Password reset flow in Firebase - Time & Space Complexity

Time Complexity: Password reset flow

O(n)

Understanding Time Complexity

When users reset their passwords using Firebase, the system makes calls to send reset emails and verify tokens.

We want to understand how the number of these calls grows as more users request password resets.

Scenario Under Consideration

Analyze the time complexity of the following operation sequence.

const auth = getAuth();

function sendPasswordReset(email) {
  return sendPasswordResetEmail(auth, email);
}

// Later, user clicks link and token is verified
function verifyResetCode(code) {
  return verifyPasswordResetCode(auth, code);
}

This sequence sends a password reset email and then verifies the reset code when the user clicks the link.

Identify Repeating Operations

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

• Primary operation: Sending password reset emails via sendPasswordResetEmail.
• How many times: Once per user request for password reset.
• Secondary operation: Verifying reset codes via verifyPasswordResetCode, once per user clicking the reset link.

How Execution Grows With Input

Each password reset request triggers one email send operation.

Input Size (n)	Approx. Api Calls/Operations
10	10 email sends
100	100 email sends
1000	1000 email sends

Pattern observation: The number of email sends grows directly with the number of reset requests.

Final Time Complexity

Time Complexity: O(n)

This means the time and resources needed grow in direct proportion to the number of password reset requests.

Common Mistake

[X] Wrong: "Sending one password reset email handles multiple users at once, so time stays the same regardless of requests."

[OK] Correct: Each user needs their own reset email, so the system must send one email per request, increasing work as requests grow.

Interview Connect

Understanding how user-triggered operations scale helps you design systems that handle growth smoothly and predict resource needs.

Self-Check

"What if the system batched password reset emails to send them all at once? How would the time complexity change?"

Practice

1. What does the Firebase function sendPasswordResetEmail do?

easy

A. Sends an email to the user to reset their password

B. Changes the user's password immediately

C. Deletes the user's account

D. Creates a new user account

Solution

1. Step 1: Understand the function purpose

   The function sendPasswordResetEmail is designed to send an email to the user with a link to reset their password.

2. Step 2: Differentiate from other actions

   This function does not change the password directly or affect the account status; it only initiates the reset process by sending an email.

3. Final Answer:

   Sends an email to the user to reset their password -> Option A

4. Quick Check:

   sendPasswordResetEmail = Sends reset email [OK]

Hint: Remember: sendPasswordResetEmail only sends the reset link [OK]

Common Mistakes:

• Thinking it changes the password immediately
• Confusing it with account deletion
• Assuming it creates a new user

2. Which of the following is the correct syntax to send a password reset email in Firebase using JavaScript?

easy

A. firebase.auth().sendPasswordResetEmail(email)

B. firebase.auth.sendPasswordResetEmail(email)

C. firebase.auth().sendPasswordReset(email)

D. firebase.auth().resetPasswordEmail(email)

Solution

1. Step 1: Recall the correct Firebase method

   The correct method to send a password reset email is sendPasswordResetEmail called on the auth object.

2. Step 2: Check method call syntax

   The auth object is accessed by firebase.auth(), so the full call is firebase.auth().sendPasswordResetEmail(email).

3. Final Answer:

   firebase.auth().sendPasswordResetEmail(email) -> Option A

4. Quick Check:

   Correct method call syntax = firebase.auth().sendPasswordResetEmail(email) [OK]

Hint: Remember auth() must be called as a function before methods [OK]

Common Mistakes:

• Omitting parentheses after auth
• Using wrong method names like sendPasswordReset
• Swapping method words order

3. Consider this code snippet:

firebase.auth().sendPasswordResetEmail('[e-mail]')
  .then(() => console.log('Email sent'))
  .catch(error => console.log(error.message));

What will be printed if the email is successfully sent?

medium

A. Error message

B. Nothing

C. undefined

D. Email sent

Solution

1. Step 1: Analyze the promise resolution

   The sendPasswordResetEmail returns a promise that resolves when the email is sent successfully.

2. Step 2: Check the then and catch handlers

   On success, the then callback logs 'Email sent'. On failure, the catch logs the error message.

3. Final Answer:

   Email sent -> Option D

4. Quick Check:

   Success logs 'Email sent' [OK]

Hint: Success triggers then(), failure triggers catch() [OK]

Common Mistakes:

• Confusing catch output with success
• Expecting no output on success
• Misreading promise behavior

4. You wrote this code but the password reset email never arrives:

firebase.auth.sendPasswordResetEmail('[e-mail]')

What is the likely error?

medium

A. Email address is invalid

B. Missing parentheses after auth()

C. sendPasswordResetEmail is not a Firebase method

D. No internet connection

Solution

1. Step 1: Check method call syntax

   The code calls firebase.auth.sendPasswordResetEmail without parentheses after auth, which is incorrect.

2. Step 2: Understand correct usage

   The correct call is firebase.auth().sendPasswordResetEmail(email) because auth is a function that returns the auth object.

3. Final Answer:

   Missing parentheses after auth() -> Option B

4. Quick Check:

   auth() must be called as a function [OK]

Hint: Always call auth() with parentheses before methods [OK]

Common Mistakes:

• Omitting parentheses after auth
• Assuming method names are wrong
• Ignoring syntax errors

5. You want to implement a password reset flow that shows a success message only if the email was sent, and an error message otherwise. Which code snippet correctly achieves this?

hard

A. firebase.auth().sendPasswordResetEmail(email)
.then(() => alert('Failed to send email'))
.catch(() => alert('Reset email sent'))

B. firebase.auth().sendPasswordResetEmail(email)
.catch(() => alert('Reset email sent'))
.then(() => alert('Failed to send email'))

C. firebase.auth().sendPasswordResetEmail(email)
.then(() => alert('Reset email sent'))
.catch(() => alert('Failed to send email'))

D. firebase.auth().sendPasswordResetEmail(email)
.finally(() => alert('Reset email sent'))

Solution

1. Step 1: Understand promise handlers order

   The then handler runs on success, and catch runs on failure.

2. Step 2: Match messages to handlers

   Success should show 'Reset email sent', failure should show 'Failed to send email'. Only firebase.auth().sendPasswordResetEmail(email) .then(() => alert('Reset email sent')) .catch(() => alert('Failed to send email')) matches this logic correctly.

3. Final Answer:

   firebase.auth().sendPasswordResetEmail(email) .then(() => alert('Reset email sent')) .catch(() => alert('Failed to send email')) -> Option C

4. Quick Check:

   then() = success, catch() = error [OK]

Hint: Use then() for success, catch() for errors [OK]

Common Mistakes:

• Swapping then and catch handlers
• Using finally for success message
• Showing error message on success