



"""simple docstring"""
from __future__ import annotations

_lowerCAmelCase    :Union[str, Any]     =					{
    'A': ['B', 'C', 'E'],
    'B': ['A', 'D', 'E'],
    'C': ['A', 'F', 'G'],
    'D': ['B'],
    'E': ['A', 'B', 'D'],
    'F': ['C'],
    'G': ['C'],
}
class 							_UpperCAmelCase							:





     '''simple docstring'''



     def __init__(					self       ,	A       ,	A		)							->					None:
         _UpperCAmelCase							:  Union[str, Any]											=    graph
         # mapping node to its parent in resulting breadth first tree
         _UpperCAmelCase							:  dict[str, str | None]											=    {}
         _UpperCAmelCase							:  List[str]											=    source_vertex





     def  __lowerCAmelCase	(					self		)							->					None:
         _UpperCAmelCase							:  Optional[int]											=    {self.source_vertex}
         _UpperCAmelCase							:  Optional[Any]											=    None
         _UpperCAmelCase							:  Optional[Any]											=    [self.source_vertex]  # first in first out queue

         while queue:
             _UpperCAmelCase							:  int											=    queue.pop(0		)
             for adjacent_vertex in self.graph[vertex]:
                 if adjacent_vertex not in visited:
                     visited.add(A		)
                     _UpperCAmelCase							:  List[Any]											=    vertex
                     queue.append(A		)





     def  __lowerCAmelCase	(					self       ,	A		)							->					str:
         if target_vertex == self.source_vertex:
             return self.source_vertex

         _UpperCAmelCase							:  Dict											=    self.parent.get(A		)
         if target_vertex_parent is None:
             _UpperCAmelCase							:  int											=    (
                 f'No path from vertex: {self.source_vertex} to vertex: {target_vertex}'
             )
             raise ValueError(A		)

         return self.shortest_path(A		) + f'->{target_vertex}'


if __name__ == "__main__":
  _lowerCAmelCase    :List[str]     =					Graph(graph, 'G')
  g.breath_first_search()
  print(g.shortest_path('D'))
  print(g.shortest_path('G'))
  print(g.shortest_path('Foo'))







"""simple docstring"""
import math

from numpy import inf
from scipy.integrate import quad





def  lowerCamelCase_						(UpperCamelCase__		:		float							):
    if num <= 0:
        raise ValueError('''math domain error'''							)

    return quad(UpperCamelCase__     ,       0     ,       UpperCamelCase__     ,       args=(UpperCamelCase__)							)[0]





def  lowerCamelCase_						(UpperCamelCase__		:		float     ,       UpperCamelCase__		:		float							):
    return math.pow(UpperCamelCase__     ,       z - 1							) * math.exp(-x							)


if __name__ == "__main__":
  from doctest import testmod

  testmod()


