name = "__codelineno-31-11" href = "#__codelineno-31-11" > < / 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-31-12" name = "__codelineno-31-12" href = "#__codelineno-31-12" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-31-13" name = "__codelineno-31-13" href = "#__codelineno-31-13" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-31-14" name = "__codelineno-31-14" href = "#__codelineno-31-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-31-15" name = "__codelineno-31-15" href = "#__codelineno-31-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝二：从 start 开始遍历，避免生成重复子集< / span >
< a id = "__codelineno-31-16" name = "__codelineno-31-16" href = "#__codelineno-31-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝三：从 start 开始遍历，避免重复选择同一元素< / span >
< a id = "__codelineno-31-17" name = "__codelineno-31-17" href = "#__codelineno-31-17" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > start< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "nx" > choices< / span > < span class = "p" > .< / span > < span class = "nx" > length< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-31-18" name = "__codelineno-31-18" href = "#__codelineno-31-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝一：若子集和超过 target ，则直接结束循环< / span >
< a id = "__codelineno-31-19" name = "__codelineno-31-19" href = "#__codelineno-31-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 这是因为数组已排序，后边元素更大，子集和一定超过 target< / span >
< a id = "__codelineno-31-20" name = "__codelineno-31-20" href = "#__codelineno-31-20" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > target< / 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" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-31-21" name = "__codelineno-31-21" href = "#__codelineno-31-21" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-31-22" name = "__codelineno-31-22" href = "#__codelineno-31-22" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-31-23" name = "__codelineno-31-23" href = "#__codelineno-31-23" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝四：如果该元素与左边元素相等，说明该搜索分支重复，直接跳过< / span >
< a id = "__codelineno-31-24" name = "__codelineno-31-24" href = "#__codelineno-31-24" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "nx" > start< / 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" > i< / span > < span class = "p" > ]< / 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" > i< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ])< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-31-25" name = "__codelineno-31-25" href = "#__codelineno-31-25" > < / a > < span class = "w" > < / span > < span class = "k" > continue< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-31-26" name = "__codelineno-31-26" href = "#__codelineno-31-26" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-31-27" name = "__codelineno-31-27" href = "#__codelineno-31-27" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新 target, start< / span >
< a id = "__codelineno-31-28" name = "__codelineno-31-28" href = "#__codelineno-31-28" > < / 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" > choices< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ]);< / span >
< a id = "__codelineno-31-29" name = "__codelineno-31-29" href = "#__codelineno-31-29" > < / a > < span class = "w" > < / span > < span class = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-31-30" name = "__codelineno-31-30" href = "#__codelineno-31-30" > < / 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" > target< / 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" > i< / 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" > i< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-31-31" name = "__codelineno-31-31" href = "#__codelineno-31-31" > < / 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-31-32" name = "__codelineno-31-32" href = "#__codelineno-31-32" > < / 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-31-33" name = "__codelineno-31-33" href = "#__codelineno-31-33" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-31-34" name = "__codelineno-31-34" href = "#__codelineno-31-34" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-31-35" name = "__codelineno-31-35" href = "#__codelineno-31-35" > < / a >
< a id = "__codelineno-31-36" name = "__codelineno-31-36" href = "#__codelineno-31-36" > < / a > < span class = "cm" > /* 求解子集和 II */< / span >
< a id = "__codelineno-31-37" name = "__codelineno-31-37" href = "#__codelineno-31-37" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > subsetSumII< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > [],< / span > < span class = "w" > < / span > < span class = "nx" > target< / 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-31-38" name = "__codelineno-31-38" href = "#__codelineno-31-38" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [];< / span > < span class = "w" > < / span > < span class = "c1" > // 状态（子集）< / span >
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< a id = "__codelineno-31-39" name = "__codelineno-31-39" href = "#__codelineno-31-39" > < / a > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "p" > .< / span > < span class = "nx" > sort< / span > < span class = "p" > ((< / span > < span class = "nx" > a< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > b< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > => < / span > < span class = "w" > < / span > < span class = "nx" > a< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "nx" > b< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 对 nums 进行排序< / span >
2023-09-04 03:17:06 +08:00
< a id = "__codelineno-31-40" name = "__codelineno-31-40" href = "#__codelineno-31-40" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > start< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 遍历起始点< / span >
