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knapsack/knapsack_memoization.py
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@ -22,8 +22,10 @@ Dynamic Programming
for more information visit https://en.wikipedia.org/wiki/Memoization for more information visit https://en.wikipedia.org/wiki/Memoization
""" """
def knapsack(values:list, weights:list, num_of_items:int, max_weight:int, dp:list
) -> int: def knapsack(
values: list, weights: list, num_of_items: int, max_weight: int, dp: list
) -> int:
""" """
Function description is as follows- Function description is as follows-
:param weights: Take a list of weights :param weights: Take a list of weights
@ -64,25 +66,30 @@ def knapsack(values:list, weights:list, num_of_items:int, max_weight:int, dp:lis
>>> knapsack(values,wt,n,w,dp) >>> knapsack(values,wt,n,w,dp)
75 75
""" """
#no profit gain if any of these two become zero # no profit gain if any of these two become zero
if max_weight == 0 or num_of_items == 0: if max_weight == 0 or num_of_items == 0:
dp[num_of_items][max_weight] = 0 dp[num_of_items][max_weight] = 0
return 0 return 0
#if this case is previously encountered => maximum gain for this case is already # if this case is previously encountered => maximum gain for this case is already
elif dp[num_of_items][max_weight] != -1: elif dp[num_of_items][max_weight] != -1:
#in dp table # in dp table
return dp[num_of_items][max_weight] return dp[num_of_items][max_weight]
#if the item can be included in the bag # if the item can be included in the bag
elif weights[num_of_items-1] <= max_weight: elif weights[num_of_items - 1] <= max_weight:
# ans1 stores the maximum profit if the item at # ans1 stores the maximum profit if the item at
# index num_of_items -1 is included in the bag # index num_of_items -1 is included in the bag
incl = knapsack(values,weights,num_of_items-1, incl = knapsack(
max_weight-weights[num_of_items-1],dp) values,
weights,
num_of_items - 1,
max_weight - weights[num_of_items - 1],
dp,
)
ans1 = values[num_of_items - 1] + incl ans1 = values[num_of_items - 1] + incl
# ans2 stores the maximum profit if the item at # ans2 stores the maximum profit if the item at
# index num_of_items -1 is not included in the bag # index num_of_items -1 is not included in the bag
ans2 = knapsack(values, weights, num_of_items-1, max_weight, dp) ans2 = knapsack(values, weights, num_of_items - 1, max_weight, dp)
# the final answer is the maximum profit gained from any of ans1 or ans2 # the final answer is the maximum profit gained from any of ans1 or ans2
dp[num_of_items][max_weight] = max(ans1, ans2) dp[num_of_items][max_weight] = max(ans1, ans2)
return dp[num_of_items][max_weight] return dp[num_of_items][max_weight]
@ -90,12 +97,13 @@ def knapsack(values:list, weights:list, num_of_items:int, max_weight:int, dp:lis
# if the item's weight exceeds the max_weight of the bag # if the item's weight exceeds the max_weight of the bag
# => it cannot be included in the bag # => it cannot be included in the bag
else: else:
dp[num_of_items][max_weight] = knapsack(values, weights, dp[num_of_items][max_weight] = knapsack(
num_of_items-1, max_weight, dp) values, weights, num_of_items - 1, max_weight, dp
)
return dp[num_of_items][max_weight] return dp[num_of_items][max_weight]
if __name__ == "__main__":
if __name__ == '__main__':
import doctest import doctest
doctest.testmod(name='knapsack', verbose=True)
doctest.testmod(name="knapsack", verbose=True)