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Added code for memory function implementation #331

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Merged
christianbender merged 3 commits into from
Jul 23, 2018
Merged

Added code for memory function implementation #331

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a9f9062
Added code for memory function implementation
bharath-123 Jul 22, 2018
bd7054a
updated testcase
bharath-123 Jul 23, 2018
dc5e42a
Merge branch 'master' into patch-2
bharath-123 Jul 23, 2018
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32 changes: 25 additions & 7 deletions dynamic_programming/knapsack.py
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Original file line number Diff line number Diff line change
@@ -1,6 +1,21 @@
"""
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)]

Expand All @@ -12,13 +27,16 @@ def knapsack(W, wt, val, n):
dp[i][w] = dp[i-1][w]

return dp[n][w]
if __name__ == "__main__":

if __name__ == '__main__':
'''
Adding test case for knapsack
'''
val = [3,2,4,4]
wt = [4,3,2,3]
W = 6
n = 4
'''
Should give 8
'''
print(knapsack(W,wt,val,n))

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