< a id = "__codelineno-31-41" name = "__codelineno-31-41" href = "#__codelineno-31-41" > < / 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 > < span class = "w" > < / span > < span class = "c1" > // 结果列表（子集列表）< / span >
< a id = "__codelineno-31-42" name = "__codelineno-31-42" href = "#__codelineno-31-42" > < / 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" > target< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > start< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-31-43" name = "__codelineno-31-43" href = "#__codelineno-31-43" > < / 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-31-44" name = "__codelineno-31-44" href = "#__codelineno-31-44" > < / a > < span class = "p" > }< / span >
2023-06-21 02:55:52 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-09-04 03:17:06 +08:00
< div class = "highlight" > < span class = "filename" > subset_sum_ii.dart< / span > < pre > < span > < / span > < code > < a id = "__codelineno-32-1" name = "__codelineno-32-1" href = "#__codelineno-32-1" > < / a > < span class = "cm" > /* 回溯算法：子集和 II */< / span >
< a id = "__codelineno-32-2" name = "__codelineno-32-2" href = "#__codelineno-32-2" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "n" > backtrack< / span > < span class = "p" > (< / span >
< a id = "__codelineno-32-3" name = "__codelineno-32-3" href = "#__codelineno-32-3" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-32-4" name = "__codelineno-32-4" href = "#__codelineno-32-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > target< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-32-5" name = "__codelineno-32-5" href = "#__codelineno-32-5" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-32-6" name = "__codelineno-32-6" href = "#__codelineno-32-6" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > start< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-32-7" name = "__codelineno-32-7" href = "#__codelineno-32-7" > < / 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 = "p" > ,< / span >
< a id = "__codelineno-32-8" name = "__codelineno-32-8" href = "#__codelineno-32-8" > < / a > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-32-9" name = "__codelineno-32-9" href = "#__codelineno-32-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子集和等于 target 时，记录解< / span >
< a id = "__codelineno-32-10" name = "__codelineno-32-10" href = "#__codelineno-32-10" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > target< / 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 = "p" > {< / span >
< a id = "__codelineno-32-11" name = "__codelineno-32-11" href = "#__codelineno-32-11" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > add< / span > < span class = "p" > (< / span > < span class = "n" > List< / span > < span class = "p" > .< / span > < span class = "n" > from< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-32-12" name = "__codelineno-32-12" href = "#__codelineno-32-12" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-32-13" name = "__codelineno-32-13" href = "#__codelineno-32-13" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-32-14" name = "__codelineno-32-14" href = "#__codelineno-32-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-32-15" name = "__codelineno-32-15" href = "#__codelineno-32-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝二：从 start 开始遍历，避免生成重复子集< / span >
< a id = "__codelineno-32-16" name = "__codelineno-32-16" href = "#__codelineno-32-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝三：从 start 开始遍历，避免重复选择同一元素< / span >
< a id = "__codelineno-32-17" name = "__codelineno-32-17" href = "#__codelineno-32-17" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > start< / 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-32-18" name = "__codelineno-32-18" href = "#__codelineno-32-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝一：若子集和超过 target ，则直接结束循环< / span >
< a id = "__codelineno-32-19" name = "__codelineno-32-19" href = "#__codelineno-32-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 这是因为数组已排序，后边元素更大，子集和一定超过 target< / span >
< a id = "__codelineno-32-20" name = "__codelineno-32-20" href = "#__codelineno-32-20" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > target< / 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 > < 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 = "p" > {< / span >
< a id = "__codelineno-32-21" name = "__codelineno-32-21" href = "#__codelineno-32-21" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-32-22" name = "__codelineno-32-22" href = "#__codelineno-32-22" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-32-23" name = "__codelineno-32-23" href = "#__codelineno-32-23" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝四：如果该元素与左边元素相等，说明该搜索分支重复，直接跳过< / span >
< a id = "__codelineno-32-24" name = "__codelineno-32-24" href = "#__codelineno-32-24" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > start< / 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 > < 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 = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ])< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-32-25" name = "__codelineno-32-25" href = "#__codelineno-32-25" > < / a > < span class = "w" > < / span > < span class = "k" > continue< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-32-26" name = "__codelineno-32-26" href = "#__codelineno-32-26" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-32-27" name = "__codelineno-32-27" href = "#__codelineno-32-27" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新 target, start< / span >
< a id = "__codelineno-32-28" name = "__codelineno-32-28" href = "#__codelineno-32-28" > < / 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" > choices< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]);< / span >
