For loop in Javascript - 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 (let i = 0; i < n; i++) {
  console.log(i);
}
    

This code prints numbers from 0 up to n-1, running the loop n times.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The loop runs and prints a number each time.
• How many times: Exactly n times, where n is the input size.

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; if n doubles, work doubles.

Final Time Complexity

Time Complexity: O(n)

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

Common Mistake

[X] Wrong: "The loop runs faster as n gets bigger because computers are fast."

[OK] Correct: Even though computers are fast, the loop still does more work when n is bigger, so it takes more time.

Interview Connect

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

Self-Check

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

Practice

1.

What does a for loop do in JavaScript?

easy

A. Changes the value of a variable once

B. Stops the program immediately

C. Repeats a block of code a set number of times

D. Creates a new variable

Solution

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

   A for loop is designed to repeat code multiple times based on a condition.

2. Step 2: Compare options with the for loop behavior

   Only Repeats a block of code a set number of times correctly describes repeating code multiple times.

3. Final Answer:

   Repeats a block of code a set number of times -> Option C

4. Quick Check:

   For loop = repeat code [OK]

Hint: For loops repeat code multiple times [OK]

Common Mistakes:

• Thinking for loop stops program
• Confusing variable creation with looping
• Assuming for loop runs only once

2.

Which of the following is the correct syntax for a basic for loop in JavaScript?

for (___; ___; ___) {
  // code
}

easy

A. for (i = 0; i < 5; i++)

B. for i = 0; i < 5; i++

C. for (i < 5; i = 0; i++)

D. for (i = 0; i++; i < 5)

Solution

1. Step 1: Recall the for loop syntax

   The correct syntax is: for (start; condition; change) { ... }

2. Step 2: Check each option against syntax

   for (i = 0; i < 5; i++) matches the correct syntax with initialization, condition, and increment.

3. Final Answer:

   for (i = 0; i < 5; i++) -> Option A

4. Quick Check:

   Syntax = for (init; cond; change) [OK]

Hint: For loop needs three parts inside parentheses [OK]

Common Mistakes:

• Missing parentheses around for loop parts
• Wrong order of parts inside for loop
• Using semicolons incorrectly

3.

What will be the output of this code?

let result = '';
for (let i = 1; i <= 3; i++) {
  result += i + ' ';
}
console.log(result.trim());

medium

A. "3 2 1"

B. "1 2 3"

C. "123"

D. "1 2 3 4"

Solution

1. Step 1: Understand the loop iterations

   The loop runs with i = 1, 2, 3 because i <= 3.

2. Step 2: Track the string concatenation

   Each iteration adds the number and a space to result: "1 ", then "1 2 ", then "1 2 3 ". trim() removes the last space.

3. Final Answer:

   "1 2 3" -> Option B

4. Quick Check:

   Loop 1 to 3 adds numbers with spaces [OK]

Hint: Check loop range and string building carefully [OK]

Common Mistakes:

• Ignoring the spaces added
• Forgetting trim() removes trailing space
• Assuming loop includes 4

4.

Find the error in this for loop code:

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

medium

A. Missing curly braces around loop body

B. Incorrect variable declaration 'let i = 0'

C. Wrong loop condition 'i < 5'

D. Missing increment operator 'i++' in the loop

Solution

1. Step 1: Check the loop increment part

   The loop has 'i' instead of 'i++' which means i never changes.

2. Step 2: Understand the effect of missing increment

   Without increment, the loop runs forever or does not progress, causing an error or infinite loop.

3. Final Answer:

   Missing increment operator 'i++' in the loop -> Option D

4. Quick Check:

   Increment needed to change loop variable [OK]

Hint: Check all three parts of for loop syntax carefully [OK]

Common Mistakes:

• Forgetting to increment loop variable
• Using wrong condition syntax
• Missing braces but allowed in single line

5.

You want to create a for loop that prints only even numbers from 2 to 10 inclusive. Which code snippet does this correctly?

hard

A. for (let i = 2; i <= 10; i += 2) { console.log(i); }

B. for (let i = 0; i <= 10; i++) { if (i % 2 === 0) console.log(i); }

C. for (let i = 2; i < 10; i++) { if (i % 2 === 0) console.log(i); }

D. for (let i = 2; i <= 10; i++) { if (i % 2 === 1) console.log(i); }

Solution

1. Step 1: Identify the range and condition for even numbers

   We want numbers 2, 4, 6, 8, 10 inclusive.

2. Step 2: Check each option for correctness

   for (let i = 2; i <= 10; i += 2) { console.log(i); } increments by 2 starting at 2, printing only even numbers up to 10. for (let i = 0; i <= 10; i++) { if (i % 2 === 0) console.log(i); } starts from 0 and prints 0 which is outside the 2-10 range. for (let i = 2; i < 10; i++) { if (i % 2 === 0) console.log(i); } misses 10 because it uses i < 10. for (let i = 2; i <= 10; i++) { if (i % 2 === 1) console.log(i); } prints odd numbers, which is wrong.

3. Final Answer:

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

4. Quick Check:

   Increment by 2 prints evens directly [OK]

Hint: Use i += 2 to skip odd numbers [OK]

Common Mistakes:

• Using wrong loop condition (i < 10)
• Printing odd numbers by mistake
• Not incrementing properly to skip odds