




from __future__ import annotations

from statistics import mean
def 						lowerCAmelCase_       (	__a )       ->			list[int]:





							"""simple docstring"""





							SCREAMING_SNAKE_CASE			: Any	     =2
							SCREAMING_SNAKE_CASE			: Any	     =list(__a )
							SCREAMING_SNAKE_CASE			: Optional[Any]	     =[0] * len(__a )
							SCREAMING_SNAKE_CASE			: int	     =0
							while True:
														SCREAMING_SNAKE_CASE			: Union[str, Any]	     =True
														for i, burst_time in enumerate(__a ):
																					if rem_burst_times[i] > 0:
																												SCREAMING_SNAKE_CASE			: Dict	     =False
																												if rem_burst_times[i] > quantum:
																																			t += quantum
																																			rem_burst_times[i] -= quantum
																												else:
																																			t += rem_burst_times[i]
																																			SCREAMING_SNAKE_CASE			: Optional[int]	     =t - burst_time
																																			SCREAMING_SNAKE_CASE			: int	     =0
														if done is True:
																					return waiting_times
def 						lowerCAmelCase_       (	__a	,	__a )       ->			list[int]:





							"""simple docstring"""





							return [burst + waiting for burst, waiting in zip(__a	,	__a )]


if __name__ == "__main__":
							_A							    =	[3, 5, 7]
							_A							    =	calculate_waiting_times(burst_times)
							_A							    =	calculate_turn_around_times(burst_times, waiting_times)
							print("""Process ID \tBurst Time \tWaiting Time \tTurnaround Time""")
							for i, burst_time in enumerate(burst_times):
														print(
														    F'''  {i + 1}\t\t  {burst_time}\t\t  {waiting_times[i]}\t\t  '''
														    F'''{turn_around_times[i]}'''
														)
							print(F'''\nAverage waiting time = {mean(waiting_times):.5f}''')
							print(F'''Average turn around time = {mean(turn_around_times):.5f}''')












from typing import Any

import numpy as np


class 							_lowerCAmelCase		:




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

											SCREAMING_SNAKE_CASE			: Tuple	     =tableau
											SCREAMING_SNAKE_CASE     ,							SCREAMING_SNAKE_CASE			: Tuple	     =tableau.shape

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

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

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

											# Number of slack variables added to make inequalities into equalities
											SCREAMING_SNAKE_CASE			: Optional[int]	     =self.n_rows - self.n_stages

											# Objectives for each stage
											SCREAMING_SNAKE_CASE			: str	     =['''max''']

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

											SCREAMING_SNAKE_CASE			: Dict	     =['''''']

											# Index of current pivot row and column
											SCREAMING_SNAKE_CASE			: str	     =None
											SCREAMING_SNAKE_CASE			: Optional[Any]	     =None

											# Does objective row only contain (non)-negative values?
											SCREAMING_SNAKE_CASE			: Dict	     =False




				@staticmethod
				def     __a		( *snake_case_							)    ->      list[str]:
											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
											SCREAMING_SNAKE_CASE			: Any	     =['''x''', '''s''', '''a''']
											SCREAMING_SNAKE_CASE			: int	     =[]
											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     __a		( self		,		snake_case_							)    ->      tuple[Any, Any]:
											SCREAMING_SNAKE_CASE			: Optional[int]	     =self.objectives[-1]

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

											# RHS
											SCREAMING_SNAKE_CASE			: Dict	     =tableau[s, -1]

											# Elements of pivot column within slice
											SCREAMING_SNAKE_CASE			: Tuple	     =tableau[s, col_idx]

											# Array filled with nans
											SCREAMING_SNAKE_CASE			: Union[str, Any]	     =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
											SCREAMING_SNAKE_CASE			: Optional[Any]	     =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
											SCREAMING_SNAKE_CASE			: List[Any]	     =np.nanargmin(snake_case_							) + self.n_stages
											return row_idx, col_idx




				def     __a		( self		,		snake_case_		,		snake_case_		,		snake_case_							)    ->      np.ndarray:
											SCREAMING_SNAKE_CASE			: Tuple	     =tableau[row_idx].copy()

											SCREAMING_SNAKE_CASE			: Optional[Any]	     =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
											SCREAMING_SNAKE_CASE			: Dict	     =piv_row
											return tableau




				def     __a		( self		,		snake_case_							)    ->      np.ndarray:
											self.objectives.pop()

											if not self.objectives:
																		return tableau

											# Slice containing ids for artificial columns
											SCREAMING_SNAKE_CASE			: Optional[int]	     =slice(-self.n_art_vars - 1		,		-1							)

											# Delete the artificial variable columns
											SCREAMING_SNAKE_CASE			: Optional[int]	     =np.delete(snake_case_		,		snake_case_		,		axis=1							)

											# Delete the objective row of the first stage
											SCREAMING_SNAKE_CASE			: str	     =np.delete(snake_case_		,		0		,		axis=0							)

											SCREAMING_SNAKE_CASE			: Any	     =1
											self.n_rows -= 1
											SCREAMING_SNAKE_CASE			: Optional[Any]	     =0
											SCREAMING_SNAKE_CASE			: List[str]	     =False
											return tableau




				def     __a		( self							)    ->      dict[Any, Any]:
											# Stop simplex algorithm from cycling.
											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:
																									SCREAMING_SNAKE_CASE			: int	     =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							)

																		SCREAMING_SNAKE_CASE     ,							SCREAMING_SNAKE_CASE			: Any	     =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
																									SCREAMING_SNAKE_CASE			: Optional[int]	     =self.change_stage(self.tableau							)
																		else:
																									SCREAMING_SNAKE_CASE			: Dict	     =self.pivot(self.tableau		,		snake_case_		,		snake_case_							)
											return {}







				def     __a		( self		,		snake_case_		,		snake_case_							)    ->      dict[str, float]:
											SCREAMING_SNAKE_CASE			: Any	     ={'''P''': abs(tableau[0, -1]							)}

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

																		# First entry in the nonzero ids
																		SCREAMING_SNAKE_CASE			: List[str]	     =nonzero[0][0]
																		SCREAMING_SNAKE_CASE			: Any	     =tableau[nonzero_rowidx, i]

																		# If there is only one nonzero value in column, which is one
																		if n_nonzero == nonzero_val == 1:
																									SCREAMING_SNAKE_CASE			: Union[str, Any]	     =tableau[nonzero_rowidx, -1]
																									SCREAMING_SNAKE_CASE			: Any	     =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()






