






from __future__ import annotations

from queue import Queue



def      UpperCAmelCase						( lowerCAmelCase__					,     lowerCAmelCase__	):


		'''simple docstring'''

		a ^= b
		b ^= a
		a ^= b
		return a, b



def      UpperCAmelCase						( lowerCAmelCase__					,     lowerCAmelCase__	):


		'''simple docstring'''

		__A    =							1
		while (1 << j) < max_node:
				for i in range(1					,     max_node + 1	):
						__A    =							parent[j - 1][parent[j - 1][i]]
				j += 1
		return parent



def      UpperCAmelCase						( lowerCAmelCase__					,     lowerCAmelCase__					,     lowerCAmelCase__					,     lowerCAmelCase__	):


		'''simple docstring'''

		if level[u] < level[v]:
				__A ,   __A    =							swap(lowerCAmelCase__					,     lowerCAmelCase__	)
		# making depth of u same as depth of v
		for i in range(18					,     -1					,     -1	):
				if level[u] - (1 << i) >= level[v]:
						__A    =							parent[i][u]
    # at the same depth if u==v that mean lca is found
		if u == v:
				return u
		# moving both nodes upwards till lca in found
		for i in range(18					,     -1					,     -1	):
				if parent[i][u] not in [0, parent[i][v]]:
						__A ,   __A    =							parent[i][u], parent[i][v]
    # returning longest common ancestor of u,v
		return parent[0][u]



def      UpperCAmelCase						( lowerCAmelCase__					,     lowerCAmelCase__					,     lowerCAmelCase__					,     lowerCAmelCase__					,     lowerCAmelCase__ = 1					,     ):


		'''simple docstring'''

		__A    =							0
		__A    =							Queue(maxsize=lowerCAmelCase__	)
		q.put(lowerCAmelCase__	)
		while q.qsize() != 0:
				__A    =							q.get()
				for v in graph[u]:
						if level[v] == -1:
								__A    =							level[u] + 1
								q.put(lowerCAmelCase__	)
								__A    =							u
		return level, parent



def      UpperCAmelCase						( ):


		'''simple docstring'''

		__A    =							13
		# initializing with 0
		__A    =							[[0 for _ in range(max_node + 10	)] for _ in range(20	)]
		# initializing with -1 which means every node is unvisited
		__A    =							[-1 for _ in range(max_node + 10	)]
		__A    =							{
		    1: [2, 3, 4],
		    2: [5],
		    3: [6, 7],
		    4: [8],
		    5: [9, 10],
		    6: [11],
		    7: [],
		    8: [12, 13],
		    9: [],
		    10: [],
		    11: [],
		    12: [],
		    13: [],
		}
		__A ,   __A    =							breadth_first_search(lowerCAmelCase__					,     lowerCAmelCase__					,     lowerCAmelCase__					,     lowerCAmelCase__					,     1	)
		__A    =							create_sparse(lowerCAmelCase__					,     lowerCAmelCase__	)
		print("LCA of node 1 and 3 is: "					,     lowest_common_ancestor(1					,     3					,     lowerCAmelCase__					,     lowerCAmelCase__	)	)
		print("LCA of node 5 and 6 is: "					,     lowest_common_ancestor(5					,     6					,     lowerCAmelCase__					,     lowerCAmelCase__	)	)
		print("LCA of node 7 and 11 is: "					,     lowest_common_ancestor(7					,     11					,     lowerCAmelCase__					,     lowerCAmelCase__	)	)
		print("LCA of node 6 and 7 is: "					,     lowest_common_ancestor(6					,     7					,     lowerCAmelCase__					,     lowerCAmelCase__	)	)
		print("LCA of node 4 and 12 is: "					,     lowest_common_ancestor(4					,     12					,     lowerCAmelCase__					,     lowerCAmelCase__	)	)
		print("LCA of node 8 and 8 is: "					,     lowest_common_ancestor(8					,     8					,     lowerCAmelCase__					,     lowerCAmelCase__	)	)


if __name__ == "__main__":
					main()



from __future__ import annotations

from queue import Queue


class 	UpperCamelCase__       :

						'''simple docstring'''



						def __init__(  self	)  ->None:
									UpperCAmelCase__		:dict[int, list[int]] 		=    {}


						def    A__       (  self	)  ->None:
									for i in self.vertices:
												print(A  , ' : '  , ' -> '.join([str(A	) for j in self.vertices[i]]	)	)


						def    A__       (  self  , A  , A	)  ->None:
									if from_vertex in self.vertices:
												self.vertices[from_vertex].append(A	)
									else:
												UpperCAmelCase__		:Union[str, Any] 		=    [to_vertex]


						def    A__       (  self  , A	)  ->set[int]:
									UpperCAmelCase__		:str 		=    set()

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

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

									while not queue.empty():
												UpperCAmelCase__		:List[str] 		=    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(A	)
																		visited.add(A	)
									return visited


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

						testmod(verbose=True)

						__snake_case					:							Any           =							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]





