正则表达式匹配

leetcode:Regular Expression Matching

Implement regular expression matching with support for ‘.’ and ‘*’.
‘.’ 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

class Solution {
public:
    bool isMatch(string s, string p) {
        /**
        * f[i][j]: if s[0..i-1] matches p[0..j-1]
        * if p[j - 1] != ‘*‘
        *      f[i][j] = f[i - 1][j - 1] && s[i - 1] == p[j - 1]
        * if p[j - 1] == ‘*‘, denote p[j - 2] with x
        *      f[i][j] is true iff any of the following is true
        *      1) "x*" repeats 0 time and matches empty: f[i][j - 2]
        *      2) "x*" repeats >= 1 times and matches "x*x": s[i - 1] == x && f[i - 1][j]
        * ‘.‘ matches any single character
        */
        int m = s.size(), n = p.size();
        vector<vector<bool>> f(m + 1, vector<bool>(n + 1, false));

        f[0][0] = true;
        for (int i = 1; i <= m; i++)
            f[i][0] = false;
        // p[0.., j - 3, j - 2, j - 1] matches empty iff p[j - 1] is ‘*‘ and p[0..j - 3] matches empty
        for (int j = 1; j <= n; j++)
            f[0][j] = j > 1 && ‘*‘ == p[j - 1] && f[0][j - 2];

        for (int i = 1; i <= m; i++)
        for (int j = 1; j <= n; j++)
        if (p[j - 1] != ‘*‘)
            f[i][j] = f[i - 1][j - 1] && (s[i - 1] == p[j - 1] || ‘.‘ == p[j - 1]);
        else
            // p[0] cannot be ‘*‘ so no need to check "j > 1" here
            f[i][j] = f[i][j - 2] || (s[i - 1] == p[j - 2] || ‘.‘ == p[j - 2]) && f[i - 1][j];

        return f[m][n];
    }
};