Topic-based messaging in Firebase - Time & Space Complexity

Time Complexity: Topic-based messaging

O(n)

Understanding Time Complexity

When sending messages to many devices using topics, it is important to know how the time to send grows as more devices subscribe.

We want to understand how the number of devices affects the work done by Firebase when sending a topic message.

Scenario Under Consideration

Analyze the time complexity of the following operation sequence.

const message = {
  topic: 'news',
  notification: {
    title: 'Hello',
    body: 'World'
  }
};

admin.messaging().send(message)
  .then(response => console.log('Sent message:', response))
  .catch(error => console.error('Error sending message:', error));
    

This code sends a notification message to all devices subscribed to the 'news' topic.

Identify Repeating Operations

Identify the API calls, resource provisioning, data transfers that repeat.

• Primary operation: Sending one message to the topic via Firebase API.
• How many times: The send call is made once per message, but Firebase internally delivers to all subscribed devices.

How Execution Grows With Input

As the number of devices subscribed to the topic grows, Firebase must deliver the message to each device.

Input Size (n)	Approx. Api Calls/Operations
10	1 send call, 10 device deliveries
100	1 send call, 100 device deliveries
1000	1 send call, 1000 device deliveries

Pattern observation: The single API call triggers work that grows linearly with the number of subscribed devices.

Final Time Complexity

Time Complexity: O(n)

This means the work to deliver messages grows in direct proportion to the number of devices subscribed to the topic.

Common Mistake

[X] Wrong: "Sending one message to a topic is always a single quick operation regardless of subscribers."

[OK] Correct: Although the API call is one, Firebase must deliver the message to every subscribed device, so the total work grows with the number of devices.

Interview Connect

Understanding how message delivery scales with subscribers helps you design efficient notification systems and answer questions about system behavior under load.

Self-Check

"What if we send messages to multiple topics at once? How would the time complexity change?"

Practice

1. What is the main purpose of topic-based messaging in Firebase Cloud Messaging?

easy

A. To send messages to multiple devices subscribed to a topic

B. To send messages only to a single device

C. To store messages in a database

D. To authenticate users before sending messages

Solution

1. Step 1: Understand topic-based messaging concept

   Topic-based messaging allows grouping devices under a topic to send messages to all subscribers at once.

2. Step 2: Identify the main purpose

   The main purpose is to send messages to multiple devices subscribed to the same topic efficiently.

3. Final Answer:

   To send messages to multiple devices subscribed to a topic -> Option A

4. Quick Check:

   Topic-based messaging = send to many devices [OK]

Hint: Topic messaging targets groups, not single devices [OK]

Common Mistakes:

• Confusing topic messaging with single device messaging
• Thinking it stores messages in database
• Assuming it handles user authentication

2. Which Firebase function is used to subscribe a device to a topic?

easy

A. unsubscribeFromTopic()

B. sendToTopic()

C. getToken()

D. subscribeToTopic()

Solution

1. Step 1: Identify subscription function

   To add a device to a topic, Firebase provides the subscribeToTopic() function.

2. Step 2: Differentiate from other functions

   sendToTopic() sends messages, getToken() gets device token, unsubscribeFromTopic() removes subscription.

3. Final Answer:

   subscribeToTopic() -> Option D

4. Quick Check:

   Subscribe device = subscribeToTopic() [OK]

Hint: Subscribe uses subscribeToTopic(), not sendToTopic() [OK]

Common Mistakes:

• Confusing sendToTopic() with subscription
• Using getToken() to subscribe
• Mixing unsubscribe with subscribe

3. Given this code snippet, what will happen?

const message = {
  topic: 'news',
  notification: { title: 'Hello', body: 'World' }
};
admin.messaging().sendToTopic(message.topic, message.notification);

medium

A. A notification with title 'Hello' and body 'World' is sent to all devices subscribed to 'news'

B. An error occurs because sendToTopic requires a message object, not separate topic and notification

C. The message is sent only to one device

D. The message is stored but not sent

Solution

1. Step 1: Analyze sendToTopic usage

   The sendToTopic method expects a topic string followed by a payload object. Here, message.topic provides the string 'news' and message.notification provides the payload {title: 'Hello', body: 'World'}.

2. Step 2: Determine the outcome

   This correctly sends the notification to all devices subscribed to the 'news' topic.

3. Final Answer:

   A notification with title 'Hello' and body 'World' is sent to all devices subscribed to 'news' -> Option A

4. Quick Check:

   sendToTopic(topic, payload) sends to subscribers [OK]

Hint: sendToTopic(topic_string, payload_object) sends to topic subscribers [OK]

Common Mistakes:

• Confusing sendToTopic(topic, payload) with send(full_message_object)
• Thinking it sends only to one device
• Believing the message is stored but not sent

4. You wrote this code to send a message to a topic:

const message = {
  topic: 'sports',
  notification: { title: 'Game', body: 'Tonight at 8' }
};
admin.messaging().sendToTopic(message);

But it throws an error. What is the likely cause?

medium

A. sendToTopic expects the message object, but you passed only the topic string

B. The topic field should be inside the notification object

C. sendToTopic expects a topic string, not a message object

D. sendToTopic expects the message object, but you passed the whole object correctly

Solution

1. Step 1: Check sendToTopic parameter type

   In Firebase Admin SDK, sendToTopic expects two parameters: topic string and payload object, not a single message object.

2. Step 2: Identify mismatch

   Passing the whole message object as one argument causes an error because the function signature is different.

3. Final Answer:

   sendToTopic expects a topic string, not a message object -> Option C

4. Quick Check:

   sendToTopic(topic, payload) not sendToTopic(message) [OK]

Hint: sendToTopic needs topic string first, then payload [OK]

Common Mistakes:

• Passing message object instead of topic string
• Putting topic inside notification
• Assuming one argument is accepted

5. You want to send a message only to devices subscribed to both 'news' and 'sports' topics. How can you achieve this using Firebase topic messaging?

hard

A. Send two separate messages, one to 'news' and one to 'sports' topics

B. Use condition parameter with "'news' in topics && 'sports' in topics" in sendToTopic

C. Subscribe devices to a combined topic 'news_sports' and send to that topic

D. Send a message to 'news' topic and filter devices manually

Solution

1. Step 1: Understand topic combination options

   Firebase supports sending messages to multiple topics using conditions with logical operators.

2. Step 2: Use condition parameter for AND logic

   Using condition: "'news' in topics && 'sports' in topics" sends message only to devices subscribed to both topics.

3. Step 3: Evaluate other options

   Sending two messages sends to each topic separately, subscribing to combined topic requires extra setup, filtering manually is inefficient.

4. Final Answer:

   Use condition parameter with "'news' in topics && 'sports' in topics" in sendToTopic -> Option B

5. Quick Check:

   Use condition for multiple topic targeting [OK]

Hint: Use condition with && for multiple topic targeting [OK]

Common Mistakes:

• Sending separate messages instead of using condition
• Creating combined topic unnecessarily
• Filtering devices manually after sending