< a id = "__codelineno-32-29" name = "__codelineno-32-29" href = "#__codelineno-32-29" > < / a > < span class = "w" > < / span > < span class = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-32-30" name = "__codelineno-32-30" href = "#__codelineno-32-30" > < / 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" > target< / 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 > < span class = "w" > < / span > < span class = "n" > choices< / 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 = "m" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-32-31" name = "__codelineno-32-31" href = "#__codelineno-32-31" > < / 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-32-32" name = "__codelineno-32-32" href = "#__codelineno-32-32" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > removeLast< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-32-33" name = "__codelineno-32-33" href = "#__codelineno-32-33" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-32-34" name = "__codelineno-32-34" href = "#__codelineno-32-34" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-32-35" name = "__codelineno-32-35" href = "#__codelineno-32-35" > < / a >
< a id = "__codelineno-32-36" name = "__codelineno-32-36" href = "#__codelineno-32-36" > < / a > < span class = "cm" > /* 求解子集和 II */< / span >
< a id = "__codelineno-32-37" name = "__codelineno-32-37" href = "#__codelineno-32-37" > < / 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" > subsetSumII< / 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" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > target< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-32-38" name = "__codelineno-32-38" href = "#__codelineno-32-38" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [];< / span > < span class = "w" > < / span > < span class = "c1" > // 状态（子集）< / span >
< a id = "__codelineno-32-39" name = "__codelineno-32-39" href = "#__codelineno-32-39" > < / a > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > .< / span > < span class = "n" > sort< / span > < span class = "p" > ();< / span > < span class = "w" > < / span > < span class = "c1" > // 对 nums 进行排序< / span >
< a id = "__codelineno-32-40" name = "__codelineno-32-40" href = "#__codelineno-32-40" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > start< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 遍历起始点< / span >
< a id = "__codelineno-32-41" name = "__codelineno-32-41" href = "#__codelineno-32-41" > < / 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 = "p" > [];< / span > < span class = "w" > < / span > < span class = "c1" > // 结果列表（子集列表）< / span >
< a id = "__codelineno-32-42" name = "__codelineno-32-42" href = "#__codelineno-32-42" > < / 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" > target< / 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" > start< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-32-43" name = "__codelineno-32-43" href = "#__codelineno-32-43" > < / 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-32-44" name = "__codelineno-32-44" href = "#__codelineno-32-44" > < / a > < span class = "p" > }< / span >
2023-06-21 02:55:52 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-09-04 03:17:06 +08:00
< div class = "highlight" > < span class = "filename" > subset_sum_ii.rs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-33-1" name = "__codelineno-33-1" href = "#__codelineno-33-1" > < / a > < span class = "cm" > /* 回溯算法：子集和 II */< / span >
< a id = "__codelineno-33-2" name = "__codelineno-33-2" href = "#__codelineno-33-2" > < / a > < span class = "k" > fn< / span > < span class = "nf" > backtrack< / span > < span class = "p" > (< / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > state< / span > : < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "kt" > i32< / span > < span class = "o" > > < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > target< / span > : < span class = "kt" > i32< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > choices< / span > : < span class = "kp" > & < / span > < span class = "p" > [< / span > < span class = "kt" > i32< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "n" > start< / span > : < span class = "kt" > usize< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > : < span class = "kp" > & < / span > < span class = "nc" > mut< / span > < span class = "w" > < / span > < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "kt" > i32< / span > < span class = "o" > > > < / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-33-3" name = "__codelineno-33-3" href = "#__codelineno-33-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子集和等于 target 时，记录解< / span >
< a id = "__codelineno-33-4" name = "__codelineno-33-4" href = "#__codelineno-33-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "n" > target< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-33-5" name = "__codelineno-33-5" href = "#__codelineno-33-5" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > push< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > );< / span >
< a id = "__codelineno-33-6" name = "__codelineno-33-6" href = "#__codelineno-33-6" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-33-7" name = "__codelineno-33-7" href = "#__codelineno-33-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-33-8" name = "__codelineno-33-8" href = "#__codelineno-33-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-33-9" name = "__codelineno-33-9" href = "#__codelineno-33-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝二：从 start 开始遍历，避免生成重复子集< / span >
< a id = "__codelineno-33-10" name = "__codelineno-33-10" href = "#__codelineno-33-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝三：从 start 开始遍历，避免重复选择同一元素< / span >
