





"""simple docstring"""


from math import log

from scipy.constants import Boltzmann, physical_constants

lowerCamelCase__				  =   300  # TEMPERATURE (unit = K)




def 					lowercase__    (					lowercase_		,lowercase_		,lowercase_		,)					->		float:




      """simple docstring"""

      if donor_conc <= 0:
            raise ValueError("Donor concentration should be positive"			)
      elif acceptor_conc <= 0:
            raise ValueError("Acceptor concentration should be positive"			)
      elif intrinsic_conc <= 0:
            raise ValueError("Intrinsic concentration should be positive"			)
      elif donor_conc <= intrinsic_conc:
            raise ValueError(
                "Donor concentration should be greater than intrinsic concentration"			)
      elif acceptor_conc <= intrinsic_conc:
            raise ValueError(
                "Acceptor concentration should be greater than intrinsic concentration"			)
      else:
            return (
                Boltzmann
                * T
                * log((donor_conc * acceptor_conc) / intrinsic_conc**2			)
                / physical_constants["electron volt"][0]
            )


if __name__ == "__main__":
    import doctest

    doctest.testmod()







"""simple docstring"""


def 					lowercase__    (					lowercase_			)					->		set:




      """simple docstring"""

      _UpperCamelCase      :	Union[str, Any]						=       set()
      # edges = list of graph's edges
      _UpperCamelCase      :	Union[str, Any]						=       get_edges(lowercase_			)

      # While there are still elements in edges list, take an arbitrary edge
      # (from_node, to_node) and add his extremity to chosen_vertices and then
      # remove all arcs adjacent to the from_node and to_node
      while edges:
            _UpperCamelCase,  _UpperCamelCase      :	str						=       edges.pop()
            chosen_vertices.add(lowercase_			)
            chosen_vertices.add(lowercase_			)
            for edge in edges.copy():
                  if from_node in edge or to_node in edge:
                        edges.discard(lowercase_			)
      return chosen_vertices




def 					lowercase__    (					lowercase_			)					->		set:




      """simple docstring"""

      _UpperCamelCase      :	List[str]						=       set()
      for from_node, to_nodes in graph.items():
            for to_node in to_nodes:
                  edges.add((from_node, to_node)			)
      return edges


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  # graph = {0: [1, 3], 1: [0, 3], 2: [0, 3, 4], 3: [0, 1, 2], 4: [2, 3]}
  # print(f"Matching vertex cover:\n{matching_min_vertex_cover(graph)}")
