Fractional Knapsack Problem in Java

This is a java program to implement a standard fractional knapsack problem. It is an algorithmic problem in combinatorial optimization in which the goal is to fill a container (the “knapsack”) with fractional amounts of different materials chosen to maximize the value of the selected materials.

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

//This is a sample program to implement a fractional knapsack problem

```
import java.io.IOException;
```
```
import java.util.Scanner;
```
```
 
```
```
class Fractional_Knapsack  
```
```
{  
```

    public static void main(String args[]) throws IOException

```
    {  
```
```
        int i,j=0,max_qty,m,n;  
```
```
        float sum=0,max;  
```

        Scanner sc = new Scanner(System.in);

```
        int array[][]=new int[2][20];  
```

        System.out.println("Enter no of items");

```
        n=sc.nextInt(); 
```
```
 
```

        System.out.println("Enter the weights of each items");

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

            array[0][i]=sc.nextInt();

```
 
```

        System.out.println("Enter the values of each items");

```
        for(i=0;i<n;i++)  
```
```
            array[1][i]=sc.nextInt(); 
```
```
 
```

        System.out.println("Enter maximum volume of knapsack :");

```
        max_qty=sc.nextInt();  
```
```
 
```
```
        m=max_qty;  
```
```
        while(m>=0)  
```
```
        {  
```
```
            max=0;  
```
```
            for(i=0;i<n;i++)  
```
```
            {  
```

                if(((float)array[1][i])/((float)array[0][i])>max)

```
                {  
```

                    max=((float)array[1][i])/((float)array[0][i]);

```
                    j=i;  
```
```
                }  
```
```
            }  
```
```
            if(array[0][j]>m)  
```
```
            {  
```

                System.out.println("Quantity of item number: " +  (j+1) + " added is " +m);

```
                sum+=m*max;  
```
```
                m=-1;  
```
```
            }  
```
```
            else  
```
```
            {  
```

                System.out.println("Quantity of item number: " + (j+1) + " added is " + array[0][j]);

```
                m-=array[0][j];  
```

                sum+=(float)array[1][j];

```
                array[1][j]=0;  
```
```
            }  
```
```
        }  
```

        System.out.println("The total profit is " + sum);

```
        sc.close();
```
```
    }  
```
```
}
```

Output:

$ javac Fractional_Knapsack.java
$ java Fractional_Knapsack
 
Enter no of items
5
Enter the weights of each items
10 20 30 40 50
Enter the values of each items
5 4 3 2 1
Enter maximum volume of knapsack :
80
Quantity of item number: 1 added is 10
Quantity of item number: 2 added is 20
Quantity of item number: 3 added is 30
Quantity of item number: 4 added is 20
The total profit is 13.0

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