Regex Matching – Finite State Machine

Given an input string (s) and a pattern (p), implement wildcard pattern matching with support for '?' and '*'.

'?' Matches any single character.
'*' Matches any sequence of characters (including the empty sequence).

The matching should cover the entire input string (not partial).


  • s could be empty and contains only lowercase letters a-z.
  • p could be empty and contains only lowercase letters a-z, and characters like ? or *.


class Solution:
    def isMatch(self, s: str, p: str) -> bool:
        :type s: str
        :type p: str
        :rtype: bool
        transfer = {}
        state = 0

        # Build a Finite State Machine(FSM)
        for char in p:
            # If pattern is *, it can stay in the current state, or move to the next state via transfer links.
            if char == '*':
                transfer[state, char] = state
            # If pattern is ? or characters, we move to the next state.
                transfer[state, char] = state + 1
                state += 1

        # the last state (Final one) is the accept state
        accept = state

        # the initial state starts from 0
        state = {0}

        for char in s:
            # There are two ways to achieve state transfer.
            # 1) We can use two rolling sets saving previous and current situations
            # 2) We also can use python syntactic sugar (Actually as same as the first method)
            # I personally think the first method is more readable.

            new_state = set()

            for token in [char, '*', '?']:
                for at in state:
                    # For each previous state, we can parallelly move to next states
                    new_state.add(transfer.get((at, token)))

            # Set the current state as the previous one
            state = new_state

            # the second method (elegant but not readable)
            # state = set([transfer.get((at, token)) for at in state for token in [char, '*', '?']])

        return accept in state

if __name__ == "__main__":
    obj = Solution()
    result = obj.isMatch("aa", "aa")