



'''simple docstring'''





from __future__ import annotations

import math




def lowerCAmelCase						(__A						,			__A):



     """simple docstring"""



     if len(__A) != 2 or len(a[0]) != 2 or len(__A) != 2 or len(b[0]) != 2:
          raise Exception('''Matrices are not 2x2''')
     _a											=						[
         [a[0][0] * b[0][0] + a[0][1] * b[1][0], a[0][0] * b[0][1] + a[0][1] * b[1][1]],
         [a[1][0] * b[0][0] + a[1][1] * b[1][0], a[1][0] * b[0][1] + a[1][1] * b[1][1]],
     ]
     return new_matrix




def lowerCAmelCase						(__A						,			__A):



     """simple docstring"""



     return [
         [matrix_a[row][col] + matrix_b[row][col] for col in range(len(matrix_a[row]))]
         for row in range(len(__A))
     ]




def lowerCAmelCase						(__A						,			__A):



     """simple docstring"""



     return [
         [matrix_a[row][col] - matrix_b[row][col] for col in range(len(matrix_a[row]))]
         for row in range(len(__A))
     ]




def lowerCAmelCase						(__A):



     """simple docstring"""



     if len(__A) % 2 != 0 or len(a[0]) % 2 != 0:
          raise Exception('''Odd matrices are not supported!''')

     _a											=						len(__A)
     _a											=						matrix_length // 2

     _a											=						[[a[i][j] for j in range(__A						,			__A)] for i in range(__A)]
     _a											=						[
         [a[i][j] for j in range(__A						,			__A)] for i in range(__A						,			__A)
     ]

     _a											=						[[a[i][j] for j in range(__A)] for i in range(__A)]
     _a											=						[[a[i][j] for j in range(__A)] for i in range(__A						,			__A)]

     return top_left, top_right, bot_left, bot_right




def lowerCAmelCase						(__A):



     """simple docstring"""



     return len(__A), len(matrix[0])




def lowerCAmelCase						(__A):



     """simple docstring"""



     print('''\n'''.join(str(__A) for line in matrix))




def lowerCAmelCase						(__A						,			__A):



     """simple docstring"""



     if matrix_dimensions(__A) == (2, 2):
          return default_matrix_multiplication(__A						,			__A)

     _a						,					_a						,					_a						,					_a											=						split_matrix(__A)
     _a						,					_a						,					_a						,					_a											=						split_matrix(__A)

     _a											=						actual_strassen(__A						,			matrix_subtraction(__A						,			__A))
     _a											=						actual_strassen(matrix_addition(__A						,			__A)						,			__A)
     _a											=						actual_strassen(matrix_addition(__A						,			__A)						,			__A)
     _a											=						actual_strassen(__A						,			matrix_subtraction(__A						,			__A))
     _a											=						actual_strassen(matrix_addition(__A						,			__A)						,			matrix_addition(__A						,			__A))
     _a											=						actual_strassen(matrix_subtraction(__A						,			__A)						,			matrix_addition(__A						,			__A))
     _a											=						actual_strassen(matrix_subtraction(__A						,			__A)						,			matrix_addition(__A						,			__A))

     _a											=						matrix_addition(matrix_subtraction(matrix_addition(__A						,			__A)						,			__A)						,			__A)
     _a											=						matrix_addition(__A						,			__A)
     _a											=						matrix_addition(__A						,			__A)
     _a											=						matrix_subtraction(matrix_subtraction(matrix_addition(__A						,			__A)						,			__A)						,			__A)

     # construct the new matrix from our 4 quadrants
     _a											=						[]
     for i in range(len(__A)):
          new_matrix.append(top_left[i] + top_right[i])
     for i in range(len(__A)):
          new_matrix.append(bot_left[i] + bot_right[i])
     return new_matrix




def lowerCAmelCase						(__A						,			__A):



     """simple docstring"""



     if matrix_dimensions(__A)[1] != matrix_dimensions(__A)[0]:
          _a											=						(
              '''Unable to multiply these matrices, please check the dimensions.\n'''
              F'''Matrix A: {matrixa}\n'''
              F'''Matrix B: {matrixa}'''
          )
          raise Exception(__A)
     _a											=						matrix_dimensions(__A)
     _a											=						matrix_dimensions(__A)

     if dimensiona[0] == dimensiona[1] and dimensiona[0] == dimensiona[1]:
          return [matrixa, matrixa]

     _a											=						max(*__A						,			*__A)
     _a											=						int(math.pow(2						,			math.ceil(math.loga(__A))))
     _a											=						matrixa
     _a											=						matrixa

     # Adding zeros to the matrices so that the arrays dimensions are the same and also
     # power of 2
     for i in range(0						,			__A):
          if i < dimensiona[0]:
               for _ in range(dimensiona[1]						,			__A):
                    new_matrixa[i].append(0)
          else:
               new_matrixa.append([0] * maxim)
          if i < dimensiona[0]:
               for _ in range(dimensiona[1]						,			__A):
                    new_matrixa[i].append(0)
          else:
               new_matrixa.append([0] * maxim)

     _a											=						actual_strassen(__A						,			__A)

     # Removing the additional zeros
     for i in range(0						,			__A):
          if i < dimensiona[0]:
               for _ in range(dimensiona[1]						,			__A):
                    final_matrix[i].pop()
          else:
               final_matrix.pop()
     return final_matrix


if __name__ == "__main__":
  lowercase_	 =						[
      [2, 3, 4, 5],
      [6, 4, 3, 1],
      [2, 3, 6, 7],
      [3, 1, 2, 4],
      [2, 3, 4, 5],
      [6, 4, 3, 1],
      [2, 3, 6, 7],
      [3, 1, 2, 4],
      [2, 3, 4, 5],
      [6, 2, 3, 1],
  ]
  lowercase_	 =						[[0, 2, 1, 1], [16, 2, 3, 3], [2, 2, 7, 7], [13, 11, 22, 4]]
  print(strassen(matrixa, matrixa))








'''simple docstring'''





from __future__ import annotations

import math




def lowerCAmelCase						(__A						,			__A						,			__A						,			__A						,			__A):



     """simple docstring"""



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

     if not scores:
          raise ValueError('''Scores cannot be empty''')

     if depth == height:
          return scores[node_index]

     return (
         max(
             minimax(depth + 1						,			node_index * 2						,			__A						,			__A						,			__A)						,			minimax(depth + 1						,			node_index * 2 + 1						,			__A						,			__A						,			__A)						,			)
         if is_max
         else min(
             minimax(depth + 1						,			node_index * 2						,			__A						,			__A						,			__A)						,			minimax(depth + 1						,			node_index * 2 + 1						,			__A						,			__A						,			__A)						,			)
     )




def lowerCAmelCase						():



     """simple docstring"""



     _a											=						[90, 23, 6, 33, 21, 65, 123, 34_423]
     _a											=						math.log(len(__A)						,			2)
     print(F'''Optimal value : {minimax(0						,			0						,			__A						,			__A						,			__A)}''')


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  main()



