Problem Description

This problem asks you to design a system that tracks tweets and analyzes their frequency over different time periods.

You need to implement a TweetCounts class with the following functionality:

1. Store tweets: Record tweets with their name and timestamp (in seconds)
2. Analyze tweet frequency: Count how many tweets occurred in specific time intervals

The key challenge is partitioning time periods into chunks based on different frequencies:

• Minute: 60-second chunks
• Hour: 3600-second chunks
• Day: 86400-second chunks

For example, if you want to analyze tweets from time 10 to 10000:

• With "minute" frequency: You get chunks [10,69], [70,129], [130,189], etc.
• With "hour" frequency: You get chunks [10,3609], [3610,7209], [7210,10000]
• With "day" frequency: You get a single chunk [10,10000]

The last chunk might be shorter than the standard chunk size - it always ends at the specified endTime.

The class methods are:

• TweetCounts(): Initialize the data structure
• recordTweet(tweetName, time): Store a tweet with its name and timestamp
• getTweetCountsPerFrequency(freq, tweetName, startTime, endTime): Return a list where each element represents the count of tweets in each time chunk within [startTime, endTime]

The solution uses a defaultdict of SortedList to store tweets efficiently. Each tweet name maps to a sorted list of timestamps. When querying, it uses binary search (bisect_left) to quickly find how many tweets fall within each time chunk, iterating through chunks of size determined by the frequency parameter.

Intuition

The core insight is that we need to efficiently count tweets within specific time ranges. Since we'll be querying different time intervals repeatedly, we need a data structure that allows fast range queries.

The first observation is that tweets for different names are independent - we can store them separately. This leads us to use a dictionary where keys are tweet names.

For each tweet name, we need to store timestamps in a way that allows quick counting within any given range [start, end]. If we store timestamps in sorted order, we can use binary search to find:

• The position where our range starts
• The position where our range ends
• The count is simply the difference between these positions

This is why SortedList is perfect - it maintains sorted order automatically when we insert new tweets, and provides bisect_left for efficient binary search.

When getting tweet counts per frequency, we need to divide the time period [startTime, endTime] into chunks. The chunk size depends on the frequency:

• "minute" → 60 seconds
• "hour" → 3600 seconds
• "day" → 86400 seconds

We iterate through the time period, creating chunks of the appropriate size. For each chunk [t, t+f) where f is the frequency size, we:

1. Find the index of the first tweet at or after time t using bisect_left(t)
2. Find the index of the first tweet at or after time t+f (or endTime+1 if that's smaller) using bisect_left(min(t+f, endTime+1))
3. The difference gives us the count of tweets in this chunk

The key optimization is using binary search instead of linear scanning, reducing the time complexity from O(n) to O(log n) for each chunk query, where n is the number of tweets for that name.

Learn more about Binary Search and Sorting patterns.

Solution Approach

The solution uses a dictionary of sorted lists to efficiently store and query tweet data.

Data Structure Design:

• self.d: A dictionary mapping frequency strings to their corresponding seconds ({"minute": 60, "hour": 3600, "day": 86400})
• self.data: A defaultdict(SortedList) where each key is a tweet name and the value is a sorted list of timestamps

Method Implementation:

1. __init__(): Initializes the two data structures mentioned above. Using defaultdict ensures we don't need to check if a tweet name exists before adding timestamps.

2. recordTweet(tweetName, time): Simply adds the timestamp to the sorted list for the given tweet name. The SortedList automatically maintains sorted order with O(log n) insertion time.

   self.data[tweetName].add(time)

3. getTweetCountsPerFrequency(freq, tweetName, startTime, endTime): This is the core method that partitions the time range and counts tweets.

