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This is a C++ Program to solve 0-1 knapsack problem. 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 0-1 Knapsack Problem. The C++ program is successfully compiled and run on a Linux system. The program output is also shown below.

```
#include<stdio.h>
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#include<conio.h>
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#include<iostream>
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using namespace std;
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```

// A utility function that returns maximum of two integers

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int max(int a, int b)
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{
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    return (a > b) ? a : b;
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}
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// Returns the maximum value that can be put in a knapsack of capacity W

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

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{
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    // Base Case
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    if (n == 0 || W == 0)
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        return 0;
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    // If weight of the nth item is more than Knapsack capacity W, then

    // this item cannot be included in the optimal solution

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    if (wt[n - 1] > W)
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        return knapSack(W, wt, val, n - 1);

```
 
```

    // Return the maximum of two cases: (1) nth item included (2) not included

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    else
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        return max(val[n - 1] + knapSack(W - wt[n - 1], wt, val, n - 1),

                knapSack(W, wt, val, n - 1));

```
}
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```
 
```

// Driver program to test above function

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int main()
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{
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    cout << "Enter the number of items in a Knapsack:";

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    int n, W;
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    cin >> n;
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    int val[n], wt[n];
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    for (int i = 0; i < n; i++)
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    {
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        cout << "Enter value and weight for item " << i << ":";

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        cin >> val[i];
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        cin >> wt[i];
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    }
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    //    int val[] = { 60, 100, 120 };
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    //    int wt[] = { 10, 20, 30 };
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    //    int W = 50;
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    cout << "Enter the capacity of knapsack";

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

$ g++ 0-1Knapsack.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