



from __future__ import annotations
def 				UpperCAmelCase__		(					_SCREAMING_SNAKE_CASE :						list[int]					)->list[int]:
      _lowerCAmelCase			      =	[0] * len(_SCREAMING_SNAKE_CASE					)
      for i in range(1  ,					len(_SCREAMING_SNAKE_CASE					)					):
            _lowerCAmelCase			      =	duration_times[i - 1] + waiting_times[i - 1]
      return waiting_times
def 				UpperCAmelCase__		(					_SCREAMING_SNAKE_CASE :						list[int]  ,					_SCREAMING_SNAKE_CASE :						list[int]					)->list[int]:
      return [
          duration_time + waiting_times[i]
          for i, duration_time in enumerate(_SCREAMING_SNAKE_CASE					)
      ]
def 				UpperCAmelCase__		(					_SCREAMING_SNAKE_CASE :						list[int]					)->float:
      return sum(_SCREAMING_SNAKE_CASE					) / len(_SCREAMING_SNAKE_CASE					)
def 				UpperCAmelCase__		(					_SCREAMING_SNAKE_CASE :						list[int]					)->float:
      return sum(_SCREAMING_SNAKE_CASE					) / len(_SCREAMING_SNAKE_CASE					)


if __name__ == "__main__":
    # process id's
    UpperCAmelCase_          =				[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_          =				[1_9, 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_          =				calculate_waiting_times(duration_times)
    UpperCAmelCase_          =				calculate_turnaround_times(duration_times, waiting_times)

    # get the average times
    UpperCAmelCase_          =				calculate_average_waiting_time(waiting_times)
    UpperCAmelCase_          =				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}""")




import numpy as np
def 				UpperCAmelCase__		(					_SCREAMING_SNAKE_CASE :						Tuple					)->Union[str, Any]:
      _lowerCAmelCase      , _lowerCAmelCase			      =	a.shape
      _lowerCAmelCase			      =	min(_SCREAMING_SNAKE_CASE  ,					_SCREAMING_SNAKE_CASE					)
      _lowerCAmelCase			      =	np.eye(_SCREAMING_SNAKE_CASE					)
      _lowerCAmelCase			      =	a.copy()

      for k in range(t - 1					):
            # select a column of modified matrix A':
            _lowerCAmelCase			      =	r[k:, [k]]
            # construct first basis vector
            _lowerCAmelCase			      =	np.zeros_like(_SCREAMING_SNAKE_CASE					)
            _lowerCAmelCase			      =	1.0
            # determine scaling factor
            _lowerCAmelCase			      =	np.linalg.norm(_SCREAMING_SNAKE_CASE					)
            # construct vector v for Householder reflection
            _lowerCAmelCase			      =	x + np.sign(x[0]					) * alpha * ea
            v /= np.linalg.norm(_SCREAMING_SNAKE_CASE					)

            # construct the Householder matrix
            _lowerCAmelCase			      =	np.eye(m - k					) - 2.0 * v @ v.T
            # pad with ones and zeros as necessary
            _lowerCAmelCase			      =	np.block([[np.eye(_SCREAMING_SNAKE_CASE					), np.zeros((k, m - k)					)], [np.zeros((m - k, k)					), q_k]]					)

            _lowerCAmelCase			      =	q @ q_k.T
            _lowerCAmelCase			      =	q_k @ r

      return q, r


if __name__ == "__main__":
    import doctest

    doctest.testmod()