Added minimum waiting time problem solution using greedy algorithm

DIRECTORY.md

@@ -449,6 +449,7 @@
  * [Fractional Knapsack](greedy_methods/fractional_knapsack.py)
  * [Fractional Knapsack 2](greedy_methods/fractional_knapsack_2.py)
  * [Optimal Merge Pattern](greedy_methods/optimal_merge_pattern.py)
+ * [Minimum Waiting Time ](greedy_methods/minimum_waiting_time.py)
 
 ## Hashes
  * [Adler32](hashes/adler32.py)

greedy_methods/minimum_waiting_time.py

@@ -0,0 +1,48 @@
+"""
+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()