






'''simple docstring'''







from __future__ import annotations


def 						_UpperCamelCase							(     snake_case__							,			snake_case__							):
      __A		   =      [None] * (len(a_							) + len(a_							))

      __A		   =      0  # pointer to current index for left Half
      __A		   =      0  # pointer to current index for the right Half
      __A		   =      0  # pointer to current index for the sorted array Half

      while pointera < len(a_							) and pointera < len(a_							):
            if left_half[pointera] < right_half[pointera]:
                  __A		   =      left_half[pointera]
                  pointera += 1
                  index += 1
            else:
                  __A		   =      right_half[pointera]
                  pointera += 1
                  index += 1
      while pointera < len(a_							):
            __A		   =      left_half[pointera]
            pointera += 1
            index += 1

      while pointera < len(a_							):
            __A		   =      right_half[pointera]
            pointera += 1
            index += 1

      return sorted_array


def 						_UpperCamelCase							(     snake_case__							):
      if len(a_							) <= 1:
            return array
      # the actual formula to calculate the middle element = left + (right - left) // 2
      # this avoids integer overflow in case of large N
      __A		   =      0 + (len(a_							) - 0) // 2

      # Split the array into halves till the array length becomes equal to One
      # merge the arrays of single length returned by mergeSort function and
      # pass them into the merge arrays function which merges the array
      __A		   =      array[:middle]
      __A		   =      array[middle:]

      return merge(merge_sort(a_							)							,			merge_sort(a_							)							)


if __name__ == "__main__":
       import doctest

       doctest.testmod()










'''simple docstring'''







from __future__ import annotations

from queue import Queue






class 					a__    :
     '''simple docstring'''







     def __init__(self    :	Any					)  ->       None:
           __A		   =      {}






     def     _UpperCamelCase   (self    :	Optional[int]					)  ->       None:
           for i in self.vertices:
                 print(lowercase__				,				" : "				,				" -> ".join([str(lowercase__					) for j in self.vertices[i]]					)					)






     def     _UpperCamelCase   (self    :	Union[str, Any]				,				lowercase__    :	int				,				lowercase__    :	int					)  ->       None:
           if from_vertex in self.vertices:
                 self.vertices[from_vertex].append(lowercase__					)
           else:
                 __A		   =      [to_vertex]






     def     _UpperCamelCase   (self    :	Optional[int]				,				lowercase__    :	int					)  ->       set[int]:
           __A		   =      set()

           # create a first in first out queue to store all the vertices for BFS
           __A		   =      Queue()

           # mark the source node as visited and enqueue it
           visited.add(lowercase__					)
           queue.put(lowercase__					)

           while not queue.empty():
                 __A		   =      queue.get()

                 # loop through all adjacent vertex and enqueue it if not yet visited
                 for adjacent_vertex in self.vertices[vertex]:
                       if adjacent_vertex not in visited:
                             queue.put(lowercase__					)
                             visited.add(lowercase__					)
           return visited


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

       testmod(verbose=True)

       __A      :       Dict      =	Graph()
       g.add_edge(0, 1)
       g.add_edge(0, 2)
       g.add_edge(1, 2)
       g.add_edge(2, 0)
       g.add_edge(2, 3)
       g.add_edge(3, 3)

       g.print_graph()
       # 0  :  1 -> 2
       # 1  :  2
       # 2  :  0 -> 3
       # 3  :  3

       assert sorted(g.bfs(2)) == [0, 1, 2, 3]


