User authentication basics in Raspberry Pi - Time & Space Complexity

Time Complexity: User authentication basics

O(n)

Understanding Time Complexity

When checking user login details, the time it takes depends on how many users we check. We want to understand how this time grows as more users are added.

How does the program's work increase when the number of users grows?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

users = ["alice", "bob", "carol", "dave"]
passwords = ["123", "abc", "xyz", "pass"]

input_user = "bob"
input_pass = "abc"

for i in range(len(users)):
    if users[i] == input_user and passwords[i] == input_pass:
        print("Access granted")
        break
else:
    print("Access denied")
    

This code checks if the entered username and password match any stored user data by going through the list one by one.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Looping through the list of users and passwords to compare each entry.
• How many times: Up to once for each user in the list, until a match is found or the list ends.

How Execution Grows With Input

As the number of users grows, the program may need to check more entries before finding a match or giving up.

Input Size (n)	Approx. Operations
10	Up to 10 checks
100	Up to 100 checks
1000	Up to 1000 checks

Pattern observation: The number of checks grows directly with the number of users. More users mean more work.

Final Time Complexity

Time Complexity: O(n)

This means the time to check login grows in a straight line with the number of users. Double the users, double the checks.

Common Mistake

[X] Wrong: "The program always checks all users no matter what."

[OK] Correct: The loop stops as soon as it finds a matching user and password, so it may check fewer users.

Interview Connect

Understanding how checking user data grows with more users helps you explain how programs handle bigger data smoothly. This skill shows you can think about program speed and efficiency.

Self-Check

"What if we stored users in a special way that lets us find them instantly? How would the time complexity change?"

Practice

1. What is the main purpose of user authentication on a Raspberry Pi?

easy

A. To speed up the Raspberry Pi's processing power

B. To verify the identity of a user before allowing access

C. To install new software automatically

D. To connect to the internet faster

Solution

1. Step 1: Understand user authentication

   User authentication is about checking who you are before access is granted.

2. Step 2: Identify the correct purpose

   Only To verify the identity of a user before allowing access describes verifying identity before access, which matches authentication.

3. Final Answer:

   To verify the identity of a user before allowing access -> Option B

4. Quick Check:

   User authentication = verify identity [OK]

Hint: Authentication means checking who you are [OK]

Common Mistakes:

• Confusing authentication with performance or internet speed
• Thinking authentication installs software
• Mixing authentication with network connection

2. Which of the following is the correct way to check a username and password in Python on Raspberry Pi?

easy

A. if username = 'pi' and password = 'raspberry':

B. if username = 'pi' or password = 'raspberry':

C. if username == 'pi' and password == 'raspberry':

D. if username == 'pi' or password == 'raspberry':

Solution

1. Step 1: Identify correct comparison operator

   In Python, '==' checks equality; '=' assigns values.

2. Step 2: Check logical operators for authentication

   Both username and password must match, so use 'and' not 'or'.

3. Final Answer:

   if username == 'pi' and password == 'raspberry': -> Option C

4. Quick Check:

   Use '==' and 'and' for correct check [OK]

Hint: Use '==' to compare and 'and' to require both true [OK]

Common Mistakes:

• Using '=' instead of '==' for comparison
• Using 'or' instead of 'and' to check both credentials
• Mixing assignment and comparison operators

3. What will be the output of this Python code on Raspberry Pi?

username = 'pi'
password = 'raspberry'
input_user = 'pi'
input_pass = 'wrongpass'

if input_user == username and input_pass == password:
    print('Access granted')
else:
    print('Access denied')

medium

A. Access granted

B. SyntaxError

C. No output

D. Access denied

Solution

1. Step 1: Compare input username and password

   input_user matches username 'pi', but input_pass is 'wrongpass', not 'raspberry'.

2. Step 2: Evaluate the if condition

   Since password check fails, condition is false, so else block runs.

3. Final Answer:

   Access denied -> Option D

4. Quick Check:

   Password mismatch means access denied [OK]

Hint: Both username and password must match exactly [OK]

Common Mistakes:

• Assuming partial match grants access
• Confusing syntax error with logic error
• Ignoring else block output

4. Find the error in this Raspberry Pi Python authentication code:

username = 'pi'
password = 'raspberry'
input_user = input('Enter username: ')
input_pass = input('Enter password: ')

if input_user = username and input_pass = password:
    print('Access granted')
else:
    print('Access denied')

medium

A. Using '=' instead of '==' in if condition

B. Missing colon ':' after if statement

C. input() function is used incorrectly

D. Print statements are missing parentheses

Solution

1. Step 1: Check the if condition syntax

   The code uses '=' which assigns values, but '==' is needed to compare values.

2. Step 2: Verify other syntax parts

   Colons are present, input() usage is correct, and print() has parentheses.

3. Final Answer:

   Using '=' instead of '==' in if condition -> Option A

4. Quick Check:

   Use '==' to compare, not '=' [OK]

Hint: Use '==' for comparison, '=' is assignment [OK]

Common Mistakes:

• Confusing assignment '=' with comparison '=='
• Forgetting colon after if statement
• Misusing input() or print() syntax

5. You want to improve a Raspberry Pi login program to lock the user out after 3 failed attempts. Which approach is best?

hard

A. Use a counter variable to track failed attempts and stop after 3

B. Change the password automatically after 3 tries

C. Print 'Access granted' even if password is wrong 3 times

D. Restart the Raspberry Pi after each failed attempt

Solution

1. Step 1: Understand the goal of locking out after 3 failures

   We need to count failed tries and stop allowing login after 3.

2. Step 2: Evaluate options for implementing this

   Using a counter variable to track attempts is the correct and simple method.

3. Final Answer:

   Use a counter variable to track failed attempts and stop after 3 -> Option A

4. Quick Check:

   Counting attempts controls login lockout [OK]

Hint: Count failed tries with a variable to limit attempts [OK]

Common Mistakes:

• Changing password automatically without user consent
• Allowing access despite wrong passwords
• Restarting device unnecessarily on failure