






"""simple docstring"""





import functools
from math import sqrt
from time import time






def 							A(    snake_case_		,  *snake_case_		,  **snake_case_						):
       """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) * 1000:0.4f} ms"""						)
       return output






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





       def fib_recursive_term(snake_case_						) -> 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 							A(    snake_case_						):
       """simple docstring"""





       @functools.cache
       def fib_recursive_term(snake_case_						) -> 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 							A(    snake_case_						):
       """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_						) -> 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 							A(    snake_case_						):
       """simple docstring"""





       if n < 0:
              raise Exception("n is negative"						)
       if n >= 1475:
              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__":
  UpperCamelCase					=     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'''







from __future__ import annotations

from collections.abc import Generator






def 					_SCREAMING_SNAKE_CASE		(						snake_case_	):
	if not isinstance(snake_case_							,       snake_case_	) or n < 1:
		raise Exception("""Sequence only defined for positive integers"""	)

	yield n
	while n != 1:
		if n % 2 == 0:
			n //= 2
		else:
			_lowercase							=     3 * n + 1
		yield n






def 					_SCREAMING_SNAKE_CASE		(						):
	_lowercase							=     43
	_lowercase							=     tuple(collatz_sequence(snake_case_	)	)
	print(snake_case_	)
	print(F"""Collatz sequence from {n} took {len(snake_case_	)} steps."""	)


if __name__ == "__main__":
							main()




