Loop execution flow in Javascript - Time & Space Complexity

Time Complexity: Loop execution flow

O(n)

Understanding Time Complexity

When we run a loop in code, it repeats some steps many times. Understanding how this repetition grows helps us know how long the code might take as the input gets bigger.

We want to find out how the number of steps changes when the loop runs more times.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

function printNumbers(n) {
  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 number.

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: If you double n, the work doubles too. The growth is steady and direct.

Final Time Complexity

Time Complexity: O(n)

This means the time it takes grows directly with the size of the input n.

Common Mistake

[X] Wrong: "The loop runs faster because it just prints simple numbers."

[OK] Correct: Even simple steps inside a loop add up when repeated many times. The number of repetitions matters more than what happens inside.

Interview Connect

Understanding how loops grow with input size is a key skill. It helps you explain how your code behaves and shows you can think about efficiency clearly.

Self-Check

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

Practice

1. What does a for loop do in JavaScript?

easy

A. Stops the program immediately

B. Runs code only once

C. Creates a new variable

D. Repeats code a set number of times

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: Identify the correct description

   Among the options, only repeating code a set number of times matches the for loop behavior.

3. Final Answer:

   Repeats code a set number of times -> Option D

4. Quick Check:

   for loop = repeat fixed times [OK]

Hint: For loops repeat code a fixed number of times [OK]

Common Mistakes:

• Thinking for loops run only once
• Confusing for loops with if statements
• Believing for loops stop the program

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

easy

A. for i = 0 to 5 { }

B. for (let i = 0; i < 5; i++) { }

C. loop (i = 0; i < 5; i++) { }

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

Solution

1. Step 1: Recall JavaScript for loop syntax

   The correct syntax uses for (initialization; condition; increment) { }.

2. Step 2: Compare options to syntax

   Only for (let i = 0; i < 5; i++) { } matches the correct syntax with let i = 0; i < 5; i++.

3. Final Answer:

   for (let i = 0; i < 5; i++) { } -> Option B

4. Quick Check:

   for loop syntax = initialization; condition; increment [OK]

Hint: Remember for loop uses three parts inside parentheses [OK]

Common Mistakes:

• Using incorrect keywords like 'loop'
• Swapping initialization and condition
• Missing semicolons inside for parentheses

3. What will be the output of this code?

let sum = 0;
for (let i = 1; i <= 3; i++) {
  sum += i;
}
console.log(sum);

medium

A. 6

B. 3

C. 0

D. Error

Solution

1. Step 1: Trace the loop iterations

   The loop runs with i = 1, 2, 3. Each time, sum adds i: 0+1=1, 1+2=3, 3+3=6.

2. Step 2: Determine final sum value

   After the loop, sum is 6, which is printed by console.log.

3. Final Answer:

   6 -> Option A

4. Quick Check:

   Sum 1+2+3 = 6 [OK]

Hint: Add numbers step-by-step inside the loop [OK]

Common Mistakes:

• Stopping loop early
• Adding wrong values
• Confusing sum initialization

4. Find the error in this loop:

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

medium

A. Console.log is incorrect

B. Syntax error in for loop

C. The loop will run infinitely because i decreases

D. Variable i is not declared

Solution

1. Step 1: Analyze the loop increment/decrement

   The loop uses i--, so i decreases each time starting from 0.

2. Step 2: Check loop condition

   The condition is i < 5, which is true for all i less than 5, including negative numbers. Since i decreases, it never reaches 5 or more, so loop never ends.

3. Final Answer:

   The loop will run infinitely because i decreases -> Option C

4. Quick Check:

   Decrement with < condition causes infinite loop [OK]

Hint: Check if increment matches loop condition direction [OK]

Common Mistakes:

• Confusing i-- with i++
• Ignoring loop condition logic
• Assuming loop stops automatically

5. How many times will this loop run?

let count = 0;
let i = 10;
while (i > 0) {
  i -= 3;
  count++;
}
console.log(count);

hard

A. 4

B. 3

C. 5

D. 6

Solution

1. Step 1: Trace the while loop iterations

   Start i=10, count=0. Each loop: i decreases by 3, count increases by 1.
   Iterations:
   1) i=7, count=1
   2) i=4, count=2
   3) i=1, count=3
   4) i=-2, count=4 (loop stops after this because i > 0 is false)

2. Step 2: Count total iterations

   The loop runs 4 times before i becomes -2 and condition fails.

3. Final Answer:

   4 -> Option A

4. Quick Check:

   Subtract 3 until i ≤ 0 counts 4 times [OK]

Hint: Count how many times i decreases by 3 until ≤ 0 [OK]

Common Mistakes:

• Counting one less or more iteration
• Not updating count correctly
• Misunderstanding while loop condition