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Hello 算法
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15.2 分数背包问题
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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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< a href = "../../chapter_computational_complexity/" class = "md-nav__link " >
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第 2 章 时空复杂度
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第 2 章 时空复杂度
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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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< a href = "../../chapter_data_structure/" class = "md-nav__link " >
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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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< a href = "../../chapter_array_and_linkedlist/" class = "md-nav__link " >
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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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4.4 小结
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< a href = "../../chapter_stack_and_queue/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z" / > < / svg >
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第 5 章 栈与队列
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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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< a href = "../../chapter_hashing/" class = "md-nav__link " >
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第 6 章 哈希表
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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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< a href = "../../chapter_tree/" class = "md-nav__link " >
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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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< a href = "../../chapter_heap/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z" / > < / svg >
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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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< a href = "../../chapter_graph/" class = "md-nav__link " >
< 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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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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< a href = "../../chapter_searching/" class = "md-nav__link " >
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第 10 章 搜索
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第 10 章 搜索
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10.1 二分查找
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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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10.4 哈希优化策略
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10.5 重识搜索算法
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10.6 小结
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< a href = "../../chapter_sorting/" class = "md-nav__link " >
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第 11 章 排序
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第 11 章 排序
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11.1 排序算法
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11.2 选择排序
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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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< a href = "../../chapter_divide_and_conquer/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z" / > < / svg >
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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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12.2 分治搜索策略
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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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< a href = "../../chapter_backtracking/" class = "md-nav__link " >
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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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13.4 N 皇后问题
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13.5 小结
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< a href = "../../chapter_dynamic_programming/" class = "md-nav__link " >
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第 14 章 动态规划
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第 14 章 动态规划
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14.1 初探动态规划
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14.2 DP 问题特性
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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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14.5 完全背包问题
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14.6 编辑距离问题
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14.7 小结
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< a href = "../" class = "md-nav__link " >
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第 15 章 贪心
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第 15 章 贪心
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15.2 分数背包问题
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15.3 最大容量问题
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< h1 id = "152" > 15.2 分数背包问题< a class = "headerlink" href = "#152" title = "Permanent link" > ¶ < / a > < / h1 >
< div class = "admonition question" >
< p class = "admonition-title" > Question< / p >
< p > 给定 < span class = "arithmatex" > \(n\)< / span > 个物品，第 < span class = "arithmatex" > \(i\)< / span > 个物品的重量为 < span class = "arithmatex" > \(wgt[i-1]\)< / span > 、价值为 < span class = "arithmatex" > \(val[i-1]\)< / span > ，和一个容量为 < span class = "arithmatex" > \(cap\)< / span > 的背包。每个物品只能选择一次，< strong > 但可以选择物品的一部分，价值根据选择的重量比例计算< / strong > ，问在不超过背包容量下背包中物品的最大价值。< / p >
< / div >
< p > < img alt = "分数背包问题的示例数据" src = "../fractional_knapsack_problem.assets/fractional_knapsack_example.png" / > < / p >
< p align = "center" > 图 15-3 分数背包问题的示例数据 < / p >
< p > 分数背包和 0-1 背包整体上非常相似，状态包含当前物品 < span class = "arithmatex" > \(i\)< / span > 和容量 < span class = "arithmatex" > \(c\)< / span > ，目标是求不超过背包容量下的最大价值。< / p >
< p > 不同点在于，本题允许只选择物品的一部分。如图 15-4 所示，< strong > 我们可以对物品任意地进行切分，并按照重量比例来计算物品价值< / strong > 。< / p >
< ol >
< li > 对于物品 < span class = "arithmatex" > \(i\)< / span > ，它在单位重量下的价值为 < span class = "arithmatex" > \(val[i-1] / wgt[i-1]\)< / span > ，简称为单位价值。< / li >
< li > 假设放入一部分物品 < span class = "arithmatex" > \(i\)< / span > ，重量为 < span class = "arithmatex" > \(w\)< / span > ，则背包增加的价值为 < span class = "arithmatex" > \(w \times val[i-1] / wgt[i-1]\)< / span > 。< / li >
< / ol >
< p > < img alt = "物品在单位重量下的价值" src = "../fractional_knapsack_problem.assets/fractional_knapsack_unit_value.png" / > < / p >
< p align = "center" > 图 15-4 物品在单位重量下的价值 < / p >
< h3 id = "1" > 1. 贪心策略确定< a class = "headerlink" href = "#1" title = "Permanent link" > ¶ < / a > < / h3 >
< p > 最大化背包内物品总价值，< strong > 本质上是要最大化单位重量下的物品价值< / strong > 。由此便可推出图 15-5 所示的贪心策略：< / p >
< ol >
< li > 将物品按照单位价值从高到低进行排序。< / li >
< li > 遍历所有物品，< strong > 每轮贪心地选择单位价值最高的物品< / strong > 。< / li >
< li > 若剩余背包容量不足，则使用当前物品的一部分填满背包即可。< / li >
< / ol >
< p > < img alt = "分数背包的贪心策略" src = "../fractional_knapsack_problem.assets/fractional_knapsack_greedy_strategy.png" / > < / p >
< p align = "center" > 图 15-5 分数背包的贪心策略 < / p >
< h3 id = "2" > 2. 代码实现< a class = "headerlink" href = "#2" title = "Permanent link" > ¶ < / a > < / h3 >
< p > 我们建立了一个物品类 < code > Item< / code > ，以便将物品按照单位价值进行排序。循环进行贪心选择，当背包已满时跳出并返回解。< / p >
< 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" > Java< / label > < label for = "__tabbed_1_2" > C++< / label > < label for = "__tabbed_1_3" > Python< / label > < label for = "__tabbed_1_4" > Go< / label > < label for = "__tabbed_1_5" > JS< / label > < label for = "__tabbed_1_6" > TS< / label > < label for = "__tabbed_1_7" > C< / label > < label for = "__tabbed_1_8" > C#< / label > < label for = "__tabbed_1_9" > Swift< / label > < label for = "__tabbed_1_10" > Zig< / label > < label for = "__tabbed_1_11" > Dart< / label > < label for = "__tabbed_1_12" > Rust< / label > < / div >
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< div class = "highlight" > < span class = "filename" > fractional_knapsack.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-0-1" name = "__codelineno-0-1" href = "#__codelineno-0-1" > < / a > < span class = "cm" > /* 物品 */< / span >
