mirror of
https://hub.njuu.cf/TheAlgorithms/Python.git
synced 2023-10-11 13:06:12 +08:00
[pre-commit.ci] auto fixes from pre-commit.com hooks
for more information, see https://pre-commit.ci
This commit is contained in:
parent
0e789ce3ec
commit
1d756e4621
@ -15,24 +15,26 @@ Calculate:
|
||||
The maximum profit that the shopkeeper can make given maxmum weight that can
|
||||
be carried.
|
||||
|
||||
This problem is implemented here with MEMOIZATION method using the concept of
|
||||
This problem is implemented here with MEMOIZATION method using the concept of
|
||||
Dynamic Programming
|
||||
"""
|
||||
"""
|
||||
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-
|
||||
:param weights: Take a list of weights
|
||||
:param values: Take a list of profits corresponding to the weights
|
||||
:param number_of_items: number of items available to pick from
|
||||
:param max_weight: Maximum weight that could be carried
|
||||
:param dp: it is a list of list, i.e, a table whose (i,j)
|
||||
:param dp: it is a list of list, i.e, a table whose (i,j)
|
||||
cell represents the maximum profit earned
|
||||
for i items and j as the maximum weight allowed, it
|
||||
for i items and j as the maximum weight allowed, it
|
||||
is an essential part for implementing this problem
|
||||
using memoization dynamic programming
|
||||
:return: Maximum expected gain
|
||||
@ -64,38 +66,44 @@ def knapsack(values:list, weights:list, num_of_items:int, max_weight:int, dp:lis
|
||||
>>> knapsack(values,wt,n,w,dp)
|
||||
75
|
||||
"""
|
||||
#no profit gain if any of these two become zero
|
||||
if max_weight == 0 or num_of_items == 0:
|
||||
# no profit gain if any of these two become zero
|
||||
if max_weight == 0 or num_of_items == 0:
|
||||
dp[num_of_items][max_weight] = 0
|
||||
return 0
|
||||
#if this case is previously encountered => maximum gain for this case is already
|
||||
elif dp[num_of_items][max_weight] != -1:
|
||||
#in dp table
|
||||
# if this case is previously encountered => maximum gain for this case is already
|
||||
elif dp[num_of_items][max_weight] != -1:
|
||||
# in dp table
|
||||
return dp[num_of_items][max_weight]
|
||||
|
||||
#if the item can be included in the bag
|
||||
elif weights[num_of_items-1] <= max_weight:
|
||||
|
||||
# if the item can be included in the bag
|
||||
elif weights[num_of_items - 1] <= max_weight:
|
||||
# ans1 stores the maximum profit if the item at
|
||||
# index num_of_items -1 is included in the bag
|
||||
incl = knapsack(values,weights,num_of_items-1,
|
||||
max_weight-weights[num_of_items-1],dp)
|
||||
incl = knapsack(
|
||||
values,
|
||||
weights,
|
||||
num_of_items - 1,
|
||||
max_weight - weights[num_of_items - 1],
|
||||
dp,
|
||||
)
|
||||
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
|
||||
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
|
||||
dp[num_of_items][max_weight] = max(ans1, ans2)
|
||||
return dp[num_of_items][max_weight]
|
||||
|
||||
|
||||
# if the item's weight exceeds the max_weight of the bag
|
||||
# => it cannot be included in the bag
|
||||
else:
|
||||
dp[num_of_items][max_weight] = knapsack(values, weights,
|
||||
num_of_items-1, max_weight, dp)
|
||||
else:
|
||||
dp[num_of_items][max_weight] = knapsack(
|
||||
values, weights, num_of_items - 1, max_weight, dp
|
||||
)
|
||||
return dp[num_of_items][max_weight]
|
||||
|
||||
|
||||
|
||||
if __name__ == '__main__':
|
||||
if __name__ == "__main__":
|
||||
import doctest
|
||||
doctest.testmod(name='knapsack', verbose=True)
|
||||
|
||||
doctest.testmod(name="knapsack", verbose=True)
|
||||
|
Loading…
Reference in New Issue
Block a user