Variable declaration using let in Javascript - Time & Space Complexity

Time Complexity: Variable declaration using let

O(n)

Understanding Time Complexity

Let's see how declaring variables with let affects the time it takes for code to run.

We want to know if using let changes how long the program takes as it grows.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

for (let i = 0; i < n; i++) {
  let x = i * 2;
  console.log(x);
}
    

This code runs a loop from 0 to n-1, declares a variable x each time, and prints it.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The for loop runs n times.
• How many times: Variable x is declared and assigned inside the loop each time, so n times.

How Execution Grows With Input

As n grows, the loop runs more times, doing the same steps each time.

Input Size (n)	Approx. Operations
10	About 10 times the loop runs and declares x.
100	About 100 times the loop runs and declares x.
1000	About 1000 times the loop runs and declares x.

Pattern observation: The work grows directly with n. Double n, double the work.

Final Time Complexity

Time Complexity: O(n)

This means the time to run grows in a straight line with the number of times the loop runs.

Common Mistake

[X] Wrong: "Declaring a variable with let inside a loop makes the code slower in a way that changes the time complexity."

[OK] Correct: Declaring let inside the loop happens each time, but it only adds a small fixed step per loop. It doesn't change how the total time grows with n.

Interview Connect

Understanding how variable declarations inside loops affect time helps you explain code efficiency clearly and confidently.

Self-Check

"What if we moved the let x declaration outside the loop? How would the time complexity change?"

Practice

1. What does the let keyword do in JavaScript?

easy

A. Declares a constant variable that cannot change

B. Declares a variable that can change value and has block scope

C. Declares a variable with global scope only

D. Declares a function

Solution

1. Step 1: Understand let behavior

   let declares variables that can be reassigned new values.

2. Step 2: Understand scope of let

   Variables declared with let are limited to the block they are declared in (block scope).

3. Final Answer:

   Declares a variable that can change value and has block scope -> Option B

4. Quick Check:

   let = variable with block scope [OK]

Hint: Remember: let = changeable variable inside blocks [OK]

Common Mistakes:

• Confusing let with const (constant)
• Thinking let variables have global scope
• Mixing let with function declarations

2. Which of the following is the correct syntax to declare a variable named score using let?

easy

A. let = score 10;

B. let score: 10;

C. score let = 10;

D. let score = 10;

Solution

1. Step 1: Recall correct variable declaration syntax

   The correct syntax is: let variableName = value;

2. Step 2: Match syntax with options

   let score = 10; matches the correct syntax exactly.

3. Final Answer:

   let score = 10; -> Option D

4. Quick Check:

   Correct syntax = let score = 10; [OK]

Hint: Use: let variableName = value; [OK]

Common Mistakes:

• Placing let after variable name
• Using colon instead of equal sign
• Missing semicolon (though optional)

3. What will be the output of this code?

let x = 5;
x = 10;
console.log(x);

medium

A. 10

B. Error

C. undefined

D. 5

Solution

1. Step 1: Understand variable assignment and reassignment

   Variable x is first set to 5, then changed to 10.

2. Step 2: Check console.log output

   Since x was reassigned to 10, console.log(x) prints 10.

3. Final Answer:

   10 -> Option A

4. Quick Check:

   Reassigned let variable prints new value [OK]

Hint: let variables can change value, so print latest [OK]

Common Mistakes:

• Thinking let variables cannot be reassigned
• Expecting original value to print
• Confusing with const behavior

4. Find the error in this code:

if (true) {
  let message = "Hello";
}
console.log(message);

medium

A. ReferenceError: message is not defined

B. SyntaxError: Unexpected token

C. No error, prints Hello

D. TypeError: message is undefined

Solution

1. Step 1: Understand block scope of let

   Variable message is declared inside the if block and only exists there.

2. Step 2: Check console.log outside block

   Trying to access message outside the block causes a ReferenceError.

3. Final Answer:

   ReferenceError: message is not defined -> Option A

4. Quick Check:

   let variables have block scope, so error outside block [OK]

Hint: let variables only exist inside their block [OK]

Common Mistakes:

• Assuming let variables are global
• Confusing ReferenceError with SyntaxError
• Trying to access block variables outside

5. Consider this code:

let total = 0;
for (let i = 0; i < 3; i++) {
  let total = i * 2;
}
console.log(total);

What will be printed and why?

hard

A. 6, because total sums all i*2 values

B. 4, because total accumulates inside the loop

C. 0, because the outer total is unchanged by inner block

D. ReferenceError, total is redeclared

Solution

1. Step 1: Identify variable scopes

   There are two total variables: one outside the loop and one declared inside the loop block.

2. Step 2: Understand variable shadowing

   The inner total inside the loop is a new variable that does not affect the outer total.

3. Step 3: Check final console.log

   The outer total remains 0, so console.log(total) prints 0.

4. Final Answer:

   0, because the outer total is unchanged by inner block -> Option C

5. Quick Check:

   Inner let shadows outer variable, outer stays 0 [OK]

Hint: Inner let creates new variable, outer stays same [OK]

Common Mistakes:

• Thinking inner total changes outer total
• Assuming let variables are global
• Confusing variable shadowing with reassignment