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hello-algo/zh-hant/codes/cpp/chapter_greedy/fractional_knapsack.cpp

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/**
* File: fractional_knapsack.cpp
* Created Time: 2023-07-20
* Author: krahets (krahets@163.com)
*/
#include "../utils/common.hpp"
/* 物品 */
class Item {
public:
int w; // 物品重量
int v; // 物品價值
Item(int w, int v) : w(w), v(v) {
}
};
/* 分數背包:貪婪 */
double fractionalKnapsack(vector<int> &wgt, vector<int> &val, int cap) {
// 建立物品串列,包含兩個屬性:重量、價值
vector<Item> items;
for (int i = 0; i < wgt.size(); i++) {
items.push_back(Item(wgt[i], val[i]));
}
// 按照單位價值 item.v / item.w 從高到低進行排序
sort(items.begin(), items.end(), [](Item &a, Item &b) { return (double)a.v / a.w > (double)b.v / b.w; });
// 迴圈貪婪選擇
double res = 0;
for (auto &item : items) {
if (item.w <= cap) {
// 若剩餘容量充足,則將當前物品整個裝進背包
res += item.v;
cap -= item.w;
} else {
// 若剩餘容量不足,則將當前物品的一部分裝進背包
res += (double)item.v / item.w * cap;
// 已無剩餘容量,因此跳出迴圈
break;
}
}
return res;
}
/* Driver Code */
int main() {
vector<int> wgt = {10, 20, 30, 40, 50};
vector<int> val = {50, 120, 150, 210, 240};
int cap = 50;
// 貪婪演算法
double res = fractionalKnapsack(wgt, val, cap);
cout << "不超過背包容量的最大物品價值為 " << res << endl;
return 0;
}