Variable declaration using var in Javascript - Time & Space Complexity

Time Complexity: Variable declaration using var

O(1)

Understanding Time Complexity

Let's see how declaring variables with var affects the speed of a program.

We want to know how the time to run changes when we declare variables using var.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

var a = 5;
var b = 10;
var c = a + b;
console.log(c);
    

This code declares three variables using var and prints their sum.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Variable declarations and simple arithmetic.
• How many times: Each line runs once, no loops or repeats.

How Execution Grows With Input

Since there are no loops or repeated steps, the time to run grows linearly with the number of variables we declare.

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

Pattern observation: Time grows directly with the number of variable declarations.

Final Time Complexity

Time Complexity: O(n)

This means the time grows in a straight line as you add more var declarations.

Common Mistake

[X] Wrong: "Declaring variables with var takes constant time no matter how many variables."

[OK] Correct: Each variable declaration is a separate step, so more variables mean more steps and more time.

Interview Connect

Understanding how simple statements like variable declarations affect time helps build a strong foundation for analyzing bigger code pieces.

Self-Check

"What if we replaced var with let or const? How would the time complexity change?"