10. 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

Solution:

1. DP[i][j] means for s from (0,i-1] and p from (0, j-1) matches.
2. initialize
   1. DP[0][0] == true, and other dp[i][0] = false ----> do not need to update
   2. DP[0][j] = true when string p can be empty ----> XXXXX*
3. when p.charAt(j-1) != *
   1. if(p.charAt(j-1) == s.charAt(j-1) || p.charAt(j-1) =='.') ----> dp[i][j] = dp[i-1][j-1]
4. when p.charAt(j-1) == *
   1. when the character before * != character of s.charAt(i-1) ---> element should be treated as represent 0 times
      1. p.charAt(j-2)!=s.charAt(i-1) && p.charAt(j-2) != '.'
         1. dp[i][j] = dp[i][j-2];
   2. when the character before* == character of s.charAt(i-1) ----> element can be taken as 0 times, 1/more times
      1. dp[i][j] == dp[i][j-2] || dp[i][j-1] || dp[i-1][j]

 public boolean isMatch(String s, String p) {
        if(s == null || p == null) {
            return false;
        }
        boolean[][] state = new boolean[s.length() + 1][p.length() + 1];
        state[0][0] = true;

        for (int j = 1; j < state[0].length; j++) {
            if (p.charAt(j - 1) == '*') {
                if (state[0][j - 1] || (j > 1 && state[0][j - 2])) {
                    state[0][j] = true;
                }
            } 
        }
        for (int i = 1; i < state.length; i++) {
            for (int j = 1; j < state[0].length; j++) {
                if (s.charAt(i - 1) == p.charAt(j - 1) || p.charAt(j - 1) == '.') {
                    state[i][j] = state[i - 1][j - 1];
                }
                if (p.charAt(j - 1) == '*') {
                    if (s.charAt(i - 1) != p.charAt(j - 2) && p.charAt(j - 2) != '.') {
                        state[i][j] = state[i][j - 2];//0 element
                    } else {
                        state[i][j] = state[i - 1][j] || state[i][j - 1] || state[i][j - 2];
                    }
                }
            }
        }
        return state[s.length()][p.length()];
    }