< a id = "__codelineno-33-11" name = "__codelineno-33-11" href = "#__codelineno-33-11" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "k" > in< / span > < span class = "w" > < / span > < span class = "n" > start< / span > < span class = "o" > ..< / span > < span class = "n" > choices< / span > < span class = "p" > .< / span > < span class = "n" > len< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-33-12" name = "__codelineno-33-12" href = "#__codelineno-33-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝一：若子集和超过 target ，则直接结束循环< / span >
< a id = "__codelineno-33-13" name = "__codelineno-33-13" href = "#__codelineno-33-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 这是因为数组已排序，后边元素更大，子集和一定超过 target< / span >
< a id = "__codelineno-33-14" name = "__codelineno-33-14" href = "#__codelineno-33-14" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "n" > target< / 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 > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-33-15" name = "__codelineno-33-15" href = "#__codelineno-33-15" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-33-16" name = "__codelineno-33-16" href = "#__codelineno-33-16" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-33-17" name = "__codelineno-33-17" href = "#__codelineno-33-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝四：如果该元素与左边元素相等，说明该搜索分支重复，直接跳过< / span >
< a id = "__codelineno-33-18" name = "__codelineno-33-18" href = "#__codelineno-33-18" > < / a > < span class = "w" > < / span > < span class = "k" > if< / 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" > start< / 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 > < 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 = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-33-19" name = "__codelineno-33-19" href = "#__codelineno-33-19" > < / a > < span class = "w" > < / span > < span class = "k" > continue< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-33-20" name = "__codelineno-33-20" href = "#__codelineno-33-20" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-33-21" name = "__codelineno-33-21" href = "#__codelineno-33-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新 target, start< / span >
< a id = "__codelineno-33-22" name = "__codelineno-33-22" href = "#__codelineno-33-22" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > push< / span > < span class = "p" > (< / span > < span class = "n" > choices< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]);< / span >
< a id = "__codelineno-33-23" name = "__codelineno-33-23" href = "#__codelineno-33-23" > < / a > < span class = "w" > < / span > < span class = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-33-24" name = "__codelineno-33-24" href = "#__codelineno-33-24" > < / 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 = "n" > clone< / span > < span class = "p" > (),< / span > < span class = "w" > < / span > < span class = "n" > target< / 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 > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-33-25" name = "__codelineno-33-25" href = "#__codelineno-33-25" > < / 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-33-26" name = "__codelineno-33-26" href = "#__codelineno-33-26" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > pop< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-33-27" name = "__codelineno-33-27" href = "#__codelineno-33-27" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-33-28" name = "__codelineno-33-28" href = "#__codelineno-33-28" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-33-29" name = "__codelineno-33-29" href = "#__codelineno-33-29" > < / a >
< a id = "__codelineno-33-30" name = "__codelineno-33-30" href = "#__codelineno-33-30" > < / a > < span class = "cm" > /* 求解子集和 II */< / span >
< a id = "__codelineno-33-31" name = "__codelineno-33-31" href = "#__codelineno-33-31" > < / a > < span class = "k" > fn< / span > < span class = "nf" > subset_sum_ii< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > : < span class = "kp" > & < / span > < span class = "nc" > mut< / span > < span class = "w" > < / span > < span class = "p" > [< / span > < span class = "kt" > i32< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "n" > target< / span > : < span class = "kt" > i32< / span > < span class = "p" > )< / span > < span class = "w" > < / span > -> < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "kt" > i32< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-33-32" name = "__codelineno-33-32" href = "#__codelineno-33-32" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > Vec< / span > ::< span class = "n" > new< / span > < span class = "p" > ();< / span > < span class = "w" > < / span > < span class = "c1" > // 状态（子集）< / span >
< a id = "__codelineno-33-33" name = "__codelineno-33-33" href = "#__codelineno-33-33" > < / a > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > .< / span > < span class = "n" > sort< / span > < span class = "p" > ();< / span > < span class = "w" > < / span > < span class = "c1" > // 对 nums 进行排序< / span >
< a id = "__codelineno-33-34" name = "__codelineno-33-34" href = "#__codelineno-33-34" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "n" > start< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 遍历起始点< / span >
< a id = "__codelineno-33-35" name = "__codelineno-33-35" href = "#__codelineno-33-35" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > Vec< / span > ::< span class = "n" > new< / span > < span class = "p" > ();< / span > < span class = "w" > < / span > < span class = "c1" > // 结果列表（子集列表）< / span >
