




"""simple docstring"""







from typing import Any

import numpy as np

class 							snake_case_ :







			"""simple docstring"""




			def __init__(		self					,				lowerCamelCase_					,				lowerCamelCase_)							->      Optional[Any]:
							# Check if RHS is negative
							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      UpperCAmelCase__ (		*lowerCamelCase_)							->      Dict:
							if len(__snake_case) != 3:
											raise ValueError('''Must provide n_vars, n_slack, and n_art_vars''')

							if not all(x >= 0 and isinstance(__snake_case					,				__snake_case) 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      UpperCAmelCase__ (		self					,				lowerCamelCase_)							->      Union[str, Any]:
							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(__snake_case					,				__snake_case					,				out=__snake_case					,				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(__snake_case) + self.n_stages
							return row_idx, col_idx







			def      UpperCAmelCase__ (		self					,				lowerCamelCase_					,				lowerCamelCase_					,				lowerCamelCase_)							->      List[str]:
							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      UpperCAmelCase__ (		self					,				lowerCamelCase_)							->      Any:
							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(__snake_case					,				__snake_case					,				axis=1)

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

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







			def      UpperCAmelCase__ (		self)							->      int:
							# Stop simplex algorithm from cycling.
							for _ in range(1_0_0):
											# 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					,				__snake_case					,				__snake_case)
							return {}







			def      UpperCAmelCase__ (		self					,				lowerCamelCase_					,				lowerCamelCase_)							->      List[Any]:
							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(__snake_case					,				0)
							return output_dict


if __name__ == "__main__":
		import doctest

		doctest.testmod()





"""simple docstring"""







class 							snake_case_ :







   """simple docstring"""




   def __init__(		self					,				lowerCamelCase_=None)							->      Tuple:
       UpperCamelCase										=  data
       UpperCamelCase										=  None







   def __repr__(		self)							->      Union[str, Any]:
       UpperCamelCase										=  ''''''
       UpperCamelCase										=  self
       while temp:
           string_rep += F'<{temp.data}> ---> '
           UpperCamelCase										=  temp.next
       string_rep += "<END>"
       return string_rep





def     __snake_case   (							_lowercase						):


    """simple docstring"""







    if not elements_list:
        raise Exception('''The Elements List is empty'''						)

    # Set first element as Head
    UpperCamelCase										=  Node(elements_list[0]						)
    UpperCamelCase										=  head
    # Loop through elements from position 1
    for data in elements_list[1:]:
        UpperCamelCase										=  Node(_lowercase						)
        UpperCamelCase										=  current.next
    return head


SCREAMING_SNAKE_CASE_      =					[1, 3, 5, 32, 44, 12, 43]
print(f'List: {list_data}')
print('Creating Linked List from List.')
SCREAMING_SNAKE_CASE_      =					make_linked_list(list_data)
print('Linked List:')


print(linked_list)