C++ Program to Solve Knapsack Problem Using Dynamic Programming

This is a C++ program to solve 0-1 knapsack problem using dynamic programming. In 0-1 knapsack problem, a set of items are given, each with a weight and a value. We need to determine the number of each item to include in a collection so that the total weight is less than or equal to the given limit and the total value is large as possible.

Algorithm

Begin
Input set of items each with a weight and a value
Set knapsack capacity
Create a function that returns maximum of two integers.
Create a function which returns the maximum value that can be put in a knapsack of capacity W
int knapSack(int W, int w[], int v[], int n)
int i, wt;
int K[n + 1][W + 1]
for i = 0 to n
for wt = 0 to W
if (i == 0 or wt == 0)
   Do K[i][wt] = 0
else if (w[i - 1] <= wt)
   Compute: K[i][wt] = max(v[i - 1] + K[i - 1][wt - w[i - 1]], K[i -1][wt])
else
   K[i][wt] = K[i - 1][wt]
   return K[n][W]
   Call the function and print.
End

Example Code

#include <iostream>
using namespace std;
int max(int x, int y) {
   return (x > y) ? x : y;
}
int knapSack(int W, int w[], int v[], int n) {
   int i, wt;
   int K[n + 1][W + 1];
   for (i = 0; i <= n; i++) {
      for (wt = 0; wt <= W; wt++) {
         if (i == 0 || wt == 0)
         K[i][wt] = 0;
         else if (w[i - 1] <= wt)
            K[i][wt] = max(v[i - 1] + K[i - 1][wt - w[i - 1]], K[i - 1][wt]);
         else
        K[i][wt] = K[i - 1][wt];
      }
   }
   return K[n][W];
}
int main() {
   cout << "Enter the number of items in a Knapsack:";
   int n, W;
   cin >> n;
   int v[n], w[n];
   for (int i = 0; i < n; i++) {
      cout << "Enter value and weight for item " << i << ":";
      cin >> v[i];
      cin >> w[i];
   }
   cout << "Enter the capacity of knapsack";
   cin >> W;
   cout << knapSack(W, w, v, n);
   return 0;
}

Output

Enter the number of items in a Knapsack:4
Enter value and weight for item 0:10
50
Enter value and weight for item 1:20
60
Enter value and weight for item 2:30
70
Enter value and weight for item 3:40
90
Enter the capacity of knapsack100
40