Question

I’ve run into a thinking trouble and I’m just frustrated. I have a working algorithm of the knapsack problem, using dynamic programming, where I specify

• Max load
• Items (their weight)

and the algorithm calculates the optimal fill of the knapsack using those items. But now I need to fill it completely, using least items, but I have unlimited amount of each item. (Those items have weights {1; w1; w2; ...} so it is always possible to complete).

How do I fit this in the ‘classic’ algorithm?

Thanks

Answer 1

Let

• M = Amount need to fill
• w[] = Array of weights
• dp[] = Array of optimal fill(dp[i] contains minimum number of items needed to fill weight i).

 initialize the dp array with INFINITY, dp[0] = 0;
 for(i = 0;i<size of w;i++) {
    for(j = 1;j<=M;j++) {
       if(j-w[i] >= 0) {
          dp[j] = min(dp[j], dp[j-w[i]]+1);
       }
    }
 }

 final solution is the value of dp[M];