Topics and subscriptions in GCP - Time & Space Complexity

Time Complexity: Topics and subscriptions

O(n + m)

Understanding Time Complexity

When working with topics and subscriptions in cloud messaging, it is important to understand how the time to process messages grows as the number of messages or subscriptions increases.

We want to know how the number of operations changes when we add more messages or subscribers.

Scenario Under Consideration

Analyze the time complexity of the following operation sequence.

// Create a topic
const topic = pubsub.topic('my-topic');

// Create multiple subscriptions
for (let i = 0; i < n; i++) {
  topic.createSubscription(`sub-${i}`);
}

// Publish m messages to the topic
for (let j = 0; j < m; j++) {
  topic.publishMessage({ data: Buffer.from(`message ${j}`) });
}

This sequence creates n subscriptions to a topic and publishes m messages to it.

Identify Repeating Operations

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

• Primary operation: Creating subscriptions and publishing messages.
• How many times: Creating subscriptions happens n times; publishing messages happens m times.

How Execution Grows With Input

As the number of subscriptions (n) increases, the number of subscription creation calls grows linearly. Similarly, publishing m messages grows linearly with m.

Input Size (n subscriptions, m messages)	Approx. API Calls/Operations
10, 10	About 20 calls (10 createSubscription + 10 publish)
100, 100	About 200 calls
1000, 1000	About 2000 calls

Pattern observation: The total operations grow roughly in direct proportion to the sum of subscriptions and messages.

Final Time Complexity

Time Complexity: O(n + m)

This means the time to complete these operations grows linearly with the number of subscriptions plus the number of messages.

Common Mistake

[X] Wrong: "Publishing messages to a topic with many subscriptions takes longer for each message because it sends to all subscribers at once."

[OK] Correct: Publishing a message is a single operation; the message fan-out to subscriptions happens asynchronously and does not increase the publish call time.

Interview Connect

Understanding how operations scale with the number of subscriptions and messages helps you design efficient messaging systems and answer questions about system behavior under load.

Self-Check

"What if we batch publish messages instead of publishing one by one? How would the time complexity change?"

Practice

1. What is the main role of a topic in Google Cloud Pub/Sub?

easy

A. To authenticate users

B. To receive messages from subscribers

C. To store messages permanently

D. To send messages to subscribers

Solution

1. Step 1: Understand the role of a topic

   A topic is where messages are sent or published by a publisher.

2. Step 2: Differentiate topic from subscription

   Subscriptions receive messages from topics, not the other way around.

3. Final Answer:

   To send messages to subscribers -> Option D

4. Quick Check:

   Topic = message sender [OK]

Hint: Topics send; subscriptions receive messages [OK]

Common Mistakes:

• Confusing topic as receiver instead of sender
• Thinking topics store messages permanently
• Mixing roles of topic and subscription

2. Which of the following is the correct way to create a subscription to a topic using gcloud CLI?

easy

A. gcloud pubsub subscriptions create my-sub --topic=my-topic

B. gcloud pubsub topics create my-sub --subscription=my-topic

C. gcloud pubsub subscriptions create my-topic --topic=my-sub

D. gcloud pubsub topics create my-topic --subscription=my-sub

Solution

1. Step 1: Identify correct command syntax

   The command to create a subscription uses subscriptions create with the subscription name and --topic flag for the topic.

2. Step 2: Verify gcloud pubsub subscriptions create my-sub --topic=my-topic matches syntax

   gcloud pubsub subscriptions create my-sub --topic=my-topic correctly uses gcloud pubsub subscriptions create my-sub --topic=my-topic.

3. Final Answer:

   gcloud pubsub subscriptions create my-sub --topic=my-topic -> Option A

4. Quick Check:

   Subscriptions create with --topic flag [OK]

Hint: Subscriptions created with 'subscriptions create' and --topic [OK]

Common Mistakes:

• Using topics create instead of subscriptions create
• Swapping topic and subscription names
• Using --subscription flag instead of --topic

3. Given the following code snippet, what will be printed if the subscription receives a message?

from google.cloud import pubsub_v1

subscriber = pubsub_v1.SubscriberClient()
subscription_path = subscriber.subscription_path('my-project', 'my-sub')

def callback(message):
    print(f'Received: {message.data.decode()}')
    message.ack()

streaming_pull_future = subscriber.subscribe(subscription_path, callback=callback)
print('Listening for messages...')

medium

A. Only Listening for messages...

B. Only Received:

C. Listening for messages... followed by Received:

D. Error because callback is not called

Solution

1. Step 1: Understand code flow

   The code subscribes to a topic and sets a callback to print received messages and acknowledge them.

2. Step 2: Identify output behavior

   It prints 'Listening for messages...' immediately, then prints 'Received: ...' when a message arrives.

3. Final Answer:

   Listening for messages... followed by Received: <message content> -> Option C

4. Quick Check:

   Subscribe prints listening then message received [OK]

Hint: Callback prints message after initial listening print [OK]

Common Mistakes:

• Assuming callback runs before print
• Thinking no output until message arrives
• Ignoring message acknowledgment

4. You created a subscription but messages are not being received. Which of the following is the most likely cause?

medium

A. The subscription is not attached to the correct topic

B. The topic does not exist

C. The subscription name is too long

D. The messages are too large

Solution

1. Step 1: Check subscription-topic link

   If subscription is not linked to the right topic, it won't receive messages.

2. Step 2: Evaluate other options

   Topic existence is important but usually creation fails if topic missing; name length or message size usually cause errors, not silent no messages.

3. Final Answer:

   The subscription is not attached to the correct topic -> Option A

4. Quick Check:

   Subscription-topic mismatch blocks messages [OK]

Hint: Check subscription's topic link first if no messages [OK]

Common Mistakes:

• Ignoring subscription-topic association
• Assuming message size silently blocks delivery
• Thinking subscription name length causes no messages

5. You want to ensure that messages published to a topic are delivered to multiple independent services. Which setup should you use?

hard

A. Create multiple topics, one per service, and one subscription per topic

B. Create one topic and multiple subscriptions, one per service

C. Create one subscription and multiple topics linked to it

D. Create one topic and one subscription shared by all services

Solution

1. Step 1: Understand message fan-out

   One topic can send messages to many subscriptions, allowing multiple services to receive independently.

2. Step 2: Evaluate options

   Create one topic and multiple subscriptions, one per service uses one topic with multiple subscriptions, which is the recommended pattern for multiple independent consumers.

3. Final Answer:

   Create one topic and multiple subscriptions, one per service -> Option B

4. Quick Check:

   One topic, many subscriptions for multiple services [OK]

Hint: Use multiple subscriptions on one topic for multiple receivers [OK]

Common Mistakes:

• Creating multiple topics unnecessarily
• Using one subscription shared by all services
• Linking subscriptions to multiple topics