


import math




def     __SCREAMING_SNAKE_CASE							(       lowercase_      )		->     bool:




						'''simple docstring'''







						__UpperCAmelCase			:							str	    =	math.loga(math.sqrt(4 * positive_integer + 1      ) / 2 + 1 / 2      )

						return exponent == int(lowercase_      )




def     __SCREAMING_SNAKE_CASE							(       lowercase_ = 1 / 12345      )		->     int:




						'''simple docstring'''







						__UpperCAmelCase			:							Tuple	    =	0
						__UpperCAmelCase			:							List[str]	    =	0

						__UpperCAmelCase			:							List[Any]	    =	3
						while True:
												__UpperCAmelCase			:							List[Any]	    =	(integer**2 - 1) / 4
												# if candidate is an integer, then there is a partition for k
												if partition_candidate == int(lowercase_      ):
																		__UpperCAmelCase			:							List[Any]	    =	int(lowercase_      )
																		total_partitions += 1
																		if check_partition_perfect(lowercase_      ):
																								perfect_partitions += 1
												if perfect_partitions > 0:
																		if perfect_partitions / total_partitions < max_proportion:
																								return int(lowercase_      )
												integer += 1


if __name__ == "__main__":
				print(F'{solution() = }')





import unittest

from knapsack import greedy_knapsack as kp




class 							lowerCamelCase   (  unittest.TestCase ):


	def  A(    self):
							__UpperCAmelCase			:							Optional[Any]	    =	[1_0, 2_0, 3_0, 4_0, 5_0, 6_0]
							__UpperCAmelCase			:							str	    =	[2, 4, 6, 8, 1_0, 1_2]
							__UpperCAmelCase			:							List[Any]	    =	1_0_0
							self.assertEqual(kp.calc_profit(lowercase__				,     lowercase__				,     lowercase__)				,     2_1_0)


	def  A(    self):
							self.assertRaisesRegex(lowercase__				,     '''max_weight must greater than zero.''')


	def  A(    self):
							self.assertRaisesRegex(lowercase__				,     '''Weight can not be negative.''')


	def  A(    self):
							self.assertRaisesRegex(lowercase__				,     '''Profit can not be negative.''')


	def  A(    self):
							self.assertRaisesRegex(lowercase__				,     '''max_weight must greater than zero.''')


	def  A(    self):
							self.assertRaisesRegex(
							    lowercase__				,     '''The length of profit and weight must be same.''')


if __name__ == "__main__":
				unittest.main()