< a id = "__codelineno-0-2" name = "__codelineno-0-2" href = "#__codelineno-0-2" > < / a > < span class = "kd" > class< / span > < span class = "nc" > Item< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-0-3" name = "__codelineno-0-3" href = "#__codelineno-0-3" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > w< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 物品重量< / span >
< a id = "__codelineno-0-4" name = "__codelineno-0-4" href = "#__codelineno-0-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > v< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 物品价值< / span >
< a id = "__codelineno-0-5" name = "__codelineno-0-5" href = "#__codelineno-0-5" > < / a >
< a id = "__codelineno-0-6" name = "__codelineno-0-6" href = "#__codelineno-0-6" > < / a > < span class = "w" > < / span > < span class = "kd" > public< / span > < span class = "w" > < / span > < span class = "nf" > Item< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > w< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > v< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-0-7" name = "__codelineno-0-7" href = "#__codelineno-0-7" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "na" > w< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > w< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-0-8" name = "__codelineno-0-8" href = "#__codelineno-0-8" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "na" > v< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > v< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-0-9" name = "__codelineno-0-9" href = "#__codelineno-0-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-0-10" name = "__codelineno-0-10" href = "#__codelineno-0-10" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-0-11" name = "__codelineno-0-11" href = "#__codelineno-0-11" > < / a >
< a id = "__codelineno-0-12" name = "__codelineno-0-12" href = "#__codelineno-0-12" > < / a > < span class = "cm" > /* 分数背包：贪心 */< / span >
< a id = "__codelineno-0-13" name = "__codelineno-0-13" href = "#__codelineno-0-13" > < / a > < span class = "kt" > double< / span > < span class = "w" > < / span > < span class = "nf" > fractionalKnapsack< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "o" > []< / span > < span class = "w" > < / span > < span class = "n" > wgt< / 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" > val< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-0-14" name = "__codelineno-0-14" href = "#__codelineno-0-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 创建物品列表，包含两个属性：重量、价值< / span >
< a id = "__codelineno-0-15" name = "__codelineno-0-15" href = "#__codelineno-0-15" > < / a > < span class = "w" > < / span > < span class = "n" > Item< / span > < span class = "o" > []< / span > < span class = "w" > < / span > < span class = "n" > items< / 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" > Item< / span > < span class = "o" > [< / span > < span class = "n" > wgt< / span > < span class = "p" > .< / span > < span class = "na" > length< / span > < span class = "o" > ]< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-0-16" name = "__codelineno-0-16" href = "#__codelineno-0-16" > < / 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 = "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" > wgt< / span > < span class = "p" > .< / span > < span class = "na" > length< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-0-17" name = "__codelineno-0-17" href = "#__codelineno-0-17" > < / a > < span class = "w" > < / span > < span class = "n" > items< / 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 = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > Item< / span > < span class = "p" > (< / span > < span class = "n" > wgt< / 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" > val< / span > < span class = "o" > [< / span > < span class = "n" > i< / span > < span class = "o" > ]< / span > < span class = "p" > );< / span >
< a id = "__codelineno-0-18" name = "__codelineno-0-18" href = "#__codelineno-0-18" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-0-19" name = "__codelineno-0-19" href = "#__codelineno-0-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 按照单位价值 item.v / item.w 从高到低进行排序< / span >
< a id = "__codelineno-0-20" name = "__codelineno-0-20" href = "#__codelineno-0-20" > < / 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" > items< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > Comparator< / span > < span class = "p" > .< / span > < span class = "na" > comparingDouble< / span > < span class = "p" > (< / span > < span class = "n" > item< / span > < span class = "w" > < / span > < span class = "o" > -> < / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "p" > ((< / span > < span class = "kt" > double< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "na" > v< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "na" > w< / span > < span class = "p" > )));< / span >
< a id = "__codelineno-0-21" name = "__codelineno-0-21" href = "#__codelineno-0-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环贪心选择< / span >
< a id = "__codelineno-0-22" name = "__codelineno-0-22" href = "#__codelineno-0-22" > < / a > < span class = "w" > < / span > < span class = "kt" > double< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-0-23" name = "__codelineno-0-23" href = "#__codelineno-0-23" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > Item< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "w" > < / span > < span class = "p" > :< / span > < span class = "w" > < / span > < span class = "n" > items< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-0-24" name = "__codelineno-0-24" href = "#__codelineno-0-24" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "na" > w< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-0-25" name = "__codelineno-0-25" href = "#__codelineno-0-25" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若剩余容量充足，则将当前物品整个装进背包< / span >
< a id = "__codelineno-0-26" name = "__codelineno-0-26" href = "#__codelineno-0-26" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "na" > v< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-0-27" name = "__codelineno-0-27" href = "#__codelineno-0-27" > < / a > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "w" > < / span > < span class = "o" > -=< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "na" > w< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-0-28" name = "__codelineno-0-28" href = "#__codelineno-0-28" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-0-29" name = "__codelineno-0-29" href = "#__codelineno-0-29" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若剩余容量不足，则将当前物品的一部分装进背包< / span >
< a id = "__codelineno-0-30" name = "__codelineno-0-30" href = "#__codelineno-0-30" > < / a > < 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 = "kt" > double< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "na" > v< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "na" > w< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-0-31" name = "__codelineno-0-31" href = "#__codelineno-0-31" > < / a > < span class = "w" > < / span > < span class = "c1" > // 已无剩余容量，因此跳出循环< / span >
< a id = "__codelineno-0-32" name = "__codelineno-0-32" href = "#__codelineno-0-32" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-0-33" name = "__codelineno-0-33" href = "#__codelineno-0-33" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-0-34" name = "__codelineno-0-34" href = "#__codelineno-0-34" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-0-35" name = "__codelineno-0-35" href = "#__codelineno-0-35" > < / 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-0-36" name = "__codelineno-0-36" href = "#__codelineno-0-36" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > fractional_knapsack.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-1-1" name = "__codelineno-1-1" href = "#__codelineno-1-1" > < / a > < span class = "cm" > /* 物品 */< / span >
< a id = "__codelineno-1-2" name = "__codelineno-1-2" href = "#__codelineno-1-2" > < / a > < span class = "k" > class< / span > < span class = "w" > < / span > < span class = "nc" > Item< / 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 = "k" > public< / span > < span class = "o" > :< / span >
< a id = "__codelineno-1-4" name = "__codelineno-1-4" href = "#__codelineno-1-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > w< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 物品重量< / span >
< a id = "__codelineno-1-5" name = "__codelineno-1-5" href = "#__codelineno-1-5" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > v< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 物品价值< / span >
< a id = "__codelineno-1-6" name = "__codelineno-1-6" href = "#__codelineno-1-6" > < / a >
