


'''simple docstring'''





import sys


def 		lowercase_  (     _UpperCamelCase  ):


			'''simple docstring'''







			__lowercase 					=   len(UpperCamelCase__  )
			__lowercase 					=   [[0 for x in range(UpperCamelCase__  )] for x in range(UpperCamelCase__  )]
			__lowercase 					=   [[0 for x in range(UpperCamelCase__  )] for x in range(UpperCamelCase__  )]

			for chain_length in range(2       ,			UpperCamelCase__  ):
						for a in range(1       ,			n - chain_length + 1  ):
									__lowercase 					=   a + chain_length - 1

									__lowercase 					=   sys.maxsize
									for c in range(UpperCamelCase__       ,			UpperCamelCase__  ):
												__lowercase 					=   (
												    matrix[a][c] + matrix[c + 1][b] + array[a - 1] * array[c] * array[b]
												)
												if cost < matrix[a][b]:
															__lowercase 					=   cost
															__lowercase 					=   c
			return matrix, sol


def 		lowercase_  (     _UpperCamelCase       ,			_UpperCamelCase       ,			_UpperCamelCase  ):


			'''simple docstring'''







			if i == j:
						print('''A''' + str(UpperCamelCase__  )       ,			end=''' '''  )
			else:
						print('''('''       ,			end=''' '''  )
						print_optiomal_solution(UpperCamelCase__       ,			UpperCamelCase__       ,			optimal_solution[i][j]  )
						print_optiomal_solution(UpperCamelCase__       ,			optimal_solution[i][j] + 1       ,			UpperCamelCase__  )
						print(''')'''       ,			end=''' '''  )


def 		lowercase_  (     ):


			'''simple docstring'''







			__lowercase 					=   [30, 35, 15, 5, 10, 20, 25]
			__lowercase 					=   len(UpperCamelCase__  )
			# Size of matrix created from above array will be
			# 30*35 35*15 15*5 5*10 10*20 20*25
			__lowercase 					=   matrix_chain_order(UpperCamelCase__  )

			print('''No. of Operation required: ''' + str(matrix[1][n - 1]  )  )
			print_optiomal_solution(UpperCamelCase__       ,			1       ,			n - 1  )


if __name__ == "__main__":
	main()






from __future__ import annotations

import typing
from collections.abc import Iterable

import numpy as np

a : Optional[int]		=				typing.Union[Iterable[float], Iterable[int], np.ndarray]  # noqa: UP007
a : Union[str, Any]		=				typing.Union[np.floataa, int, float]  # noqa: UP007


def 		lowercase_  (     _UpperCamelCase       ,			_UpperCamelCase  ):


			'''simple docstring'''







			return np.sqrt(np.sum((np.asarray(_UpperCamelCase  ) - np.asarray(_UpperCamelCase  )) ** 2  )  )


def 		lowercase_  (     _UpperCamelCase       ,			_UpperCamelCase  ):


			'''simple docstring'''







			return sum((va - va) ** 2 for va, va in zip(_UpperCamelCase       ,			_UpperCamelCase  )  ) ** (1 / 2)


if __name__ == "__main__":


	def 		lowercase_  (     ):


				'''simple docstring'''







				from timeit import timeit

				print('''Without Numpy'''  )
				print(
				    timeit(
				        '''euclidean_distance_no_np([1, 2, 3], [4, 5, 6])'''       ,			number=1_00_00       ,			globals=globals()       ,			)  )
				print('''With Numpy'''  )
				print(
				    timeit(
				        '''euclidean_distance([1, 2, 3], [4, 5, 6])'''       ,			number=1_00_00       ,			globals=globals()       ,			)  )





	benchmark()


