



"""simple docstring"""






import numpy as np


def     _lowercase       (						__snake_case      ,__snake_case      ,__snake_case      ,__snake_case      ,__snake_case			)		->     Dict:
			__lowerCAmelCase   :						Optional[Any]				= int(np.ceil((x_end - xa) / h			)			)
			__lowerCAmelCase   :						Optional[int]				= np.zeros((n + 1,)			)
			__lowerCAmelCase   :						Any				= ya
			__lowerCAmelCase   :						Optional[int]				= xa

			for k in range(__snake_case			):
						__lowerCAmelCase   :						Any				= f(__snake_case      ,y[k]			)
						__lowerCAmelCase   :						str				= f(x + 0.5 * h      ,y[k] + 0.5 * h * ka			)
						__lowerCAmelCase   :						Union[str, Any]				= f(x + 0.5 * h      ,y[k] + 0.5 * h * ka			)
						__lowerCAmelCase   :						str				= f(x + h      ,y[k] + h * ka			)
						__lowerCAmelCase   :						Union[str, Any]				= y[k] + (1 / 6) * h * (ka + 2 * ka + 2 * ka + ka)
						x += h

			return y


if __name__ == "__main__":
	import doctest

	doctest.testmod()




"""simple docstring"""






def     _lowercase       (						__snake_case      ,__snake_case			)		->     list:
			__lowerCAmelCase   :						List[str]				= len(__snake_case			)
			__lowerCAmelCase   :						Dict				= []
			for i in range(len(__snake_case			) - pat_len + 1			):
						__lowerCAmelCase   :						List[Any]				= True
						for j in range(__snake_case			):
									if s[i + j] != pattern[j]:
												__lowerCAmelCase   :						Union[str, Any]				= False
												break
						if match_found:
									position.append(__snake_case			)
			return position


if __name__ == "__main__":
	assert naive_pattern_search('ABCDEFG', 'DE') == [3]
	print(naive_pattern_search('ABAAABCDBBABCDDEBCABC', 'ABC'))