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 @@
+"""
+This is a pure Python implementation for minimum waiting time problem using 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):
+    """
+    This function takes a list of query times and returns the minimum waiting time
+    for all queries to be completed.
+
+    >>> minimum_waiting_time([3, 2, 1, 2, 6])
+    17
+    >>> minimum_waiting_time([3, 2, 1])
+    4
+    >>> minimum_waiting_time([1, 2, 3, 4])
+    10
+    """
+    # Base case
+    n = len(queries)
+    if n == 0 or n == 1:
+        return 0
+
+    # Sort the list in non-decreasing order
+    queries.sort()
+
+    # Calculate the total waiting time
+    total_waiting_time = 0
+    for i in range(n - 1):
+        total_waiting_time += queries[i] * (n - i - 1)
+
+    return total_waiting_time
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()