Added minimum waiting time problem solution using greedy algorithm (T…

…heAlgorithms#8701)

* Added minimum waiting time problem solution using greedy algorithm

* [pre-commit.ci] auto fixes from pre-commit.com hooks

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* ruff --fix

* Add type hints

* Added two more doc test

* Removed unnecessary comments

* updated type hints

* Updated the code as per the code review

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

DIRECTORY.md

@@ -450,6 +450,7 @@
   * [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()