A LeetCode problem requiring a custom regex matcher for the dot and asterisk characters serves as the motivation for exploring how regex engines work.
The initial linked-list implementation is not extensible enough to handle complex patterns like a real-world email validation regex.
Regular expressions can be modeled as finite automata, or state machines, which describe a set of character strings through states and transitions.
Non-deterministic Finite Automata (NFA) are more flexible for representing regex because a single input can lead to multiple possible next states.
A complex regular expression is converted into an NFA by combining smaller NFA components for concatenation, alternation, and repetition operators.
The backtracking approach, where the engine guesses a path and reverts on failure, can lead to exponential time complexity for complex patterns.
A more efficient simulation method avoids backtracking by simultaneously tracking the entire set of possible states the machine could be in at any point.
A practical implementation involves compiling the regex pattern into an NFA data structure and then iterating through the input string while tracking the current set of active states.
Production-grade regex engines often use a hybrid approach, selecting from different algorithms like NFA simulation or backtracking based on the specific pattern.
Jobs that call for the skills explored in this talk.