



'''simple docstring'''






import functools
from math import sqrt
from time import time





def 				_SCREAMING_SNAKE_CASE(					snake_case_    :     Optional[Any] ,       *snake_case_    :     List[str] ,       **snake_case_    :     List[str]  )		->Optional[Any]:






							'''simple docstring'''
							_lowercase							:		Optional[int]				=   time()
							_lowercase							:		int				=   func(*snake_case_ ,       **snake_case_  )
							_lowercase							:		Tuple				=   time()
							if int(end - start  ) > 0:
														print(F"{func.__name__} runtime: {(end - start):0.4f} s"  )
							else:
														print(F"{func.__name__} runtime: {(end - start) * 10_00:0.4f} ms"  )
							return output





def 				_SCREAMING_SNAKE_CASE(					snake_case_    :     int  )		->List[Any]:






							'''simple docstring'''





							if n < 0:
														raise Exception('''n is negative'''  )
							if n == 0:
														return [0]
							_lowercase							:		Any				=   [0, 1]
							for _ in range(n - 1  ):
														fib.append(fib[-1] + fib[-2]  )
							return fib





def 				_SCREAMING_SNAKE_CASE(					snake_case_    :     str  )		->List[str]:






							'''simple docstring'''





							def fib_recursive_term(snake_case_    :     Union[str, Any]  ) -> 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(snake_case_  ) for i in range(n + 1  )]





def 				_SCREAMING_SNAKE_CASE(					snake_case_    :     Dict  )		->Optional[Any]:






							'''simple docstring'''





							@functools.cache
							def fib_recursive_term(snake_case_    :     Any  ) -> 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(snake_case_  ) for i in range(n + 1  )]





def 				_SCREAMING_SNAKE_CASE(					snake_case_    :     List[Any]  )		->List[str]:






							'''simple docstring'''





							if n < 0:
														raise Exception('''n is negative'''  )
							# Cache must be outside recursuive function
							# other it will reset every time it calls itself.
							_lowercase							:		dict[int, int]				=   {0: 0, 1: 1, 2: 1}  # Prefilled cache

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

														_lowercase							:		Any				=   rec_fn_memoized(num - 1  ) + rec_fn_memoized(num - 2  )
														_lowercase							:		List[str]				=   value
														return value

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





def 				_SCREAMING_SNAKE_CASE(					snake_case_    :     Dict  )		->Union[str, Any]:






							'''simple docstring'''





							if n < 0:
														raise Exception('''n is negative'''  )
							if n >= 14_75:
														raise Exception('''n is too large'''  )
							_lowercase							:		Any				=   sqrt(5  )
							_lowercase							:		Optional[int]				=   (1 + sqrt_a) / 2
							return [round(phi**i / sqrt_a  ) for i in range(n + 1  )]


if __name__ == "__main__":
						lowerCamelCase__	  =		30
						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)











"""simple docstring"""





import doctest

import projectq
from projectq.ops import H, Measure






def 							A(    snake_case_						):
       """simple docstring"""





       lowercase__:							Dict         =     quantum_engine.allocate_qubit()
       H | qubit
       Measure | qubit
       return int(snake_case_						)


if __name__ == "__main__":
  doctest.testmod()

  # initialises a new quantum backend
  UpperCamelCase					=     projectq.MainEngine()

  # Generate a list of 10 random numbers
  UpperCamelCase					=     [get_random_number(quantum_engine) for _ in range(10)]

  # Flushes the quantum engine from memory
  quantum_engine.flush()

  print("""Random numbers""", random_numbers_list)