< a id = "__codelineno-33-36" name = "__codelineno-33-36" href = "#__codelineno-33-36" > < / 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" > target< / 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" > start< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-33-37" name = "__codelineno-33-37" href = "#__codelineno-33-37" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span >
< a id = "__codelineno-33-38" name = "__codelineno-33-38" href = "#__codelineno-33-38" > < / a > < span class = "p" > }< / span >
2023-06-21 02:55:52 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-09-04 03:17:06 +08:00
< div class = "highlight" > < span class = "filename" > subset_sum_ii.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-34-1" name = "__codelineno-34-1" href = "#__codelineno-34-1" > < / a > < span class = "cm" > /* 回溯算法：子集和 II */< / span >
< a id = "__codelineno-34-2" name = "__codelineno-34-2" href = "#__codelineno-34-2" > < / 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 = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > target< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > start< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > vector< / 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-34-3" name = "__codelineno-34-3" href = "#__codelineno-34-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 子集和等于 target 时，记录解< / span >
< a id = "__codelineno-34-4" name = "__codelineno-34-4" href = "#__codelineno-34-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > target< / 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 = "p" > {< / span >
< a id = "__codelineno-34-5" name = "__codelineno-34-5" href = "#__codelineno-34-5" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > tmpVector< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > newVector< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-34-6" name = "__codelineno-34-6" href = "#__codelineno-34-6" > < / a > < span class = "w" > < / span > < span class = "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" > state< / span > < span class = "o" > -> < / 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-34-7" name = "__codelineno-34-7" href = "#__codelineno-34-7" > < / a > < span class = "w" > < / span > < span class = "n" > vectorPushback< / span > < span class = "p" > (< / span > < span class = "n" > tmpVector< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "o" > -> < / span > < span class = "n" > data< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "k" > sizeof< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-34-8" name = "__codelineno-34-8" href = "#__codelineno-34-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-34-9" name = "__codelineno-34-9" href = "#__codelineno-34-9" > < / a > < span class = "w" > < / span > < span class = "n" > vectorPushback< / span > < span class = "p" > (< / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > tmpVector< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "k" > sizeof< / span > < span class = "p" > (< / span > < span class = "n" > vector< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-34-10" name = "__codelineno-34-10" href = "#__codelineno-34-10" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-34-11" name = "__codelineno-34-11" href = "#__codelineno-34-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-34-12" name = "__codelineno-34-12" href = "#__codelineno-34-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-34-13" name = "__codelineno-34-13" href = "#__codelineno-34-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝二：从 start 开始遍历，避免生成重复子集< / span >
< a id = "__codelineno-34-14" name = "__codelineno-34-14" href = "#__codelineno-34-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝三：从 start 开始遍历，避免重复选择同一元素< / span >
< a id = "__codelineno-34-15" name = "__codelineno-34-15" href = "#__codelineno-34-15" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > start< / 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 = "o" > -> < / 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-34-16" name = "__codelineno-34-16" href = "#__codelineno-34-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝一：若子集和超过 target ，则直接结束循环< / span >
< a id = "__codelineno-34-17" name = "__codelineno-34-17" href = "#__codelineno-34-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 这是因为数组已排序，后边元素更大，子集和一定超过 target< / span >
< a id = "__codelineno-34-18" name = "__codelineno-34-18" href = "#__codelineno-34-18" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > target< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > )(< / span > < span class = "n" > choices< / span > < span class = "o" > -> < / span > < span class = "n" > data< / 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 = "mi" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-34-19" name = "__codelineno-34-19" href = "#__codelineno-34-19" > < / a > < span class = "w" > < / span > < span class = "k" > continue< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-34-20" name = "__codelineno-34-20" href = "#__codelineno-34-20" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-34-21" name = "__codelineno-34-21" href = "#__codelineno-34-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝四：如果该元素与左边元素相等，说明该搜索分支重复，直接跳过< / span >
< a id = "__codelineno-34-22" name = "__codelineno-34-22" href = "#__codelineno-34-22" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > start< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > )(< / span > < span class = "n" > choices< / span > < span class = "o" > -> < / span > < span class = "n" > data< / 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 = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > )(< / span > < span class = "n" > choices< / span > < span class = "o" > -> < / span > < span class = "n" > data< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ]))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-34-23" name = "__codelineno-34-23" href = "#__codelineno-34-23" > < / a > < span class = "w" > < / span > < span class = "k" > continue< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-34-24" name = "__codelineno-34-24" href = "#__codelineno-34-24" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-34-25" name = "__codelineno-34-25" href = "#__codelineno-34-25" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新 target, start< / span >
