"""
Given weights and values of n items, put these items in a knapsack of capacity W to get the maximum total value in the knapsack.
"""
def MF_knapsack(i,wt,val,j):
 '''
 This code involves the concept of memory functions. Here we solve the subproblems which are needed
 unlike the below example
 F is a 2D array with -1s filled up
 '''
 global F # a global dp table for knapsack
 if F[i][j] < 0:
 if j < wt[i - 1]:
 val = MF_knapsack(i - 1,wt,val,j)
 else:
 val = max(MF_knapsack(i - 1,wt,val,j),MF_knapsack(i - 1,wt,val,j - wt[i - 1]) + val[i - 1])
 F[i][j] = val
 return F[i][j]

def knapsack(W, wt, val, n):
 dp = [[0 for i in range(W+1)]for j in range(n+1)]

 for i in range(1,n+1):
 for w in range(1,W+1):
 if(wt[i-1]<=w):
 dp[i][w] = max(val[i-1]+dp[i-1][w-wt[i-1]],dp[i-1][w])
 else:
 dp[i][w] = dp[i-1][w]

 return dp[n][w]

if __name__ == '__main__':
 '''
 Adding test case for knapsack
 '''
 val = [3,2,4,4]
 wt = [4,3,2,3]
 n = 4
 w = 6
 F = [[0]*(w + 1)] + [[0] + [-1 for i in range(w + 1)] for j in range(n + 1)]
 print(knapsack(w,wt,val,n))
 print(MF_knapsack(n,wt,val,w)) # switched the n and w