
'''simple docstring'''

def  a__    (    lowercase :					Dict, lowercase :					str, lowercase :					Optional[Any], lowercase :					int=None				)		->		Tuple:





     """simple docstring"""

     _UpperCamelCase       =	(path or []) + [u]
     for v in graph[u]:
          if visited_edge[u][v] is False:
               _UpperCamelCase   ,    _UpperCamelCase       =	True, True
               _UpperCamelCase       =	dfs(SCREAMING_SNAKE_CASE_, SCREAMING_SNAKE_CASE_, SCREAMING_SNAKE_CASE_, SCREAMING_SNAKE_CASE_				)
     return path







def  a__    (    lowercase :					List[Any], lowercase :					List[str]				)		->		Union[str, Any]:





     """simple docstring"""

     _UpperCamelCase       =	0
     _UpperCamelCase       =	-1
     for i in range(SCREAMING_SNAKE_CASE_				):
          if i not in graph.keys():
               continue
          if len(graph[i]				) % 2 == 1:
               odd_degree_nodes += 1
               _UpperCamelCase       =	i
     if odd_degree_nodes == 0:
          return 1, odd_node
     if odd_degree_nodes == 2:
          return 2, odd_node
     return 3, odd_node







def  a__    (    lowercase :					int, lowercase :					Any				)		->		int:





     """simple docstring"""

     _UpperCamelCase       =	[[False for _ in range(max_node + 1				)] for _ in range(max_node + 1				)]
     _UpperCamelCase   ,    _UpperCamelCase       =	check_circuit_or_path(SCREAMING_SNAKE_CASE_, SCREAMING_SNAKE_CASE_				)
     if check == 3:
          print('''graph is not Eulerian'''				)
          print('''no path'''				)
          return
     _UpperCamelCase       =	1
     if check == 2:
          _UpperCamelCase       =	odd_node
          print('''graph has a Euler path'''				)
     if check == 1:
          print('''graph has a Euler cycle'''				)
     _UpperCamelCase       =	dfs(SCREAMING_SNAKE_CASE_, SCREAMING_SNAKE_CASE_, SCREAMING_SNAKE_CASE_				)
     print(SCREAMING_SNAKE_CASE_				)







def  a__    (    )		->		List[str]:





     """simple docstring"""

     _UpperCamelCase       =	{1: [2, 3, 4], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [4]}
     _UpperCamelCase       =	{1: [2, 3, 4, 5], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [1, 4]}
     _UpperCamelCase       =	{1: [2, 3, 4], 2: [1, 3, 4], 3: [1, 2], 4: [1, 2, 5], 5: [4]}
     _UpperCamelCase       =	{1: [2, 3], 2: [1, 3], 3: [1, 2]}
     _UpperCamelCase       =	{
         1: [],
         2: []
         # all degree is zero
     }
     _UpperCamelCase       =	10
     check_euler(SCREAMING_SNAKE_CASE_, SCREAMING_SNAKE_CASE_				)
     check_euler(SCREAMING_SNAKE_CASE_, SCREAMING_SNAKE_CASE_				)
     check_euler(SCREAMING_SNAKE_CASE_, SCREAMING_SNAKE_CASE_				)
     check_euler(SCREAMING_SNAKE_CASE_, SCREAMING_SNAKE_CASE_				)
     check_euler(SCREAMING_SNAKE_CASE_, SCREAMING_SNAKE_CASE_				)


if __name__ == "__main__":
   main()










'''simple docstring'''

import importlib.metadata
from typing import Union

from packaging.version import Version, parse

from .constants import STR_OPERATION_TO_FUNC


lowercase__						:      List[Any]	=    parse(importlib.metadata.version('torch'))







def  a__    (    lowercase :					Union[str, Version], lowercase :					str, lowercase :					str				)		->		List[str]:





     """simple docstring"""

     if operation not in STR_OPERATION_TO_FUNC.keys():
          raise ValueError(F"""`operation` must be one of {list(STR_OPERATION_TO_FUNC.keys()				)}, received {operation}"""				)
     _UpperCamelCase       =	STR_OPERATION_TO_FUNC[operation]
     if isinstance(lowercase, lowercase				):
          _UpperCamelCase       =	parse(importlib.metadata.version(lowercase				)				)
     return operation(lowercase, parse(lowercase				)				)







def  a__    (    lowercase :					str, lowercase :					str				)		->		List[Any]:





     """simple docstring"""

     return compare_versions(lowercase, lowercase, lowercase				)