< a id = "__codelineno-1-7" name = "__codelineno-1-7" href = "#__codelineno-1-7" > < / a > < span class = "w" > < / span > < span class = "n" > Item< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > w< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > v< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "n" > w< / span > < span class = "p" > (< / span > < span class = "n" > w< / span > < span class = "p" > ),< / span > < span class = "w" > < / span > < span class = "n" > v< / span > < span class = "p" > (< / span > < span class = "n" > v< / span > < span class = "p" > )< / span > < 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 = "p" > }< / span >
< a id = "__codelineno-1-9" name = "__codelineno-1-9" href = "#__codelineno-1-9" > < / a > < span class = "p" > };< / span >
< a id = "__codelineno-1-10" name = "__codelineno-1-10" href = "#__codelineno-1-10" > < / a >
< a id = "__codelineno-1-11" name = "__codelineno-1-11" href = "#__codelineno-1-11" > < / a > < span class = "cm" > /* 分数背包：贪心 */< / span >
< a id = "__codelineno-1-12" name = "__codelineno-1-12" href = "#__codelineno-1-12" > < / a > < span class = "kt" > double< / span > < span class = "w" > < / span > < span class = "nf" > fractionalKnapsack< / 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" > wgt< / 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" > val< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "p" > )< / span > < span class = "w" > < / 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 = "c1" > // 创建物品列表，包含两个属性：重量、价值< / span >
< a id = "__codelineno-1-14" name = "__codelineno-1-14" href = "#__codelineno-1-14" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > Item< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > items< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-15" name = "__codelineno-1-15" href = "#__codelineno-1-15" > < / a > < span class = "w" > < / span > < span class = "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" > wgt< / 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-1-16" name = "__codelineno-1-16" href = "#__codelineno-1-16" > < / a > < span class = "w" > < / span > < span class = "n" > items< / span > < span class = "p" > .< / span > < span class = "n" > push_back< / span > < span class = "p" > (< / span > < span class = "n" > Item< / span > < span class = "p" > (< / span > < span class = "n" > wgt< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]));< / span >
< a id = "__codelineno-1-17" name = "__codelineno-1-17" href = "#__codelineno-1-17" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-1-18" name = "__codelineno-1-18" href = "#__codelineno-1-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 按照单位价值 item.v / item.w 从高到低进行排序< / span >
< a id = "__codelineno-1-19" name = "__codelineno-1-19" href = "#__codelineno-1-19" > < / a > < span class = "w" > < / span > < span class = "n" > sort< / span > < span class = "p" > (< / span > < span class = "n" > items< / span > < span class = "p" > .< / span > < span class = "n" > begin< / span > < span class = "p" > (),< / span > < span class = "w" > < / span > < span class = "n" > items< / span > < span class = "p" > .< / span > < span class = "n" > end< / span > < span class = "p" > (),< / span > < span class = "w" > < / span > < span class = "p" > [](< / span > < span class = "n" > Item< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > a< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > Item< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > b< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > double< / span > < span class = "p" > )< / span > < span class = "n" > a< / span > < span class = "p" > .< / span > < span class = "n" > v< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "n" > a< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > double< / span > < span class = "p" > )< / span > < span class = "n" > b< / span > < span class = "p" > .< / span > < span class = "n" > v< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "n" > b< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "p" > ;< / span > < span class = "w" > < / 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 = "c1" > // 循环贪心选择< / span >
< a id = "__codelineno-1-21" name = "__codelineno-1-21" href = "#__codelineno-1-21" > < / a > < span class = "w" > < / span > < span class = "kt" > double< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-22" name = "__codelineno-1-22" href = "#__codelineno-1-22" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "k" > auto< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > item< / span > < span class = "w" > < / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "n" > items< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-23" name = "__codelineno-1-23" href = "#__codelineno-1-23" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-24" name = "__codelineno-1-24" href = "#__codelineno-1-24" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若剩余容量充足，则将当前物品整个装进背包< / span >
< a id = "__codelineno-1-25" name = "__codelineno-1-25" href = "#__codelineno-1-25" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > v< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-26" name = "__codelineno-1-26" href = "#__codelineno-1-26" > < / a > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "w" > < / span > < span class = "o" > -=< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-27" name = "__codelineno-1-27" href = "#__codelineno-1-27" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-28" name = "__codelineno-1-28" href = "#__codelineno-1-28" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若剩余容量不足，则将当前物品的一部分装进背包< / span >
< a id = "__codelineno-1-29" name = "__codelineno-1-29" href = "#__codelineno-1-29" > < / a > < 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 = "kt" > double< / span > < span class = "p" > )< / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > v< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-30" name = "__codelineno-1-30" href = "#__codelineno-1-30" > < / a > < span class = "w" > < / span > < span class = "c1" > // 已无剩余容量，因此跳出循环< / span >
< a id = "__codelineno-1-31" name = "__codelineno-1-31" href = "#__codelineno-1-31" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-32" name = "__codelineno-1-32" href = "#__codelineno-1-32" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-1-33" name = "__codelineno-1-33" href = "#__codelineno-1-33" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-1-34" name = "__codelineno-1-34" href = "#__codelineno-1-34" > < / 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-1-35" name = "__codelineno-1-35" href = "#__codelineno-1-35" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > fractional_knapsack.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-2-1" name = "__codelineno-2-1" href = "#__codelineno-2-1" > < / a > < span class = "k" > class< / span > < span class = "nc" > Item< / span > < span class = "p" > :< / span >
< a id = "__codelineno-2-2" name = "__codelineno-2-2" href = "#__codelineno-2-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 物品" " " < / span >
< a id = "__codelineno-2-3" name = "__codelineno-2-3" href = "#__codelineno-2-3" > < / a >
< a id = "__codelineno-2-4" name = "__codelineno-2-4" href = "#__codelineno-2-4" > < / a > < span class = "k" > def< / span > < span class = "fm" > __init__< / span > < span class = "p" > (< / span > < span class = "bp" > self< / span > < span class = "p" > ,< / span > < span class = "n" > w< / span > < span class = "p" > :< / span > < span class = "nb" > int< / span > < span class = "p" > ,< / span > < span class = "n" > v< / span > < span class = "p" > :< / span > < span class = "nb" > int< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-2-5" name = "__codelineno-2-5" href = "#__codelineno-2-5" > < / a > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > w< / span > < span class = "o" > =< / span > < span class = "n" > w< / span > < span class = "c1" > # 物品重量< / span >
< a id = "__codelineno-2-6" name = "__codelineno-2-6" href = "#__codelineno-2-6" > < / a > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > v< / span > < span class = "o" > =< / span > < span class = "n" > v< / span > < span class = "c1" > # 物品价值< / span >
< a id = "__codelineno-2-7" name = "__codelineno-2-7" href = "#__codelineno-2-7" > < / a >
< a id = "__codelineno-2-8" name = "__codelineno-2-8" href = "#__codelineno-2-8" > < / a > < span class = "k" > def< / span > < span class = "nf" > fractional_knapsack< / span > < span class = "p" > (< / span > < span class = "n" > wgt< / 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" > val< / 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" > cap< / span > < span class = "p" > :< / span > < span class = "nb" > int< / span > < span class = "p" > )< / span > < span class = "o" > -> < / span > < span class = "nb" > int< / span > < span class = "p" > :< / span >
