While loop execution model in C Sharp (C#) - Time & Space Complexity

Time Complexity: While loop execution model

O(n)

Understanding Time Complexity

We want to understand how the time a while loop takes changes as the input grows.

Specifically, how many times the loop runs affects the total work done.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

int i = 0;
while (i < n)
{
    Console.WriteLine(i);
    i++;
}
    

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

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The while loop runs and prints a number each time.
• How many times: It runs once for each number from 0 to n-1, so n times.

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 prints
100	100 prints
1000	1000 prints

Pattern observation: The work grows directly with n; doubling n doubles the work.

Final Time Complexity

Time Complexity: O(n)

This means the time taken grows in a straight line with the size of n.

Common Mistake

[X] Wrong: "The while loop runs a fixed number of times no matter what n is."

[OK] Correct: The loop runs once for each number up to n, so if n grows, the loop runs more times.

Interview Connect

Understanding how loops grow with input size helps you explain your code clearly and shows you can think about efficiency.

Self-Check

"What if we changed the loop to increase i by 2 each time? How would the time complexity change?"