


"""simple docstring"""






from typing import Any

import numpy as np


class       lowerCamelCase_		:





				"""simple docstring"""







				def __init__(    self							,		UpperCAmelCase__							,		UpperCAmelCase__  ):
								# Check if RHS is negative
								if np.any(tableau[:, -1]							,		where=tableau[:, -1] < 0  ):
												raise ValueError("RHS must be > 0"  )

								SCREAMING_SNAKE_CASE__  				=					tableau
								SCREAMING_SNAKE_CASE__				,   SCREAMING_SNAKE_CASE__  				=					tableau.shape

								# Number of decision variables x1, x2, x3...
								SCREAMING_SNAKE_CASE__  				=					n_vars

								# Number of artificial variables to be minimised
								SCREAMING_SNAKE_CASE__  				=					len(np.where(tableau[self.n_vars : -1] == -1  )[0]  )

								# 2 if there are >= or == constraints (nonstandard), 1 otherwise (std)
								SCREAMING_SNAKE_CASE__  				=					(self.n_art_vars > 0) + 1

								# Number of slack variables added to make inequalities into equalities
								SCREAMING_SNAKE_CASE__  				=					self.n_rows - self.n_stages

								# Objectives for each stage
								SCREAMING_SNAKE_CASE__  				=					["max"]

								# In two stage simplex, first minimise then maximise
								if self.n_art_vars:
												self.objectives.append("min"  )

								SCREAMING_SNAKE_CASE__  				=					[""]

								# Index of current pivot row and column
								SCREAMING_SNAKE_CASE__  				=					None
								SCREAMING_SNAKE_CASE__  				=					None

								# Does objective row only contain (non)-negative values?
								SCREAMING_SNAKE_CASE__  				=					False



				@staticmethod
				def 	lowerCAmelCase__		(    *UpperCAmelCase__  ):
								if len(UpperCAmelCase__  ) != 3:
												raise ValueError("Must provide n_vars, n_slack, and n_art_vars"  )

								if not all(x >= 0 and isinstance(UpperCAmelCase__							,		UpperCAmelCase__  ) for x in args  ):
												raise ValueError("All arguments must be non-negative integers"  )

								# decision | slack | artificial
								SCREAMING_SNAKE_CASE__  				=					["x", "s", "a"]
								SCREAMING_SNAKE_CASE__  				=					[]
								for i in range(3  ):
												for j in range(args[i]  ):
																titles.append(string_starts[i] + str(j + 1  )  )
								titles.append("RHS"  )
								return titles



				def 	lowerCAmelCase__		(    self							,		UpperCAmelCase__  ):
								SCREAMING_SNAKE_CASE__  				=					self.objectives[-1]

								# Find entries of highest magnitude in objective rows
								SCREAMING_SNAKE_CASE__  				=					(objective == "min") - (objective == "max")
								SCREAMING_SNAKE_CASE__  				=					np.argmax(sign * tableau[0, : self.n_vars]  )

								# Choice is only valid if below 0 for maximise, and above for minimise
								if sign * self.tableau[0, col_idx] <= 0:
												SCREAMING_SNAKE_CASE__  				=					True
												return 0, 0

								# Pivot row is chosen as having the lowest quotient when elements of
								# the pivot column divide the right-hand side

								# Slice excluding the objective rows
								SCREAMING_SNAKE_CASE__  				=					slice(self.n_stages							,		self.n_rows  )

								# RHS
								SCREAMING_SNAKE_CASE__  				=					tableau[s, -1]

								# Elements of pivot column within slice
								SCREAMING_SNAKE_CASE__  				=					tableau[s, col_idx]

								# Array filled with nans
								SCREAMING_SNAKE_CASE__  				=					np.full(self.n_rows - self.n_stages							,		np.nan  )

								# If element in pivot column is greater than zeron_stages, return
								# quotient or nan otherwise
								SCREAMING_SNAKE_CASE__  				=					np.divide(UpperCAmelCase__							,		UpperCAmelCase__							,		out=UpperCAmelCase__							,		where=divisor > 0  )

								# Arg of minimum quotient excluding the nan values. n_stages is added
								# to compensate for earlier exclusion of objective columns
								SCREAMING_SNAKE_CASE__  				=					np.nanargmin(UpperCAmelCase__  ) + self.n_stages
								return row_idx, col_idx



				def 	lowerCAmelCase__		(    self							,		UpperCAmelCase__							,		UpperCAmelCase__							,		UpperCAmelCase__  ):
								SCREAMING_SNAKE_CASE__  				=					tableau[row_idx].copy()

								SCREAMING_SNAKE_CASE__  				=					piv_row[col_idx]

								# Entry becomes 1
								piv_row *= 1 / piv_val

								# Variable in pivot column becomes basic, ie the only non-zero entry
								for idx, coeff in enumerate(tableau[:, col_idx]  ):
												tableau[idx] += -coeff * piv_row
								SCREAMING_SNAKE_CASE__  				=					piv_row
								return tableau



				def 	lowerCAmelCase__		(    self							,		UpperCAmelCase__  ):
								self.objectives.pop()

								if not self.objectives:
												return tableau

								# Slice containing ids for artificial columns
								SCREAMING_SNAKE_CASE__  				=					slice(-self.n_art_vars - 1							,		-1  )

								# Delete the artificial variable columns
								SCREAMING_SNAKE_CASE__  				=					np.delete(UpperCAmelCase__							,		UpperCAmelCase__							,		axis=1  )

