While loop in C++ - Time & Space Complexity

Time Complexity: While loop

O(n)

Understanding Time Complexity

We want to understand how the time a while loop takes changes when the input size changes.

Specifically, how many times does the loop run as input grows?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

int i = 0;
while (i < n) {
    // some constant time work
    i++;
}
    

This code runs a loop from 0 up to n-1, doing a small task each time.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

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

How Execution Grows With Input

As n gets bigger, the loop runs more times, growing in a straight line with n.

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

Pattern observation: If you double n, the work roughly doubles too.

Final Time Complexity

Time Complexity: O(n)

This means the time grows directly in proportion to the input size.

Common Mistake

[X] Wrong: "The while loop runs forever or a fixed number of times regardless of n."

[OK] Correct: The loop clearly depends on n and runs exactly n times, so the time changes with input size.

Interview Connect

Understanding how loops grow with input is a key skill that helps you explain code efficiency clearly and confidently.

Self-Check

"What if we changed the increment from i++ to i += 2? How would the time complexity change?"

Practice

1.

What does a while loop do in C++?

easy

A. Executes code only once

B. Repeats code a fixed number of times

C. Stops the program immediately

D. Repeats code while a condition is true

Solution

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

   A while loop runs the code inside it repeatedly as long as the condition is true.

2. Step 2: Compare options with definition

   Only Repeats code while a condition is true correctly states this behavior.

3. Final Answer:

   Repeats code while a condition is true -> Option D

4. Quick Check:

   while loop = repeat while true [OK]

Hint: While loops run as long as condition is true [OK]

Common Mistakes:

• Thinking while loops run a fixed number of times
• Confusing while with if statement
• Assuming while loops always run once

2.

Which of the following is the correct syntax for a while loop in C++?

???
{
    // code
}

easy

A. while condition

B. while {condition}

C. while (condition)

D. while: (condition)

Solution

1. Step 1: Recall correct while loop syntax

   The condition must be inside parentheses after the keyword while.

2. Step 2: Check each option

   while (condition) uses while (condition), which is correct syntax in C++.

3. Final Answer:

   while (condition) -> Option C

4. Quick Check:

   while loop syntax = while (condition) [OK]

Hint: Condition in while must be inside parentheses [OK]

Common Mistakes:

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

3.

What is the output of this C++ code?

int i = 1;
while (i <= 3) {
    std::cout << i << " ";
    i++;
}

medium

A. 1 2 3 4

B. 1 2 3

C. 0 1 2

D. 3 2 1

Solution

1. Step 1: Analyze loop condition and increments

   Variable i starts at 1 and increases by 1 each loop until i > 3.

2. Step 2: Trace output values

   i = 1 prints "1 ", then 2 prints "2 ", then 3 prints "3 ". Loop stops after i becomes 4.

3. Final Answer:

   1 2 3 -> Option B

4. Quick Check:

   Prints 1 to 3 with spaces [OK]

Hint: Count from start to condition limit inclusive [OK]

Common Mistakes:

• Printing extra number after loop ends
• Starting count from 0 instead of 1
• Printing numbers in reverse

4.

Find the error in this code snippet:

int count = 5;
while (count > 0)
    std::cout << count << " ";

medium

A. Infinite loop because count is never changed

B. Variable count is not declared

C. Syntax error in while condition

D. Missing semicolon after cout statement

Solution

1. Step 1: Check loop body and variable changes

   The loop prints count but does not change it inside the loop.

2. Step 2: Understand loop behavior

   Since count stays 5, condition is always true, causing an infinite loop.

3. Final Answer:

   Infinite loop because count is never changed -> Option A

4. Quick Check:

   Loop variable must change to avoid infinite loop [OK]

Hint: Update loop variable inside while to avoid infinite loop [OK]

Common Mistakes:

• Forgetting to change loop variable
• Assuming loop ends automatically
• Misreading syntax as error

5.

Write a while loop in C++ that prints all even numbers from 2 to 10 inclusive.

Which code snippet correctly does this?

???

hard

A. int n = 2;
while (n <= 10) {
std::cout << n << " ";
n += 2;
}

B. int n = 1;
while (n < 10) {
if (n % 2 == 0) std::cout << n << " ";
n++;
}

C. int n = 2;
while (n < 10) {
std::cout << n << " ";
n += 2;
}

D. int n = 0;
while (n <= 10) {
std::cout << n << " ";
n += 2;
}

Solution

1. Step 1: Understand the requirement

   We need to print even numbers from 2 to 10 inclusive, so numbers: 2,4,6,8,10.

2. Step 2: Check each option

   int n = 2; while (n <= 10) { std::cout << n << " "; n += 2; } starts at 2, increments by 2, and stops at 10 inclusive, printing correct numbers.

3. Final Answer:

   2 4 6 8 10 -> Option A

4. Quick Check:

   Start at 2, add 2 each time, stop at 10 [OK]

Hint: Start at 2, add 2, stop at 10 inclusive [OK]

Common Mistakes:

• Stopping before 10 (using < instead of <=)
• Starting at 1 and missing even numbers
• Including 0 which is not in range