Token refresh mechanism in Rest API - Time & Space Complexity

Time Complexity: Token refresh mechanism

O(n)

Understanding Time Complexity

When working with token refresh mechanisms, it's important to understand how the time to process requests grows as more users or tokens are involved.

We want to know how the system's work changes when refreshing tokens for many users.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

// Pseudocode for token refresh
POST /refresh-token
  receive refreshToken
  user = findUserByRefreshToken(refreshToken)
  if user exists and token valid:
    newAccessToken = generateAccessToken(user)
    return newAccessToken
  else:
    return error
    

This code receives a refresh token, finds the user linked to it, checks validity, and returns a new access token.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Searching for the user by refresh token.
• How many times: Once per token refresh request.

How Execution Grows With Input

As the number of users grows, finding the user by refresh token may take longer if not optimized.

Input Size (n)	Approx. Operations
10	10 lookups
100	100 lookups
1000	1000 lookups

Pattern observation: Without indexing, the search grows linearly with the number of users.

Final Time Complexity

Time Complexity: O(n)

This means the time to find the user grows in direct proportion to the number of users.

Common Mistake

[X] Wrong: "Finding a user by token always takes the same time no matter how many users exist."

[OK] Correct: If the system searches users one by one, more users mean more time. Without a fast lookup, time grows with user count.

Interview Connect

Understanding how token refresh scales helps you design APIs that stay fast as users grow. This skill shows you can think about real system performance.

Self-Check

"What if we used a hash map to store refresh tokens instead of searching a list? How would the time complexity change?"