
from __future__ import annotations

__UpperCAmelCase   						=     [2, 1, 4, 5, 6, 0, 8, 9, 1, 2, 0, 6, 4, 2, 0, 6, 5, 3, 2, 7]





class 				UpperCamelCase__		:






       """simple docstring"""


       def __init__(							self ,     _A	)				->				List[Any]:
          SCREAMING_SNAKE_CASE_	=      -1
          SCREAMING_SNAKE_CASE_	=      -1
          SCREAMING_SNAKE_CASE_	=      [-1] * length
          SCREAMING_SNAKE_CASE_	=      None
          SCREAMING_SNAKE_CASE_	=      None




       def __repr__(							self	)				->				List[str]:
          return F'''Node(min_value={self.minn} max_value={self.maxx})'''







def  A__ (       __lowerCamelCase						):
   SCREAMING_SNAKE_CASE_	=      Node(len(_SCREAMING_SNAKE_CASE						)						)
   SCREAMING_SNAKE_CASE_	, SCREAMING_SNAKE_CASE_	=      min(_SCREAMING_SNAKE_CASE						), max(_SCREAMING_SNAKE_CASE						)
   # Leaf node case where the node contains only one unique value
   if root.minn == root.maxx:
      return root
   SCREAMING_SNAKE_CASE_	=      (root.minn + root.maxx) // 2

   SCREAMING_SNAKE_CASE_	=      []
   SCREAMING_SNAKE_CASE_	=      []

   for index, num in enumerate(_SCREAMING_SNAKE_CASE						):
      if num <= pivot:
         left_arr.append(_SCREAMING_SNAKE_CASE						)
      else:
         right_arr.append(_SCREAMING_SNAKE_CASE						)
      SCREAMING_SNAKE_CASE_	=      len(_SCREAMING_SNAKE_CASE						)
   SCREAMING_SNAKE_CASE_	=      build_tree(_SCREAMING_SNAKE_CASE						)
   SCREAMING_SNAKE_CASE_	=      build_tree(_SCREAMING_SNAKE_CASE						)
   return root


def  A__ (       __lowerCamelCase,  __lowerCamelCase,  __lowerCamelCase						):


   if index < 0 or node is None:
      return 0
   # Leaf node cases
   if node.minn == node.maxx:
      return index + 1 if node.minn == num else 0
   SCREAMING_SNAKE_CASE_	=      (node.minn + node.maxx) // 2
   if num <= pivot:
      # go the left subtree and map index to the left subtree
      return rank_till_index(node.left,  _SCREAMING_SNAKE_CASE,  node.map_left[index] - 1						)
   else:
      # go to the right subtree and map index to the right subtree
      return rank_till_index(node.right,  _SCREAMING_SNAKE_CASE,  index - node.map_left[index]						)


def  A__ (       __lowerCamelCase,  __lowerCamelCase,  __lowerCamelCase,  __lowerCamelCase						):


   if start > end:
      return 0
   SCREAMING_SNAKE_CASE_	=      rank_till_index(_SCREAMING_SNAKE_CASE,  _SCREAMING_SNAKE_CASE,  _SCREAMING_SNAKE_CASE						)
   SCREAMING_SNAKE_CASE_	=      rank_till_index(_SCREAMING_SNAKE_CASE,  _SCREAMING_SNAKE_CASE,  start - 1						)
   return rank_till_end - rank_before_start


def  A__ (       __lowerCamelCase,  __lowerCamelCase,  __lowerCamelCase,  __lowerCamelCase						):


   if index > (end - start) or start > end or node is None:
      return -1
   # Leaf node case
   if node.minn == node.maxx:
      return node.minn
   # Number of elements in the left subtree in interval [start, end]
   SCREAMING_SNAKE_CASE_	=      node.map_left[end] - (
       node.map_left[start - 1] if start else 0
   )
   if num_elements_in_left_tree > index:
      return quantile(
          node.left,  _SCREAMING_SNAKE_CASE,  (node.map_left[start - 1] if start else 0),  node.map_left[end] - 1,  )
   else:
      return quantile(
          node.right,  index - num_elements_in_left_tree,  start - (node.map_left[start - 1] if start else 0),  end - node.map_left[end],  )


def  A__ (       __lowerCamelCase,  __lowerCamelCase,  __lowerCamelCase,  __lowerCamelCase,  __lowerCamelCase						):


   if (
       start > end
       or node is None
       or start_num > end_num
       or node.minn > end_num
       or node.maxx < start_num
   ):
      return 0
   if start_num <= node.minn and node.maxx <= end_num:
      return end - start + 1
   SCREAMING_SNAKE_CASE_	=      range_counting(
       node.left,  (node.map_left[start - 1] if start else 0),  node.map_left[end] - 1,  _SCREAMING_SNAKE_CASE,  _SCREAMING_SNAKE_CASE,  )
   SCREAMING_SNAKE_CASE_	=      range_counting(
       node.right,  start - (node.map_left[start - 1] if start else 0),  end - node.map_left[end],  _SCREAMING_SNAKE_CASE,  _SCREAMING_SNAKE_CASE,  )
   return left + right


if __name__ == "__main__":
   import doctest

   doctest.testmod()





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}')


