


"""simple docstring"""




def       a_ (	lowercase__ :str,			lowercase__ :int     ):
			return [sentence[i : i + ngram_size] for i in range(len(lowercase__     ) - ngram_size + 1     )]


if __name__ == "__main__":
					from doctest import testmod

					testmod()








"""simple docstring"""




from collections.abc import Callable





def       a_ (	lowercase__ :Callable[[float], float],			lowercase__ :float,			lowercase__ :float     ):
			__lowerCamelCase          =      a
			__lowerCamelCase          =      b
			if function(lowercase__     ) == 0:  # one of the a or b is a root for the function
						return a
			elif function(lowercase__     ) == 0:
						return b
			elif (
			    function(lowercase__     ) * function(lowercase__     ) > 0
			):  # if none of these are root and they are both positive or negative,
						# then this algorithm can't find the root
						raise ValueError("""could not find root in given interval."""     )
			else:
						__lowerCamelCase          =      start + (end - start) / 2.0
						while abs(start - mid     ) > 10**-7:  # until precisely equals to 10^-7
									if function(lowercase__     ) == 0:
												return mid
									elif function(lowercase__     ) * function(lowercase__     ) < 0:
												__lowerCamelCase          =      mid
									else:
												__lowerCamelCase          =      mid
									__lowerCamelCase          =      start + (end - start) / 2.0
						return mid





def       a_ (	lowercase__ :float     ):
			return x**3 - 2 * x - 5


if __name__ == "__main__":
					print(bisection(f, 1, 1_0_0_0))

					import doctest

					doctest.testmod()




