While loop in Javascript - Time & Space Complexity

Time Complexity: While loop

O(n)

Understanding Time Complexity

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

How does the number of steps grow when the loop runs more times?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

let i = 0;
while (i < n) {
  console.log(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 repeats exactly n times, increasing i by 1 each time.

How Execution Grows With Input

Each time n grows, the loop runs more times, directly matching n.

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

Pattern observation: The number of steps grows evenly as n grows.

Final Time Complexity

Time Complexity: O(n)

This means the time grows in a straight line with the input size.

Common Mistake

[X] Wrong: "The while loop always takes the same time no matter what."

[OK] Correct: The loop runs more times when n is bigger, so it takes longer.

Interview Connect

Understanding how loops grow with input helps you explain your code clearly and shows you know how to write efficient programs.

Self-Check

"What if we increased i by 2 each time instead of 1? How would the time complexity change?"

Practice

1. What does a while loop do in JavaScript?

easy

A. Repeats code while a condition is true

B. Runs code only once

C. Runs code a fixed number of times

D. Stops the program immediately

Solution

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

   A while loop runs repeatedly as long as its condition stays true.

2. Step 2: Compare options with the definition

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

3. Final Answer:

   Repeats code while a condition is true -> Option A

4. Quick Check:

   while loop = repeats while true [OK]

Hint: Remember: while loops run only if condition is true [OK]

Common Mistakes:

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

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

easy

A. while condition { /* code */ }

B. while (condition) { /* code */ }

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

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

Solution

1. Step 1: Recall JavaScript while loop syntax

   The correct syntax uses parentheses around the condition and curly braces for the code block: while (condition) { ... }.

2. Step 2: Check each option

   while (condition) { /* code */ } matches the correct syntax exactly.

3. Final Answer:

   while (condition) { /* code */ } -> Option B

4. Quick Check:

   Correct syntax = while (condition) { } [OK]

Hint: Look for parentheses around condition and braces for code [OK]

Common Mistakes:

• Omitting parentheses around the condition
• Using a semicolon after while condition
• Adding a colon after while keyword

3. What will be the output of this code?

let count = 1;
while (count <= 3) {
  console.log(count);
  count++;
}

medium

A. 0 1 2 3

B. 1 2 3 4

C. 3 2 1

D. 1 2 3

Solution

1. Step 1: Analyze the loop condition and increments

   The loop starts with count = 1 and runs while count is less than or equal to 3. Each time, it prints count and then adds 1.

2. Step 2: Trace the output values

   It prints 1, then 2, then 3. When count becomes 4, the condition fails and loop stops.

3. Final Answer:

   1 2 3 -> Option D

4. Quick Check:

   Prints 1 to 3 inclusive [OK]

Hint: Count starts at 1 and stops after 3 [OK]

Common Mistakes:

• Including 4 in output
• Starting count at 0 instead of 1
• Printing in reverse order

4. Find the error in this code snippet:

let i = 0;
while i < 5 {
  console.log(i);
  i++;
}

medium

A. Missing semicolon after console.log

B. Variable i is not declared

C. Missing parentheses around the condition

D. Increment operator is incorrect

Solution

1. Step 1: Check while loop syntax

   JavaScript requires parentheses around the condition in a while loop.

2. Step 2: Identify the error in the code

   The code has while i < 5 { but it should be while (i < 5) {.

3. Final Answer:

   Missing parentheses around the condition -> Option C

4. Quick Check:

   while needs (condition) [OK]

Hint: Always put condition inside parentheses in while [OK]

Common Mistakes:

• Forgetting parentheses around condition
• Adding semicolon after while condition
• Misusing increment operator

5. You want to print all even numbers from 2 to 10 using a while loop. Which code correctly does this?

hard

A. let num = 2;
while (num <= 10) {
console.log(num);
num += 2;
}

B. let num = 1;
while (num < 10) {
if (num % 2 === 0) console.log(num);
num++;
}

C. let num = 2;
while (num < 10) {
console.log(num);
num += 2;
}

D. let num = 0;
while (num <= 10) {
console.log(num);
num += 2;
}

Solution

1. Step 1: Understand the goal and loop conditions

   We want to print even numbers from 2 to 10 inclusive. So the loop must start at 2 and run while number is less than or equal to 10.

2. Step 2: Check each option for correctness

   let num = 2; while (num <= 10) { console.log(num); num += 2; } starts at 2, prints number, then adds 2, stopping at 10. This prints 2,4,6,8,10 correctly. let num = 1; while (num < 10) { if (num % 2 === 0) console.log(num); num++; } starts at 1, uses modulo check, but since num < 10 stops after 9, printing 2,4,6,8 missing 10. let num = 2; while (num < 10) { console.log(num); num += 2; } stops before 10, missing 10. let num = 0; while (num <= 10) { console.log(num); num += 2; } starts at 0, which is not in the required range.

3. Final Answer:

   let num = 2; while (num <= 10) { console.log(num); num += 2; } -> Option A

4. Quick Check:

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

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

Common Mistakes:

• Starting at 0 or 1 instead of 2
• Stopping before 10
• Not incrementing by 2