

# using dfs for finding eulerian path traversal




def 			UpperCAmelCase__				(			_A      : List[str]	,      _A      : Tuple	,      _A      : List[Any]	,      _A      : List[Any]=None							):





  '''simple docstring'''







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




def 			UpperCAmelCase__				(			_A      : Dict	,      _A      : Any							):





  '''simple docstring'''







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




def 			UpperCAmelCase__				(			_A      : Optional[Any]	,      _A      : Tuple							):





  '''simple docstring'''







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




def 			UpperCAmelCase__				(			):





  '''simple docstring'''







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


if __name__ == "__main__":
       main()



from __future__ import annotations




def 			UpperCAmelCase__				(			_A      : float	,      _A      : float	,      _A      : float	,      ):





  '''simple docstring'''







  if (electron_conc, hole_conc, intrinsic_conc).count(0							) != 1:
    raise ValueError('''You cannot supply more or less than 2 values'''							)
  elif electron_conc < 0:
    raise ValueError('''Electron concentration cannot be negative in a semiconductor'''							)
  elif hole_conc < 0:
    raise ValueError('''Hole concentration cannot be negative in a semiconductor'''							)
  elif intrinsic_conc < 0:
    raise ValueError(
        '''Intrinsic concentration cannot be negative in a semiconductor'''							)
  elif electron_conc == 0:
    return (
        "electron_conc",
        intrinsic_conc**2 / hole_conc,
    )
  elif hole_conc == 0:
    return (
        "hole_conc",
        intrinsic_conc**2 / electron_conc,
    )
  elif intrinsic_conc == 0:
    return (
        "intrinsic_conc",
        (electron_conc * hole_conc) ** 0.5,
    )
  else:
    return (-1, -1)


if __name__ == "__main__":
       import doctest

       doctest.testmod()
