Problem Description

You have a system with a certain number of users that can be online or offline. You need to track how many times each user gets mentioned across various message events.

The problem gives you:

• numberOfUsers: The total number of users (indexed from 0 to numberOfUsers-1)
• events: An array where each event has 3 elements describing either a message or an offline event

There are two types of events:

1. Message Event: ["MESSAGE", "timestamp", "mentions_string"]

• Occurs at a specific timestamp
• The mentions_string can contain:
  • id<number>: Mentions a specific user (e.g., "id0", "id5"). Multiple ids can be separated by spaces and duplicates count as separate mentions
  • ALL: Mentions every single user in the system
  • HERE: Mentions only users who are currently online

2. Offline Event: ["OFFLINE", "timestamp", "user_id"]

• Indicates that a user goes offline at the given timestamp
• The user stays offline for exactly 60 time units
• The user automatically comes back online at timestamp + 60

Important rules:

• All users start as online
• If events happen at the same timestamp, offline/online status changes are processed BEFORE message events
• A user can be mentioned multiple times in a single message, and each mention counts separately
• Offline users can still be mentioned with their specific id

Your task is to return an array where the value at index i represents the total number of times user i was mentioned across all message events.

For example, if user 0 is mentioned 3 times across different messages (including being part of an "ALL" mention), the result array at index 0 should be 3.

Intuition

The key insight is that we need to process events in chronological order while carefully managing user online/offline states. Since status changes must be processed before messages at the same timestamp, we need a way to ensure proper ordering.

First, let's think about sorting. We sort events by timestamp, but when timestamps are equal, we need offline events to come first. This is achieved by comparing the third character of the event type string (e[0][2]) - "OFFLINE" has 'F' at index 2 while "MESSAGE" has 'S' at index 2, and 'F' comes before 'S' alphabetically.

For tracking online status, we can use an array online_t where each element represents when that user will next be online. If online_t[i] <= current_time, user i is online. When a user goes offline at time t, we set online_t[i] = t + 60.

The "ALL" mentions present an interesting optimization opportunity. Instead of immediately adding 1 to every user's count when we see "ALL", we can use a lazy evaluation approach. We accumulate these global mentions in a lazy counter and apply them all at once at the end. This is more efficient than updating every user's count multiple times.

For "HERE" mentions, we need to check each user's online status at the current timestamp and increment their count if they're online.

For specific user mentions (like "id0 id2 id0"), we parse the string, extract the user IDs, and increment their counts directly. Note that duplicates count separately, so if "id0" appears twice, user 0 gets 2 mentions.

The beauty of this approach is that by properly ordering events and maintaining just the next online time for each user, we can efficiently simulate the entire system without complex state management. The lazy evaluation for "ALL" mentions further optimizes performance by deferring work until necessary.

Learn more about Math and Sorting patterns.

Solution Approach

Let's walk through the implementation step by step:

1. Sorting the Events

events.sort(key=lambda e: (int(e[1]), e[0][2]))

We sort events primarily by timestamp (int(e[1])). For events with the same timestamp, we use the third character of the event type (e[0][2]) as a tiebreaker. This ensures "OFFLINE" events (with 'F' at index 2) come before "MESSAGE" events (with 'S' at index 2).

2. Initialize Data Structures

ans = [0] * numberOfUsers      # Stores mention count for each user
online_t = [0] * numberOfUsers  # Stores next online time for each user
lazy = 0                        # Accumulates "ALL" mentions

• ans: The result array tracking mentions for each user
• online_t: Initially all zeros, meaning all users are online (since 0 <= any timestamp)
• lazy: Counter for deferred "ALL" mentions

3. Process Each Event

for etype, ts, s in events:
    cur = int(ts)

We iterate through sorted events and convert the timestamp to an integer for comparison.

4. Handle Different Event Types

OFFLINE Event:

if etype[0] == "O":
    online_t[int(s)] = cur + 60

Set the user's next online time to current time + 60.

MESSAGE Event with "ALL":

elif s[0] == "A":
    lazy += 1

Instead of immediately incrementing all users' counts, we defer this operation by incrementing lazy.

MESSAGE Event with "HERE":

elif s[0] == "H":
    for i, t in enumerate(online_t):
        if t <= cur:
            ans[i] += 1

Check each user's online status. If online_t[i] <= cur, the user is online and gets mentioned.

MESSAGE Event with Specific IDs:

else:
    for a in s.split():
        ans[int(a[2:])] += 1

Split the mention string by spaces, extract user IDs (skipping "id" prefix with a[2:]), and increment their counts. Duplicates are counted separately.

5. Apply Lazy Updates

if lazy:
    for i in range(numberOfUsers):
        ans[i] += lazy

Finally, apply all accumulated "ALL" mentions to every user.

This approach efficiently handles the simulation with O(n log n) time complexity for sorting and O(n × m) for processing events (where n is the number of events and m is the number of users), while maintaining O(m) space complexity for the tracking arrays.

