


'''simple docstring'''

from typing import Any

import numpy as np







class  UpperCAmelCase :

	def __init__( self :	Optional[Any],					a_ :	np.ndarray,					a_ :	int					):





				"""simple docstring"""



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

				UpperCamelCase__ 						=						tableau
				UpperCamelCase__						,		UpperCamelCase__ 						=						tableau.shape

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

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

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

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

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

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

				UpperCamelCase__ 						=						[""]

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

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

	@staticmethod
	def 		lowercase_						( *a_ :	int					):





				"""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__ 						=						["x", "s", "a"]
				UpperCamelCase__ 						=						[]
				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 		lowercase_						( self :	int,					a_ :	np.ndarray					):





				"""simple docstring"""



				UpperCamelCase__ 						=						self.objectives[-1]

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

				# RHS
				UpperCamelCase__ 						=						tableau[s, -1]

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

				# Array filled with nans
				UpperCamelCase__ 						=						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__ 						=						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__ 						=						np.nanargmin(a_					) + self.n_stages
				return row_idx, col_idx

	def 		lowercase_						( self :	List[Any],					a_ :	np.ndarray,					a_ :	int,					a_ :	int					):





				"""simple docstring"""



				UpperCamelCase__ 						=						tableau[row_idx].copy()

				UpperCamelCase__ 						=						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__ 						=						piv_row
				return tableau

	def 		lowercase_						( self :	Dict,					a_ :	np.ndarray					):





				"""simple docstring"""



				self.objectives.pop()

				if not self.objectives:
							return tableau

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

				# Delete the artificial variable columns
				UpperCamelCase__ 						=						np.delete(a_,					a_,					axis=1					)

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

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

	def 		lowercase_						( self :	Optional[int]					):





				"""simple docstring"""



				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:
										UpperCamelCase__ 						=						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__						,		UpperCamelCase__ 						=						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__ 						=						self.change_stage(self.tableau					)
							else:
										UpperCamelCase__ 						=						self.pivot(self.tableau,					a_,					a_					)
				return {}

	def 		lowercase_						( self :	List[Any],					a_ :	np.ndarray,					a_ :	list[str]					):





				"""simple docstring"""



				UpperCamelCase__ 						=						{"P": abs(tableau[0, -1]					)}

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

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

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

from dataclasses import dataclass

__lowercase:		List[str]							=     "0.1"
__lowercase:		Union[str, Any]							=     "Lucia Harcekova"







@dataclass
class  UpperCAmelCase :
 _lowerCamelCase :					int
 _lowerCamelCase :					int
 _lowerCamelCase :					str

 def __repr__( self :	List[str]					):





    """simple docstring"""



    return f'({self.offset}, {self.length}, {self.indicator})'







class  UpperCAmelCase :

 def __init__( self :	Optional[int],					a_ :	int = 13,					a_ :	int = 6					):





    """simple docstring"""



    UpperCamelCase__ 						=						window_size
    UpperCamelCase__ 						=						lookahead_buffer_size
    UpperCamelCase__ 						=						self.window_size - self.lookahead_buffer_size

 def 		lowercase_						( self :	Optional[int],					a_ :	str					):





    """simple docstring"""



    UpperCamelCase__ 						=						[]
    UpperCamelCase__ 						=						""

    # while there are still characters in text to compress
    while text:
       # find the next encoding phrase
       # - triplet with offset, length, indicator (the next encoding character)
       UpperCamelCase__ 						=						self._find_encoding_token(a_,					a_					)

       # update the search buffer:
       # - add new characters from text into it
       # - check if size exceed the max search buffer size, if so, drop the
       #   oldest elements
       search_buffer += text[: token.length + 1]
       if len(a_					) > self.search_buffer_size:
          UpperCamelCase__ 						=						search_buffer[-self.search_buffer_size :]

       # update the text
       UpperCamelCase__ 						=						text[token.length + 1 :]

       # append the token to output
       output.append(a_					)

    return output

 def 		lowercase_						( self :	List[Any],					a_ :	list[Token]					):





    """simple docstring"""



    UpperCamelCase__ 						=						""

    for token in tokens:
       for _ in range(token.length					):
          output += output[-token.offset]
       output += token.indicator

    return output

 def 		lowercase_						( self :	Any,					a_ :	str,					a_ :	str					):





    """simple docstring"""



    if not text:
       raise ValueError("We need some text to work with."					)

    # Initialise result parameters to default values
    UpperCamelCase__						,		UpperCamelCase__ 						=						0, 0

    if not search_buffer:
       return Token(a_,					a_,					text[length]					)

    for i, character in enumerate(a_					):
       UpperCamelCase__ 						=						len(a_					) - i
       if character == text[0]:
          UpperCamelCase__ 						=						self._match_length_from_index(a_,					a_,					0,					a_					)
          # if the found length is bigger than the current or if it's equal,
          # which means it's offset is smaller: update offset and length
          if found_length >= length:
             UpperCamelCase__						,		UpperCamelCase__ 						=						found_offset, found_length

    return Token(a_,					a_,					text[length]					)

 def 		lowercase_						( self :	Optional[int],					a_ :	str,					a_ :	str,					a_ :	int,					a_ :	int					):





    """simple docstring"""



    if not text or text[text_index] != window[window_index]:
       return 0
    return 1 + self._match_length_from_index(
        a_,					window + text[text_index],					text_index + 1,					window_index + 1					)


if __name__ == "__main__":
       from doctest import testmod

       testmod()
       # Initialize compressor class
       __lowercase:		Optional[Any]							=     LZaaCompressor(window_size=13, lookahead_buffer_size=6)

       # Example
       __lowercase:		Union[str, Any]							=     "cabracadabrarrarrad"
       __lowercase:		Optional[int]							=     lzaa_compressor.compress(TEXT)
       print(lzaa_compressor.compress("ababcbababaa"))
       __lowercase:		Optional[int]							=     lzaa_compressor.decompress(compressed_text)
       assert decompressed_text == TEXT, "The LZ77 algorithm returned the invalid result."