For loop in C - Time & Space Complexity

Time Complexity: For loop

O(n)

Understanding Time Complexity

We want to understand how the time a for loop takes changes as we increase the number of times it runs.

How does the work grow when the loop runs more times?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

for (int i = 0; i < n; i++) {
    printf("%d\n", i);
}
    

This code prints numbers from 0 up to n-1 using a for loop.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The for loop runs the print statement.
• How many times: Exactly n times, once for each number from 0 to n-1.

How Execution Grows With Input

As n grows, the number of times the loop runs grows the same way.

Input Size (n)	Approx. Operations
10	10 print operations
100	100 print operations
1000	1000 print operations

Pattern observation: The work grows directly with n. Double n, double the work.

Final Time Complexity

Time Complexity: O(n)

This means the time grows in a straight line with the number of loop runs.

Common Mistake

[X] Wrong: "The loop runs faster because it just prints numbers quickly."

[OK] Correct: The speed of printing does not change how many times the loop runs. The loop still runs n times, so time grows with n.

Interview Connect

Understanding how loops affect time helps you explain how your code scales and shows you can think about efficiency clearly.

Self-Check

"What if we added a second nested for loop inside this one? How would the time complexity change?"