
from typing import Any

import numpy as np

class        UpperCamelCase__:

	"""simple docstring"""

	def __init__(      self				:			Union[str, Any]							,			snake_case__				:			np.ndarray							,			snake_case__				:			int ):
			"""simple docstring"""





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

			A				=tableau
			A			,    A				=tableau.shape

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

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

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

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

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

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

			A				=[""]

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

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







	@staticmethod
	def        _a					(      *snake_case__				:			int ):
			"""simple docstring"""





			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
			A				=["x", "s", "a"]
			A				=[]
			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				:			Any							,			snake_case__				:			np.ndarray ):
			"""simple docstring"""





			A				=self.objectives[-1]

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

			# RHS
			A				=tableau[s, -1]

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

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







	def        _a					(      self				:			List[str]							,			snake_case__				:			np.ndarray							,			snake_case__				:			int							,			snake_case__				:			int ):
			"""simple docstring"""





			A				=tableau[row_idx].copy()

			A				=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
			A				=piv_row
			return tableau







	def        _a					(      self				:			Dict							,			snake_case__				:			np.ndarray ):
			"""simple docstring"""





			self.objectives.pop()

			if not self.objectives:
					return tableau

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

			# Delete the artificial variable columns
			A				=np.delete(snake_case__							,			snake_case__							,			axis=1 )

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

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







	def        _a					(      self				:			Dict ):
			"""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:
							A				=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 )

					A			,    A				=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
							A				=self.change_stage(self.tableau )
					else:
							A				=self.pivot(self.tableau							,			snake_case__							,			snake_case__ )
			return {}







	def        _a					(      self				:			List[str]							,			snake_case__				:			np.ndarray							,			snake_case__				:			list[str] ):
			"""simple docstring"""





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

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

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

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






import functools
from math import sqrt
from time import time

def    UpperCamelCase_ (	a_  ,				*a_  ,				**a_		)     ->List[Any]:
		A				=time()
		A				=func(*a_  ,				**a_		)
		A				=time()
		if int(end - start		) > 0:
				print(f'''{func.__name__} runtime: {(end - start):0.4f} s'''		)
		else:
				print(f'''{func.__name__} runtime: {(end - start) * 1000:0.4f} ms'''		)
		return output

def    UpperCamelCase_ (	a_		)     ->list[int]:
		if n < 0:
				raise Exception("n is negative"		)
		if n == 0:
				return [0]
		A				=[0, 1]
		for _ in range(n - 1		):
				fib.append(fib[-1] + fib[-2]		)
		return fib

def    UpperCamelCase_ (	a_		)     ->list[int]:

		def fib_recursive_term(a_		) -> int:
				if i < 0:
						raise Exception("n is negative"		)
				if i < 2:
						return i
				return fib_recursive_term(i - 1		) + fib_recursive_term(i - 2		)

		if n < 0:
				raise Exception("n is negative"		)
		return [fib_recursive_term(a_		) for i in range(n + 1		)]

def    UpperCamelCase_ (	a_		)     ->list[int]:

		@functools.cache
		def fib_recursive_term(a_		) -> int:
				if i < 0:
						raise Exception("n is negative"		)
				if i < 2:
						return i
				return fib_recursive_term(i - 1		) + fib_recursive_term(i - 2		)

		if n < 0:
				raise Exception("n is negative"		)
		return [fib_recursive_term(a_		) for i in range(n + 1		)]

def    UpperCamelCase_ (	a_		)     ->list[int]:
		if n < 0:
				raise Exception("n is negative"		)
		# Cache must be outside recursuive function
		# other it will reset every time it calls itself.
		A				={0: 0, 1: 1, 2: 1}  # Prefilled cache

		def rec_fn_memoized(a_		) -> int:
				if num in cache:
						return cache[num]

				A				=rec_fn_memoized(num - 1		) + rec_fn_memoized(num - 2		)
				A				=value
				return value

		return [rec_fn_memoized(a_		) for i in range(n + 1		)]

def    UpperCamelCase_ (	a_		)     ->list[int]:
		if n < 0:
				raise Exception("n is negative"		)
		if n >= 1475:
				raise Exception("n is too large"		)
		A				=sqrt(5		)
		A				=(1 + sqrt_a) / 2
		return [round(phi**i / sqrt_a		) for i in range(n + 1		)]


if __name__ == "__main__":
	__a							  =						3_0
	time_func(fib_iterative, num)
	time_func(fib_recursive, num)  # Around 3s runtime
	time_func(fib_recursive_cached, num)  # Around 0ms runtime
	time_func(fib_memoization, num)
	time_func(fib_binet, num)




