




from __future__ import annotations

import math







def SCREAMING_SNAKE_CASE       ( lowercase_				,       lowercase_		)     -> list:



       """simple docstring"""

       if len(lowercase_		) != 2 or len(a[0]		) != 2 or len(lowercase_		) != 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 SCREAMING_SNAKE_CASE       ( lowercase_				,       lowercase_		)     -> Optional[int]:



       """simple docstring"""

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







def SCREAMING_SNAKE_CASE       ( lowercase_				,       lowercase_		)     -> Any:



       """simple docstring"""

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







def SCREAMING_SNAKE_CASE       ( lowercase_		)     -> tuple[list, list, list, list]:



       """simple docstring"""

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

       A__   				=					len(lowercase_		)
       A__   				=					matrix_length // 2

       A__   				=					[[a[i][j] for j in range(lowercase_				,       lowercase_		)] for i in range(lowercase_		)]
       A__   				=					[
           [a[i][j] for j in range(lowercase_				,       lowercase_		)] for i in range(lowercase_				,       lowercase_		)
       ]

       A__   				=					[[a[i][j] for j in range(lowercase_		)] for i in range(lowercase_		)]
       A__   				=					[[a[i][j] for j in range(lowercase_		)] for i in range(lowercase_				,       lowercase_		)]

       return top_left, top_right, bot_left, bot_right







def SCREAMING_SNAKE_CASE       ( lowercase_		)     -> tuple[int, int]:



       """simple docstring"""

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







def SCREAMING_SNAKE_CASE       ( lowercase_		)     -> None:



       """simple docstring"""

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







def SCREAMING_SNAKE_CASE       ( lowercase_				,       lowercase_		)     -> list:



       """simple docstring"""

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

       A__				,							A__				,							A__				,							A__   				=					split_matrix(lowercase_		)
       A__				,							A__				,							A__				,							A__   				=					split_matrix(lowercase_		)

       A__   				=					actual_strassen(lowercase_				,       matrix_subtraction(lowercase_				,       lowercase_		)		)
       A__   				=					actual_strassen(matrix_addition(lowercase_				,       lowercase_		)				,       lowercase_		)
       A__   				=					actual_strassen(matrix_addition(lowercase_				,       lowercase_		)				,       lowercase_		)
       A__   				=					actual_strassen(lowercase_				,       matrix_subtraction(lowercase_				,       lowercase_		)		)
       A__   				=					actual_strassen(matrix_addition(lowercase_				,       lowercase_		)				,       matrix_addition(lowercase_				,       lowercase_		)		)
       A__   				=					actual_strassen(matrix_subtraction(lowercase_				,       lowercase_		)				,       matrix_addition(lowercase_				,       lowercase_		)		)
       A__   				=					actual_strassen(matrix_subtraction(lowercase_				,       lowercase_		)				,       matrix_addition(lowercase_				,       lowercase_		)		)

       A__   				=					matrix_addition(matrix_subtraction(matrix_addition(lowercase_				,       lowercase_		)				,       lowercase_		)				,       lowercase_		)
       A__   				=					matrix_addition(lowercase_				,       lowercase_		)
       A__   				=					matrix_addition(lowercase_				,       lowercase_		)
       A__   				=					matrix_subtraction(matrix_subtraction(matrix_addition(lowercase_				,       lowercase_		)				,       lowercase_		)				,       lowercase_		)

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







def SCREAMING_SNAKE_CASE       ( lowercase_				,       lowercase_		)     -> list:



       """simple docstring"""

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

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

       A__   				=					max(*lowercase_				,       *lowercase_		)
       A__   				=					int(math.pow(2				,       math.ceil(math.loga(lowercase_		)		)		)		)
       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				,       lowercase_		):
              if i < dimensiona[0]:
                     for _ in range(dimensiona[1]				,       lowercase_		):
                            new_matrixa[i].append(0		)
              else:
                     new_matrixa.append([0] * maxim		)
              if i < dimensiona[0]:
                     for _ in range(dimensiona[1]				,       lowercase_		):
                            new_matrixa[i].append(0		)
              else:
                     new_matrixa.append([0] * maxim		)

       A__   				=					actual_strassen(lowercase_				,       lowercase_		)

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


if __name__ == "__main__":
  _lowerCamelCase			:	Tuple							 =     [
      [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],
  ]
  _lowerCamelCase			:	List[str]							 =     [[0, 2, 1, 1], [16, 2, 3, 3], [2, 2, 7, 7], [13, 11, 22, 4]]
  print(strassen(matrixa, matrixa))








def SCREAMING_SNAKE_CASE       ( lowercase_				,       lowercase_		)     -> float:



       """simple docstring"""

       def get_matched_characters(lowercase_				,       lowercase_		) -> str:
              A__   				=					[]
              A__   				=					min(len(_stra		)				,       len(_stra		)		) // 2
              for i, l in enumerate(_stra		):
                     A__   				=					int(max(0				,       i - limit		)		)
                     A__   				=					int(min(i + limit + 1				,       len(_stra		)		)		)
                     if l in _stra[left:right]:
                            matched.append(lowercase_		)
                            A__   				=					f"""{_stra[0:_stra.index(lowercase_		)]} {_stra[_stra.index(lowercase_		) + 1:]}"""

              return "".join(lowercase_		)

       # matching characters
       A__   				=					get_matched_characters(lowercase_				,       lowercase_		)
       A__   				=					get_matched_characters(lowercase_				,       lowercase_		)
       A__   				=					len(lowercase_		)

       # transposition
       A__   				=					(
           len([(ca, ca) for ca, ca in zip(lowercase_				,       lowercase_		) if ca != ca]		) // 2
       )

       if not match_count:
              A__   				=					0.0
       else:
              A__   				=					(
                  1
                  / 3
                  * (
                      match_count / len(lowercase_		)
                      + match_count / len(lowercase_		)
                      + (match_count - transpositions) / match_count
                  )
              )

       # common prefix up to 4 characters
       A__   				=					0
       for ca, ca in zip(stra[:4]				,       stra[:4]		):
              if ca == ca:
                     prefix_len += 1
              else:
                     break

       return jaro + 0.1 * prefix_len * (1 - jaro)


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  print(jaro_winkler("""hello""", """world"""))


