Operator precedence in Javascript - Time & Space Complexity

Time Complexity: Operator precedence

O(1)

Understanding Time Complexity

When we look at operator precedence, we want to understand how the order of operations affects the steps a program takes.

We ask: how does the program decide which operation to do first, and does that change how long it takes?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

const a = 5 + 3 * 2;
const b = (5 + 3) * 2;
const c = 10 / 2 + 7;
const d = 10 / (2 + 7);

This code uses different operators with and without parentheses to show how operator precedence works.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Simple arithmetic operations (+, *, /) executed once each.
• How many times: Each operation runs only once, no loops or repeated steps.

How Execution Grows With Input

Since each operation runs once, the total steps stay the same no matter the numbers used.

Input Size (n)	Approx. Operations
10	4 operations
100	4 operations
1000	4 operations

Pattern observation: The number of operations does not grow with input size; it stays constant.

Final Time Complexity

Time Complexity: O(1)

This means the time to run these operations stays the same no matter what numbers we use.

Common Mistake

[X] Wrong: "More complex expressions always take longer to run because of operator precedence."

[OK] Correct: Operator precedence only changes the order of operations, not how many operations happen or how long they take.

Interview Connect

Understanding operator precedence helps you read and write code clearly and predict how it runs, a skill useful in many coding situations.

Self-Check

"What if we added a loop that repeats the expression 100 times? How would the time complexity change?"

Practice

1. Which operator has the highest precedence in the expression 3 + 4 * 2?

easy

A. Multiplication (*)

B. Addition (+)

C. Subtraction (-)

D. Division (/)

Solution

1. Step 1: Recall operator precedence rules

   Multiplication and division have higher precedence than addition and subtraction.

2. Step 2: Identify operators in the expression

   The expression has addition (+) and multiplication (*). Multiplication runs first.

3. Final Answer:

   Multiplication (*) -> Option A

4. Quick Check:

   Multiplication > Addition [OK]

Hint: Multiplication/division run before addition/subtraction [OK]

Common Mistakes:

• Thinking addition runs before multiplication
• Ignoring operator precedence
• Assuming left-to-right always applies

2. Which of the following expressions is syntactically correct in JavaScript?

easy

A. 5 + (3 * 2)

B. 5 + * 3

C. 5 + 3 * )2(

D. 5 + 3 * 2)

Solution

1. Step 1: Check each expression for syntax errors

   5 + * 3 has two operators in a row (+ *), which is invalid. 5 + 3 * )2( has misplaced parentheses. 5 + 3 * 2) has an unmatched closing parenthesis.

2. Step 2: Confirm correct syntax

   5 + (3 * 2) uses parentheses correctly and has valid operators and operands.

3. Final Answer:

   5 + (3 * 2) -> Option A

4. Quick Check:

   Valid parentheses and operators [OK]

Hint: Check parentheses and operator placement carefully [OK]

Common Mistakes:

• Misplacing parentheses
• Using two operators together
• Unmatched parentheses

3. What is the output of the following code?

console.log(10 - 2 * 3 + 4 / 2);

medium

A. 8

B. 12

C. 6

D. 10

Solution

1. Step 1: Apply operator precedence

   Multiplication (*) and division (/) run before addition (+) and subtraction (-). Calculate 2 * 3 = 6 and 4 / 2 = 2 first.

2. Step 2: Calculate remaining expression

   Expression becomes 10 - 6 + 2. Calculate left to right: 10 - 6 = 4, then 4 + 2 = 6.

3. Final Answer:

   6 -> Option C

4. Quick Check:

   10 - 6 + 2 = 6 [OK]

Hint: Do * and / before + and -, then left to right [OK]

Common Mistakes:

• Adding before multiplying
• Ignoring division precedence
• Calculating right to left

4. Find the error in this expression:

let result = 5 + 3 * / 2;

medium

A. No error, expression is valid

B. Incorrect use of parentheses

C. Division operator should be replaced with subtraction

D. Missing operand between * and /

Solution

1. Step 1: Analyze the operator sequence

   The expression has '* /' operators together without a number between them, which is invalid syntax.

2. Step 2: Identify the syntax error

   Every operator needs operands on both sides. Here, the '*' operator is missing its right operand before the '/' operator.

3. Final Answer:

   Missing operand between * and / -> Option D

4. Quick Check:

   Operators need operands on both sides [OK]

Hint: Operators must have numbers on both sides [OK]

Common Mistakes:

• Ignoring missing operand
• Assuming expression is valid
• Confusing operator roles

5. Given the expression let x = 4 + 3 * 2 ** 2 / (1 + 1);, what is the value of x?

hard

A. 13

B. 10

C. 11

D. 14

Solution

1. Step 1: Evaluate parentheses and exponentiation first

   Parentheses: (1 + 1) = 2. Exponentiation: 2 ** 2 = 4.

2. Step 2: Calculate multiplication and division left to right

   Expression becomes 4 + 3 * 4 / 2. Calculate 3 * 4 = 12, then 12 / 2 = 6.

3. Step 3: Perform addition

   Finally, 4 + 6 = 10.

4. Final Answer:

   10 -> Option B

5. Quick Check:

   Parentheses & exponentiation first, then * /, then + [OK]

Hint: Do parentheses, then **, then * /, then + [OK]

Common Mistakes:

• Ignoring exponentiation precedence
• Doing addition before multiplication
• Miscomputing parentheses