"""simple docstring"""






from typing import Any

import numpy as np






class     A:

		"""simple docstring"""





		def __init__(   self				,							SCREAMING_SNAKE_CASE__				,							SCREAMING_SNAKE_CASE__      )			->  None:

					"""simple docstring"""



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

					_UpperCamelCase				:List[Any]				    =  tableau
					_UpperCamelCase				:List[str]				    =  tableau.shape

					# Number of decision variables x1, x2, x3...
					_UpperCamelCase				:Optional[Any]				    =  n_vars

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

					# 2 if there are >= or == constraints (nonstandard), 1 otherwise (std)
					_UpperCamelCase				:List[str]				    =  (self.n_art_vars > 0) + 1

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

					# Objectives for each stage
					_UpperCamelCase				:List[Any]				    =  ['max']

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

					_UpperCamelCase				:List[Any]				    =  ['']

					# Index of current pivot row and column
					_UpperCamelCase				:Dict				    =  None
					_UpperCamelCase				:List[str]				    =  None

					# Does objective row only contain (non)-negative values?
					_UpperCamelCase				:Optional[int]				    =  False
		@staticmethod
		def      _UpperCamelCase(   *SCREAMING_SNAKE_CASE__      )			->  list[str]:

					"""simple docstring"""



					if len(_A      ) != 3:
								raise ValueError('''Must provide n_vars, n_slack, and n_art_vars'''      )

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

					# decision | slack | artificial
					_UpperCamelCase				:Union[str, Any]				    =  ['x', 's', 'a']
					_UpperCamelCase				:List[str]				    =  []
					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				,							SCREAMING_SNAKE_CASE__      )			->  tuple[Any, Any]:

					"""simple docstring"""



					_UpperCamelCase				:int				    =  self.objectives[-1]

					# Find entries of highest magnitude in objective rows
					_UpperCamelCase				:Optional[int]				    =  (objective == 'min') - (objective == 'max')
					_UpperCamelCase				:Tuple				    =  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:
								_UpperCamelCase				:List[str]				    =  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
					_UpperCamelCase				:Optional[Any]				    =  slice(self.n_stages				,							self.n_rows      )

					# RHS
					_UpperCamelCase				:int				    =  tableau[s, -1]

					# Elements of pivot column within slice
					_UpperCamelCase				:Dict				    =  tableau[s, col_idx]

					# Array filled with nans
					_UpperCamelCase				:Tuple				    =  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
					_UpperCamelCase				:Tuple				    =  np.divide(_A				,							_A				,							out=_A				,							where=divisor > 0      )

					# Arg of minimum quotient excluding the nan values. n_stages is added
					# to compensate for earlier exclusion of objective columns
					_UpperCamelCase				:Tuple				    =  np.nanargmin(_A      ) + self.n_stages
					return row_idx, col_idx
		def      _UpperCamelCase(   self				,							SCREAMING_SNAKE_CASE__				,							SCREAMING_SNAKE_CASE__				,							SCREAMING_SNAKE_CASE__      )			->  np.ndarray:

					"""simple docstring"""



					_UpperCamelCase				:Optional[int]				    =  tableau[row_idx].copy()

					_UpperCamelCase				:Tuple				    =  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
					_UpperCamelCase				:List[Any]				    =  piv_row
					return tableau
		def      _UpperCamelCase(   self				,							SCREAMING_SNAKE_CASE__      )			->  np.ndarray:

					"""simple docstring"""



					self.objectives.pop()

					if not self.objectives:
								return tableau

					# Slice containing ids for artificial columns
					_UpperCamelCase				:List[str]				    =  slice(-self.n_art_vars - 1				,							-1      )

					# Delete the artificial variable columns
					_UpperCamelCase				:Union[str, Any]				    =  np.delete(_A				,							_A				,							axis=1      )

					# Delete the objective row of the first stage
					_UpperCamelCase				:Any				    =  np.delete(_A				,							0				,							axis=0      )

					_UpperCamelCase				:int				    =  1
					self.n_rows -= 1
					_UpperCamelCase				:Tuple				    =  0
					_UpperCamelCase				:str				    =  False
					return tableau
		def      _UpperCamelCase(   self      )			->  dict[Any, Any]:

					"""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:
											_UpperCamelCase				:Optional[Any]				    =  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      )

								_UpperCamelCase				:int				    =  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
											_UpperCamelCase				:Optional[int]				    =  self.change_stage(self.tableau      )
								else:
											_UpperCamelCase				:int				    =  self.pivot(self.tableau				,							_A				,							_A      )
					return {}





		def      _UpperCamelCase(   self				,							SCREAMING_SNAKE_CASE__				,							SCREAMING_SNAKE_CASE__      )			->  dict[str, float]:

					"""simple docstring"""



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

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

								# First entry in the nonzero ids
								_UpperCamelCase				:Tuple				    =  nonzero[0][0]
								_UpperCamelCase				:Union[str, Any]				    =  tableau[nonzero_rowidx, i]

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


if __name__ == "__main__":
					import doctest

					doctest.testmod()





"""simple docstring"""






def 							A_					(   snake_case__		)				->     str:
			_UpperCamelCase				:Tuple				    =  word.upper()
			_UpperCamelCase				:Dict				    =  0
			_UpperCamelCase				:Union[str, Any]				    =  {}
			_UpperCamelCase				:Optional[int]				    =  []

			for letter in word:
						if letter not in letter_nums:
									_UpperCamelCase				:Dict				    =  str(snake_case__		)
									next_num += 1
						word_pattern.append(letter_nums[letter]		)
			return ".".join(snake_case__		)


if __name__ == "__main__":
					import pprint
					import time

					UpperCamelCase__							:Dict       =  time.time()
					with open("""dictionary.txt""") as in_file:
										UpperCamelCase__							:str       =  in_file.read().splitlines()

					UpperCamelCase__							:dict       =  {}
					for word in word_list:
										UpperCamelCase__							:List[Any]       =  get_word_pattern(word)
										if pattern in all_patterns:
															all_patterns[pattern].append(word)
										else:
															UpperCamelCase__							:Tuple       =  [word]

					with open("""word_patterns.txt""", """w""") as out_file:
										out_file.write(pprint.pformat(all_patterns))

					UpperCamelCase__							:Dict       =  round(time.time() - start_time, 2)
					print(F"""Done!  {len(all_patterns):,} word patterns found in {total_time} seconds.""")
					# Done!  9,581 word patterns found in 0.58 seconds.

