Question

Write an algorithm that uses dynamic program to find a solution to the knapsack problem.

The input is the capacity of the knapsack then each row of the table of values and weights.

The output is the resulting maximum value of the items that can be put in the knapsack.

Code submitted in C++

Sample Input 1:

11
1 1
6 2
18 5
22 6
28 7

Sample Output 1:

40

Sample Input 2:

8
15 1
10 5
9 3
5 4

Sample Output 2:

29

Sample Input 3:

5
1 1
2 1
3 1
4 1
5 1

Sample Output 3:

15

Sample Input 4:

5
1 1
2 1
3 1
4 5

Sample Output 4:

6

Sample Input 5:

5
1 1
2 1
3 1
10 5

Sample Output 5:

10

Sample Input 6:

5
10 5
1 1
2 1
3 1

Sample Output 6:

10

Answer 1

CODE

#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()

{

int n;

cin >> n;

int W;

cin >> W;

  int val[n];

  int wt[n];

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

cin >> val[i];

cin >> wt[i];

}

  cout << knapSack(W, wt, val, n);

  return 0;

}