code: 
  
  """simple docstring"""
  
  
  
  
  def      __SCREAMING_SNAKE_CASE		(		lowercase__   ):
  					"""simple docstring"""
  					A    =      len(lowercase__   )
  
  					# Set the gap value to be decreased by a factor of 1.3
  					# after each iteration
  					A    =      1.3
  
  					# Continue sorting until the gap is 1
  					while gap > 1:
  										# Decrease the gap value
  										A    =      int(gap / shrink   )
  
  										# Sort the elements using insertion sort
  										for i in range(lowercase__    ,							len(lowercase__   )   ):
  															A    =      collection[i]
  															A    =      i
  															while j >= gap and collection[j - gap] > temp:
  																				A    =      collection[j - gap]
  																				j -= gap
  															A    =      temp
  
  					return collection
  
  
  if __name__ == "__main__":
  	import doctest
  
  	doctest.testmod()
  
  
  
  
  
  
style_context: 
  
  """simple docstring"""
  
  
  
  
  import functools
  from math import sqrt
  from time import time
  def      __SCREAMING_SNAKE_CASE		(		lowercase__    ,							*lowercase__    ,							**lowercase__   ):
  					"""simple docstring"""
  					A    =      time()
  					A    =      func(*lowercase__    ,							**lowercase__   )
  					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) * 1_000:0.4f} ms"""   )
  					return output
  def      __SCREAMING_SNAKE_CASE		(		lowercase__   ):
  					"""simple docstring"""
  					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      __SCREAMING_SNAKE_CASE		(		lowercase__   ):
  					"""simple docstring"""
  
  					def fib_recursive_term(lowercase__   ) -> 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(lowercase__   ) for i in range(n + 1   )]
  def      __SCREAMING_SNAKE_CASE		(		lowercase__   ):
  					"""simple docstring"""
  
  					@functools.cache
  					def fib_recursive_term(lowercase__   ) -> 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(lowercase__   ) for i in range(n + 1   )]
  def      __SCREAMING_SNAKE_CASE		(		lowercase__   ):
  					"""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.
  					A    =      {0: 0, 1: 1, 2: 1}  # Prefilled cache
  
  					def rec_fn_memoized(lowercase__   ) -> 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(lowercase__   ) for i in range(n + 1   )]
  def      __SCREAMING_SNAKE_CASE		(		lowercase__   ):
  					"""simple docstring"""
  					if n < 0:
  										raise Exception("n is negative"   )
  					if n >= 1_475:
  										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  :					Optional[Any]												=	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)
  
  
  
  
  
  