


'''simple docstring'''
from __future__ import annotations

import sys






class 				__lowerCAmelCase      :

						"""simple docstring"""






						def __init__(     self       :			Tuple   ,     lowerCAmelCase       :			str   ,     lowerCAmelCase       :			int  ):
													A_ 						=		letter
													A_ 						=		freq
													A_ 						=		{}






						def __repr__(     self       :			Optional[int]  ):
													return F"{self.letter}:{self.freq}"






class 				__lowerCAmelCase      :

						"""simple docstring"""






						def __init__(     self       :			List[str]   ,     lowerCAmelCase       :			int   ,     lowerCAmelCase       :			Letter | TreeNode   ,     lowerCAmelCase       :			Letter | TreeNode  ):
													A_ 						=		freq
													A_ 						=		left
													A_ 						=		right







def 			a_							(  UpperCamelCase_   ):
							A_ 						=		{}
							with open(UpperCamelCase_   ) as f:
														while True:
																					A_ 						=		f.read(1   )
																					if not c:
																												break
																					A_ 						=		chars[c] + 1 if c in chars else 1
							return sorted((Letter(UpperCamelCase_	,     UpperCamelCase_   ) for c, f in chars.items())	,     key=lambda UpperCamelCase_   : x.freq   )







def 			a_							(  UpperCamelCase_   ):
							A_ 						=		letters  # type: ignore
							while len(UpperCamelCase_   ) > 1:
														A_ 						=		response.pop(0   )
														A_ 						=		response.pop(0   )
														A_ 						=		left.freq + right.freq
														A_ 						=		TreeNode(UpperCamelCase_	,     UpperCamelCase_	,     UpperCamelCase_   )
														response.append(UpperCamelCase_   )
														response.sort(key=lambda UpperCamelCase_   : x.freq   )
							return response[0]







def 			a_							(  UpperCamelCase_	,     UpperCamelCase_   ):
							if isinstance(UpperCamelCase_	,     UpperCamelCase_   ):
														A_ 						=		bitstring
														return [root]
							A_ 						=		root  # type: ignore
							A_ 						=		[]
							letters += traverse_tree(treenode.left	,     bitstring + "0"   )
							letters += traverse_tree(treenode.right	,     bitstring + "1"   )
							return letters







def 			a_							(  UpperCamelCase_   ):
							A_ 						=		parse_file(UpperCamelCase_   )
							A_ 						=		build_tree(UpperCamelCase_   )
							A_ 						=		{
							    k: v for letter in traverse_tree(UpperCamelCase_	,     ""   ) for k, v in letter.bitstring.items()
							}
							print(f"Huffman Coding  of {file_path}: "   )
							with open(UpperCamelCase_   ) as f:
														while True:
																					A_ 						=		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])









'''simple docstring'''
def 			a_							(  UpperCamelCase_	,     UpperCamelCase_ = 1_0_0_0   ):
							if (not isinstance(UpperCamelCase_	,     UpperCamelCase_   )) or (digit_position <= 0):
														raise ValueError("Digit position must be a positive integer"   )
							elif (not isinstance(UpperCamelCase_	,     UpperCamelCase_   )) or (precision < 0):
														raise ValueError("Precision must be a nonnegative integer"   )

							# compute an approximation of (16 ** (n - 1)) * pi whose fractional part is mostly
							# accurate
							A_ 						=		(
							    4 * _subsum(UpperCamelCase_	,     1	,     UpperCamelCase_   )
							    - 2 * _subsum(UpperCamelCase_	,     4	,     UpperCamelCase_   )
							    - _subsum(UpperCamelCase_	,     5	,     UpperCamelCase_   )
							    - _subsum(UpperCamelCase_	,     6	,     UpperCamelCase_   )
							)

							# return the first hex digit of the fractional part of the result
							return hex(int((sum_result % 1) * 1_6   )   )[2:]







def 			a_							(  UpperCamelCase_	,     UpperCamelCase_	,     UpperCamelCase_   ):
							A_ 						=		0.0
							for sum_index in range(digit_pos_to_extract + precision   ):
														A_ 						=		8 * sum_index + denominator_addend
														if sum_index < digit_pos_to_extract:
																					# if the exponential term is an integer and we mod it by the denominator
																					# before dividing, only the integer part of the sum will change;
																					# the fractional part will not
																					A_ 						=		pow(
																					    1_6	,     digit_pos_to_extract - 1 - sum_index	,     UpperCamelCase_   )
														else:
																					A_ 						=		pow(1_6	,     digit_pos_to_extract - 1 - sum_index   )
														total += exponential_term / denominator
							return total


if __name__ == "__main__":
							import doctest

							doctest.testmod()





