



def       UpperCamelCase(  __UpperCamelCase							:		dict					,__UpperCamelCase							:		int			):
		if not root or root not in binary_tree_mirror_dictionary:
				return
		lowerCAmelCase_ ,  lowerCAmelCase_      :					Dict     =			binary_tree_mirror_dictionary[root][:2]
		lowerCAmelCase_      :					Optional[int]     =			[right_child, left_child]
		binary_tree_mirror_dict(__UpperCamelCase					,__UpperCamelCase			)
		binary_tree_mirror_dict(__UpperCamelCase					,__UpperCamelCase			)


def       UpperCamelCase(  __UpperCamelCase							:		dict					,__UpperCamelCase							:		int = 1			):
		if not binary_tree:
				raise ValueError('''binary tree cannot be empty'''			)
		if root not in binary_tree:
				lowerCAmelCase_      :					Tuple     =			f"""root {root} is not present in the binary_tree"""
				raise ValueError(__UpperCamelCase			)
		lowerCAmelCase_      :					List[str]     =			dict(__UpperCamelCase			)
		binary_tree_mirror_dict(__UpperCamelCase					,__UpperCamelCase			)
		return binary_tree_mirror_dictionary


if __name__ == "__main__":
						A__  :  Tuple       = {1: [2, 3], 2: [4, 5], 3: [6, 7], 7: [8, 9]}
						print(F'''Binary tree: {binary_tree}''')
						A__  :  Dict       = binary_tree_mirror(binary_tree, 5)
						print(F'''Binary tree mirror: {binary_tree_mirror_dictionary}''')










A__  :  str       = 1000


def       UpperCamelCase(  __UpperCamelCase							:		float			):
		return x * x


def       UpperCamelCase(  __UpperCamelCase							:		Optional[int]					,__UpperCamelCase							:		float					,__UpperCamelCase							:		float					,__UpperCamelCase							:		int = 4			):
		assert callable(
		    __UpperCamelCase			), f"""the function(object) passed should be callable your input : {function}"""
		assert isinstance(__UpperCamelCase					,(float, int)			), f"""a should be float or integer your input : {a}"""
		assert isinstance(function(__UpperCamelCase			)					,(float, int)			), (
		    "the function should return integer or float return type of your function, "
		    f"""{type(__UpperCamelCase			)}"""
		)
		assert isinstance(__UpperCamelCase					,(float, int)			), f"""b should be float or integer your input : {b}"""
		assert (
		    isinstance(__UpperCamelCase					,__UpperCamelCase			) and precision > 0
		), f"""precision should be positive integer your input : {precision}"""

		# just applying the formula of simpson for approximate integration written in
		# mentioned article in first comment of this file and above this function

		lowerCAmelCase_      :					List[str]     =			(b - a) / N_STEPS
		lowerCAmelCase_      :					str     =			function(__UpperCamelCase			) + function(__UpperCamelCase			)

		for i in range(1					,__UpperCamelCase			):
				lowerCAmelCase_      :					Optional[Any]     =			a + h * i
				result += function(__UpperCamelCase			) * (4 if i % 2 else 2)

		result *= h / 3
		return round(__UpperCamelCase					,__UpperCamelCase			)


if __name__ == "__main__":
						import doctest

						doctest.testmod()