< a id = "__codelineno-2-9" name = "__codelineno-2-9" href = "#__codelineno-2-9" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 分数背包：贪心" " " < / span >
< a id = "__codelineno-2-10" name = "__codelineno-2-10" href = "#__codelineno-2-10" > < / a > < span class = "c1" > # 创建物品列表，包含两个属性：重量、价值< / span >
< a id = "__codelineno-2-11" name = "__codelineno-2-11" href = "#__codelineno-2-11" > < / a > < span class = "n" > items< / span > < span class = "o" > =< / span > < span class = "p" > [< / span > < span class = "n" > Item< / span > < span class = "p" > (< / span > < span class = "n" > w< / span > < span class = "p" > ,< / span > < span class = "n" > v< / span > < span class = "p" > )< / span > < span class = "k" > for< / span > < span class = "n" > w< / span > < span class = "p" > ,< / span > < span class = "n" > v< / span > < span class = "ow" > in< / span > < span class = "nb" > zip< / span > < span class = "p" > (< / span > < span class = "n" > wgt< / span > < span class = "p" > ,< / span > < span class = "n" > val< / span > < span class = "p" > )]< / span >
< a id = "__codelineno-2-12" name = "__codelineno-2-12" href = "#__codelineno-2-12" > < / a > < span class = "c1" > # 按照单位价值 item.v / item.w 从高到低进行排序< / span >
< a id = "__codelineno-2-13" name = "__codelineno-2-13" href = "#__codelineno-2-13" > < / a > < span class = "n" > items< / span > < span class = "o" > .< / span > < span class = "n" > sort< / span > < span class = "p" > (< / span > < span class = "n" > key< / span > < span class = "o" > =< / span > < span class = "k" > lambda< / span > < span class = "n" > item< / span > < span class = "p" > :< / span > < span class = "n" > item< / span > < span class = "o" > .< / span > < span class = "n" > v< / span > < span class = "o" > /< / span > < span class = "n" > item< / span > < span class = "o" > .< / span > < span class = "n" > w< / span > < span class = "p" > ,< / span > < span class = "n" > reverse< / span > < span class = "o" > =< / span > < span class = "kc" > True< / span > < span class = "p" > )< / span >
< a id = "__codelineno-2-14" name = "__codelineno-2-14" href = "#__codelineno-2-14" > < / a > < span class = "c1" > # 循环贪心选择< / span >
< a id = "__codelineno-2-15" name = "__codelineno-2-15" href = "#__codelineno-2-15" > < / a > < span class = "n" > res< / span > < span class = "o" > =< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-2-16" name = "__codelineno-2-16" href = "#__codelineno-2-16" > < / a > < span class = "k" > for< / span > < span class = "n" > item< / span > < span class = "ow" > in< / span > < span class = "n" > items< / span > < span class = "p" > :< / span >
< a id = "__codelineno-2-17" name = "__codelineno-2-17" href = "#__codelineno-2-17" > < / a > < span class = "k" > if< / span > < span class = "n" > item< / span > < span class = "o" > .< / span > < span class = "n" > w< / span > < span class = "o" > < =< / span > < span class = "n" > cap< / span > < span class = "p" > :< / span >
< a id = "__codelineno-2-18" name = "__codelineno-2-18" href = "#__codelineno-2-18" > < / a > < span class = "c1" > # 若剩余容量充足，则将当前物品整个装进背包< / span >
< a id = "__codelineno-2-19" name = "__codelineno-2-19" href = "#__codelineno-2-19" > < / a > < span class = "n" > res< / span > < span class = "o" > +=< / span > < span class = "n" > item< / span > < span class = "o" > .< / span > < span class = "n" > v< / span >
< a id = "__codelineno-2-20" name = "__codelineno-2-20" href = "#__codelineno-2-20" > < / a > < span class = "n" > cap< / span > < span class = "o" > -=< / span > < span class = "n" > item< / span > < span class = "o" > .< / span > < span class = "n" > w< / span >
< a id = "__codelineno-2-21" name = "__codelineno-2-21" href = "#__codelineno-2-21" > < / a > < span class = "k" > else< / span > < span class = "p" > :< / span >
< a id = "__codelineno-2-22" name = "__codelineno-2-22" href = "#__codelineno-2-22" > < / a > < span class = "c1" > # 若剩余容量不足，则将当前物品的一部分装进背包< / span >
< a id = "__codelineno-2-23" name = "__codelineno-2-23" href = "#__codelineno-2-23" > < / a > < span class = "n" > res< / span > < span class = "o" > +=< / span > < span class = "p" > (< / span > < span class = "n" > item< / span > < span class = "o" > .< / span > < span class = "n" > v< / span > < span class = "o" > /< / span > < span class = "n" > item< / span > < span class = "o" > .< / span > < span class = "n" > w< / span > < span class = "p" > )< / span > < span class = "o" > *< / span > < span class = "n" > cap< / span >
< a id = "__codelineno-2-24" name = "__codelineno-2-24" href = "#__codelineno-2-24" > < / a > < span class = "c1" > # 已无剩余容量，因此跳出循环< / span >
< a id = "__codelineno-2-25" name = "__codelineno-2-25" href = "#__codelineno-2-25" > < / a > < span class = "k" > break< / span >
< a id = "__codelineno-2-26" name = "__codelineno-2-26" href = "#__codelineno-2-26" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > fractional_knapsack.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-3-1" name = "__codelineno-3-1" href = "#__codelineno-3-1" > < / a > < span class = "cm" > /* 物品 */< / span >
< a id = "__codelineno-3-2" name = "__codelineno-3-2" href = "#__codelineno-3-2" > < / a > < span class = "kd" > type< / span > < span class = "w" > < / span > < span class = "nx" > Item< / span > < span class = "w" > < / span > < span class = "kd" > struct< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-3" name = "__codelineno-3-3" href = "#__codelineno-3-3" > < / a > < span class = "w" > < / span > < span class = "nx" > w< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "c1" > // 物品重量< / span >
< a id = "__codelineno-3-4" name = "__codelineno-3-4" href = "#__codelineno-3-4" > < / a > < span class = "w" > < / span > < span class = "nx" > v< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "c1" > // 物品价值< / span >
< a id = "__codelineno-3-5" name = "__codelineno-3-5" href = "#__codelineno-3-5" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-3-6" name = "__codelineno-3-6" href = "#__codelineno-3-6" > < / a >
< a id = "__codelineno-3-7" name = "__codelineno-3-7" href = "#__codelineno-3-7" > < / a > < span class = "cm" > /* 分数背包：贪心 */< / span >
< a id = "__codelineno-3-8" name = "__codelineno-3-8" href = "#__codelineno-3-8" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > fractionalKnapsack< / span > < span class = "p" > (< / span > < span class = "nx" > wgt< / 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" > val< / 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" > cap< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "kt" > float64< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-9" name = "__codelineno-3-9" href = "#__codelineno-3-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 创建物品列表，包含两个属性：重量、价值< / span >
< a id = "__codelineno-3-10" name = "__codelineno-3-10" href = "#__codelineno-3-10" > < / a > < span class = "w" > < / span > < span class = "nx" > items< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nb" > make< / span > < span class = "p" > ([]< / span > < span class = "nx" > Item< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "nx" > wgt< / span > < span class = "p" > ))< / span >
< a id = "__codelineno-3-11" name = "__codelineno-3-11" href = "#__codelineno-3-11" > < / a > < span class = "w" > < / span > < span class = "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 = "nx" > wgt< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-12" name = "__codelineno-3-12" href = "#__codelineno-3-12" > < / a > < span class = "w" > < / span > < span class = "nx" > items< / 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" > Item< / span > < span class = "p" > {< / span > < span class = "nx" > wgt< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "nx" > val< / span > < span class = "p" > [< / span > < span class = "nx" > i< / 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" > // 按照单位价值 item.v / item.w 从高到低进行排序< / span >
