



"""simple docstring"""

from __future__ import annotations







def 							SCREAMING_SNAKE_CASE__      (		SCREAMING_SNAKE_CASE__ :  list[int | str]			):



					"""simple docstring"""





					create_state_space_tree(SCREAMING_SNAKE_CASE__				,    []				,    0				,    [0 for i in range(len(SCREAMING_SNAKE_CASE__			)			)]			)







def 							SCREAMING_SNAKE_CASE__      (		SCREAMING_SNAKE_CASE__ :  list[int | str]				,    SCREAMING_SNAKE_CASE__ :  list[int | str]				,    SCREAMING_SNAKE_CASE__ :  int				,    SCREAMING_SNAKE_CASE__ :  list[int]				,    ):



					"""simple docstring"""





					if index == len(SCREAMING_SNAKE_CASE__			):
										print(SCREAMING_SNAKE_CASE__			)
										return

					for i in range(len(SCREAMING_SNAKE_CASE__			)			):
										if not index_used[i]:
															current_sequence.append(sequence[i]			)
															snake_case_					:		List[Any] 					=					True
															create_state_space_tree(SCREAMING_SNAKE_CASE__				,    SCREAMING_SNAKE_CASE__				,    index + 1				,    SCREAMING_SNAKE_CASE__			)
															current_sequence.pop()
															snake_case_					:		int 					=					False
a_			   =					[3, 1, 2, 4]
generate_all_permutations(sequence)

a_			   =					["A", "B", "C"]


generate_all_permutations(sequence_a)









"""simple docstring"""

import random







def 							SCREAMING_SNAKE_CASE__      (		SCREAMING_SNAKE_CASE__ :  int				,    SCREAMING_SNAKE_CASE__ :  float				,    SCREAMING_SNAKE_CASE__ :  bool = False			):



					"""simple docstring"""





					snake_case_					:		dict 					=					{i: [] for i in range(SCREAMING_SNAKE_CASE__			)}

					# if probability is greater or equal than 1, then generate a complete graph
					if probability >= 1:
										return complete_graph(SCREAMING_SNAKE_CASE__			)
					# 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(SCREAMING_SNAKE_CASE__			):
										for j in range(i + 1				,    SCREAMING_SNAKE_CASE__			):
															if random.random() < probability:
																				graph[i].append(SCREAMING_SNAKE_CASE__			)
																				if not directed:
																									# if the graph is undirected, add an edge in from j to i, either
																									graph[j].append(SCREAMING_SNAKE_CASE__			)
					return graph







def 							SCREAMING_SNAKE_CASE__      (		SCREAMING_SNAKE_CASE__ :  int			):



					"""simple docstring"""





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


if __name__ == "__main__":
			import doctest

			doctest.testmod()




