






from __future__ import annotations

import math

def      __lowercase					( snake_case,  snake_case ):







    """simple docstring"""






    if len(snake_case ) != 2 or len(a[0] ) != 2 or len(snake_case ) != 2 or len(b[0] ) != 2:
        raise Exception('''Matrices are not 2x2''' )
    __magic_name__		:str        =      [
        [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      __lowercase					( snake_case,  snake_case ):







    """simple docstring"""






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

def      __lowercase					( snake_case,  snake_case ):







    """simple docstring"""






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

def      __lowercase					( snake_case ):







    """simple docstring"""






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

    __magic_name__		:Tuple        =      len(snake_case )
    __magic_name__		:List[Any]        =      matrix_length // 2

    __magic_name__		:Optional[int]        =      [[a[i][j] for j in range(snake_case,  snake_case )] for i in range(snake_case )]
    __magic_name__		:int        =      [
        [a[i][j] for j in range(snake_case,  snake_case )] for i in range(snake_case,  snake_case )
    ]

    __magic_name__		:Dict        =      [[a[i][j] for j in range(snake_case )] for i in range(snake_case )]
    __magic_name__		:Optional[Any]        =      [[a[i][j] for j in range(snake_case )] for i in range(snake_case,  snake_case )]

    return top_left, top_right, bot_left, bot_right

def      __lowercase					( snake_case ):







    """simple docstring"""






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

def      __lowercase					( snake_case ):







    """simple docstring"""






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

def      __lowercase					( snake_case,  snake_case ):







    """simple docstring"""






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

    __magic_name__		:Tuple        =      split_matrix(snake_case )
    __magic_name__		:List[str]        =      split_matrix(snake_case )

    __magic_name__		:Tuple        =      actual_strassen(snake_case,  matrix_subtraction(snake_case,  snake_case ) )
    __magic_name__		:Tuple        =      actual_strassen(matrix_addition(snake_case,  snake_case ),  snake_case )
    __magic_name__		:Dict        =      actual_strassen(matrix_addition(snake_case,  snake_case ),  snake_case )
    __magic_name__		:Dict        =      actual_strassen(snake_case,  matrix_subtraction(snake_case,  snake_case ) )
    __magic_name__		:Union[str, Any]        =      actual_strassen(matrix_addition(snake_case,  snake_case ),  matrix_addition(snake_case,  snake_case ) )
    __magic_name__		:Optional[int]        =      actual_strassen(matrix_subtraction(snake_case,  snake_case ),  matrix_addition(snake_case,  snake_case ) )
    __magic_name__		:int        =      actual_strassen(matrix_subtraction(snake_case,  snake_case ),  matrix_addition(snake_case,  snake_case ) )

    __magic_name__		:int        =      matrix_addition(matrix_subtraction(matrix_addition(snake_case,  snake_case ),  snake_case ),  snake_case )
    __magic_name__		:List[str]        =      matrix_addition(snake_case,  snake_case )
    __magic_name__		:List[Any]        =      matrix_addition(snake_case,  snake_case )
    __magic_name__		:Optional[int]        =      matrix_subtraction(matrix_subtraction(matrix_addition(snake_case,  snake_case ),  snake_case ),  snake_case )

    # construct the new matrix from our 4 quadrants
    __magic_name__		:Union[str, Any]        =      []
    for i in range(len(snake_case ) ):
        new_matrix.append(top_left[i] + top_right[i] )
    for i in range(len(snake_case ) ):
        new_matrix.append(bot_left[i] + bot_right[i] )
    return new_matrix

def      __lowercase					( snake_case,  snake_case ):







    """simple docstring"""






    if matrix_dimensions(snake_case )[1] != matrix_dimensions(snake_case )[0]:
        __magic_name__		:Union[str, Any]        =      (
            '''Unable to multiply these matrices, please check the dimensions.\n'''
            f'''Matrix A: {matrixa}\n'''
            f'''Matrix B: {matrixa}'''
        )
        raise Exception(snake_case )
    __magic_name__		:List[str]        =      matrix_dimensions(snake_case )
    __magic_name__		:Union[str, Any]        =      matrix_dimensions(snake_case )

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

    __magic_name__		:Tuple        =      max(*snake_case,  *snake_case )
    __magic_name__		:Union[str, Any]        =      int(math.pow(2,  math.ceil(math.loga(snake_case ) ) ) )
    __magic_name__		:Optional[int]        =      matrixa
    __magic_name__		:int        =      matrixa

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

    __magic_name__		:List[Any]        =      actual_strassen(snake_case,  snake_case )

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


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














SCREAMING_SNAKE_CASE__      :			str							=		"""Alexander Joslin"""

import operator as op

from .stack import Stack

def      __lowercase					( snake_case ):







				"""simple docstring"""






				__magic_name__		:Optional[int]        =      {'''*''': op.mul, '''/''': op.truediv, '''+''': op.add, '''-''': op.sub}

				__magic_name__		:Stack[int]        =      Stack()
				__magic_name__		:Stack[str]        =      Stack()

				for i in equation:
								if i.isdigit():
												# RULE 1
												operand_stack.push(int(snake_case ) )
								elif i in operators:
												# RULE 2
												operator_stack.push(snake_case )
								elif i == ")":
												# RULE 4
												__magic_name__		:Optional[int]        =      operator_stack.peek()
												operator_stack.pop()
												__magic_name__		:List[str]        =      operand_stack.peek()
												operand_stack.pop()
												__magic_name__		:Optional[Any]        =      operand_stack.peek()
												operand_stack.pop()

												__magic_name__		:Optional[int]        =      operators[opr](snake_case,  snake_case )
												operand_stack.push(snake_case )

    # RULE 5
				return operand_stack.peek()


if __name__ == "__main__":
					SCREAMING_SNAKE_CASE__      :			Any							=		"""(5 + ((4 * 2) * (2 + 3)))"""
					# answer = 45
					print(f"{equation} = {dijkstras_two_stack_algorithm(equation)}")