< a id = "__codelineno-3-15" name = "__codelineno-3-15" href = "#__codelineno-3-15" > < / a > < span class = "w" > < / span > < span class = "nx" > sort< / span > < span class = "p" > .< / span > < span class = "nx" > Slice< / span > < span class = "p" > (< / span > < span class = "nx" > items< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kd" > func< / span > < span class = "p" > (< / span > < span class = "nx" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > j< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "kt" > bool< / span > < span class = "w" > < / 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 = "k" > return< / span > < span class = "w" > < / span > < span class = "nb" > float64< / span > < span class = "p" > (< / span > < span class = "nx" > items< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ].< / span > < span class = "nx" > v< / span > < span class = "p" > )< / span > < span class = "o" > /< / span > < span class = "nb" > float64< / span > < span class = "p" > (< / span > < span class = "nx" > items< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ].< / span > < span class = "nx" > w< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > > < / span > < span class = "w" > < / span > < span class = "nb" > float64< / span > < span class = "p" > (< / span > < span class = "nx" > items< / span > < span class = "p" > [< / span > < span class = "nx" > j< / span > < span class = "p" > ].< / span > < span class = "nx" > v< / span > < span class = "p" > )< / span > < span class = "o" > /< / span > < span class = "nb" > float64< / span > < span class = "p" > (< / span > < span class = "nx" > items< / span > < span class = "p" > [< / span > < span class = "nx" > j< / span > < span class = "p" > ].< / span > < span class = "nx" > w< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-17" name = "__codelineno-3-17" href = "#__codelineno-3-17" > < / a > < span class = "w" > < / span > < span class = "p" > })< / span >
< a id = "__codelineno-3-18" name = "__codelineno-3-18" href = "#__codelineno-3-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环贪心选择< / span >
< a id = "__codelineno-3-19" name = "__codelineno-3-19" href = "#__codelineno-3-19" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mf" > 0.0< / span >
< a id = "__codelineno-3-20" name = "__codelineno-3-20" href = "#__codelineno-3-20" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > _< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > item< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "k" > range< / span > < span class = "w" > < / span > < span class = "nx" > items< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-21" name = "__codelineno-3-21" href = "#__codelineno-3-21" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > item< / span > < span class = "p" > .< / span > < span class = "nx" > w< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "nx" > cap< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-22" name = "__codelineno-3-22" href = "#__codelineno-3-22" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若剩余容量充足，则将当前物品整个装进背包< / span >
< a id = "__codelineno-3-23" name = "__codelineno-3-23" href = "#__codelineno-3-23" > < / 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" > float64< / span > < span class = "p" > (< / span > < span class = "nx" > item< / span > < span class = "p" > .< / span > < span class = "nx" > v< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-24" name = "__codelineno-3-24" href = "#__codelineno-3-24" > < / a > < span class = "w" > < / span > < span class = "nx" > cap< / span > < span class = "w" > < / span > < span class = "o" > -=< / span > < span class = "w" > < / span > < span class = "nx" > item< / span > < span class = "p" > .< / span > < span class = "nx" > w< / span >
< a id = "__codelineno-3-25" name = "__codelineno-3-25" href = "#__codelineno-3-25" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-26" name = "__codelineno-3-26" href = "#__codelineno-3-26" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若剩余容量不足，则将当前物品的一部分装进背包< / span >
< a id = "__codelineno-3-27" name = "__codelineno-3-27" href = "#__codelineno-3-27" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "nb" > float64< / span > < span class = "p" > (< / span > < span class = "nx" > item< / span > < span class = "p" > .< / span > < span class = "nx" > v< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "nb" > float64< / span > < span class = "p" > (< / span > < span class = "nx" > item< / span > < span class = "p" > .< / span > < span class = "nx" > w< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "nb" > float64< / span > < span class = "p" > (< / span > < span class = "nx" > cap< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-28" name = "__codelineno-3-28" href = "#__codelineno-3-28" > < / a > < span class = "w" > < / span > < span class = "c1" > // 已无剩余容量，因此跳出循环< / span >
< a id = "__codelineno-3-29" name = "__codelineno-3-29" href = "#__codelineno-3-29" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span >
< a id = "__codelineno-3-30" name = "__codelineno-3-30" href = "#__codelineno-3-30" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-31" name = "__codelineno-3-31" href = "#__codelineno-3-31" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-32" name = "__codelineno-3-32" href = "#__codelineno-3-32" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span >
< a id = "__codelineno-3-33" name = "__codelineno-3-33" href = "#__codelineno-3-33" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > fractional_knapsack.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-4-1" name = "__codelineno-4-1" href = "#__codelineno-4-1" > < / a > < span class = "p" > [< / span > < span class = "kd" > class< / span > < span class = "p" > ]{< / span > < span class = "nx" > Item< / span > < span class = "p" > }< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "nx" > func< / span > < span class = "p" > ]{}< / span >
< a id = "__codelineno-4-2" name = "__codelineno-4-2" href = "#__codelineno-4-2" > < / a >
< a id = "__codelineno-4-3" name = "__codelineno-4-3" href = "#__codelineno-4-3" > < / a > < span class = "p" > [< / span > < span class = "kd" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "nx" > func< / span > < span class = "p" > ]{< / span > < span class = "nx" > fractionalKnapsack< / span > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > fractional_knapsack.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-5-1" name = "__codelineno-5-1" href = "#__codelineno-5-1" > < / a > < span class = "p" > [< / span > < span class = "kd" > class< / span > < span class = "p" > ]{< / span > < span class = "nx" > Item< / span > < span class = "p" > }< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "nx" > func< / span > < span class = "p" > ]{}< / span >
< a id = "__codelineno-5-2" name = "__codelineno-5-2" href = "#__codelineno-5-2" > < / a >
< a id = "__codelineno-5-3" name = "__codelineno-5-3" href = "#__codelineno-5-3" > < / a > < span class = "p" > [< / span > < span class = "kd" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "nx" > func< / span > < span class = "p" > ]{< / span > < span class = "nx" > fractionalKnapsack< / span > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > fractional_knapsack.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-6-1" name = "__codelineno-6-1" href = "#__codelineno-6-1" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{< / span > < span class = "n" > Item< / span > < span class = "p" > }< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{}< / span >
< a id = "__codelineno-6-2" name = "__codelineno-6-2" href = "#__codelineno-6-2" > < / a >
< a id = "__codelineno-6-3" name = "__codelineno-6-3" href = "#__codelineno-6-3" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > fractionalKnapsack< / span > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > fractional_knapsack.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-7-1" name = "__codelineno-7-1" href = "#__codelineno-7-1" > < / a > < span class = "cm" > /* 物品 */< / span >
< a id = "__codelineno-7-2" name = "__codelineno-7-2" href = "#__codelineno-7-2" > < / a > < span class = "k" > class< / span > < span class = "w" > < / span > < span class = "nc" > Item< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-3" name = "__codelineno-7-3" href = "#__codelineno-7-3" > < / a > < span class = "w" > < / span > < span class = "k" > public< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > w< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 物品重量< / span >
< a id = "__codelineno-7-4" name = "__codelineno-7-4" href = "#__codelineno-7-4" > < / a > < span class = "w" > < / span > < span class = "k" > public< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > v< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 物品价值< / span >
< a id = "__codelineno-7-5" name = "__codelineno-7-5" href = "#__codelineno-7-5" > < / a >
< a id = "__codelineno-7-6" name = "__codelineno-7-6" href = "#__codelineno-7-6" > < / a > < span class = "w" > < / span > < span class = "k" > public< / span > < span class = "w" > < / span > < span class = "nf" > Item< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > w< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > v< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-7" name = "__codelineno-7-7" href = "#__codelineno-7-7" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > w< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-8" name = "__codelineno-7-8" href = "#__codelineno-7-8" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "n" > v< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > v< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-9" name = "__codelineno-7-9" href = "#__codelineno-7-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-7-10" name = "__codelineno-7-10" href = "#__codelineno-7-10" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-7-11" name = "__codelineno-7-11" href = "#__codelineno-7-11" > < / a >
