Lookahead and lookbehind in PHP - Time & Space Complexity

Time Complexity: Lookahead and lookbehind

O(n)

Understanding Time Complexity

We want to understand how the time it takes to run a PHP regex with lookahead and lookbehind changes as the input grows.

How does the pattern matching cost grow when using these special checks?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

$string = "abc123xyz456";
$pattern = '/(?<=\D)\d+(?=\D)/';
preg_match_all($pattern, $string, $matches);

// This finds numbers surrounded by non-digits.

This code uses lookbehind and lookahead to find numbers that have non-digit characters before and after them.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The regex engine scans the string character by character to check for matches.
• How many times: It checks each position in the string once, applying lookbehind and lookahead at each step.

How Execution Grows With Input

As the string gets longer, the regex engine does more checks, roughly one per character.

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

Pattern observation: The work grows roughly in direct proportion to the input size.

Final Time Complexity

Time Complexity: O(n)

This means the time to find matches grows linearly as the string gets longer.

Common Mistake

[X] Wrong: "Lookahead and lookbehind make regex run much slower, like exponentially slower."

[OK] Correct: While these checks add some work, they only look at fixed positions around each character, so the overall time still grows linearly with input size.

Interview Connect

Understanding how regex features like lookahead and lookbehind affect performance helps you write efficient pattern matching in real projects and interviews.

Self-Check

"What if the lookbehind pattern was variable length instead of fixed length? How would the time complexity change?"