




from __future__ import annotations




class    snake_case__							:
				"""simple docstring"""



				def __init__(				self    :					Tuple ,				__lowerCamelCase    :					int = 0							) ->					None:
							a   =      value
							a   =      None
							a   =      None




def       __magic_name__    (			A		: Node | None,  A		: Node | None       ):






			'''simple docstring'''







			if treea is None:
						return treea
			if treea is None:
						return treea

			a   =      treea.value + treea.value
			a   =      merge_two_binary_trees(treea.left,  treea.left       )
			a   =      merge_two_binary_trees(treea.right,  treea.right       )
			return treea




def       __magic_name__    (			A		: Node | None       ):






			'''simple docstring'''







			if root:
						print(root.value       )
						print_preorder(root.left       )
						print_preorder(root.right       )


if __name__ == "__main__":
		__lowerCAmelCase		:    int	      =		Node(1)
		__lowerCAmelCase		:    Tuple	      =		Node(2)
		__lowerCAmelCase		:    Tuple	      =		Node(3)
		__lowerCAmelCase		:    Any	      =		Node(4)

		__lowerCAmelCase		:    int	      =		Node(2)
		__lowerCAmelCase		:    Optional[int]	      =		Node(4)
		__lowerCAmelCase		:    List[str]	      =		Node(6)
		__lowerCAmelCase		:    str	      =		Node(9)
		__lowerCAmelCase		:    int	      =		Node(5)

		print('Tree1 is: ')
		print_preorder(treea)
		print('Tree2 is: ')
		print_preorder(treea)
		__lowerCAmelCase		:    str	      =		merge_two_binary_trees(treea, treea)
		print('Merged Tree is: ')
		print_preorder(merged_tree)












from typing import Any

import numpy as np




class    snake_case__							:
				"""simple docstring"""



				def __init__(				self    :					Tuple ,				__lowerCamelCase    :					np.ndarray ,				__lowerCamelCase    :					int							) ->					None:
							# Check if RHS is negative
							if np.any(tableau[:, -1] ,				where=tableau[:, -1] < 0							):
										raise ValueError("RHS must be > 0"							)

							a   =      tableau
							a   ,		a   =      tableau.shape

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

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

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

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

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

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

							a   =      [""]

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

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





				@staticmethod
				def 							__UpperCAmelCase							(				*__lowerCamelCase    :					int							) ->					list[str]:
							if len(__lowerCamelCase							) != 3:
										raise ValueError("Must provide n_vars, n_slack, and n_art_vars"							)

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

							# decision | slack | artificial
							a   =      ["x", "s", "a"]
							a   =      []
							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 							__UpperCAmelCase							(				self    :					Tuple ,				__lowerCamelCase    :					np.ndarray							) ->					tuple[Any, Any]:
							a   =      self.objectives[-1]

							# Find entries of highest magnitude in objective rows
							a   =      (objective == "min") - (objective == "max")
							a   =      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:
										a   =      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
							a   =      slice(self.n_stages ,				self.n_rows							)

							# RHS
							a   =      tableau[s, -1]

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

							# Array filled with nans
							a   =      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
							a   =      np.divide(__lowerCamelCase ,				__lowerCamelCase ,				out=__lowerCamelCase ,				where=divisor > 0							)

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





				def 							__UpperCAmelCase							(				self    :					List[Any] ,				__lowerCamelCase    :					np.ndarray ,				__lowerCamelCase    :					int ,				__lowerCamelCase    :					int							) ->					np.ndarray:
							a   =      tableau[row_idx].copy()

							a   =      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
							a   =      piv_row
							return tableau





				def 							__UpperCAmelCase							(				self    :					Tuple ,				__lowerCamelCase    :					np.ndarray							) ->					np.ndarray:
							self.objectives.pop()

							if not self.objectives:
										return tableau

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

							# Delete the artificial variable columns
							a   =      np.delete(__lowerCamelCase ,				__lowerCamelCase ,				axis=1							)

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

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





				def 							__UpperCAmelCase							(				self    :					Any							) ->					dict[Any, Any]:
							# Stop simplex algorithm from cycling.
							for _ in range(1_00							):
										# Completion of each stage removes an objective. If both stages
										# are complete, then no objectives are left
										if not self.objectives:
													a   =      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							)

										a   ,		a   =      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
													a   =      self.change_stage(self.tableau							)
										else:
													a   =      self.pivot(self.tableau ,				__lowerCamelCase ,				__lowerCamelCase							)
							return {}





				def 							__UpperCAmelCase							(				self    :					int ,				__lowerCamelCase    :					np.ndarray ,				__lowerCamelCase    :					list[str]							) ->					dict[str, float]:
							a   =      {"P": abs(tableau[0, -1]							)}

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

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

										# If there is only one nonzero value in column, which is one
										if n_nonzero == nonzero_val == 1:
													a   =      tableau[nonzero_rowidx, -1]
													a   =      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(__lowerCamelCase ,				0							)
							return output_dict


if __name__ == "__main__":
		import doctest

		doctest.testmod()






