Publishing messages in GCP - Time & Space Complexity

Time Complexity: Publishing messages

O(n)

Understanding Time Complexity

When sending messages to a cloud messaging service, it is important to understand how the time taken grows as we send more messages.

We want to know how the number of messages affects the total time and operations involved.

Scenario Under Consideration

Analyze the time complexity of the following operation sequence.

// Publish multiple messages to a Pub/Sub topic
for (int i = 0; i < n; i++) {
  publisher.publish(PubsubMessage.newBuilder()
    .setData(ByteString.copyFromUtf8("Message " + i))
    .build());
}
    

This code sends n messages one by one to a Pub/Sub topic.

Identify Repeating Operations

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

• Primary operation: The publish API call to send a single message.
• How many times: This call happens once for each message, so n times.

How Execution Grows With Input

Each message requires one API call, so as the number of messages grows, the total calls grow at the same rate.

Input Size (n)	Approx. API Calls/Operations
10	10 publish calls
100	100 publish calls
1000	1000 publish calls

Pattern observation: The number of API calls grows directly in proportion to the number of messages.

Final Time Complexity

Time Complexity: O(n)

This means the time to publish messages grows linearly with the number of messages sent.

Common Mistake

[X] Wrong: "Publishing multiple messages at once takes the same time as publishing one message."

[OK] Correct: Each message requires its own API call, so more messages mean more calls and more time.

Interview Connect

Understanding how message publishing scales helps you design efficient cloud systems and answer questions about performance growth confidently.

Self-Check

"What if we batch multiple messages into a single publish call? How would the time complexity change?"