





import functools
from math import sqrt
from time import time






def 			SCREAMING_SNAKE_CASE__							(    UpperCamelCase__:							Optional[Any]   ,				*UpperCamelCase__:							Optional[Any]   ,				**UpperCamelCase__:							Tuple      ):
		SCREAMING_SNAKE_CASE__								= time()
		SCREAMING_SNAKE_CASE__								= func(*UpperCamelCase__   ,				**UpperCamelCase__      )
		SCREAMING_SNAKE_CASE__								= time()
		if int(end - start      ) > 0:
				print(f'''{func.__name__} runtime: {(end - start):0.4f} s'''      )
		else:
				print(f'''{func.__name__} runtime: {(end - start) * 1_000:0.4f} ms'''      )
		return output






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






def 			SCREAMING_SNAKE_CASE__							(    UpperCamelCase__:							int      ):

		def fib_recursive_term(UpperCamelCase__:							int      ) -> 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(UpperCamelCase__      ) for i in range(n + 1      )]






def 			SCREAMING_SNAKE_CASE__							(    UpperCamelCase__:							int      ):

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






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

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

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

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






def 			SCREAMING_SNAKE_CASE__							(    UpperCamelCase__:							int      ):
		if n < 0:
				raise Exception("""n is negative"""      )
		if n >= 1_475:
				raise Exception("""n is too large"""      )
		SCREAMING_SNAKE_CASE__								= sqrt(5      )
		SCREAMING_SNAKE_CASE__								= (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)






from __future__ import annotations






def 			SCREAMING_SNAKE_CASE__							(    UpperCamelCase__:							list[int | float]      ):
		if len(UpperCamelCase__      ) == 0:
				raise ValueError("""find_min() arg is an empty sequence"""      )
		SCREAMING_SNAKE_CASE__								= nums[0]
		for num in nums:
				SCREAMING_SNAKE_CASE__								= min(UpperCamelCase__   ,				UpperCamelCase__      )
		return min_num


if __name__ == "__main__":
	import doctest

	doctest.testmod(verbose=True)