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C++ Program to Solve the Fractional Knapsack Problem

This is a C++ Program to solve fractional knapsack. The knapsack problem or rucksack problem is a problem in combinatorial optimization: Given a set of items, each with a mass and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible. It derives its name from the problem faced by someone who is constrained by a fixed-size knapsack and must fill it with the most valuable items.

Here is source code of the C++ Program to Solve the Fractional Knapsack Problem. The C++ program is successfully compiled and run on a Linux system. The program output is also shown below.

/* program to implement fractional knapsack problem using greedy programming */

```
#include<iostream>
```
```
using namespace std;
```
```
int main()
```
```
{
```

    int array[2][100], n, w, i, curw, used[100], maxi = -1, totalprofit = 0;

```
    //input number of objects
```

    cout << "Enter number of objects: ";

```
    cin >> n;
```
```
    //input max weight of knapsack
```

    cout << "Enter the weight of the knapsack: ";

```
    cin >> w;
```

    /* Array's first row is to store weights

```
     second row is to store profits */
```
```
    for (i = 0; i < n; i++)
```
```
    {
```

        cin >> array[0][i] >> array[1][i];

```
    }
```
```
    for (i = 0; i < n; i++)
```
```
    {
```
```
        used[i] = 0;
```
```
    }
```
```
    curw = w;
```
```
    //loop until knapsack is full
```
```
    while (curw >= 0)
```
```
    {
```
```
        maxi = -1;
```

        //loop to find max profit object

```
        for (i = 0; i < n; i++)
```
```
        {
```

            if ((used[i] == 0) && ((maxi == -1) || (((float) array[1][i]

                    / (float) array[0][i]) > ((float) array[1][maxi]

                    / (float) array[0][maxi]))))

```
            {
```
```
                maxi = i;
```
```
            }
```
```
        }
```
```
        used[maxi] = 1;
```
```
        //decrease current wight
```
```
        curw -= array[0][maxi];
```
```
        //increase total profit
```
```
        totalprofit += array[1][maxi];
```
```
        if (curw >= 0)
```
```
        {
```

            cout << "\nAdded object " << maxi + 1 << " Weight: "

                    << array[0][maxi] << " Profit: " << array[1][maxi]

                    << " completely in the bag, Space left: " << curw;

```
        }
```
```
        else
```
```
        {
```

            cout << "\nAdded object " << maxi + 1 << " Weight: "

                    << (array[0][maxi] + curw) << " Profit: "

                    << (array[1][maxi] / array[0][maxi]) * (array[0][maxi]

                            + curw) << " partially in the bag, Space left: 0"

                    << " Weight added is: " << curw + array[0][maxi];

            totalprofit -= array[1][maxi];

            totalprofit += ((array[1][maxi] / array[0][maxi]) * (array[0][maxi]

```
                    + curw));
```
```
        }
```
```
    }
```

    //print total worth of objects filled in knapsack

    cout << "\nBags filled with objects worth: " << totalprofit;

```
    return 0;
```
```
}
```

Output:

$ g++ FractionalKnapsack.cpp
$ a.out
 
Enter number of objects: 3
Enter the weight of the knapsack: 50
10 60
20 100
30 120
 
Added object 1 Weight: 10 Profit: 60 completely in the bag, Space left: 40
Added object 2 Weight: 20 Profit: 100 completely in the bag, Space left: 20
Added object 3 Weight: 20 Profit: 80 partially in the bag, Space left: 0 Weight added is: 20
Bags filled with objects worth: 240

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C++ Program to Solve the Fractional Knapsack Problem

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