< a id = "__codelineno-34-26" name = "__codelineno-34-26" href = "#__codelineno-34-26" > < / a > < span class = "w" > < / span > < span class = "n" > vectorPushback< / 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 = "o" > -> < / span > < span class = "n" > data< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "k" > sizeof< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-34-27" name = "__codelineno-34-27" href = "#__codelineno-34-27" > < / a > < span class = "w" > < / span > < span class = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-34-28" name = "__codelineno-34-28" href = "#__codelineno-34-28" > < / 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" > target< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > )(< / span > < span class = "n" > choices< / span > < span class = "o" > -> < / span > < span class = "n" > data< / span > < span class = "p" > [< / span > < span class = "n" > i< / 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" > i< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-34-29" name = "__codelineno-34-29" href = "#__codelineno-34-29" > < / 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-34-30" name = "__codelineno-34-30" href = "#__codelineno-34-30" > < / a > < span class = "w" > < / span > < span class = "n" > vectorPopback< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > );< / span >
< a id = "__codelineno-34-31" name = "__codelineno-34-31" href = "#__codelineno-34-31" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-34-32" name = "__codelineno-34-32" href = "#__codelineno-34-32" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-34-33" name = "__codelineno-34-33" href = "#__codelineno-34-33" > < / a >
< a id = "__codelineno-34-34" name = "__codelineno-34-34" href = "#__codelineno-34-34" > < / a > < span class = "cm" > /* 求解子集和 II */< / span >
< a id = "__codelineno-34-35" name = "__codelineno-34-35" href = "#__codelineno-34-35" > < / a > < span class = "n" > vector< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nf" > subsetSumII< / span > < span class = "p" > (< / span > < span class = "n" > vector< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > target< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-34-36" name = "__codelineno-34-36" href = "#__codelineno-34-36" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > state< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > newVector< / span > < span class = "p" > ();< / span > < span class = "w" > < / span > < span class = "c1" > // 状态（子集）< / span >
< a id = "__codelineno-34-37" name = "__codelineno-34-37" href = "#__codelineno-34-37" > < / a > < span class = "w" > < / span > < span class = "n" > qsort< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "o" > -> < / span > < span class = "n" > data< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "o" > -> < / span > < span class = "n" > size< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "k" > sizeof< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > ),< / span > < span class = "w" > < / span > < span class = "n" > comp< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 对 nums 进行排序< / span >
< a id = "__codelineno-34-38" name = "__codelineno-34-38" href = "#__codelineno-34-38" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > start< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 子集和< / span >
< a id = "__codelineno-34-39" name = "__codelineno-34-39" href = "#__codelineno-34-39" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > newVector< / span > < span class = "p" > ();< / span > < span class = "w" > < / span > < span class = "c1" > // 结果列表（子集列表）< / span >
< a id = "__codelineno-34-40" name = "__codelineno-34-40" href = "#__codelineno-34-40" > < / 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" > target< / 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" > start< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-34-41" name = "__codelineno-34-41" href = "#__codelineno-34-41" > < / 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-34-42" name = "__codelineno-34-42" href = "#__codelineno-34-42" > < / a > < span class = "p" > }< / span >
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< div class = "highlight" > < span class = "filename" > subset_sum_ii.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-35-1" name = "__codelineno-35-1" href = "#__codelineno-35-1" > < / 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-35-2" name = "__codelineno-35-2" href = "#__codelineno-35-2" > < / a >
< a id = "__codelineno-35-3" name = "__codelineno-35-3" href = "#__codelineno-35-3" > < / 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" > subsetSumII< / span > < span class = "p" > }< / span >
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< p > 图 13-14 展示了数组 < span class = "arithmatex" > \([4, 4, 5]\)< / span > 和目标元素 < span class = "arithmatex" > \(9\)< / span > 的回溯过程，共包含四种剪枝操作。请你将图示与代码注释相结合，理解整个搜索过程，以及每种剪枝操作是如何工作的。< / p >
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< p > < a class = "glightbox" href = "../subset_sum_problem.assets/subset_sum_ii.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "子集和 II 回溯过程" src = "../subset_sum_problem.assets/subset_sum_ii.png" / > < / a > < / p >
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< p align = "center" > 图 13-14 子集和 II 回溯过程 < / p >
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