

def        _UpperCAmelCase							(	_SCREAMING_SNAKE_CASE       :		list[list[int]]							):





    """simple docstring"""


    if len(_SCREAMING_SNAKE_CASE							) == 0 or not all(len(_SCREAMING_SNAKE_CASE							) == 2 for pair in coordinates							):
        raise ValueError('The program cannot work out a fitting polynomial.'							)

    if len({tuple(_SCREAMING_SNAKE_CASE							) for pair in coordinates}							) != len(_SCREAMING_SNAKE_CASE							):
        raise ValueError('The program cannot work out a fitting polynomial.'							)

    SCREAMING_SNAKE_CASE_						=    {x for x, _ in coordinates}
    if len(_SCREAMING_SNAKE_CASE							) == 1:
        return f"""x={coordinates[0][0]}"""

    if len(_SCREAMING_SNAKE_CASE							) != len(_SCREAMING_SNAKE_CASE							):
        raise ValueError('The program cannot work out a fitting polynomial.'							)

    SCREAMING_SNAKE_CASE_						=    len(_SCREAMING_SNAKE_CASE							)

    SCREAMING_SNAKE_CASE_						=    0
    SCREAMING_SNAKE_CASE_						=    []
    # put the x and x to the power values in a matrix
    while count_of_line < x:
        SCREAMING_SNAKE_CASE_						=    0
        SCREAMING_SNAKE_CASE_						=    coordinates[count_of_line][0]
        SCREAMING_SNAKE_CASE_						=    []
        while count_in_line < x:
            count_line.append(a ** (x - (count_in_line + 1))							)
            count_in_line += 1
        matrix.append(_SCREAMING_SNAKE_CASE							)
        count_of_line += 1

    SCREAMING_SNAKE_CASE_						=    0
    # put the y values into a vector
    SCREAMING_SNAKE_CASE_						=    []
    while count_of_line < x:
        vector.append(coordinates[count_of_line][1]							)
        count_of_line += 1

    SCREAMING_SNAKE_CASE_						=    0

    while count < x:
        SCREAMING_SNAKE_CASE_						=    0
        while zahlen < x:
            if count == zahlen:
                zahlen += 1
            if zahlen == x:
                break
            SCREAMING_SNAKE_CASE_						=    matrix[zahlen][count] / matrix[count][count]
            for counting_columns, item in enumerate(matrix[count]							):
                # manipulating all the values in the matrix
                matrix[zahlen][counting_columns] -= item * bruch
            # manipulating the values in the vector
            vector[zahlen] -= vector[count] * bruch
            zahlen += 1
        count += 1

    SCREAMING_SNAKE_CASE_						=    0
    # make solutions
    SCREAMING_SNAKE_CASE_						=    []
    while count < x:
        solution.append(str(vector[count] / matrix[count][count]							)							)
        count += 1

    SCREAMING_SNAKE_CASE_						=    0
    SCREAMING_SNAKE_CASE_						=    'f(x)='

    while count < x:
        SCREAMING_SNAKE_CASE_						=    solution[count].split('E'							)
        if len(_SCREAMING_SNAKE_CASE							) > 1:
            SCREAMING_SNAKE_CASE_						=    f"""{remove_e[0]}*10^{remove_e[1]}"""
        solved += f"""x^{x - (count + 1)}*{solution[count]}"""
        if count + 1 != x:
            solved += "+"
        count += 1

    return solved


if __name__ == "__main__":
       print(points_to_polynomial([]))
       print(points_to_polynomial([[]]))
       print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
       print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
       print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
       print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
       print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
       print(points_to_polynomial([[1, 3], [2, 6], [3, 11]]))
       print(points_to_polynomial([[1, -3], [2, -6], [3, -11]]))
       print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))





from __future__ import annotations


def        _UpperCAmelCase							(	_SCREAMING_SNAKE_CASE       :		list[int]							):





    """simple docstring"""


    SCREAMING_SNAKE_CASE_						=    [0] * len(_SCREAMING_SNAKE_CASE							)
    for i in range(1			, len(_SCREAMING_SNAKE_CASE							)							):
        SCREAMING_SNAKE_CASE_						=    duration_times[i - 1] + waiting_times[i - 1]
    return waiting_times


def        _UpperCAmelCase							(	_SCREAMING_SNAKE_CASE       :		list[int]			, _SCREAMING_SNAKE_CASE       :		list[int]							):





    """simple docstring"""


    return [
        duration_time + waiting_times[i]
        for i, duration_time in enumerate(_SCREAMING_SNAKE_CASE							)
    ]


def        _UpperCAmelCase							(	_SCREAMING_SNAKE_CASE       :		list[int]							):





    """simple docstring"""


    return sum(_SCREAMING_SNAKE_CASE							) / len(_SCREAMING_SNAKE_CASE							)


def        _UpperCAmelCase							(	_SCREAMING_SNAKE_CASE       :		list[int]							):





    """simple docstring"""


    return sum(_SCREAMING_SNAKE_CASE							) / len(_SCREAMING_SNAKE_CASE							)


if __name__ == "__main__":
       # process id's
       UpperCamelCase__	:   List[str]								=     [1, 2, 3]

       # ensure that we actually have processes
       if len(processes) == 0:
              print("Zero amount of processes")
              raise SystemExit(0)

       # duration time of all processes
       UpperCamelCase__	:   Any								=     [19, 8, 9]

       # ensure we can match each id to a duration time
       if len(duration_times) != len(processes):
              print("Unable to match all id's with their duration time")
              raise SystemExit(0)

       # get the waiting times and the turnaround times
       UpperCamelCase__	:   List[str]								=     calculate_waiting_times(duration_times)
       UpperCamelCase__	:   Union[str, Any]								=     calculate_turnaround_times(duration_times, waiting_times)

       # get the average times
       UpperCamelCase__	:   str								=     calculate_average_waiting_time(waiting_times)
       UpperCamelCase__	:   List[Any]								=     calculate_average_turnaround_time(turnaround_times)

       # print all the results
       print("Process ID\tDuration Time\tWaiting Time\tTurnaround Time")
       for i, process in enumerate(processes):
              print(
                  F'{process}\t\t{duration_times[i]}\t\t{waiting_times[i]}\t\t'
                  F'{turnaround_times[i]}'
              )
       print(F'Average waiting time = {average_waiting_time}')
       print(F'Average turn around time = {average_turnaround_time}')