   • First, get the chunk size f from the frequency dictionary
   • Retrieve the sorted list of timestamps for the tweet name
   • Initialize time pointer t at startTime
   • For each chunk:

     l = tweets.bisect_left(t)  # Find first tweet >= t
     r = tweets.bisect_left(min(t + f, endTime + 1))  # Find first tweet >= end of chunk
     ans.append(r - l)  # Count = difference in indices
     t += f  # Move to next chunk

   The key insight is using min(t + f, endTime + 1) for the right boundary. This ensures:

   • Regular chunks use t + f as the boundary
   • The last chunk is capped at endTime + 1 (since we want tweets up to and including endTime)

   The bisect_left operations find the leftmost position where we could insert the given value while maintaining sorted order, effectively giving us the index of the first element >= the search value.

Time Complexity:

• recordTweet: O(log n) where n is the number of tweets for that name
• getTweetCountsPerFrequency: O(k * log n) where k is the number of chunks and n is the number of tweets for that name

Space Complexity:

• O(m * n) where m is the number of unique tweet names and n is the average number of tweets per name

Example Walkthrough

Let's walk through a concrete example to understand how the solution works.

Setup:

tc = TweetCounts()

Recording tweets:

tc.recordTweet("tweet1", 10)
tc.recordTweet("tweet1", 80)
tc.recordTweet("tweet1", 150)
tc.recordTweet("tweet1", 3650)

After these operations, our data structure looks like:

self.data = {
    "tweet1": SortedList([10, 80, 150, 3650])
}

Query: Get tweet counts per minute from time 0 to 3700

result = tc.getTweetCountsPerFrequency("minute", "tweet1", 0, 3700)

Let's trace through the execution:

1. Initialize variables:

   • f = 60 (chunk size for "minute")
   • tweets = [10, 80, 150, 3650]
   • t = 0 (starting time)
   • ans = [] (result array)

2. Process chunks:

   Chunk 1: [0, 60)

   • l = bisect_left(0) = 0 (index where 0 would be inserted)
   • r = bisect_left(min(0+60, 3701)) = bisect_left(60) = 1 (index where 60 would be inserted)
   • Count = r - l = 1 - 0 = 1 (only tweet at time 10 is in this range)
   • ans = [1], t = 60

   Chunk 2: [60, 120)

   • l = bisect_left(60) = 1
   • r = bisect_left(120) = 2
   • Count = 2 - 1 = 1 (only tweet at time 80)
   • ans = [1, 1], t = 120

   Chunk 3: [120, 180)

   • l = bisect_left(120) = 2
   • r = bisect_left(180) = 3
   • Count = 3 - 2 = 1 (only tweet at time 150)
   • ans = [1, 1, 1], t = 180

   Chunks 4-61: [180, 240), [240, 300), ..., [3600, 3660)

   • All these chunks have no tweets, so we append 0s
   • ans = [1, 1, 1, 0, 0, ..., 0] (58 zeros)
   • t = 3660

   Final Chunk: [3660, 3700]

   • l = bisect_left(3660) = 4
   • r = bisect_left(min(3660+60, 3701)) = bisect_left(3701) = 4
   • Count = 4 - 4 = 0 (tweet at 3650 is before this chunk)
   • Final ans = [1, 1, 1, 0, 0, ..., 0] (total 62 elements)

Key Observations:

1. Binary search efficiency: Instead of checking every tweet for each chunk, bisect_left finds the boundaries in O(log n) time.

2. Handling the last chunk: Notice how we use min(t + f, endTime + 1). In the final chunk, instead of going to 3720 (3660+60), we cap it at 3701 (3700+1), ensuring we only count tweets up to and including time 3700.

3. Empty chunks: The solution correctly handles chunks with no tweets (returning 0).

4. Sorted order maintenance: The SortedList automatically keeps timestamps in order, making our binary searches valid even as we add new tweets.

