refactor(algorithms, intervals, count days): add type hints

Co-authored-by: coderabbitai[bot] <136622811+coderabbitai[bot]@users.noreply.github.com>

Author: BrianLusina

algorithms/intervals/count_days/__init__.py

@@ -54,7 +54,22 @@ def count_days(days: int, meetings: List[List[int]]) -> int:
     return free_days + (days - last_busy_day)
 
 
-def count_days_2(days, meetings):
+def count_days_2(days: int, meetings: List[List[int]]) -> int:
+    """
+    Counts the number of days the employee is available for work but has no scheduled meetings.
+    
+    This implementation merges overlapping meetings and counts total occupied days.
+    
+    Time Complexity: O(n log n) due to sorting
+    Space Complexity: O(1) excluding sort overhead
+    
+    Args:
+        days (int): The total number of days the employee is available for work
+        meetings (List[List[int]]): A list of meetings, where each meeting is represented as a list of two integers [start, end]
+            Note: This function modifies the input list by sorting it in place.
+    Returns:
+        int: The number of days the employee is available for work but has no scheduled meetings
+    """
     # Sort the meetings based on their start time to process them in order
     meetings.sort()