Authorization code flow in Rest API - Time & Space Complexity

Time Complexity: Authorization code flow

O(n)

Understanding Time Complexity

We want to understand how the time needed to complete the authorization code flow changes as more users or requests happen.

Specifically, how does the process scale when handling multiple authorization requests?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

POST /authorize
  - User sends request with client_id and redirect_uri
  - Server validates client and user credentials
  - Server generates authorization code

POST /token
  - Client sends authorization code
  - Server validates code and issues access token

This code snippet shows the main steps of the authorization code flow in a REST API.

Identify Repeating Operations

Look for repeated actions that affect time.

• Primary operation: Validating user and client data, and generating tokens for each request.
• How many times: Once per authorization request and once per token request.

How Execution Grows With Input

Each authorization request requires a fixed set of steps.

Input Size (n)	Approx. Operations
10 requests	About 10 sets of validation and token generation
100 requests	About 100 sets of validation and token generation
1000 requests	About 1000 sets of validation and token generation

Pattern observation: The time grows directly with the number of requests, doubling requests roughly doubles the work.

Final Time Complexity

Time Complexity: O(n)

This means the time needed grows linearly with the number of authorization requests.

Common Mistake

[X] Wrong: "The authorization code flow takes the same time no matter how many requests happen."

[OK] Correct: Each request requires separate validation and token generation, so more requests mean more work and more time.

Interview Connect

Understanding how the authorization code flow scales helps you design APIs that handle many users efficiently and reliably.

Self-Check

"What if the server cached validation results for clients? How would that affect the time complexity?"