


from __future__ import annotations

import sys





class       _a							:




	def __init__(      self		:	int	,      _SCREAMING_SNAKE_CASE		:	str	,      _SCREAMING_SNAKE_CASE		:	int	)-> List[Any]:
			lowerCAmelCase__     :    str					  =      letter
			lowerCAmelCase__     :    int					  =      freq
			lowerCAmelCase__     :    dict[str, str]					  =      {}




	def __repr__(      self		:	Any	)-> str:
			return F'{self.letter}:{self.freq}'





class       _a							:




	def __init__(      self		:	List[str]	,      _SCREAMING_SNAKE_CASE		:	int	,      _SCREAMING_SNAKE_CASE		:	Letter | TreeNode	,      _SCREAMING_SNAKE_CASE		:	Letter | TreeNode	)-> int:
			lowerCAmelCase__     :    int					  =      freq
			lowerCAmelCase__     :    Letter | TreeNode					  =      left
			lowerCAmelCase__     :    Letter | TreeNode					  =      right






def   lowerCamelCase_					( _a ):




		"""simple docstring"""






		lowerCAmelCase__     :    dict[str, int]					  =      {}
		with open(_a ) as f:
				while True:
						lowerCAmelCase__     :    Union[str, Any]					  =      f.read(1 )
						if not c:
								break
						lowerCAmelCase__     :    Optional[int]					  =      chars[c] + 1 if c in chars else 1
		return sorted((Letter(_a			,     _a ) for c, f in chars.items())			,     key=lambda _a : x.freq )






def   lowerCamelCase_					( _a ):




		"""simple docstring"""






		lowerCAmelCase__     :    list[Letter | TreeNode]					  =      letters  # type: ignore
		while len(_a ) > 1:
				lowerCAmelCase__     :    Tuple					  =      response.pop(0 )
				lowerCAmelCase__     :    Optional[Any]					  =      response.pop(0 )
				lowerCAmelCase__     :    List[str]					  =      left.freq + right.freq
				lowerCAmelCase__     :    Union[str, Any]					  =      TreeNode(_a			,     _a			,     _a )
				response.append(_a )
				response.sort(key=lambda _a : x.freq )
		return response[0]






def   lowerCamelCase_					( _a			,     _a ):




		"""simple docstring"""






		if isinstance(_a			,     _a ):
				lowerCAmelCase__     :    Optional[Any]					  =      bitstring
				return [root]
		lowerCAmelCase__     :    TreeNode					  =      root  # type: ignore
		lowerCAmelCase__     :    List[Any]					  =      []
		letters += traverse_tree(treenode.left			,     bitstring + '''0''' )
		letters += traverse_tree(treenode.right			,     bitstring + '''1''' )
		return letters






def   lowerCamelCase_					( _a ):




		"""simple docstring"""






		lowerCAmelCase__     :    Optional[Any]					  =      parse_file(_a )
		lowerCAmelCase__     :    str					  =      build_tree(_a )
		lowerCAmelCase__     :    int					  =      {
		    k: v for letter in traverse_tree(_a			,     '''''' ) for k, v in letter.bitstring.items()
		}
		print(f'Huffman Coding  of {file_path}: ' )
		with open(_a ) as f:
				while True:
						lowerCAmelCase__     :    List[str]					  =      f.read(1 )
						if not c:
								break
						print(letters[c]			,     end=''' ''' )
		print()


if __name__ == "__main__":
		# pass the file path to the huffman function
		huffman(sys.argv[1])








from itertools import count
from math import asin, pi, sqrt






def   lowerCamelCase_					( _a ):




		"""simple docstring"""






		return (
		    (1 - 2 * point) * sqrt(point - point**2 ) + 2 * point + asin(sqrt(1 - point ) )
		) / 4






def   lowerCamelCase_					( _a ):




		"""simple docstring"""






		lowerCAmelCase__     :    Union[str, Any]					  =      (circles_number + 1 - sqrt(2 * circles_number )) / (
		    2 * (circles_number**2 + 1)
		)
		lowerCAmelCase__     :    Tuple					  =      circles_number * intersection_y

		lowerCAmelCase__     :    Any					  =      intersection_x * intersection_y / 2
		lowerCAmelCase__     :    Optional[Any]					  =      circle_bottom_arc_integral(
		    1 / 2 ) - circle_bottom_arc_integral(_a )

		return triangle_area + concave_region_area






def   lowerCamelCase_					( _a = 1 / 1_000 ):




		"""simple docstring"""






		lowerCAmelCase__     :    Any					  =      (1 - pi / 4) / 4

		for n in count(1 ):
				if concave_triangle_area(_a ) / l_section_area < fraction:
						return n

		return -1


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




