





from __future__ import annotations

from collections.abc import Callable

__A							:			int         =			list[list[float | int]]





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)							-> Matrix:




    """simple docstring"""




    _A     =							len(_SCREAMING_SNAKE_CASE				)
    _A     =							[[0 for _ in range(size + 1				)] for _ in range(_SCREAMING_SNAKE_CASE				)]
    _A     =							42
    _A     =							42
    _A     =							42
    _A     =							42
    _A     =							42
    _A     =							42

    for row in range(_SCREAMING_SNAKE_CASE				):
        for col in range(_SCREAMING_SNAKE_CASE				):
            _A     =							matrix[row][col]

        _A     =							vector[row][0]

    _A     =							0
    _A     =							0
    while row < size and col < size:
        # pivoting
        _A     =							max((abs(augmented[rowa][col]				), rowa) for rowa in range(_SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)				)[
            1
        ]
        if augmented[pivot_row][col] == 0:
            col += 1
            continue
        else:
            _A,			_A     =							augmented[pivot_row], augmented[row]

        for rowa in range(row + 1							,     _SCREAMING_SNAKE_CASE				):
            _A     =							augmented[rowa][col] / augmented[row][col]
            _A     =							0
            for cola in range(col + 1							,     size + 1				):
                augmented[rowa][cola] -= augmented[row][cola] * ratio

        row += 1
        col += 1

    # back substitution
    for col in range(1							,     _SCREAMING_SNAKE_CASE				):
        for row in range(_SCREAMING_SNAKE_CASE				):
            _A     =							augmented[row][col] / augmented[col][col]
            for cola in range(_SCREAMING_SNAKE_CASE							,     size + 1				):
                augmented[row][cola] -= augmented[col][cola] * ratio

    # round to get rid of numbers like 2.000000000000004
    return [
        [round(augmented[row][size] / augmented[row][row]							,     10				)] for row in range(_SCREAMING_SNAKE_CASE				)
    ]





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE				)							-> Callable[[int], int]:




    """simple docstring"""




    _A     =							len(_SCREAMING_SNAKE_CASE				)
    _A     =							[[0 for _ in range(_SCREAMING_SNAKE_CASE				)] for _ in range(_SCREAMING_SNAKE_CASE				)]
    _A     =							[[0] for _ in range(_SCREAMING_SNAKE_CASE				)]
    _A     =							42
    _A     =							42
    _A     =							42
    _A     =							42

    for x_val, y_val in enumerate(_SCREAMING_SNAKE_CASE				):
        for col in range(_SCREAMING_SNAKE_CASE				):
            _A     =							(x_val + 1) ** (size - col - 1)
        _A     =							y_val

    _A     =							solve(_SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)

    def interpolated_func(_SCREAMING_SNAKE_CASE				) -> int:
        return sum(
            round(coeffs[x_val][0]				) * (var ** (size - x_val - 1))
            for x_val in range(_SCREAMING_SNAKE_CASE				)				)

    return interpolated_func





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE				)							-> int:




    """simple docstring"""




    return (
        1
        - variable
        + variable**2
        - variable**3
        + variable**4
        - variable**5
        + variable**6
        - variable**7
        + variable**8
        - variable**9
        + variable**10
    )





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE = question_function							,     _SCREAMING_SNAKE_CASE = 10				)							-> int:




    """simple docstring"""




    _A     =							[func(_SCREAMING_SNAKE_CASE				) for x_val in range(1							,     order + 1				)]

    _A     =							[
        interpolate(data_points[:max_coeff]				) for max_coeff in range(1							,     order + 1				)
    ]

    _A     =							0
    _A     =							42
    _A     =							42

    for poly in polynomials:
        _A     =							1
        while func(_SCREAMING_SNAKE_CASE				) == poly(_SCREAMING_SNAKE_CASE				):
            x_val += 1

        ret += poly(_SCREAMING_SNAKE_CASE				)

    return ret


if __name__ == "__main__":
 print(f"{solution() = }")












__A							:			Dict         =			"Alexander Joslin"

import operator as op

from .stack import Stack





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE				)							-> int:




    """simple docstring"""




    _A     =							{'*': op.mul, '/': op.truediv, '+': op.add, '-': op.sub}

    _A     =							Stack()
    _A     =							Stack()

    for i in equation:
        if i.isdigit():
            # RULE 1
            operand_stack.push(int(_SCREAMING_SNAKE_CASE				)				)
        elif i in operators:
            # RULE 2
            operator_stack.push(_SCREAMING_SNAKE_CASE				)
        elif i == ")":
            # RULE 4
            _A     =							operator_stack.peek()
            operator_stack.pop()
            _A     =							operand_stack.peek()
            operand_stack.pop()
            _A     =							operand_stack.peek()
            operand_stack.pop()

            _A     =							operators[opr](_SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)
            operand_stack.push(_SCREAMING_SNAKE_CASE				)

    # RULE 5
    return operand_stack.peek()


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





