Solution Explanation: Design Log Storage System

This problem requires designing a LogSystem that can store logs with timestamps and retrieve logs within a specified range based on a given granularity. The solution uses a simple approach leveraging string manipulation and comparison for efficiency.

Approach:

The core idea is to store logs as pairs of (ID, timestamp). Retrieving logs involves comparing truncated timestamps based on the specified granularity.

1. put(id, timestamp): This method simply appends the log (ID, timestamp) to a list of logs. The timestamp is stored as a string in "Year:Month:Day:Hour:Minute:Second" format. This operation has a time complexity of O(1) as it involves a single append operation to the list.

2. retrieve(start, end, granularity): This is where the main logic resides.

   • A granularity map is used to determine the index up to which the timestamp string needs to be truncated (e.g., "Year" -> truncate up to the 4th character, "Day" -> up to the 10th character).
   • The start and end timestamps are truncated based on the granularity.
   • The method iterates through the stored logs. For each log, its timestamp is also truncated based on the granularity.
   • The truncated timestamp is then compared with the truncated start and end timestamps. If it falls within the range (inclusive), the corresponding ID is added to the result list.
   • Finally, the list of IDs is returned. This operation has a time complexity of O(n) where n is the number of stored logs because it iterates through the entire list.

Time and Space Complexity:

• Time Complexity:

  • put(): O(1) - Constant time for appending to the list.
  • retrieve(): O(n) - Linear time complexity due to the iteration through the list of logs.

• Space Complexity:

  • O(n), where n is the number of logs stored. The space used is primarily for storing the logs in the logs list.

Code Implementation Details (Python3 Example):

class LogSystem:
    def __init__(self):
        self.logs = []  # List to store logs as (id, timestamp) pairs
        self.d = {  # Map for granularity to index mapping
            "Year": 4,
            "Month": 7,
            "Day": 10,
            "Hour": 13,
            "Minute": 16,
            "Second": 19,
        }
 
    def put(self, id: int, timestamp: str) -> None:
        self.logs.append((id, timestamp))
 
    def retrieve(self, start: str, end: str, granularity: str) -> List[int]:
        i = self.d[granularity]  # Get the truncation index
        return [id for id, ts in self.logs if start[:i] <= ts[:i] <= end[:i]] #Efficient list comprehension for filtering

The Python code uses a list comprehension for concisely filtering logs based on the truncated timestamps. Other language implementations (Java, C++, Go) follow a similar structure, using appropriate data structures and syntax for their respective languages. The core algorithmic approach remains consistent across all implementations.