< a id = "__codelineno-7-12" name = "__codelineno-7-12" href = "#__codelineno-7-12" > < / a > < span class = "cm" > /* 分数背包：贪心 */< / span >
< a id = "__codelineno-7-13" name = "__codelineno-7-13" href = "#__codelineno-7-13" > < / a > < span class = "kt" > double< / span > < span class = "w" > < / span > < span class = "nf" > fractionalKnapsack< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "n" > wgt< / 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" > val< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "p" > )< / span > < 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" > // 创建物品列表，包含两个属性：重量、价值< / span >
< a id = "__codelineno-7-15" name = "__codelineno-7-15" href = "#__codelineno-7-15" > < / a > < span class = "w" > < / span > < span class = "n" > Item< / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "n" > items< / 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" > Item< / span > < span class = "p" > [< / span > < span class = "n" > wgt< / span > < span class = "p" > .< / span > < span class = "n" > Length< / 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 = "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" > wgt< / span > < span class = "p" > .< / span > < span class = "n" > Length< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-17" name = "__codelineno-7-17" href = "#__codelineno-7-17" > < / a > < span class = "w" > < / span > < span class = "n" > items< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > Item< / span > < span class = "p" > (< / span > < span class = "n" > wgt< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > [< / span > < span class = "n" > i< / 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 = "p" > }< / span >
< a id = "__codelineno-7-19" name = "__codelineno-7-19" href = "#__codelineno-7-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 按照单位价值 item.v / item.w 从高到低进行排序< / span >
< a id = "__codelineno-7-20" name = "__codelineno-7-20" href = "#__codelineno-7-20" > < / 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" > items< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > x< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > y< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > => < / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > y< / span > < span class = "p" > .< / span > < span class = "n" > v< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "n" > y< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "p" > ).< / span > < span class = "n" > CompareTo< / span > < span class = "p" > (< / span > < span class = "n" > x< / span > < span class = "p" > .< / span > < span class = "n" > v< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "n" > x< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-7-21" name = "__codelineno-7-21" href = "#__codelineno-7-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环贪心选择< / span >
< a id = "__codelineno-7-22" name = "__codelineno-7-22" href = "#__codelineno-7-22" > < / a > < span class = "w" > < / span > < span class = "kt" > double< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-23" name = "__codelineno-7-23" href = "#__codelineno-7-23" > < / a > < span class = "w" > < / span > < span class = "k" > foreach< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > Item< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "w" > < / span > < span class = "k" > in< / span > < span class = "w" > < / span > < span class = "n" > items< / span > < span class = "p" > )< / span > < span class = "w" > < / 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 = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-25" name = "__codelineno-7-25" href = "#__codelineno-7-25" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若剩余容量充足，则将当前物品整个装进背包< / span >
< a id = "__codelineno-7-26" name = "__codelineno-7-26" href = "#__codelineno-7-26" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > v< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-27" name = "__codelineno-7-27" href = "#__codelineno-7-27" > < / a > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "w" > < / span > < span class = "o" > -=< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-28" name = "__codelineno-7-28" href = "#__codelineno-7-28" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-29" name = "__codelineno-7-29" href = "#__codelineno-7-29" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若剩余容量不足，则将当前物品的一部分装进背包< / span >
< a id = "__codelineno-7-30" name = "__codelineno-7-30" href = "#__codelineno-7-30" > < / a > < 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 = "kt" > double< / span > < span class = "p" > )< / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > v< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > cap< / 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 = "c1" > // 已无剩余容量，因此跳出循环< / span >
< a id = "__codelineno-7-32" name = "__codelineno-7-32" href = "#__codelineno-7-32" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-33" name = "__codelineno-7-33" href = "#__codelineno-7-33" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-7-34" name = "__codelineno-7-34" href = "#__codelineno-7-34" > < / a > < span class = "w" > < / span > < span class = "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 = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-36" name = "__codelineno-7-36" href = "#__codelineno-7-36" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > fractional_knapsack.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-8-1" name = "__codelineno-8-1" href = "#__codelineno-8-1" > < / a > < span class = "p" > [< / span > < span class = "kd" > class< / span > < span class = "p" > ]{< / span > < span class = "n" > Item< / span > < span class = "p" > }< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "kd" > func< / span > < span class = "p" > ]{}< / span >
< a id = "__codelineno-8-2" name = "__codelineno-8-2" href = "#__codelineno-8-2" > < / a >
< a id = "__codelineno-8-3" name = "__codelineno-8-3" href = "#__codelineno-8-3" > < / a > < span class = "p" > [< / span > < span class = "kd" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "kd" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > fractionalKnapsack< / span > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > fractional_knapsack.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-9-1" name = "__codelineno-9-1" href = "#__codelineno-9-1" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{< / span > < span class = "n" > Item< / span > < span class = "p" > }< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{}< / span >
< a id = "__codelineno-9-2" name = "__codelineno-9-2" href = "#__codelineno-9-2" > < / a >
< a id = "__codelineno-9-3" name = "__codelineno-9-3" href = "#__codelineno-9-3" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > fractionalKnapsack< / span > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > fractional_knapsack.dart< / span > < pre > < span > < / span > < code > < a id = "__codelineno-10-1" name = "__codelineno-10-1" href = "#__codelineno-10-1" > < / a > < span class = "cm" > /* 物品 */< / span >
< a id = "__codelineno-10-2" name = "__codelineno-10-2" href = "#__codelineno-10-2" > < / a > < span class = "kd" > class< / span > < span class = "w" > < / span > < span class = "nc" > Item< / 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 = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > w< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 物品重量< / span >
< a id = "__codelineno-10-4" name = "__codelineno-10-4" href = "#__codelineno-10-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > v< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 物品价值< / span >
< a id = "__codelineno-10-5" name = "__codelineno-10-5" href = "#__codelineno-10-5" > < / a >
< a id = "__codelineno-10-6" name = "__codelineno-10-6" href = "#__codelineno-10-6" > < / a > < span class = "w" > < / span > < span class = "n" > Item< / span > < span class = "p" > (< / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "n" > v< / span > < span class = "p" > );< / span >
< a id = "__codelineno-10-7" name = "__codelineno-10-7" href = "#__codelineno-10-7" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-10-8" name = "__codelineno-10-8" href = "#__codelineno-10-8" > < / a >
