Logical operators in PHP - Time & Space Complexity

Time Complexity: Logical operators

O(n)

Understanding Time Complexity

Logical operators combine true or false values to make decisions in code.

We want to see how the time to run code with logical operators changes as input grows.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

function checkConditions(array $data) {
    foreach ($data as $item) {
        if ($item > 10 && $item % 2 === 0) {
            echo "Even and greater than 10: $item\n";
        }
    }
}
    

This code checks each number in an array to see if it is even and greater than 10.

Identify Repeating Operations

• Primary operation: Looping through each item in the array.
• How many times: Once for every element in the input array.

How Execution Grows With Input

As the array gets bigger, the code checks more items one by one.

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

Pattern observation: The number of checks grows directly with the number of items.

Final Time Complexity

Time Complexity: O(n)

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

Common Mistake

[X] Wrong: "Logical operators make the code run slower exponentially."

[OK] Correct: Logical operators just combine conditions and run once per item, so they don't multiply the work by input size.

Interview Connect

Understanding how logical checks scale helps you write efficient code and explain your reasoning clearly in interviews.

Self-Check

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

Practice

1. Which logical operator in PHP returns true only if both conditions are true?

easy

A. && (AND)

B. || (OR)

C. ! (NOT)

D. xor

Solution

1. Step 1: Understand the AND operator

   The AND operator && returns true only if both conditions it connects are true.

2. Step 2: Compare with other operators

   The OR operator || returns true if at least one condition is true, NOT ! negates a condition, and xor returns true if exactly one condition is true.

3. Final Answer:

   && (AND) -> Option A

4. Quick Check:

   AND = both true [OK]

Hint: AND means both must be true to get true [OK]

Common Mistakes:

• Confusing OR (||) with AND (&&)
• Thinking NOT (!) combines two conditions
• Assuming xor behaves like AND

2. Which of the following is the correct syntax for the logical OR operator in PHP?

easy

A. !

B. &&

C. ||

D. and

Solution

1. Step 1: Identify the OR operator syntax

   In PHP, the logical OR operator is written as ||.

2. Step 2: Differentiate from other operators

   && is AND, ! is NOT, and and is a lower precedence alternative but not the common OR operator symbol.

3. Final Answer:

   || -> Option C

4. Quick Check:

   OR = || symbol [OK]

Hint: OR operator is double vertical bars || [OK]

Common Mistakes:

• Using single | instead of ||
• Confusing AND (&&) with OR (||)
• Using 'and' keyword instead of ||

3. What will be the output of the following PHP code?

$a = true;
$b = false;
if ($a && !$b) {
    echo 'Yes';
} else {
    echo 'No';
}

medium

A. No

B. Yes

C. Syntax Error

D. Nothing

Solution

1. Step 1: Evaluate the NOT operator on $b

   $b is false, so !$b becomes true.

2. Step 2: Evaluate the AND condition

   $a is true and !$b is true, so $a && !$b is true.

3. Final Answer:

   Yes -> Option B

4. Quick Check:

   true AND true = true [OK]

Hint: NOT flips false to true, AND needs both true [OK]

Common Mistakes:

• Ignoring the NOT operator effect
• Assuming false && true is true
• Confusing output strings

4. Find the error in this PHP code snippet:

$x = true;
$y = false;
if ($x || ! $y) {
    echo 'True';
 else {
    echo 'False';
}

medium

A. Missing closing brace for if block

B. Missing semicolon after echo statement

C. Incorrect use of logical OR operator

D. Missing closing parenthesis in if condition

Solution

1. Step 1: Check the if statement syntax

   The if condition has correct parentheses and logical operators.

2. Step 2: Check the braces for if-else blocks

   The if block opens with { but does not have a closing } before the else block starts.

3. Final Answer:

   Missing closing brace for if block -> Option A

4. Quick Check:

   Braces must match for if-else [OK]

Hint: Count opening and closing braces carefully [OK]

Common Mistakes:

• Assuming missing parenthesis causes error
• Thinking logical OR syntax is wrong
• Ignoring missing brace errors

5. Given the variables:

$a = false;
$b = true;
$c = false;

Which expression evaluates to true?
($a || $b) && !$c

hard

A. null

B. false

C. Syntax Error

D. true

Solution

1. Step 1: Evaluate the OR inside parentheses

   $a is false, $b is true, so $a || $b is true.

2. Step 2: Evaluate the NOT operator on $c

   $c is false, so !$c is true.

3. Step 3: Evaluate the AND between results

   true AND true equals true.

4. Final Answer:

   true -> Option D

5. Quick Check:

   (false OR true) AND NOT false = true [OK]

Hint: Evaluate inside parentheses first, then NOT, then AND [OK]

Common Mistakes:

• Ignoring operator precedence
• Misapplying NOT operator
• Assuming OR returns false if one operand is false