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C++ Program to Solve Knapsack Problem Using Dynamic Programming

This is a C++ Program to knapsack problem using dynamic programming. 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 Knapsack Problem Using Dynamic Programming. The C++ program is successfully compiled and run on a Linux system. The program output is also shown below.

// A Dynamic Programming based solution for 0-1 Knapsack problem

```
#include <iostream>
```
```
 
```
```
using namespace std;
```
```
 
```

// A utility function that returns maximum of two integers

```
int max(int a, int b)
```
```
{
```
```
    return (a > b) ? a : b;
```
```
}
```
```
 
```

// Returns the maximum value that can be put in a knapsack of capacity W

int knapSack(int W, int wt[], int val[], int n)

```
{
```
```
    int i, w;
```
```
    int K[n + 1][W + 1];
```
```
 
```

    // Build table K[][] in bottom up manner

```
    for (i = 0; i <= n; i++)
```
```
    {
```
```
        for (w = 0; w <= W; w++)
```
```
        {
```
```
            if (i == 0 || w == 0)
```
```
                K[i][w] = 0;
```
```
            else if (wt[i - 1] <= w)
```
```
                K[i][w]
```

                        = max(val[i - 1] + K[i - 1][w - wt[i - 1]], K[i - 1][w]);

```
            else
```
```
                K[i][w] = K[i - 1][w];
```
```
        }
```
```
    }
```
```
 
```
```
    return K[n][W];
```
```
}
```
```
 
```
```
int main()
```
```
{
```

    cout << "Enter the number of items in a Knapsack:";

```
    int n, W;
```
```
    cin >> n;
```
```
    int val[n], wt[n];
```
```
    for (int i = 0; i < n; i++)
```
```
    {
```

        cout << "Enter value and weight for item " << i << ":";

```
        cin >> val[i];
```
```
        cin >> wt[i];
```
```
    }
```
```
 
```
```
    //    int val[] = { 60, 100, 120 };
```
```
    //    int wt[] = { 10, 20, 30 };
```
```
    //    int W = 50;
```

    cout << "Enter the capacity of knapsack";

```
    cin >> W;
```
```
    cout << knapSack(W, wt, val, n);
```
```
 
```
```
    return 0;
```
```
}
```

Output:

$ g++ DPKnapsack.cpp
$ a.out
 
Enter the number of items in a Knapsack:5
Enter value and weight for item 0:11 111
Enter value and weight for item 1:22 121
Enter value and weight for item 2:33 131
Enter value and weight for item 3:44 141
Enter value and weight for item 4:55 151
Enter the capacity of knapsack 300
99

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C++ Program to Solve Knapsack Problem Using Dynamic Programming

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