



'''simple docstring'''




def    __lowerCamelCase						(      _lowercase	)   ->    set:
							UpperCAmelCase  :	Any							  =	set()
							# edges = list of graph's edges
							UpperCAmelCase  :	Dict							  =	get_edges(_lowercase	)

							# While there are still elements in edges list, take an arbitrary edge
							# (from_node, to_node) and add his extremity to chosen_vertices and then
							# remove all arcs adjacent to the from_node and to_node
							while edges:
														UpperCAmelCase  ,  UpperCAmelCase  :	Optional[Any]							  =	edges.pop()
														chosen_vertices.add(_lowercase	)
														chosen_vertices.add(_lowercase	)
														for edge in edges.copy():
																					if from_node in edge or to_node in edge:
																												edges.discard(_lowercase	)
							return chosen_vertices



def    __lowerCamelCase						(      _lowercase	)   ->    set:
							UpperCAmelCase  :	Any							  =	set()
							for from_node, to_nodes in graph.items():
														for to_node in to_nodes:
																					edges.add((from_node, to_node)	)
							return edges


if __name__ == "__main__":
							import doctest

							doctest.testmod()

							# graph = {0: [1, 3], 1: [0, 3], 2: [0, 3, 4], 3: [0, 1, 2], 4: [2, 3]}
							# print(f"Matching vertex cover:\n{matching_min_vertex_cover(graph)}")






'''simple docstring'''




a     :    List[Any]      						=					"""Alexander Joslin"""

import operator as op

from .stack import Stack



def    __lowerCamelCase						(      _lowercase	)   ->    int:
							UpperCAmelCase  :	Dict							  =	{"""*""": op.mul, """/""": op.truediv, """+""": op.add, """-""": op.sub}

							UpperCAmelCase  :	Stack[int]							  =	Stack()
							UpperCAmelCase  :	Stack[str]							  =	Stack()

							for i in equation:
														if i.isdigit():
																					# RULE 1
																					operand_stack.push(int(_lowercase	)	)
														elif i in operators:
																					# RULE 2
																					operator_stack.push(_lowercase	)
														elif i == ")":
																					# RULE 4
																					UpperCAmelCase  :	List[Any]							  =	operator_stack.peek()
																					operator_stack.pop()
																					UpperCAmelCase  :	str							  =	operand_stack.peek()
																					operand_stack.pop()
																					UpperCAmelCase  :	str							  =	operand_stack.peek()
																					operand_stack.pop()

																					UpperCAmelCase  :	List[Any]							  =	operators[opr](_lowercase			,       _lowercase	)
																					operand_stack.push(_lowercase	)

    # RULE 5
							return operand_stack.peek()


if __name__ == "__main__":
							a     :    Tuple      						=					"""(5 + ((4 * 2) * (2 + 3)))"""
							# answer = 45
							print(F'''{equation} = {dijkstras_two_stack_algorithm(equation)}''')

