Operator precedence and evaluation in PHP - Time & Space Complexity

Time Complexity: Operator precedence and evaluation

O(n)

Understanding Time Complexity

When we use operators in PHP, the order they run in can affect how many steps the program takes.

We want to see how the order of operations changes the work done as input grows.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

$sum = 0;
for ($i = 0; $i < $n; $i++) {
    $sum += $i * 2 + 1;
}
echo $sum;
    

This code adds up a series of numbers calculated with operators inside a loop.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The loop runs and does addition and multiplication each time.
• How many times: The loop runs once for each number from 0 up to n-1.

How Execution Grows With Input

Each time n gets bigger, the loop runs more times, doing the same steps each time.

Input Size (n)	Approx. Operations
10	About 10 times the addition and multiplication
100	About 100 times the addition and multiplication
1000	About 1000 times the addition and multiplication

Pattern observation: The work grows directly with n; if n doubles, work doubles.

Final Time Complexity

Time Complexity: O(n)

This means the time to finish grows in a straight line as the input size grows.

Common Mistake

[X] Wrong: "Because there are multiple operators inside the loop, the time grows faster than n."

[OK] Correct: The operators run a fixed number of times per loop, so they only add a small constant amount of work each time, not extra loops.

Interview Connect

Understanding how operator order affects repeated work helps you explain code efficiency clearly and confidently.

Self-Check

"What if we added another loop inside the current loop? How would the time complexity change?"

Practice

1. In PHP, which operator has the highest precedence among these: +, *, -, /?

easy

A. All have the same precedence

B. Addition (+)

C. Subtraction (-)

D. Multiplication (*) and division (/)

Solution

1. Step 1: Recall operator precedence rules

   Multiplication (*) and division (/) have higher precedence than addition (+) and subtraction (-).

2. Step 2: Compare given operators

   Among +, -, *, /, the * and / operators are evaluated first.

3. Final Answer:

   Multiplication (*) and division (/) -> Option D

4. Quick Check:

   Higher precedence = * and / [OK]

Hint: Remember: multiply/divide before add/subtract [OK]

Common Mistakes:

• Thinking addition has higher precedence
• Assuming all operators have equal precedence
• Confusing subtraction with division precedence

2. Which of the following PHP expressions is syntactically correct and respects operator precedence?

easy

A. $result = 5 + 3 * 2;

B. $result = 5 + * 3 2;

C. $result = 5 + (3 * 2;

D. $result = 5 + 3 *;

Solution

1. Step 1: Check syntax of each expression

   $result = 5 + 3 * 2; is a valid PHP expression with correct operator placement. Options B, C, and D have syntax errors like misplaced operators or missing parentheses.

2. Step 2: Confirm operator precedence in $result = 5 + 3 * 2;

   Multiplication (*) happens before addition (+), so expression is valid and clear.

3. Final Answer:

   $result = 5 + 3 * 2; -> Option A

4. Quick Check:

   Valid syntax and precedence = $result = 5 + 3 * 2; [OK]

Hint: Check for misplaced operators and balanced parentheses [OK]

Common Mistakes:

• Leaving out parentheses
• Placing operators without operands
• Unbalanced parentheses

3. What is the output of the following PHP code?

$a = 4 + 2 * 3 - 1;

medium

A. 11

B. 17

C. 9

D. 15

Solution

1. Step 1: Apply operator precedence

   Multiplication (*) happens before addition (+) and subtraction (-). So calculate 2 * 3 = 6 first.

2. Step 2: Calculate the full expression

   Expression becomes 4 + 6 - 1 = 9. Then 4 + 6 = 10, 10 - 1 = 9.

3. Final Answer:

   9 -> Option A

4. Quick Check:

   Multiplication first, then add/subtract = 9 [OK]

Hint: Multiply before adding or subtracting [OK]

Common Mistakes:

• Adding before multiplying
• Subtracting before multiplying
• Ignoring operator precedence

4. Find the error in this PHP expression:

$result = 10 - 4 / 2 *;

medium

A. Division operator used incorrectly

B. Missing operand after the last operator

C. Subtraction operator has wrong precedence

D. Expression is correct

Solution

1. Step 1: Analyze the expression syntax

   The expression ends with an operator '*', but no operand follows it. This is a syntax error.

2. Step 2: Confirm the error type

   Operators must have operands on both sides. Missing operand after '*' causes error.

3. Final Answer:

   Missing operand after the last operator -> Option B

4. Quick Check:

   Operator must have operands both sides [OK]

Hint: Check if every operator has two operands [OK]

Common Mistakes:

• Ignoring missing operand errors
• Thinking operator precedence causes error
• Assuming expression is valid

5. Given the PHP expression:

$value = 8 + 2 * (5 - 3) / 2 - 1;

What is the correct value of $value after evaluation?

hard

A. 9

B. 10

C. 8

D. 11

Solution

1. Step 1: Evaluate parentheses first

   Calculate (5 - 3) = 2.

2. Step 2: Apply multiplication and division next

   Calculate 2 * 2 = 4, then 4 / 2 = 2.

3. Step 3: Perform addition and subtraction left to right

   Calculate 8 + 2 = 10, then 10 - 1 = 9.

4. Final Answer:

   8 -> Option C

5. Quick Check:

   Parentheses, then multiply/divide, then add/subtract = 8 [OK]

Hint: Calculate parentheses first, then multiply/divide, then add/subtract [OK]

Common Mistakes:

• Ignoring parentheses
• Doing addition before multiplication
• Dividing before multiplying inside parentheses