



import sys




def lowerCAmelCase						(__A):



     """simple docstring"""



     _a											=						len(__A)
     _a											=						[[0 for x in range(__A)] for x in range(__A)]
     _a											=						[[0 for x in range(__A)] for x in range(__A)]

     for chain_length in range(2						,			__A):
          for a in range(1						,			n - chain_length + 1):
               _a											=						a + chain_length - 1

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




def lowerCAmelCase						(__A						,			__A						,			__A):



     """simple docstring"""



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




def lowerCAmelCase						():



     """simple docstring"""



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

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


if __name__ == "__main__":
  main()








'''simple docstring'''





from __future__ import annotations

import typing
from collections.abc import Iterable

import numpy as np

lowercase_	 =						typing.Union[Iterable[float], Iterable[int], np.ndarray]  # noqa: UP007
lowercase_	 =						typing.Union[np.floataa, int, float]  # noqa: UP007




def lowerCAmelCase						(__A						,			__A):



     """simple docstring"""



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




def lowerCAmelCase						(__A						,			__A):



     """simple docstring"""



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


if __name__ == "__main__":




  def lowerCAmelCase						():



       """simple docstring"""



       from timeit import timeit

       print('''Without Numpy''')
       print(
           timeit(
               '''euclidean_distance_no_np([1, 2, 3], [4, 5, 6])'''						,			number=10_000						,			globals=globals()						,			))
       print('''With Numpy''')
       print(
           timeit(
               '''euclidean_distance([1, 2, 3], [4, 5, 6])'''						,			number=10_000						,			globals=globals()						,			))
  benchmark()



