Examveda

What is the time complexity of the following dynamic programming implementation of the Knapsack problem with n items and a maximum weight of W?
#include<stdio.h>
int find_max(int a, int b)
{
      if(a > b)
         return a;
      return b;
}
int knapsack(int W, int *wt, int *val,int n)
{
     int ans[n + 1][W + 1];
     int itm,w;
     for(itm = 0; itm <= n; itm++)
         ans[itm][0] = 0;
     for(w = 0;w <= W; w++)
        ans[0][w] = 0;
     for(itm = 1; itm <= n; itm++)
     {
          for(w = 1; w <= W; w++)
          {
               if(wt[itm - 1] <= w)
                 ans[itm][w] = find_max(ans[itm - 1][w-wt[itm - 1]]+val[itm - 1], ans[itm - 1][w]);
               else
                  ans[itm][w] = ans[itm - 1][w];
          }
     }
     return ans[n][W];
}
int main()
{
     int w[] = {10,20,30}, v[] = {60, 100, 120}, W = 50;
     int ans = knapsack(W, w, v, 3);
     printf("%d",ans);
     return 0;
}

A. O(n)

B. O(n + w)

C. O(nW)

D. O(n2)

Answer: Option C


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