su (switch user) in Linux CLI - Time & Space Complexity

Time Complexity: su (switch user)

O(n)

Understanding Time Complexity

We want to understand how the time it takes to switch users with su changes as we use it more or with different inputs.

Specifically, how does the command's execution time grow when switching users repeatedly or with different user data?

Scenario Under Consideration

Analyze the time complexity of the following command usage.

for user in user1 user2 user3 user4 user5; do
  su - $user -c 'echo Hello from $(whoami)'
done
    

This script switches to each user in a list and runs a simple command to print a greeting.

Identify Repeating Operations

Look at what repeats in the script.

• Primary operation: The su command runs once per user in the list.
• How many times: It runs exactly as many times as there are users (5 times here).

How Execution Grows With Input

Each time we add one more user to the list, the script runs su one more time.

Input Size (n)	Approx. Operations
10	10 times running su
100	100 times running su
1000	1000 times running su

Pattern observation: The total work grows directly with the number of users; doubling users doubles the work.

Final Time Complexity

Time Complexity: O(n)

This means the time to run the script grows in a straight line with the number of users you switch to.

Common Mistake

[X] Wrong: "Switching users with su takes the same time no matter how many users I switch to."

[OK] Correct: Each su command runs separately, so more users mean more commands and more total time.

Interview Connect

Understanding how repeated commands scale helps you write scripts that run efficiently and predict how long tasks will take.

Self-Check

What if we replaced the simple echo command with a longer script inside su -c? How would that affect the time complexity?