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Fractional knapsack.cpp
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Fractional knapsack.cpp
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//fractional knapsack problem:
//given items their weights and values and capacity
//find the maximum value obtainable with given capacity
//considering we can take parts of an item
#include <utility>
#include <iostream>
#include <algorithm>
#include <cstdio>
//first is value second is weight
typedef std::pair<double, double> item;
//return if first item has greater value by weight ratio than the
bool comp_item(item& a, item& b){
return a.first/a.second > b.first/b.second;
}
//find the maximum value obtainable
double mx_profit(item items[], int n, double capacity){
double mx= 0;
//sort items by their value/weight ratio in decreasing order
sort(items, items+n, comp_item);
for(int i= 0; i<n; i++){
if(items[i].second <= capacity){
capacity -= items[i].second;
mx+= items[i].first;
}
else{
mx+= items[i].first/items[i].second * capacity;
capacity= 0;
break;
}
}
return mx;
}
int main(void)
{
using namespace std;
int n;
item items[100];
double capacity;
cin>>n>>capacity;
for(int i= 0; i<n; i++){
cin>>items[i].first>>items[i].second;
}
cout<< mx_profit(items, n, capacity) <<endl;
return 0;
}
/*
//n number of items, capacity
n lines: value (of current weight) weight
3 50
60 10
100 20
120 30
*/