Solution Implementation

Time and Space Complexity

Time Complexity:

• __init__(): O(1) - Simply initializes a dictionary and a defaultdict
• recordTweet(): O(log n) where n is the number of tweets for the given tweetName - The SortedList add operation maintains sorted order using binary search insertion
• getTweetCountsPerFrequency(): O(k * log n) where k is the number of intervals (endTime - startTime) / freq and n is the number of tweets for the given tweetName
  • The while loop runs k times where k = ceiling((endTime - startTime + 1) / freq)
  • Each iteration performs two bisect_left operations, each taking O(log n) time
  • The subtraction r - l takes O(1) time
  • Therefore, total time is O(k * log n)

Space Complexity:

• Overall space: O(m * n) where m is the number of unique tweet names and n is the average number of tweets per name
• self.d: O(1) - Stores only 3 key-value pairs
• self.data: O(m * n) - Stores all tweets where m is the number of unique tweet names and n is the average number of tweets per name
• recordTweet(): O(1) additional space (not counting the space to store the tweet itself)
• getTweetCountsPerFrequency(): O(k) additional space where k is the number of intervals, used for the ans list

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

Common Pitfalls

1. Off-by-One Error with End Time Boundary

One of the most common mistakes is incorrectly handling the inclusive nature of the endTime parameter. The problem specifies that the time range is [startTime, endTime] (both inclusive), but when using bisect_left, you need to search for endTime + 1 to include tweets at exactly endTime.

Incorrect:

right_index = tweet_timestamps.bisect_left(min(current_time + interval_duration, endTime))

Correct:

right_index = tweet_timestamps.bisect_left(min(current_time + interval_duration, endTime + 1))

2. Importing SortedList Incorrectly

The SortedList is not a built-in Python data structure. It requires the sortedcontainers library, which may not be available in all coding environments.

Alternative Solution Using Built-in bisect:

from collections import defaultdict
import bisect

class TweetCounts:
    def __init__(self):
        self.frequency_duration = {"minute": 60, "hour": 3600, "day": 86400}
        self.tweet_data = defaultdict(list)
  
    def recordTweet(self, tweetName: str, time: int) -> None:
        # Use bisect.insort to maintain sorted order
        bisect.insort(self.tweet_data[tweetName], time)

3. Empty Tweet List Handling

While the current implementation handles empty tweet lists correctly (returning zeros), explicitly checking can make the code more readable and potentially more efficient:

def getTweetCountsPerFrequency(self, freq: str, tweetName: str, startTime: int, endTime: int) -> List[int]:
    interval_duration = self.frequency_duration[freq]
  
    # Early return for non-existent tweet names
    if tweetName not in self.tweet_data:
        num_intervals = (endTime - startTime) // interval_duration + 1
        return [0] * num_intervals
  
    tweet_timestamps = self.tweet_data[tweetName]
    # ... rest of the logic

4. Misunderstanding Chunk Boundaries

A common misconception is that chunks should be aligned to absolute time boundaries (e.g., minute 0-59, 60-119). However, chunks actually start from startTime, not from time 0.

Example: If startTime=10 and freq="minute":

• First chunk: [10, 69] (NOT [10, 59])
• Second chunk: [70, 129] (NOT [60, 119])

5. Integer Overflow in Large Time Ranges

For extremely large time ranges with "minute" frequency, the number of chunks could be very large, potentially causing memory issues:

def getTweetCountsPerFrequency(self, freq: str, tweetName: str, startTime: int, endTime: int) -> List[int]:
    interval_duration = self.frequency_duration[freq]
  
    # Add validation to prevent excessive memory usage
    max_chunks = (endTime - startTime) // interval_duration + 1
    if max_chunks > 10**6:  # Arbitrary large limit
        raise ValueError("Time range too large for given frequency")
  
    # ... rest of the implementation

6. Not Handling Duplicate Timestamps

The current solution correctly handles duplicate timestamps (multiple tweets at the same time), but it's worth noting that using a regular list with bisect would also handle this correctly. The key is understanding that both bisect_left and bisect_right would give different results when duplicates exist, and choosing the appropriate one based on your needs.