Problem Description

The given LeetCode problem involves creating a log system that can store log entries with a unique ID and timestamp, and then retrieve logs that fall within a given time range based on varying levels of granularity. A timestamp in this problem is given in the string format "Year:Month:Day:Hour:Minute:Second", where each part of the date-time is zero-padded. The system needs to support two operations:

• put(int id, string timestamp): This function takes a log entry's unique ID and its timestamp, then stores it in the system.

• retrieve(string start, string end, string granularity): This method returns the list of log IDs that have timestamps within the inclusive range specified by start and end. The granularity parameter determines how precise the time range should be, ranging from the year down to the second. The granularity truncates the timestamp to the specified level of detail, and only that level of detail is considered when filtering logs.

For example, if the granularity is "Day", then the logs are filtered based on their year, month, and day, without considering hours, minutes, or seconds.

Intuition

The intuition behind the solution involves storing the log entries efficiently so that they can be easily retrieved based on time range queries with varying granularities. To retrieve the correct logs, we need to compare only the parts of the timestamps that are relevant to the specified granularity. The solution defines a dictionary d that contains the cutoff indices for each granularity. These indices are used to truncate the timestamp strings to the required precision.

The retrieval function takes advantage of Python's string comparison, which can be used directly on the truncated timestamp strings. Since the timestamps are fixed-length and zero-padded, lexicographical comparison of the strings works equivalently to comparing the numerical values.

Here's the thought process for arriving at the solution approach:

1. Store all logs in a list as they are received. There's no need to sort them since we can filter them during retrieval.

2. Define a dictionary that maps each granularity to the index up to which the timestamp should be considered. For instance, if the granularity is "Year", we only consider the first four characters of the timestamp.

3. When retrieving logs within a specific range, determine the cutoff index for the timestamps based on granularity. Use slicing to truncate the start, end, and current log timestamp to the relevant precision.

4. Iterate through all stored logs, compare the truncated timestamp of each log to the truncated start and end timestamps, and filter accordingly.

5. Return the list of IDs of the logs that satisfy the range and granularity criteria.

By following this approach, we ensure that we can efficiently retrieve the correct log entries without the need for complex date-time parsing or conversion.

Solution Approach

The implementation of the LogSystem class involves two key methods: put and retrieve.

The put method is straightforward. Each call to put adds a tuple consisting of the id and timestamp to the logs list:

def put(self, id: int, timestamp: str) -> None:
    self.logs.append((id, timestamp))

Here we don't need to worry about sorting or the position of the log entry because the retrieval will handle the search based on the timestamp.

The retrieve method does the main work of filtering the log entries according to the provided time range and granularity:

def retrieve(self, start: str, end: str, granularity: str) -> List[int]:
    i = self.d[granularity]  # Find the index up to which we should compare timestamps
    return [id for id, ts in self.logs if start[:i] <= ts[:i] <= end[:i]]

The use of dictionary d to store the indices for each granularity level allows us to easily retrieve the correct substring length to compare. For example, for granularity Year, d['Year'] would be 4, so start[:4] would give us the year component of the start timestamp.

A comprehensive breakdown of the algorithm used:

1. Upon initialization (__init__), an empty list logs is created to store the log entries. A dictionary d is also initialized to map granularity to corresponding substring indices.

2. The put method simply appends the provided log entry to the logs list without any additional processing.

3. The retrieve method calculates the index i up to which the timestamps should be considered, based on the granularity. It uses list comprehension to iterate through all the stored logs and includes the ones that match the range condition.

4. For each log, the comparison is done by slicing the timestamps of the logs and the provided start and end parameters up to index i. This way, we only compare the parts of the timestamps that matter for the specified granularity.

5. We rely on Python's string comparison to compare the sliced timestamps. Since timestamps are zero-padded and have a consistent format, this works out as effectively as numerical comparison.

6. The method finally returns a list of IDs whose timestamps fall within the specified range.

This implementation is efficient as it separates the storage and querying of log entries. The dictionary d effectively eliminates complex parsing or time conversion by using string slicing based on predefined indices corresponding to each granularity.

Example Walkthrough

Let's say we instantiate a LogSystem and perform a series of put and retrieve operations as per the solution approach described.

First, we add a few logs to the system with varying timestamps:

logSystem = LogSystem()
logSystem.put(1, "2017:01:01:23:59:59")
logSystem.put(2, "2017:01:02:23:59:59")
logSystem.put(3, "2017:02:01:23:59:59")

In our logs data structure, we now have:

[(1, "2017:01:01:23:59:59"), (2, "2017:01:02:23:59:59"), (3, "2017:02:01:23:59:59")]

No sorting is needed; we just store the logs as they come.

Suppose we want to retrieve logs with timestamps in January 2017; we can call the retrieve method accordingly:

results = logSystem.retrieve("2017:01:01:00:00:00", "2017:01:31:23:59:59", "Month")

The d dictionary in the LogSystem has an entry "Month": 7, indicating that we should compare the timestamps up to the seventh character for a "Month" granularity, which corresponds to the year and month components.

The retrieve method will:

1. Determine the index i for month granularity, which is 7. Thus, we will compare timestamps up to "2017:01".

2. Iterate through the logs:

- For log (1, "2017:01:01:23:59:59"), the truncated timestamp is "2017:01" which is within the range "2017:01" to "2017:01".
- For log (2, "2017:01:02:23:59:59"), the truncated timestamp is also "2017:01", which is within the range.
- For log (3, "2017:02:01:23:59:59"), the truncated timestamp is "2017:02", which is outside the range.

3. Create a list of the IDs where the condition holds true. In this case, logs 1 and 2 match, while log 3 does not.

As a result, results will have the value [1, 2], meaning log entries with IDs 1 and 2 are the ones that fall within the desired time range and granularity.

This example demonstrates how the implementation allows us to efficiently filter logs based on a specified granularity and time range without complex parsing.

Solution Implementation

Time and Space Complexity

Time Complexity

put method: The put operation has a time complexity of O(1) since it only involves appending a tuple (ID and timestamp) to the end of the self.logs list which is a constant time operation.

retrieve method: The retrieve operation involves iterating over each log entry in self.logs and comparing the substrings of their timestamps. The time complexity is O(n * s) where n is the number of log entries and s is the length of the timestamp substring being compared. The complexity of the comparison operation is assumed to be O(1) since the length of the substring depends on the granularity and doesn't change with the size of self.logs.

Space Complexity

Overall: The space complexity of the LogSystem class is O(n), where n is the number of log entries stored in self.logs. Each log entry requires a fixed amount of space for the integer ID and a fixed-length string for the timestamp, resulting in space directly proportional to the number of entries.

put method: For the put method, it only appends the log data without needing any extra space besides the self.logs, so the space complexity incurred by this method is O(1) in addition to the overall O(n) space needed for storing the logs themselves.

retrieve method: The retrieve method creates a new list of IDs that match the criteria, the space complexity of which is O(k) where k is the number of matching log entries returned. Since k can be at most n in the worst case, the worst-case space complexity for retrieve can also be O(n).

Learn more about how to find time and space complexity quickly using problem constraints.