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ACM Greedy Mouse

攻城狮锦灏技术 2022年11月10日

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Greedy Mouse

时间限制：1000 ms | 内存限制：65535 KB难度：3

描述

A fat mouse prepared M pounds of cat food,ready to trade with the cats guarding the warehouse containing his

favorite food:peanut. The warehouse has N rooms.The ith room containsW[i] pounds of peanut and requires

F[i] pounds of cat food. Fatmouse does not have to trade for all the peanut in the room,instead,he may get

W[i]*a% pounds of peanut if he pays F[i]*a% pounds of cat food.The mouse is a stupid mouse,so can you tell

him the maximum amount of peanut he can obtain.

输入

The input consists of multiple test cases. Each test case begins with a line containing two non-negative integers M and N. Then N lines follow, each contains two non-negative integers W[i] and F[i] respectively. The test case is terminated by two -1. All integers are not greater than 1000.

输出

For each test case, print in a single line a real number accurate up to 3 decimal places, which is the maximum amount of penaut that FatMouse can obtain.

样例输入

样例输出

13.333
31.500
基本的背包问题，用贪心求解

#include <iostream>
#include <algorithm>
#include <vector>
#include <cstdio>
#include <utility>
using namespace std;
typedef pair<double,double> W;
bool cmp(const W& a,const W& b){ return a.first > b.first;}
int main(){
    double m;
    int n;
    while(cin >>  m >> n && m!=- && n!=-){
        vector<W> exchange(n);
        for(int i =  ; i < n; ++ i){
            double w,f;
            cin >>w >>f;
            exchange[i].first = w/f;
            exchange[i].second = w;
        }
        sort(exchange.begin(),exchange.end(), cmp);
        double res = ;
        for(int i =  ; i < n && m; ++i){
            if(m > exchange[i].second/exchange[i].first){
                res += exchange[i].second;
                m -= exchange[i].second/exchange[i].first;
            }else{
                res+=m*exchange[i].first;
                break;
            }
        }
        printf("%0.3f\n",res);
    }
}