< a id = "__codelineno-10-9" name = "__codelineno-10-9" href = "#__codelineno-10-9" > < / a > < span class = "cm" > /* 分数背包：贪心 */< / span >
< a id = "__codelineno-10-10" name = "__codelineno-10-10" href = "#__codelineno-10-10" > < / a > < span class = "kt" > double< / span > < span class = "w" > < / span > < span class = "n" > fractionalKnapsack< / 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" > wgt< / span > < span class = "p" > ,< / 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 = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "p" > )< / span > < span class = "w" > < / 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 = "c1" > // 创建物品列表，包含两个属性：重量、价值< / span >
< a id = "__codelineno-10-12" name = "__codelineno-10-12" href = "#__codelineno-10-12" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Item< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > items< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "p" > .< / span > < span class = "n" > generate< / span > < span class = "p" > (< / span > < span class = "n" > wgt< / span > < span class = "p" > .< / span > < span class = "n" > length< / span > < span class = "p" > ,< / span > < span class = "w" > < / 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" > Item< / span > < span class = "p" > (< / span > < span class = "n" > wgt< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]));< / span >
< a id = "__codelineno-10-13" name = "__codelineno-10-13" href = "#__codelineno-10-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 按照单位价值 item.v / item.w 从高到低进行排序< / span >
< a id = "__codelineno-10-14" name = "__codelineno-10-14" href = "#__codelineno-10-14" > < / a > < span class = "w" > < / span > < span class = "n" > items< / span > < span class = "p" > .< / span > < span class = "n" > sort< / span > < span class = "p" > ((< / span > < span class = "n" > a< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > b< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > => < / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > b< / span > < span class = "p" > .< / span > < span class = "n" > v< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "n" > b< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "p" > ).< / span > < span class = "n" > compareTo< / span > < span class = "p" > (< / span > < span class = "n" > a< / span > < span class = "p" > .< / span > < span class = "n" > v< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "n" > a< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-10-15" name = "__codelineno-10-15" href = "#__codelineno-10-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环贪心选择< / span >
< a id = "__codelineno-10-16" name = "__codelineno-10-16" href = "#__codelineno-10-16" > < / a > < span class = "w" > < / span > < span class = "kt" > double< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-17" name = "__codelineno-10-17" href = "#__codelineno-10-17" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > Item< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "w" > < / span > < span class = "k" > in< / span > < span class = "w" > < / span > < span class = "n" > items< / span > < span class = "p" > )< / span > < 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 = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-10-19" name = "__codelineno-10-19" href = "#__codelineno-10-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若剩余容量充足，则将当前物品整个装进背包< / span >
< a id = "__codelineno-10-20" name = "__codelineno-10-20" href = "#__codelineno-10-20" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > v< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-21" name = "__codelineno-10-21" href = "#__codelineno-10-21" > < / a > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "w" > < / span > < span class = "o" > -=< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > w< / 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 = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-10-23" name = "__codelineno-10-23" href = "#__codelineno-10-23" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若剩余容量不足，则将当前物品的一部分装进背包< / span >
< a id = "__codelineno-10-24" name = "__codelineno-10-24" href = "#__codelineno-10-24" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > v< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-25" name = "__codelineno-10-25" href = "#__codelineno-10-25" > < / a > < span class = "w" > < / span > < span class = "c1" > // 已无剩余容量，因此跳出循环< / span >
< a id = "__codelineno-10-26" name = "__codelineno-10-26" href = "#__codelineno-10-26" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-27" name = "__codelineno-10-27" href = "#__codelineno-10-27" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-10-28" name = "__codelineno-10-28" href = "#__codelineno-10-28" > < / a > < 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 = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-30" name = "__codelineno-10-30" href = "#__codelineno-10-30" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > fractional_knapsack.rs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-11-1" name = "__codelineno-11-1" href = "#__codelineno-11-1" > < / a > < span class = "cm" > /* 物品 */< / span >
< a id = "__codelineno-11-2" name = "__codelineno-11-2" href = "#__codelineno-11-2" > < / a > < span class = "k" > struct< / span > < span class = "nc" > Item< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-3" name = "__codelineno-11-3" href = "#__codelineno-11-3" > < / a > < span class = "w" > < / span > < span class = "n" > w< / span > : < span class = "kt" > i32< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "c1" > // 物品重量< / span >
< a id = "__codelineno-11-4" name = "__codelineno-11-4" href = "#__codelineno-11-4" > < / a > < span class = "w" > < / span > < span class = "n" > v< / span > : < span class = "kt" > i32< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "c1" > // 物品价值< / span >
< a id = "__codelineno-11-5" name = "__codelineno-11-5" href = "#__codelineno-11-5" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-11-6" name = "__codelineno-11-6" href = "#__codelineno-11-6" > < / a >
< a id = "__codelineno-11-7" name = "__codelineno-11-7" href = "#__codelineno-11-7" > < / a > < span class = "k" > impl< / span > < span class = "w" > < / span > < span class = "n" > Item< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-8" name = "__codelineno-11-8" href = "#__codelineno-11-8" > < / a > < span class = "w" > < / span > < span class = "k" > fn< / span > < span class = "nf" > new< / span > < span class = "p" > (< / span > < span class = "n" > w< / span > : < span class = "kt" > i32< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > v< / span > : < span class = "kt" > i32< / span > < span class = "p" > )< / span > < span class = "w" > < / span > -> < span class = "nc" > Self< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-9" name = "__codelineno-11-9" href = "#__codelineno-11-9" > < / a > < span class = "w" > < / span > < span class = "bp" > Self< / span > < span class = "w" > < / span > < span class = "p" > {< / span > < span class = "w" > < / span > < span class = "n" > w< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > v< / span > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-10" name = "__codelineno-11-10" href = "#__codelineno-11-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-11" name = "__codelineno-11-11" href = "#__codelineno-11-11" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-11-12" name = "__codelineno-11-12" href = "#__codelineno-11-12" > < / a >
< a id = "__codelineno-11-13" name = "__codelineno-11-13" href = "#__codelineno-11-13" > < / a > < span class = "cm" > /* 分数背包：贪心 */< / span >
< a id = "__codelineno-11-14" name = "__codelineno-11-14" href = "#__codelineno-11-14" > < / a > < span class = "k" > fn< / span > < span class = "nf" > fractional_knapsack< / span > < span class = "p" > (< / span > < span class = "n" > wgt< / 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" > val< / span > : < span class = "kp" > & < / span > < span class = "p" > [< / span > < span class = "kt" > i32< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > cap< / span > : < span class = "kt" > i32< / span > < span class = "p" > )< / span > < span class = "w" > < / span > -> < span class = "kt" > f64< / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-15" name = "__codelineno-11-15" href = "#__codelineno-11-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 创建物品列表，包含两个属性：重量、价值< / span >
< a id = "__codelineno-11-16" name = "__codelineno-11-16" href = "#__codelineno-11-16" > < / 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" > items< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > wgt< / span >
