011 Regular Expression Matching.py

"""
'.' Matches any single character.
'*' Matches zero or more of the preceding element.

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

The function prototype should be:
bool isMatch(const char *s, const char *p)

Some examples:
isMatch("aa","a") -> false
isMatch("aa","aa") -> true
isMatch("aaa","aa") -> false
isMatch("aa", "a*") -> true
isMatch("aa", ".*") -> true
isMatch("ab", ".*") -> true
isMatch("aab", "c*a*b") -> true

Author : Rajeev Ranjan
"""

class Solution:
    def isMatch_error(self, s, p):
        """
        Using FSA? It is complicated to build compared to 066 Valid Number, since you have to construct the transition
        table from the pattern

        Algorithm: simple pointer

        :param s:
        :param p:
        :return: boolean
        """
        # rename
        tape = s
        regex = p

        index = 0
        state = 0
        while index < len(tape) and state < len(regex):
            char = tape[index]
            if state+1 < len(regex) and regex[state+1] == "*":
                if regex[state] != ".":
                    if char == regex[state]:  # advance tape
                        while index < len(tape) and tape[index] == char: index += 1
                        state += 2
                    else:
                        state += 2
                else:  # .*
                    state += 2
                    if state < len(regex):
                        if regex[state] != ".":  # find until the next char in regex
                            while index < len(tape) and tape[index] != regex[state]: index += 1
                        else:  # difficult part
                            count = 1

                    else:
                        return True
            else:  # no * appended
                if char == regex[state] or regex[state] == ".":
                    index += 1
                    state += 1
                else:
                    break

        if index == len(tape) and state == len(regex):
            return True
        return False


    def isMatch_TLE(self, s, p):
        """
        Algorithm: dfs, advancing the tape
        "." is not a problem
        "*" is the problem

        :param s:
        :param p:
        :return: boolean
        """
        # rename
        tape = s
        regex = p

        index = 0
        state = 0

        # dfs terminal condition
        if not tape and not regex:
            return True
        # if not s and p or s and not p:
        if tape and not regex:  # possible "", "a*"
            return False

        if not tape and regex:
            if state+1 < len(regex) and regex[state+1] == "*":
                return self.isMatch(tape, regex[state+2:])
            else:
                return False

        if state+1 < len(regex) and regex[state+1] == "*":
            if tape[index] == regex[state] or regex[state] == ".":  # consume tokens
                return self.isMatch(tape[index+1:], regex[state:]) or \
                       self.isMatch(tape[index+1:], regex[state+2:]) or \
                       self.isMatch(tape[index:], regex[state+2:])
            else:
                return self.isMatch(tape[index:], regex[state+2:])
        else:  # without trailing *
            if tape[index] == regex[state] or regex[state] == ".":
                return self.isMatch(tape[index+1:], regex[state+1:])
            else:
                return False

    def isMatch(self, s, p):
        """
        Algorithm: dfs, advancing the tape  --> dp

        dp, similar to the dfs solution
        backward dp

          . * a * a -
        b
        b
        b
        b
        a
        -

        define dp[i][j] = tape[i:] and regex[j:] are matched
        So what is the state and how is the state transferred?
        :param s:
        :param p:
        :return: boolean
        """
        # rename
        tape = s
        regex = p

        m = len(tape)
        n = len(regex)

        dp = [[False for _ in xrange(n+1)] for _ in xrange(m+1)]

        # edge cases
        dp[m][n] = True
        for j in xrange(n-1, -1, -1):
            if regex[j] == "*":
                dp[m][j] = dp[m][j+1]
            elif j+1 < n and regex[j+1] == "*":
                dp[m][j] = dp[m][j+1]
            else:
                dp[m][j] = False

        # normal cases
        for i in xrange(m-1, -1, -1):
            for j in xrange(n-1, -1, -1):
                if regex[j] == "*":
                    if j-1 >= 0 and regex[j-1] != "*":
                        dp[i][j] = dp[i][j+1]  # skip
                    else:
                        return False  # two consecutive *
                elif j+1 < n and regex[j+1] == "*":
                    if tape[i] == regex[j] or regex[j] == ".":
                        dp[i][j] = dp[i][j+2] or dp[i+1][j] or dp[i+1][j+2]  # what is done in dfs
                    else:
                        dp[i][j] = dp[i][j+2]
                else:
                    if tape[i] == regex[j] or regex[j] == ".":
                        dp[i][j] = dp[i+1][j+1]
                    else:
                        dp[i][j] = False

        # notice that in edge cases and normal cases, checking conditions are exactly the same

        return dp[0][0]


if __name__ == "__main__":
    assert Solution().isMatch("aa", "a") == False
    assert Solution().isMatch("aa", "aa") == True
    assert Solution().isMatch("aaa", "aa") == False
    assert Solution().isMatch("aa", "a*") == True
    assert Solution().isMatch("ab", ".*") == True
    assert Solution().isMatch("aab", "c*a*b") == True
    assert Solution().isMatch("aaa", "a*a") == True
    assert Solution().isMatch("bbbba", ".*a*a") == True
    assert Solution().isMatch("a", "aa*") == True