





from __future__ import annotations

import sys

class 		__a							:



       def __init__(     self	:   Any					,			UpperCAmelCase	:   str					,			UpperCAmelCase	:   int			):
           lowerCAmelCase_					:	str						=   letter
           lowerCAmelCase_					:	int						=   freq
           lowerCAmelCase_					:	dict[str, str]						=   {}



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






class 		__a							:



       def __init__(     self	:   Any					,			UpperCAmelCase	:   int					,			UpperCAmelCase	:   Letter | TreeNode					,			UpperCAmelCase	:   Letter | TreeNode			):
           lowerCAmelCase_					:	int						=   freq
           lowerCAmelCase_					:	Letter | TreeNode						=   left
           lowerCAmelCase_					:	Letter | TreeNode						=   right






def 			__UpperCamelCase				(			lowercase__	:       str		)	->      list[Letter]:
    '''simple docstring'''





    lowerCAmelCase_					:	dict[str, int]						=   {}
    with open(lowercase__		) as f:
        while True:
            lowerCAmelCase_					:	int						=   f.read(1		)
            if not c:
                break
            lowerCAmelCase_					:	Optional[Any]						=   chars[c] + 1 if c in chars else 1
    return sorted((Letter(lowercase__		,    lowercase__		) for c, f in chars.items())		,    key=lambda lowercase__		: x.freq		)
def 			__UpperCamelCase				(			lowercase__	:       list[Letter]		)	->      Letter | TreeNode:
    '''simple docstring'''





    lowerCAmelCase_					:	list[Letter | TreeNode]						=   letters  # type: ignore
    while len(lowercase__		) > 1:
        lowerCAmelCase_					:	str						=   response.pop(0		)
        lowerCAmelCase_					:	Any						=   response.pop(0		)
        lowerCAmelCase_					:	Union[str, Any]						=   left.freq + right.freq
        lowerCAmelCase_					:	Union[str, Any]						=   TreeNode(lowercase__		,    lowercase__		,    lowercase__		)
        response.append(lowercase__		)
        response.sort(key=lambda lowercase__		: x.freq		)
    return response[0]
def 			__UpperCamelCase				(			lowercase__	:       Letter | TreeNode		,    lowercase__	:       str		)	->      list[Letter]:
    '''simple docstring'''





    if isinstance(lowercase__		,    lowercase__		):
        lowerCAmelCase_					:	Dict						=   bitstring
        return [root]
    lowerCAmelCase_					:	TreeNode						=   root  # type: ignore
    lowerCAmelCase_					:	Union[str, Any]						=   []
    letters += traverse_tree(treenode.left		,    bitstring + """0"""		)
    letters += traverse_tree(treenode.right		,    bitstring + """1"""		)
    return letters
def 			__UpperCamelCase				(			lowercase__	:       str		)	->      None:
    '''simple docstring'''





    lowerCAmelCase_					:	Any						=   parse_file(lowercase__		)
    lowerCAmelCase_					:	int						=   build_tree(lowercase__		)
    lowerCAmelCase_					:	Tuple						=   {
        k: v for letter in traverse_tree(lowercase__		,    """"""		) for k, v in letter.bitstring.items()
    }
    print(f'Huffman Coding  of {file_path}: '		)
    with open(lowercase__		) 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])









import math
def 			__UpperCamelCase				(			lowercase__	:       int		)	->      list:
    '''simple docstring'''





    if n <= 0:
        raise ValueError("""Only positive integers have prime factors"""		)
    lowerCAmelCase_					:	str						=   []
    while n % 2 == 0:
        pf.append(2		)
        lowerCAmelCase_					:	str						=   int(n / 2		)
    for i in range(3		,    int(math.sqrt(lowercase__		)		) + 1		,    2		):
        while n % i == 0:
            pf.append(lowercase__		)
            lowerCAmelCase_					:	List[Any]						=   int(n / i		)
    if n > 2:
        pf.append(lowercase__		)
    return pf
def 			__UpperCamelCase				(			lowercase__	:       int		)	->      int:
    '''simple docstring'''





    if n <= 0:
        raise ValueError("""Only positive numbers are accepted"""		)
    lowerCAmelCase_					:	Union[str, Any]						=   1
    lowerCAmelCase_					:	str						=   1
    while n % 2 == 0:
        temp += 1
        lowerCAmelCase_					:	Optional[Any]						=   int(n / 2		)
    div *= temp
    for i in range(3		,    int(math.sqrt(lowercase__		)		) + 1		,    2		):
        lowerCAmelCase_					:	Tuple						=   1
        while n % i == 0:
            temp += 1
            lowerCAmelCase_					:	Any						=   int(n / i		)
        div *= temp
    if n > 1:
        div *= 2
    return div
def 			__UpperCamelCase				(			lowercase__	:       int		)	->      int:
    '''simple docstring'''





    if n <= 0:
        raise ValueError("""Only positive numbers are accepted"""		)
    lowerCAmelCase_					:	Tuple						=   1
    lowerCAmelCase_					:	str						=   1
    while n % 2 == 0:
        temp += 1
        lowerCAmelCase_					:	Optional[int]						=   int(n / 2		)
    if temp > 1:
        s *= (2**temp - 1) / (2 - 1)
    for i in range(3		,    int(math.sqrt(lowercase__		)		) + 1		,    2		):
        lowerCAmelCase_					:	int						=   1
        while n % i == 0:
            temp += 1
            lowerCAmelCase_					:	Any						=   int(n / i		)
        if temp > 1:
            s *= (i**temp - 1) / (i - 1)
    return int(lowercase__		)
def 			__UpperCamelCase				(			lowercase__	:       int		)	->      int:
    '''simple docstring'''





    lowerCAmelCase_					:	str						=   n
    for x in set(prime_factors(lowercase__		)		):
        s *= (x - 1) / x
    return int(lowercase__		)


if __name__ == "__main__":
  import doctest

  doctest.testmod()


