[leetcode]678. Valid Parenthesis String

链接：https://leetcode.com/problems/valid-parenthesis-string/description/

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

x and y track the min and max possible number of left parenthesis as we traverse the string.

• If both the min and max fall below 0, then we have an invalid string.
• If min falls below 0 and max is above zero, set the min to 0.
• If min is zero at the end of the string, we have a valid string.

class Solution {
public:
  
    bool checkValidString(string s) {
  
      int x = 0;
      int y = 0;
      
      for (int i = 0; i < s.size(); ++i)
      {
        if (s[i] == '(')
        {
          ++x;
          ++y;
        }
        else if (s[i] == '*')
        {
          --x;
          ++y;
        }
        else
        {
          --x;
          --y;
        }
        
        if (x < 0 && y < 0)
        {
          return false;
        }
        else if (x < 0)
        {
          x = 0;
        }
      }
          
      return x == 0;
      
    }
};