< a id = "__codelineno-11-17" name = "__codelineno-11-17" href = "#__codelineno-11-17" > < / a > < span class = "w" > < / span > < span class = "p" > .< / span > < span class = "n" > iter< / span > < span class = "p" > ()< / span >
< a id = "__codelineno-11-18" name = "__codelineno-11-18" href = "#__codelineno-11-18" > < / a > < span class = "w" > < / span > < span class = "p" > .< / span > < span class = "n" > zip< / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "p" > .< / span > < span class = "n" > iter< / span > < span class = "p" > ())< / span >
< a id = "__codelineno-11-19" name = "__codelineno-11-19" href = "#__codelineno-11-19" > < / a > < span class = "w" > < / span > < span class = "p" > .< / span > < span class = "n" > map< / span > < span class = "p" > (< / span > < span class = "o" > |< / span > < span class = "p" > (< / span > < span class = "o" > & < / span > < span class = "n" > w< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > v< / span > < span class = "p" > )< / span > < span class = "o" > |< / span > < span class = "w" > < / span > < span class = "n" > Item< / span > ::< span class = "n" > new< / span > < span class = "p" > (< / span > < span class = "n" > w< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > v< / span > < span class = "p" > ))< / span >
< a id = "__codelineno-11-20" name = "__codelineno-11-20" href = "#__codelineno-11-20" > < / a > < span class = "w" > < / span > < span class = "p" > .< / span > < span class = "n" > collect< / span > ::< span class = "o" > < < / span > < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "n" > Item< / span > < span class = "o" > > > < / span > < span class = "p" > ();< / span >
< a id = "__codelineno-11-21" name = "__codelineno-11-21" href = "#__codelineno-11-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 按照单位价值 item.v / item.w 从高到低进行排序< / span >
< a id = "__codelineno-11-22" name = "__codelineno-11-22" href = "#__codelineno-11-22" > < / a > < span class = "w" > < / span > < span class = "n" > items< / span > < span class = "p" > .< / span > < span class = "n" > sort_by< / span > < span class = "p" > (< / span > < span class = "o" > |< / span > < span class = "n" > a< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > b< / span > < span class = "o" > |< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-23" name = "__codelineno-11-23" href = "#__codelineno-11-23" > < / a > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > b< / span > < span class = "p" > .< / span > < span class = "n" > v< / span > < span class = "w" > < / span > < span class = "k" > as< / span > < span class = "w" > < / span > < span class = "kt" > f64< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "n" > b< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "w" > < / span > < span class = "k" > as< / span > < span class = "w" > < / span > < span class = "kt" > f64< / span > < span class = "p" > )< / span >
< a id = "__codelineno-11-24" name = "__codelineno-11-24" href = "#__codelineno-11-24" > < / a > < span class = "w" > < / span > < span class = "p" > .< / span > < span class = "n" > partial_cmp< / span > < span class = "p" > (< / span > < span class = "o" > & < / span > < span class = "p" > (< / span > < span class = "n" > a< / span > < span class = "p" > .< / span > < span class = "n" > v< / span > < span class = "w" > < / span > < span class = "k" > as< / span > < span class = "w" > < / span > < span class = "kt" > f64< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "n" > a< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "w" > < / span > < span class = "k" > as< / span > < span class = "w" > < / span > < span class = "kt" > f64< / span > < span class = "p" > ))< / span >
< a id = "__codelineno-11-25" name = "__codelineno-11-25" href = "#__codelineno-11-25" > < / a > < span class = "w" > < / span > < span class = "p" > .< / span > < span class = "n" > unwrap< / span > < span class = "p" > ()< / span >
< a id = "__codelineno-11-26" name = "__codelineno-11-26" href = "#__codelineno-11-26" > < / a > < span class = "w" > < / span > < span class = "p" > });< / span >
< a id = "__codelineno-11-27" name = "__codelineno-11-27" href = "#__codelineno-11-27" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环贪心选择< / span >
< a id = "__codelineno-11-28" name = "__codelineno-11-28" href = "#__codelineno-11-28" > < / 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 = "mf" > 0.0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-11-29" name = "__codelineno-11-29" href = "#__codelineno-11-29" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "w" > < / span > < span class = "k" > in< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > items< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-30" name = "__codelineno-11-30" href = "#__codelineno-11-30" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-31" name = "__codelineno-11-31" href = "#__codelineno-11-31" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若剩余容量充足，则将当前物品整个装进背包< / span >
< a id = "__codelineno-11-32" name = "__codelineno-11-32" href = "#__codelineno-11-32" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > v< / span > < span class = "w" > < / span > < span class = "k" > as< / span > < span class = "w" > < / span > < span class = "kt" > f64< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-11-33" name = "__codelineno-11-33" href = "#__codelineno-11-33" > < / a > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "w" > < / span > < span class = "o" > -=< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-11-34" name = "__codelineno-11-34" href = "#__codelineno-11-34" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-35" name = "__codelineno-11-35" href = "#__codelineno-11-35" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若剩余容量不足，则将当前物品的一部分装进背包< / span >
< a id = "__codelineno-11-36" name = "__codelineno-11-36" href = "#__codelineno-11-36" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > v< / span > < span class = "w" > < / span > < span class = "k" > as< / span > < span class = "w" > < / span > < span class = "kt" > f64< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "n" > item< / span > < span class = "p" > .< / span > < span class = "n" > w< / span > < span class = "w" > < / span > < span class = "k" > as< / span > < span class = "w" > < / span > < span class = "kt" > f64< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > cap< / span > < span class = "w" > < / span > < span class = "k" > as< / span > < span class = "w" > < / span > < span class = "kt" > f64< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-11-37" name = "__codelineno-11-37" href = "#__codelineno-11-37" > < / a > < span class = "w" > < / span > < span class = "c1" > // 已无剩余容量，因此跳出循环< / span >
< a id = "__codelineno-11-38" name = "__codelineno-11-38" href = "#__codelineno-11-38" > < / a > < span class = "w" > < / span > < span class = "k" > break< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-11-39" name = "__codelineno-11-39" href = "#__codelineno-11-39" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-40" name = "__codelineno-11-40" href = "#__codelineno-11-40" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-41" name = "__codelineno-11-41" href = "#__codelineno-11-41" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span >
< a id = "__codelineno-11-42" name = "__codelineno-11-42" href = "#__codelineno-11-42" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< p > 最差情况下，需要遍历整个物品列表，< strong > 因此时间复杂度为 < span class = "arithmatex" > \(O(n)\)< / span > < / strong > ，其中 < span class = "arithmatex" > \(n\)< / span > 为物品数量。< / p >
< p > 由于初始化了一个 < code > Item< / code > 对象列表，< strong > 因此空间复杂度为 < span class = "arithmatex" > \(O(n)\)< / span > < / strong > 。< / p >
< h3 id = "3" > 3. 正确性证明< a class = "headerlink" href = "#3" title = "Permanent link" > ¶ < / a > < / h3 >
< p > 采用反证法。假设物品 < span class = "arithmatex" > \(x\)< / span > 是单位价值最高的物品，使用某算法求得最大价值为 < code > res< / code > ，但该解中不包含物品 < span class = "arithmatex" > \(x\)< / span > 。< / p >
< p > 现在从背包中拿出单位重量的任意物品，并替换为单位重量的物品 < span class = "arithmatex" > \(x\)< / span > 。由于物品 < span class = "arithmatex" > \(x\)< / span > 的单位价值最高，因此替换后的总价值一定大于 < code > res< / code > 。< strong > 这与 < code > res< / code > 是最优解矛盾，说明最优解中必须包含物品 < span class = "arithmatex" > \(x\)< / span > < / strong > 。< / p >
< p > 对于该解中的其他物品，我们也可以构建出上述矛盾。总而言之，< strong > 单位价值更大的物品总是更优选择< / strong > ，这说明贪心策略是有效的。< / p >
< p > 如图 15-6 所示，如果将物品重量和物品单位价值分别看作一个 2D 图表的横轴和纵轴，则分数背包问题可被转化为“求在有限横轴区间下的最大围成面积”。这个类比可以帮助我们从几何角度理解贪心策略的有效性。< / p >
< p > < img alt = "分数背包问题的几何表示" src = "../fractional_knapsack_problem.assets/fractional_knapsack_area_chart.png" / > < / p >
< p align = "center" > 图 15-6 分数背包问题的几何表示 < / p >
< h2 id = "__comments" > 评论< / h2 >
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