





def    __UpperCamelCase      (    a,     a,     a) ->bool:
					return not any(
					    neighbour == 1 and colored_vertices[i] == color
					    for i, neighbour in enumerate(a))





def    __UpperCamelCase      (    a,     a,     a,     a) ->bool:

					# Base Case
					if index == len(a):
										return True

					# Recursive Step
					for i in range(a):
										if valid_coloring(graph[index],     a,     a):
															# Color current vertex
															lowerCamelCase__       =       i
															# Validate coloring
															if util_color(a,     a,     a,     index + 1):
																				return True
															# Backtrack
															lowerCamelCase__       =       -1
					return False







def    __UpperCamelCase      (    a,     a) ->list[int]:
					lowerCamelCase__       =       [-1] * len(a)

					if util_color(a,     a,     a,     0):
										return colored_vertices

					return []








def    __UpperCamelCase      (    a,     a,     a=False) ->Dict:

					if isinstance(a,     a) and isinstance(a,     a):
										lowerCamelCase__       =       len(set_a.intersection(a))

										if alternative_union:
															lowerCamelCase__       =       len(a) + len(a)
										else:
															lowerCamelCase__       =       len(set_a.union(a))

										return intersection / union

					if isinstance(a,     (list, tuple)) and isinstance(a,     (list, tuple)):
										lowerCamelCase__       =       [element for element in set_a if element in set_b]

										if alternative_union:
															lowerCamelCase__       =       len(a) + len(a)
															return len(a) / union
										else:
															lowerCamelCase__       =       set_a + [element for element in set_b if element not in set_a]
															return len(a) / len(a)

										return len(a) / len(a)
					return None


if __name__ == "__main__":
						A_												=     {"a", "b", "c", "d", "e"}
						A_												=     {"c", "d", "e", "f", "h", "i"}
						print(jaccard_similarity(set_a, set_b))

