OAuth providers (Google, GitHub) in Supabase - Time & Space Complexity

Time Complexity: OAuth providers (Google, GitHub)

O(n)

Understanding Time Complexity

When using OAuth providers like Google or GitHub with Supabase, it's important to understand how the number of users affects the time it takes to authenticate them.

We want to know how the time to sign in grows as more users try to log in.

Scenario Under Consideration

Analyze the time complexity of signing in users using OAuth providers.

// User clicks sign-in button
const { data, error } = await supabase.auth.signInWithOAuth({
  provider: 'google', // or 'github'
  options: {
    redirectTo: 'https://yourapp.com/welcome'
  }
})
// Supabase handles redirect and token exchange
// User session is created or retrieved

This sequence shows a user signing in with an OAuth provider through Supabase.

Identify Repeating Operations

Each user sign-in triggers these operations:

• Primary operation: OAuth token exchange and user session creation via Supabase API.
• How many times: Once per user sign-in attempt.

How Execution Grows With Input

Each new user signing in causes one OAuth exchange and session setup.

Input Size (n)	Approx. API Calls/Operations
10	10 OAuth exchanges
100	100 OAuth exchanges
1000	1000 OAuth exchanges

Pattern observation: The number of operations grows directly with the number of users signing in.

Final Time Complexity

Time Complexity: O(n)

This means the time to handle sign-ins grows linearly with the number of users.

Common Mistake

[X] Wrong: "Signing in multiple users at once takes the same time as signing in one user."

[OK] Correct: Each user sign-in requires a separate OAuth exchange and session setup, so time grows with users.

Interview Connect

Understanding how user authentication scales helps you design systems that handle many users smoothly and reliably.

Self-Check

"What if we cached user sessions to avoid repeated OAuth exchanges? How would the time complexity change?"