"""simple docstring"""
from typing import Any

import numpy as np



class 	lowerCAmelCase_     :



				"""simple docstring"""

				def __init__(					self		,     lowerCAmelCase		,     lowerCAmelCase     ):






										"""simple docstring"""

										if np.any(tableau[:, -1]		,     where=tableau[:, -1] < 0     ):
																raise ValueError('RHS must be > 0'     )

										snake_case             =      tableau
										snake_case       ,snake_case             =      tableau.shape

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

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

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

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

										# Objectives for each stage
										snake_case             =      ['max']

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

										snake_case             =      ['']

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

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

				@staticmethod
				def 		snake_case			(					*lowerCAmelCase     ):






										"""simple docstring"""

										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
										snake_case             =      ['x', 's', 'a']
										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 		snake_case			(					self		,     lowerCAmelCase     ):






										"""simple docstring"""

										snake_case             =      self.objectives[-1]

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

										# RHS
										snake_case             =      tableau[s, -1]

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

										# Array filled with nans
										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
										snake_case             =      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
										snake_case             =      np.nanargmin(lowerCAmelCase     ) + self.n_stages
										return row_idx, col_idx

				def 		snake_case			(					self		,     lowerCAmelCase		,     lowerCAmelCase		,     lowerCAmelCase     ):






										"""simple docstring"""

										snake_case             =      tableau[row_idx].copy()

										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
										snake_case             =      piv_row
										return tableau

				def 		snake_case			(					self		,     lowerCAmelCase     ):






										"""simple docstring"""

										self.objectives.pop()

										if not self.objectives:
																return tableau

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

										# Delete the artificial variable columns
										snake_case             =      np.delete(lowerCAmelCase		,     lowerCAmelCase		,     axis=1     )

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

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

				def 		snake_case			(					self     ):






										"""simple docstring"""

										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:
																						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     )

																snake_case       ,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
																						snake_case             =      self.change_stage(self.tableau     )
																else:
																						snake_case             =      self.pivot(self.tableau		,     lowerCAmelCase		,     lowerCAmelCase     )
										return {}

				def 		snake_case			(					self		,     lowerCAmelCase		,     lowerCAmelCase     ):






										"""simple docstring"""

										snake_case             =      {'P': abs(tableau[0, -1]     )}

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

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

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


if __name__ == "__main__":
					import doctest

					doctest.testmod()



"""simple docstring"""
import os
from string import ascii_letters

SCREAMING_SNAKE_CASE__       =	ascii_letters + " \t\n"





def  lowerCAmelCase__     (      )       ->					dict[str, None]:





						"""simple docstring"""






						snake_case             =      os.path.split(os.path.realpath(_UpperCamelCase       )       )
						snake_case             =      {}
						with open(path[0] + '/dictionary.txt'       ) as dictionary_file:
												for word in dictionary_file.read().split('\n'       ):
																		snake_case             =      None
						return english_words


SCREAMING_SNAKE_CASE__       =	load_dictionary()





def  lowerCAmelCase__     (      _UpperCamelCase							:					str       )       ->					float:





						"""simple docstring"""






						snake_case             =      message.upper()
						snake_case             =      remove_non_letters(_UpperCamelCase       )
						snake_case             =      message.split()
						snake_case             =      len([word for word in possible_words if word in ENGLISH_WORDS]       )
						return float(_UpperCamelCase       ) / len(_UpperCamelCase       )





def  lowerCAmelCase__     (      _UpperCamelCase							:					str       )       ->					str:





						"""simple docstring"""






						return "".join(symbol for symbol in message if symbol in LETTERS_AND_SPACE       )





def  lowerCAmelCase__     (      _UpperCamelCase							:					str			,      _UpperCamelCase							:					int = 2_0			,      _UpperCamelCase							:					int = 8_5       )       ->					bool:





						"""simple docstring"""






						snake_case             =      get_english_count(_UpperCamelCase       ) * 1_0_0 >= word_percentage
						snake_case             =      len(remove_non_letters(_UpperCamelCase       )       )
						snake_case             =      (float(_UpperCamelCase       ) / len(_UpperCamelCase       )) * 1_0_0
						snake_case             =      message_letters_percentage >= letter_percentage
						return words_match and letters_match


if __name__ == "__main__":
					import doctest

					doctest.testmod()


