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57 lines
1.5 KiB
57 lines
1.5 KiB
/**
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* File: fractional_knapsack.cpp
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* Created Time: 2023-07-20
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* Author: Krahets (krahets@163.com)
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*/
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#include "../utils/common.hpp"
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/* 物品 */
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class Item {
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public:
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int w; // 物品重量
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int v; // 物品价值
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Item(int w, int v) : w(w), v(v) {
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}
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};
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/* 分数背包：贪心 */
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double fractionalKnapsack(vector<int> &wgt, vector<int> &val, int cap) {
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// 创建物品列表，包含两个属性：重量、价值
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vector<Item> items;
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for (int i = 0; i < wgt.size(); i++) {
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items.push_back(Item(wgt[i], val[i]));
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}
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// 按照单位价值 item.v / item.w 从高到低进行排序
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sort(items.begin(), items.end(), [](Item &a, Item &b) { return (double)a.v / a.w > (double)b.v / b.w; });
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// 循环贪心选择
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double res = 0;
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for (auto &item : items) {
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if (item.w <= cap) {
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// 若剩余容量充足，则将当前物品整个装进背包
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res += item.v;
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cap -= item.w;
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} else {
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// 若剩余容量不足，则将当前物品的一部分装进背包
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res += (double)item.v / item.w * cap;
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// 已无剩余容量，因此跳出循环
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break;
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}
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}
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return res;
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}
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/* Driver Code */
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int main() {
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vector<int> wgt = {10, 20, 30, 40, 50};
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vector<int> val = {50, 120, 150, 210, 240};
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int cap = 50;
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// 贪心算法
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double res = fractionalKnapsack(wgt, val, cap);
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cout << "不超过背包容量的最大物品价值为 " << res << endl;
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return 0;
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}
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