Example Walkthrough

Let's walk through a concrete example with 3 users and the following events:

Input:

• numberOfUsers = 3 (users 0, 1, 2)
• events = [["MESSAGE", "10", "HERE"], ["OFFLINE", "15", "1"], ["MESSAGE", "15", "id1 id2"], ["MESSAGE", "20", "ALL"]]

Step 1: Sort the events After sorting by timestamp (and OFFLINE before MESSAGE for same timestamps):

1. ["MESSAGE", "10", "HERE"] - timestamp 10
2. ["OFFLINE", "15", "1"] - timestamp 15 (comes before MESSAGE at 15)
3. ["MESSAGE", "15", "id1 id2"] - timestamp 15
4. ["MESSAGE", "20", "ALL"] - timestamp 20

Step 2: Initialize data structures

• ans = [0, 0, 0] - mention counts for users 0, 1, 2
• online_t = [0, 0, 0] - all users online initially (next online time is 0)
• lazy = 0 - deferred "ALL" mentions

Step 3: Process each event

Event 1: ["MESSAGE", "10", "HERE"] at time 10

• Check who's online: All users have online_t[i] = 0 <= 10, so all are online
• Increment each online user's count: ans = [1, 1, 1]

Event 2: ["OFFLINE", "15", "1"] at time 15

• User 1 goes offline: online_t[1] = 15 + 60 = 75
• Status now: online_t = [0, 75, 0]

Event 3: ["MESSAGE", "15", "id1 id2"] at time 15

• Parse mentions: "id1" and "id2"
• Increment user 1: ans[1] += 1 → ans = [1, 2, 1]
• Increment user 2: ans[2] += 1 → ans = [1, 2, 2]
• Note: User 1 gets mentioned even though they're offline (specific mentions work regardless of status)

Event 4: ["MESSAGE", "20", "ALL"] at time 20

• Instead of updating all users now, increment lazy: lazy = 1

Step 4: Apply lazy updates

• Add lazy = 1 to all users: ans = [2, 3, 3]

Final Result: [2, 3, 3]

• User 0: mentioned 2 times (HERE at t=10, ALL at t=20)
• User 1: mentioned 3 times (HERE at t=10, id1 at t=15, ALL at t=20)
• User 2: mentioned 3 times (HERE at t=10, id2 at t=15, ALL at t=20)

Solution Implementation

Time and Space Complexity

Time Complexity: O(m log m + m × n + L)

The time complexity breaks down as follows:

• Sorting the events takes O(m log m) where m is the number of events
• Processing each event:
  • For "OFFLINE" events: O(1) operation
  • For "MESSAGE" events with "ALL": O(1) operation (just incrementing lazy counter)
  • For "MESSAGE" events with "HERE": O(n) operation to check all users' online status
  • For "MESSAGE" events with specific mentions: O(k) where k is the number of mentioned users, and parsing the string takes O(l) where l is the length of that mention string
• The final lazy application takes O(n) to update all users

In the worst case, if all events are "HERE" messages, we get O(m × n) for processing. The total length of parsing all mention strings is L. Therefore, the overall complexity is O(m log m + m × n + L).

Space Complexity: O(n)

The space complexity consists of:

• ans array: O(n) for storing the mention count for each user
• online_t array: O(n) for storing online timestamps for each user
• lazy counter: O(1)
• The sorting operation uses O(1) extra space (in-place sorting in Python's Timsort)

Therefore, the total space complexity is O(n).

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

Common Pitfalls

1. Incorrect Timestamp Sorting for Same-Time Events

The Pitfall: When multiple events occur at the same timestamp, the order matters significantly. The original code uses event[0][2] to sort by the third character of the event type string, which works for "OFFLINE" vs "MESSAGE" but is fragile and assumes specific string formats.

Why It's a Problem:

• If a user goes offline and receives a "HERE" mention at the same timestamp, processing order determines whether they're counted as online
• The sorting key event[0][2] relies on implementation details (3rd character being 'F' for OFFLINE and 'S' for MESSAGE)
• Future event types or format changes could break this logic

Solution:

def countMentions(self, numberOfUsers: int, events: List[List[str]]) -> List[int]:
    # More explicit sorting with clear priority
    def event_priority(event):
        timestamp = int(event[1])
        # Explicitly define priority: OFFLINE events process first (priority 0)
        # MESSAGE events process second (priority 1)
        priority = 0 if event[0] == "OFFLINE" else 1
        return (timestamp, priority)
  
    events.sort(key=event_priority)

2. Misunderstanding Online/Offline Status Logic

The Pitfall: The variable name online_until in the code comments is misleading. The array actually tracks when users come back online (timestamp + 60), not when they're online until.

Why It's a Problem:

• A user is considered online when online_t[i] <= current_time
• This means online_t stores the "next time they'll be online" not "online until"
• Initially all values are 0, meaning all users start online (since 0 <= any timestamp)

Solution:

def countMentions(self, numberOfUsers: int, events: List[List[str]]) -> List[int]:
    # Better variable naming and documentation
    next_online_time = [0] * numberOfUsers  # Time when user comes back online (0 = currently online)
  
    # When processing OFFLINE event:
    if event_type == "OFFLINE":
        user_id = int(data)
        next_online_time[user_id] = current_time + 60  # User offline for 60 units
  
    # When checking if user is online:
    elif data == "HERE":
        for user_id in range(numberOfUsers):
            # User is online if current time >= their next online time
            if next_online_time[user_id] <= current_time:
                mention_counts[user_id] += 1

3. Not Handling Multiple Mentions of Same User in One Message

The Pitfall: While the code correctly handles this, developers often overlook that "id0 id0 id0" should count as 3 mentions for user 0, not 1.

Why It's a Problem:

• Natural instinct might be to use a set to track unique users mentioned
• The problem explicitly states duplicates count as separate mentions

Incorrect Approach:

# WRONG: Using a set would miss duplicate mentions
mentioned_users = set()
for mention in data.split():
    user_id = int(mention[2:])
    mentioned_users.add(user_id)
for user_id in mentioned_users:
    mention_counts[user_id] += 1  # Only counts once per message

Correct Approach (as in original code):

# CORRECT: Count each mention separately
for mention in data.split():
    user_id = int(mention[2:])
    mention_counts[user_id] += 1  # Counts every occurrence