Add docstrings to binary search functions

Added docstrings for lower_bound and upper_bound functions.

Author: shuhao-alan-fan

searches/binary_search.py

@@ -272,9 +272,19 @@ def binary_search_with_duplicates(sorted_collection: list[int], item: int) -> li
     if list(sorted_collection) != sorted(sorted_collection):
         raise ValueError("sorted_collection must be sorted in ascending order")
 
-    """find lower bounds"""
+   
 
     def lower_bound(sorted_collection: list[int], item: int) -> int:
+        """
+        Returns the index of the first element greater than or equal to the item.
+        
+        Args:
+            sorted_collection: The sorted list to search.
+            item: The item to find the lower bound for.
+
+        Returns:
+            int: The index where the item can be inserted while maintaining order.
+        """
         left = 0
         right = len(sorted_collection)
         while left < right:
@@ -286,9 +296,19 @@ def lower_bound(sorted_collection: list[int], item: int) -> int:
                 right = midpoint
         return left
 
-    """find upper bounds"""
+   
 
     def upper_bound(sorted_collection: list[int], item: int) -> int:
+        """
+        Returns the index of the first element strictly greater than the item.
+        
+        Args:
+            sorted_collection: The sorted list to search.
+            item: The item to find the upper bound for.
+
+        Returns:
+            int: The index where the item can be inserted after all existing instances.
+        """
         left = 0
         right = len(sorted_collection)
         while left < right: