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43 lines
1.3 KiB
Python
43 lines
1.3 KiB
Python
"""
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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.
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"""
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def MF_knapsack(i,wt,val,j):
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'''
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This code involves the concept of memory functions. Here we solve the subproblems which are needed
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unlike the below example
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F is a 2D array with -1s filled up
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'''
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global F # a global dp table for knapsack
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if F[i][j] < 0:
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if j < wt[i - 1]:
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val = MF_knapsack(i - 1,wt,val,j)
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else:
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val = max(MF_knapsack(i - 1,wt,val,j),MF_knapsack(i - 1,wt,val,j - wt[i - 1]) + val[i - 1])
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F[i][j] = val
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return F[i][j]
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def knapsack(W, wt, val, n):
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dp = [[0 for i in range(W+1)]for j in range(n+1)]
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for i in range(1,n+1):
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for w in range(1,W+1):
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if(wt[i-1]<=w):
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dp[i][w] = max(val[i-1]+dp[i-1][w-wt[i-1]],dp[i-1][w])
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else:
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dp[i][w] = dp[i-1][w]
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return dp[n][w]
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if __name__ == '__main__':
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'''
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Adding test case for knapsack
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'''
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val = [3,2,4,4]
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wt = [4,3,2,3]
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n = 4
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w = 6
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F = [[0]*(w + 1)] + [[0] + [-1 for i in range(w + 1)] for j in range(n + 1)]
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print(knapsack(w,wt,val,n))
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print(MF_knapsack(n,wt,val,w)) # switched the n and w
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