



"""simple docstring"""
class 							_UpperCAmelCase							:





     '''simple docstring'''



     def __init__(					self		)							->					List[str]:
         _UpperCAmelCase							:  Dict											=    ''''''
         _UpperCAmelCase							:  Dict											=    ''''''
         _UpperCAmelCase							:  int											=    []





     def  __lowerCAmelCase	(					self       ,	A       ,	A		)							->					int:
         if m == -1:
             return n + 1
         elif n == -1:
             return m + 1
         elif self.dp[m][n] > -1:
             return self.dp[m][n]
         else:
             if self.worda[m] == self.worda[n]:
                 _UpperCAmelCase							:  Optional[int]											=    self.__min_dist_top_down_dp(m - 1       ,	n - 1		)
             else:
                 _UpperCAmelCase							:  Optional[int]											=    self.__min_dist_top_down_dp(A       ,	n - 1		)
                 _UpperCAmelCase							:  Union[str, Any]											=    self.__min_dist_top_down_dp(m - 1       ,	A		)
                 _UpperCAmelCase							:  Any											=    self.__min_dist_top_down_dp(m - 1       ,	n - 1		)
                 _UpperCAmelCase							:  Tuple											=    1 + min(A       ,	A       ,	A		)

             return self.dp[m][n]





     def  __lowerCAmelCase	(					self       ,	A       ,	A		)							->					int:
         _UpperCAmelCase							:  List[Any]											=    worda
         _UpperCAmelCase							:  Dict											=    worda
         _UpperCAmelCase							:  Tuple											=    [[-1 for _ in range(len(A		)		)] for _ in range(len(A		)		)]

         return self.__min_dist_top_down_dp(len(A		) - 1       ,	len(A		) - 1		)





     def  __lowerCAmelCase	(					self       ,	A       ,	A		)							->					int:
         _UpperCAmelCase							:  Optional[int]											=    worda
         _UpperCAmelCase							:  Dict											=    worda
         _UpperCAmelCase							:  Union[str, Any]											=    len(A		)
         _UpperCAmelCase							:  List[str]											=    len(A		)
         _UpperCAmelCase							:  Tuple											=    [[0 for _ in range(n + 1		)] for _ in range(m + 1		)]

         for i in range(m + 1		):
             for j in range(n + 1		):
                 if i == 0:  # first string is empty
                     _UpperCAmelCase							:  List[str]											=    j
                 elif j == 0:  # second string is empty
                     _UpperCAmelCase							:  Dict											=    i
                 elif worda[i - 1] == worda[j - 1]:  # last characters are equal
                     _UpperCAmelCase							:  Optional[Any]											=    self.dp[i - 1][j - 1]
                 else:
                     _UpperCAmelCase							:  Any											=    self.dp[i][j - 1]
                     _UpperCAmelCase							:  Union[str, Any]											=    self.dp[i - 1][j]
                     _UpperCAmelCase							:  int											=    self.dp[i - 1][j - 1]
                     _UpperCAmelCase							:  int											=    1 + min(A       ,	A       ,	A		)
         return self.dp[m][n]


if __name__ == "__main__":
  _lowerCAmelCase    :int     =					EditDistance()

  print('****************** Testing Edit Distance DP Algorithm ******************')
  print()

  _lowerCAmelCase    :str     =					input('Enter the first string: ').strip()
  _lowerCAmelCase    :Any     =					input('Enter the second string: ').strip()

  print()
  print(f"The minimum edit distance is: {solver.min_dist_top_down(Sa, Sa)}")
  print(f"The minimum edit distance is: {solver.min_dist_bottom_up(Sa, Sa)}")
  print()
  print('*************** End of Testing Edit Distance DP Algorithm ***************')







"""simple docstring"""
from __future__ import annotations

import math





def  lowerCamelCase_						(UpperCamelCase__		:		int     ,       UpperCamelCase__		:		int     ,       UpperCamelCase__		:		bool     ,       UpperCamelCase__		:		list[int]     ,       UpperCamelCase__		:		float							):

    if depth < 0:
        raise ValueError('''Depth cannot be less than 0'''							)

    if len(UpperCamelCase__							) == 0:
        raise ValueError('''Scores cannot be empty'''							)

    if depth == height:
        return scores[node_index]

    if is_max:
        return max(
            minimax(depth + 1     ,       node_index * 2     ,       UpperCamelCase__     ,       UpperCamelCase__     ,       UpperCamelCase__							)     ,       minimax(depth + 1     ,       node_index * 2 + 1     ,       UpperCamelCase__     ,       UpperCamelCase__     ,       UpperCamelCase__							)     ,       )

    return min(
        minimax(depth + 1     ,       node_index * 2     ,       UpperCamelCase__     ,       UpperCamelCase__     ,       UpperCamelCase__							)     ,       minimax(depth + 1     ,       node_index * 2 + 1     ,       UpperCamelCase__     ,       UpperCamelCase__     ,       UpperCamelCase__							)     ,       )





def  lowerCamelCase_						():
    _UpperCAmelCase							:  Any											=    [90, 23, 6, 33, 21, 65, 123, 3_4423]
    _UpperCAmelCase							:  Any											=    math.log(len(UpperCamelCase__							)     ,       2							)
    print('''Optimal value : '''     ,       end=''''''							)
    print(minimax(0     ,       0     ,       UpperCamelCase__     ,       UpperCamelCase__     ,       UpperCamelCase__							)							)


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  main()


