[LeetCode]Valid Parenthesis String

Given a string containing only three types of characters: '(', ')' and '*', write a function to check whether this string is valid. We define the validity of a string by these rules:

1. Any left parenthesis '(' must have a corresponding right parenthesis ')'.
2. Any right parenthesis ')' must have a corresponding left parenthesis '('.
3. Left parenthesis '(' must go before the corresponding right parenthesis ')'.
4. '*' could be treated as a single right parenthesis ')' or a single left parenthesis '(' or an empty string.
5. An empty string is also valid.

Example 1:

Input: "()"
Output: True

Example 2:

Input: "(*)"
Output: True

Example 3:

Input: "(*))"
Output: True

public class Solution {
	//在不存在'*'的情況下，只要用兩個計數器就可以達到要求，現在由於還有'*' 
	public boolean checkValidString(String s) {
    		return check(s,0,0,0);
        }
	public boolean check(String s,int k,int l,int r){
		if(r>l) return false;
		if(k==s.length()){
			return l==r;
		}
		char ch=s.charAt(k);
		if(ch=='*'){
			if(check(s,k+1,l+1,r)) return true;
			if(check(s,k+1,l,r+1)) return true;
			if(check(s,k+1,l,r)) return true;
		}else {
            if(ch=='(') l++;
            else r++;
            if(check(s,k+1,l,r)) return true;
        }
		return false;
	}
}