

"""simple docstring"""



# A Bipartite Graph is a graph whose vertices can be divided into two independent sets,
# U and V such that every edge (u, v) either connects a vertex from U to V or a vertex
# from V to U. In other words, for every edge (u, v), either u belongs to U and v to V,
# or u belongs to V and v to U. We can also say that there is no edge that connects
# vertices of same set.
from queue import Queue





def 			_snake_case  (     UpperCAmelCase_	:       Tuple      ):
     A__				      =	Queue()
     A__				      =	[False] * len(UpperCAmelCase_      )
     A__				      =	[-1] * len(UpperCAmelCase_      )

     def bfs():
          while not queue.empty():
               A__				      =	queue.get()
               A__				      =	True

               for neighbour in graph[u]:
                    if neighbour == u:
                         return False

                    if color[neighbour] == -1:
                         A__				      =	1 - color[u]
                         queue.put(UpperCAmelCase_      )

                    elif color[neighbour] == color[u]:
                         return False

          return True

     for i in range(len(UpperCAmelCase_      )      ):
          if not visited[i]:
               queue.put(UpperCAmelCase_      )
               A__				      =	0
               if bfs() is False:
                    return False

     return True


if __name__ == "__main__":
 # Adjacency List of graph
 print(check_bipartite({0: [1, 3], 1: [0, 2], 2: [1, 3], 3: [0, 2]}))









"""simple docstring"""



from __future__ import annotations





def 			_snake_case  (     UpperCAmelCase_	:       list[list[int]]       , UpperCAmelCase_	:       list[list[int]]      ):
     assert len(UpperCAmelCase_      ) == len(UpperCAmelCase_      )

     A__				      =	len(UpperCAmelCase_      )
     A__				      =	list(range(UpperCAmelCase_      )      )
     A__				      =	[-1] * n  # who the donor has donated to
     A__				      =	[-1] * n  # who the recipient has received from
     A__				      =	[0] * n

     while unmatched_donors:
          A__				      =	unmatched_donors[0]
          A__				      =	donor_pref[donor]
          A__				      =	donor_preference[num_donations[donor]]
          num_donations[donor] += 1
          A__				      =	recipient_pref[recipient]
          A__				      =	rec_record[recipient]

          if prev_donor != -1:
               if rec_preference.index(UpperCAmelCase_      ) > rec_preference.index(UpperCAmelCase_      ):
                    A__				      =	donor
                    A__				      =	recipient
                    unmatched_donors.append(UpperCAmelCase_      )
                    unmatched_donors.remove(UpperCAmelCase_      )
          else:
               A__				      =	donor
               A__				      =	recipient
               unmatched_donors.remove(UpperCAmelCase_      )
     return donor_record






