





# 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.


def       UpperCamelCase__(			UpperCamelCase__     :			str    )->Any:
       A__		   =		[False] * len(UpperCamelCase__    )
       A__		   =		[-1] * len(UpperCamelCase__    )

       def dfs(UpperCamelCase__     :			List[Any]					,	UpperCamelCase__     :			str    ):
              A__		   =		True
              A__		   =		c
              for u in graph[v]:
                     if not visited[u]:
                            dfs(UpperCamelCase__					,	1 - c    )

       for i in range(len(UpperCamelCase__    )    ):
              if not visited[i]:
                     dfs(UpperCamelCase__					,	0    )

       for i in range(len(UpperCamelCase__    )    ):
              for j in graph[i]:
                     if color[i] == color[j]:
                            return False

       return True


# Adjacency list of graph
a__: Optional[Any]							   =						{0: [1, 3], 1: [0, 2], 2: [1, 3], 3: [0, 2], 4: []}
print(check_bipartite_dfs(graph))












def       UpperCamelCase__(			UpperCamelCase__     :			str = "The quick brown fox jumps over the lazy dog"					,	)->bool:
       A__		   =		set()

       # Replace all the whitespace in our sentence
       A__		   =		input_str.replace(''' '''					,	''''''    )
       for alpha in input_str:
              if "a" <= alpha.lower() <= "z":
                     frequency.add(alpha.lower()    )
       return len(UpperCamelCase__    ) == 26


def       UpperCamelCase__(			UpperCamelCase__     :			str = "The quick brown fox jumps over the lazy dog"					,	)->bool:
       A__		   =		[False] * 26
       for char in input_str:
              if char.islower():
                     A__		   =		True
              elif char.isupper():
                     A__		   =		True
       return all(UpperCamelCase__    )


def       UpperCamelCase__(			UpperCamelCase__     :			str = "The quick brown fox jumps over the lazy dog"					,	)->bool:
       return len({char for char in input_str.lower() if char.isalpha()}    ) == 26


def       UpperCamelCase__(			)->None:
       from timeit import timeit

       A__		   =		'''from __main__ import is_pangram, is_pangram_faster, is_pangram_fastest'''
       print(timeit('''is_pangram()'''					,	setup=UpperCamelCase__    )    )
       print(timeit('''is_pangram_faster()'''					,	setup=UpperCamelCase__    )    )
       print(timeit('''is_pangram_fastest()'''					,	setup=UpperCamelCase__    )    )
       # 5.348480500048026, 2.6477354579837993, 1.8470395830227062
       # 5.036091582966037, 2.644472333951853,  1.8869528750656173


if __name__ == "__main__":
       import doctest

       doctest.testmod()
       benchmark()





