
import random





def 			lowerCamelCase_ (				lowerCamelCase__	, lowerCamelCase__	, lowerCamelCase__ = False    ):
				lowerCamelCase_						=			{i: [] for i in range(lowerCamelCase__    )}

				# if probability is greater or equal than 1, then generate a complete graph
				if probability >= 1:
								return complete_graph(lowerCamelCase__    )
				# if probability is lower or equal than 0, then return a graph without edges
				if probability <= 0:
								return graph

				# for each couple of nodes, add an edge from u to v
				# if the number randomly generated is greater than probability probability
				for i in range(lowerCamelCase__    ):
								for j in range(i + 1	, lowerCamelCase__    ):
												if random.random() < probability:
																graph[i].append(lowerCamelCase__    )
																if not directed:
																				# if the graph is undirected, add an edge in from j to i, either
																				graph[j].append(lowerCamelCase__    )
				return graph





def 			lowerCamelCase_ (				lowerCamelCase__    ):
				return {
				    i: [j for j in range(lowerCamelCase__    ) if i != j] for i in range(lowerCamelCase__    )
				}


if __name__ == "__main__":
			import doctest

			doctest.testmod()




def 			lowerCamelCase_ (				lowerCamelCase__	, lowerCamelCase__    ):
				lowerCamelCase_						=			[0 for i in range(r + 1    )]
				# nc0 = 1
				lowerCamelCase_						=			1
				for i in range(1	, n + 1    ):
								# to compute current row from previous row.
								lowerCamelCase_						=			min(lowerCamelCase__	, lowerCamelCase__    )
								while j > 0:
												c[j] += c[j - 1]
												j -= 1
				return c[r]





print(binomial_coefficient(n=1_0, r=5))


