Knapsack Problem using DP in C++

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>
```
```
 
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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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    int i, w;
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    int K[n + 1][W + 1];
```
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    // Build table K[][] in bottom up manner

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

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            else
```
```
                K[i][w] = K[i - 1][w];
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        }
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    }
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    return K[n][W];
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}
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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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}
```

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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