




'''simple docstring'''



from .stack import Stack







def 	_UpperCamelCase       (_lowerCamelCase							:   str		)->      bool:




     '''simple docstring'''





     __snake_case			    =     Stack()
     __snake_case			    =     {'''(''': ''')''', '''[''': ''']''', '''{''': '''}'''}
     for bracket in parentheses:
          if bracket in bracket_pairs:
               stack.push(_lowerCamelCase		)
          elif bracket in (")", "]", "}"):
               if stack.is_empty() or bracket_pairs[stack.pop()] != bracket:
                    return False
     return stack.is_empty()


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

     testmod()

     UpperCAmelCase_				:     int     			=						['''((()))''', '''((())''', '''(()))''']
     print('''Balanced parentheses demonstration:\n''')
     for example in examples:
          UpperCAmelCase_				:     Optional[Any]     			=						'''''' if balanced_parentheses(example) else '''not '''
          print(F"""{example} is {not_str}balanced""")












'''simple docstring'''



def 	_UpperCamelCase       (_lowerCamelCase							:   list[list[int]]      ,		_lowerCamelCase							:   list[list[int]]		)->      list[list[int]]:




     '''simple docstring'''





     __snake_case			    =     []
     __snake_case			    =     len(_lowerCamelCase		)
     for i in range(_lowerCamelCase		):
          __snake_case			    =     []
          for j in range(_lowerCamelCase		):
               __snake_case			    =     0
               for k in range(_lowerCamelCase		):
                    __snake_case			    =     val + matrix_a[i][k] * matrix_b[k][j]
               list_a.append(_lowerCamelCase		)
          matrix_c.append(_lowerCamelCase		)
     return matrix_c







def 	_UpperCamelCase       (_lowerCamelCase							:   int		)->      list[list[int]]:




     '''simple docstring'''





     return [[int(row == column		) for column in range(_lowerCamelCase		)] for row in range(_lowerCamelCase		)]







def 	_UpperCamelCase       (_lowerCamelCase							:   int		)->      int:




     '''simple docstring'''





     if n <= 1:
          return n
     __snake_case			    =     identity(2		)
     __snake_case			    =     [[1, 1], [1, 0]]
     __snake_case			    =     n - 1
     while n > 0:
          if n % 2 == 1:
               __snake_case			    =     multiply(_lowerCamelCase      ,		_lowerCamelCase		)
          __snake_case			    =     multiply(_lowerCamelCase      ,		_lowerCamelCase		)
          __snake_case			    =     int(n / 2		)
     return res_matrix[0][0]







def 	_UpperCamelCase       (_lowerCamelCase							:   int		)->      int:




     '''simple docstring'''





     if n <= 1:
          return n
     __snake_case			    =     0
     __snake_case			    =     1
     for _ in range(2      ,		n + 1		):
          __snake_case    ,			__snake_case			    =     fiba, fiba + fiba
     return fiba







def 	_UpperCamelCase       ()->      None:




     '''simple docstring'''





     for ordinal in "0th 1st 2nd 3rd 10th 100th 1000th".split():
          __snake_case			    =     int(''''''.join(c for c in ordinal if c in '''0123456789'''		)		)  # 1000th --> 1000
          print(
              f'''{ordinal} fibonacci number using matrix exponentiation is '''
              f'''{nth_fibonacci_matrix(_lowerCamelCase		)} and using bruteforce is '''
              f'''{nth_fibonacci_bruteforce(_lowerCamelCase		)}\n'''		)
     # from timeit import timeit
     # print(timeit("nth_fibonacci_matrix(1000000)",
     #              "from main import nth_fibonacci_matrix", number=5))
     # print(timeit("nth_fibonacci_bruteforce(1000000)",
     #              "from main import nth_fibonacci_bruteforce", number=5))
     # 2.3342058970001744
     # 57.256506615000035


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     main()






