


'''simple docstring'''
import random


def      a (     __a					,   __a					,   __a = False  )    ->      dict:



					'''simple docstring'''






					UpperCamelCase__  :dict				   =					{i: [] for i in range(__a  )}

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


def      a (     __a  )    ->      dict:



					'''simple docstring'''






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


if __name__ == "__main__":
		import doctest

		doctest.testmod()



'''simple docstring'''
from __future__ import annotations

import math


def      a (     __a					,   __a					,   __a					,   __a					,   __a  )    ->      int:



					'''simple docstring'''






					if depth < 0:
										raise ValueError('''Depth cannot be less than 0'''  )

					if len(__a  ) == 0:
										raise ValueError('''Scores cannot be empty'''  )

					if depth == height:
										return scores[node_index]

					if is_max:
										return max(
										    minimax(depth + 1					,   node_index * 2					,   __a					,   __a					,   __a  )					,   minimax(depth + 1					,   node_index * 2 + 1					,   __a					,   __a					,   __a  )					,   )

					return min(
					    minimax(depth + 1					,   node_index * 2					,   __a					,   __a					,   __a  )					,   minimax(depth + 1					,   node_index * 2 + 1					,   __a					,   __a					,   __a  )					,   )


def      a (     )    ->      None:



					'''simple docstring'''






					UpperCamelCase__  :str				   =					[90, 23, 6, 33, 21, 65, 123, 34423]
					UpperCamelCase__  :List[Any]				   =					math.log(len(__a  )					,   2  )
					print('''Optimal value : '''					,   end=''''''  )
					print(minimax(0					,   0					,   __a					,   __a					,   __a  )  )


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		main()