								# Delete the objective row of the first stage
								SCREAMING_SNAKE_CASE__  				=					np.delete(UpperCAmelCase__							,		0							,		axis=0  )

								SCREAMING_SNAKE_CASE__  				=					1
								self.n_rows -= 1
								SCREAMING_SNAKE_CASE__  				=					0
								SCREAMING_SNAKE_CASE__  				=					False
								return tableau



				def 	lowerCAmelCase__		(    self  ):
								# Stop simplex algorithm from cycling.
								for _ in range(100  ):
												# Completion of each stage removes an objective. If both stages
												# are complete, then no objectives are left
												if not self.objectives:
																SCREAMING_SNAKE_CASE__  				=					self.generate_col_titles(
																    self.n_vars							,		self.n_slack							,		self.n_art_vars  )

																# Find the values of each variable at optimal solution
																return self.interpret_tableau(self.tableau							,		self.col_titles  )

												SCREAMING_SNAKE_CASE__				,   SCREAMING_SNAKE_CASE__  				=					self.find_pivot(self.tableau  )

												# If there are no more negative values in objective row
												if self.stop_iter:
																# Delete artificial variable columns and rows. Update attributes
																SCREAMING_SNAKE_CASE__  				=					self.change_stage(self.tableau  )
												else:
																SCREAMING_SNAKE_CASE__  				=					self.pivot(self.tableau							,		UpperCAmelCase__							,		UpperCAmelCase__  )
								return {}






				def 	lowerCAmelCase__		(    self							,		UpperCAmelCase__							,		UpperCAmelCase__  ):
								SCREAMING_SNAKE_CASE__  				=					{"P": abs(tableau[0, -1]  )}

								for i in range(self.n_vars  ):
												# Gives ids of nonzero entries in the ith column
												SCREAMING_SNAKE_CASE__  				=					np.nonzero(tableau[:, i]  )
												SCREAMING_SNAKE_CASE__  				=					len(nonzero[0]  )

												# First entry in the nonzero ids
												SCREAMING_SNAKE_CASE__  				=					nonzero[0][0]
												SCREAMING_SNAKE_CASE__  				=					tableau[nonzero_rowidx, i]

												# If there is only one nonzero value in column, which is one
												if n_nonzero == nonzero_val == 1:
																SCREAMING_SNAKE_CASE__  				=					tableau[nonzero_rowidx, -1]
																SCREAMING_SNAKE_CASE__  				=					rhs_val

        # Check for basic variables
								for title in col_titles:
												# Don't add RHS or slack variables to output dict
												if title[0] not in "R-s-a":
																output_dict.setdefault(UpperCAmelCase__							,		0  )
								return output_dict


if __name__ == "__main__":
	import doctest

	doctest.testmod()




"""simple docstring"""






class       lowerCamelCase_		:





				"""simple docstring"""







				def __init__(    self  ):
								SCREAMING_SNAKE_CASE__  				=					[0]
								SCREAMING_SNAKE_CASE__  				=					0



				def 	lowerCAmelCase__		(    self							,		UpperCAmelCase__  ):
								SCREAMING_SNAKE_CASE__  				=					self.__heap[i]
								while i // 2 > 0:
												if self.__heap[i] > self.__heap[i // 2]:
																SCREAMING_SNAKE_CASE__  				=					self.__heap[i // 2]
																SCREAMING_SNAKE_CASE__  				=					temporary
												i //= 2



				def 	lowerCAmelCase__		(    self							,		UpperCAmelCase__  ):
								self.__heap.append(UpperCAmelCase__  )
								self.__size += 1
								self.__swap_up(self.__size  )



				def 	lowerCAmelCase__		(    self							,		UpperCAmelCase__  ):
								while self.__size >= 2 * i:
												if 2 * i + 1 > self.__size:
																SCREAMING_SNAKE_CASE__  				=					2 * i
												else:
																if self.__heap[2 * i] > self.__heap[2 * i + 1]:
																				SCREAMING_SNAKE_CASE__  				=					2 * i
																else:
																				SCREAMING_SNAKE_CASE__  				=					2 * i + 1
												SCREAMING_SNAKE_CASE__  				=					self.__heap[i]
												if self.__heap[i] < self.__heap[bigger_child]:
																SCREAMING_SNAKE_CASE__  				=					self.__heap[bigger_child]
																SCREAMING_SNAKE_CASE__  				=					temporary
												SCREAMING_SNAKE_CASE__  				=					bigger_child



				def 	lowerCAmelCase__		(    self  ):
								SCREAMING_SNAKE_CASE__  				=					self.__heap[1]
								SCREAMING_SNAKE_CASE__  				=					self.__heap[self.__size]
								self.__size -= 1
								self.__heap.pop()
								self.__swap_down(1  )
								return max_value



				@property
				def 	lowerCAmelCase__		(    self  ):
								return self.__heap[1:]






				def __len__(    self  ):
								return self.__size


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	# create an instance of BinaryHeap
	_lowerCamelCase  =	BinaryHeap()
	binary_heap.insert(6)
	binary_heap.insert(10)
	binary_heap.insert(15)
	binary_heap.insert(12)
	# pop root(max-values because it is max heap)
	print(binary_heap.pop())  # 15
	print(binary_heap.pop())  # 12
	# get the list and size after operations
	print(binary_heap.get_list)
	print(len(binary_heap))
