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def is_sum_subset(arr: list[int], required_sum: int) -> bool:

"""

>>> is_sum_subset([2, 4, 6, 8], 5)

False

>>> is_sum_subset([2, 4, 6, 8], 14)

True

"""

# a subset value says 1 if that subset sum can be formed else 0

# initially no subsets can be formed hence False/0

arr_len = len(arr)

subset = [[False] * (required_sum + 1) for _ in range(arr_len + 1)]

# for each arr value, a sum of zero(0) can be formed by not taking any element

# hence True/1

for i in range(arr_len + 1):

subset[i][0] = True

# sum is not zero and set is empty then false

for i in range(1, required_sum + 1):

subset[0][i] = False

for i in range(1, arr_len + 1):

for j in range(1, required_sum + 1):

if arr[i - 1] > j:

subset[i][j] = subset[i - 1][j]

if arr[i - 1] <= j:

subset[i][j] = subset[i - 1][j] or subset[i - 1][j - arr[i - 1]]

return subset[arr_len][required_sum]

if __name__ == "__main__":

import doctest

doctest.testmod()

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