p

```
"""
Calculate the minimum waiting time using a greedy algorithm.
reference: https://www.youtube.com/watch?v=Sf3eiO12eJs
For doctests run following command:
python -m doctest -v minimum_waiting_time.py
The minimum_waiting_time function uses a greedy algorithm to calculate the minimum
time for queries to complete. It sorts the list in non-decreasing order, calculates
the waiting time for each query by multiplying its position in the list with the
sum of all remaining query times, and returns the total waiting time. A doctest
ensures that the function produces the correct output.
"""
def minimum_waiting_time(queries: list[int]) -> int:
"""
This function takes a list of query times and returns the minimum waiting time
for all queries to be completed.
Args:
queries: A list of queries measured in picoseconds
Returns:
total_waiting_time: Minimum waiting time measured in picoseconds
Examples:
>>> minimum_waiting_time([3, 2, 1, 2, 6])
17
>>> minimum_waiting_time([3, 2, 1])
4
>>> minimum_waiting_time([1, 2, 3, 4])
10
>>> minimum_waiting_time([5, 5, 5, 5])
30
>>> minimum_waiting_time([])
0
"""
n = len(queries)
if n in (0, 1):
return 0
return sum(query * (n - i - 1) for i, query in enumerate(sorted(queries)))
if __name__ == "__main__":
import doctest
doctest.testmod()
```