



'''simple docstring'''
from functools import lru_cache



@lru_cache
def 		_SCREAMING_SNAKE_CASE							(				lowerCamelCase__   :      Any				):


			'''simple docstring'''







			if not isinstance(lowerCamelCase__							,							lowerCamelCase__				):
						raise TypeError("""k must be an integer."""				)
			if k < 0:
						raise ValueError("""k integer must be greater or equal to zero."""				)
			if k == 0:
						return 0
			elif k == 1:
						return 1
			else:
						return fibonacci(k - 1				) + fibonacci(k - 2				)



def 		_SCREAMING_SNAKE_CASE							(				lowerCamelCase__   :      Union[str, Any]							,							lowerCamelCase__   :      Optional[int]				):


			'''simple docstring'''







			A:      List[Any]														=   len(lowerCamelCase__				)
			# Find m such that F_m >= n where F_i is the i_th fibonacci number.
			A:      Optional[Any]														=   0
			while True:
						if fibonacci(lowerCamelCase__				) >= len_list:
									A:      int														=   i
									break
						i += 1
			A:      str														=   0
			while fibb_k > 0:
						A:      int														=   min(
						    offset + fibonacci(fibb_k - 1				)							,							len_list - 1				)  # Prevent out of range
						A:      Any														=   arr[index_k]
						if item_k_1 == val:
									return index_k
						elif val < item_k_1:
									fibb_k -= 1
						elif val > item_k_1:
									offset += fibonacci(fibb_k - 1				)
									fibb_k -= 2
			else:
						return -1


if __name__ == "__main__":
					import doctest

					doctest.testmod()










'''simple docstring'''
from __future__ import annotations



def 		_SCREAMING_SNAKE_CASE							(				lowerCamelCase__   :      list[int]				):


			'''simple docstring'''







			A:      int														=   [0] * len(lowerCamelCase__				)
			for i in range(1							,							len(lowerCamelCase__				)				):
						A:      Dict														=   duration_times[i - 1] + waiting_times[i - 1]
			return waiting_times



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


			'''simple docstring'''







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



def 		_SCREAMING_SNAKE_CASE							(				lowerCamelCase__   :      list[int]				):


			'''simple docstring'''







			return sum(lowerCamelCase__				) / len(lowerCamelCase__				)



def 		_SCREAMING_SNAKE_CASE							(				lowerCamelCase__   :      list[int]				):


			'''simple docstring'''







			return sum(lowerCamelCase__				) / len(lowerCamelCase__				)


if __name__ == "__main__":
					# process id's
					__SCREAMING_SNAKE_CASE :      Optional[Any]             =[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
					__SCREAMING_SNAKE_CASE :      Dict             =[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
					__SCREAMING_SNAKE_CASE :      Tuple             =calculate_waiting_times(duration_times)
					__SCREAMING_SNAKE_CASE :      List[Any]             =calculate_turnaround_times(duration_times, waiting_times)

					# get the average times
					__SCREAMING_SNAKE_CASE :      List[Any]             =calculate_average_waiting_time(waiting_times)
					__SCREAMING_SNAKE_CASE :      Union[str, 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}""")





