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?"

Practice

1. What does a while loop do in C#?

easy

A. Stops the program immediately

B. Executes code only once regardless of condition

C. Repeats code a fixed number of times

D. Repeats a block of code as long as a condition is true

Solution

1. Step 1: Understand the purpose of a while loop

   A while loop runs repeatedly while its condition remains true.

2. Step 2: Compare with other options

   Options B, C, and D do not describe the behavior of a while loop correctly.

3. Final Answer:

   Repeats a block of code as long as a condition is true -> Option D

4. Quick Check:

   while loop = repeats while condition true [OK]

Hint: While loops run only if condition is true before each repeat [OK]

Common Mistakes:

• Thinking while loops run a fixed number of times
• Confusing while with do-while loops
• Assuming code runs at least once without checking condition

2. Which of the following is the correct syntax for a while loop in C#?

easy

A. while (condition) { /* code to repeat */ }

B. while condition { /* code to repeat */ }

C. while: (condition) { /* code to repeat */ }

D. while (condition); { /* code to repeat */ }

Solution

1. Step 1: Recall correct while loop syntax

   The correct syntax requires parentheses around the condition and braces for the code block.

2. Step 2: Identify syntax errors in other options

   A has a colon after while, B misses parentheses around the condition, D has a semicolon after the condition making the loop body empty.

3. Final Answer:

   while (condition) { /* code to repeat */ } -> Option A

4. Quick Check:

   Correct syntax = while (condition) { /* code to repeat */ } [OK]

Hint: Always use parentheses for condition and braces for loop body [OK]

Common Mistakes:

• Omitting parentheses around condition
• Adding semicolon after while condition
• Using colon instead of parentheses

3. What will be the output of this C# code?

int count = 3;
while (count > 0) {
    Console.Write(count + " ");
    count--;
}

medium

A. 0 1 2 3

B. 3 2 1

C. 3 2 1 0

D. 1 2 3

Solution

1. Step 1: Trace the loop iterations

   count starts at 3, prints 3, then decrements to 2, prints 2, then 1, prints 1, then decrements to 0 and stops.

2. Step 2: Confirm output sequence

   The printed numbers are "3 2 1 " exactly in that order.

3. Final Answer:

   3 2 1 -> Option B

4. Quick Check:

   Loop prints count down from 3 to 1 [OK]

Hint: Count down loops print from start to 1 before stopping [OK]

Common Mistakes:

• Including 0 in output
• Printing numbers in ascending order
• Forgetting to decrement count

4. Identify the error in this code snippet:

int i = 0;
while (i < 5)
    Console.Write(i);
    i++;

medium

A. Missing braces causes only Console.Write(i) to loop, i++ runs once

B. Syntax error due to missing semicolon after while

C. Infinite loop because i is never incremented

D. No error, code runs correctly

Solution

1. Step 1: Analyze loop body without braces

   Only the first statement after while loops; here, only Console.Write(i) is inside the loop.

2. Step 2: Understand effect on i++

   i++ runs once after the loop finishes, so i never increments inside the loop, causing an infinite loop if braces were not considered.

3. Final Answer:

   Missing braces causes only Console.Write(i) to loop, i++ runs once -> Option A

4. Quick Check:

   Braces needed to include i++ in loop [OK]

Hint: Use braces to include multiple statements in while loop [OK]

Common Mistakes:

• Assuming both statements are inside loop without braces
• Thinking missing semicolon after while is error
• Confusing infinite loop cause

5. You want to read user input repeatedly until they type "exit". Which while loop correctly implements this in C#?

hard

A. while (true) {
string input = Console.ReadLine();
if (input != "exit") break;
}

B. string input;
do {
input = Console.ReadLine();
} while (input != "exit");

C. string input = Console.ReadLine();
while (input != "exit") {
input = Console.ReadLine();
}

D. string input;
while (input != "exit") {
input = Console.ReadLine();
}

Solution

1. Step 1: Understand the need to read input before loop

   We must read input once before the while condition to avoid skipping the first input.

2. Step 2: Check each option's logic

   string input = Console.ReadLine(); while (input != "exit") { input = Console.ReadLine(); } uses priming read pattern correctly. string input; do { input = Console.ReadLine(); } while (input != "exit"); is do-while, not while loop. while (true) { string input = Console.ReadLine(); if (input != "exit") break; } breaks incorrectly on non-exit input, stopping too early. string input; while (input != "exit") { input = Console.ReadLine(); } uses uninitialized input, compile error.

3. Final Answer:

   string input = Console.ReadLine(); while (input != "exit") { input = Console.ReadLine(); } -> Option C

4. Quick Check:

   Read input before while, then loop while not "exit" [OK]

Hint: Read input once before while to check condition correctly [OK]

Common Mistakes:

• Not reading input before while loop
• Using do-while instead of while
• Using infinite loop with break instead of while condition