





from collections import deque

from .hash_table import HashTable
class 			UpperCamelCase_		(  _lowerCamelCase					):




					def __init__(		self				,						*lowerCAmelCase_				,						**lowerCAmelCase_  )		->							Any:
										super().__init__(*lowerCAmelCase_				,						**lowerCAmelCase_  )




					def 	lowerCAmelCase			(		self				,						lowerCAmelCase_				,						lowerCAmelCase_  )		->							Optional[int]:
										_snake_case									=				deque([]  ) if self.values[key] is None else self.values[key]
										self.values[key].appendleft(lowerCAmelCase_  )
										_snake_case									=				self.values[key]




					def 	lowerCAmelCase			(		self  )		->							Optional[int]:
										return (
										    sum(self.charge_factor - len(lowerCAmelCase_  ) for slot in self.values  )
										    / self.size_table
										    * self.charge_factor
										)






					def 	lowerCAmelCase			(		self				,						lowerCAmelCase_				,						lowerCAmelCase_=None  )		->							str:
										if not (
										    len(self.values[key]  ) == self.charge_factor and self.values.count(lowerCAmelCase_  ) == 0
										):
															return key
										return super()._collision_resolution(lowerCAmelCase_				,						lowerCAmelCase_  )










def 						lowerCamelCase__     (     UpperCamelCase__			:       list[int]       ,    UpperCamelCase__			:       int						)			-> bool:



					'''simple docstring'''




					_snake_case									=				len(UpperCamelCase__						)
					_snake_case									=				[[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						):
										_snake_case									=				True

					# sum is not zero and set is empty then false
					for i in range(1       ,    required_sum + 1						):
										_snake_case									=				False

					for i in range(1       ,    arr_len + 1						):
										for j in range(1       ,    required_sum + 1						):
															if arr[i - 1] > j:
																				_snake_case									=				subset[i - 1][j]
															if arr[i - 1] <= j:
																				_snake_case									=				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()



