![https://leetcode.com/problems/remove-outermost-parentheses/]

A valid parentheses string is either empty (""), “(” + A + “)”, or A + B, where A and B are valid parentheses strings, and + represents string concatenation. For example, “”, “()”, “(())()”, and “(()(()))” are all valid parentheses strings.

A valid parentheses string S is primitive if it is nonempty, and there does not exist a way to split it into S = A+B, with A and B nonempty valid parentheses strings.

Given a valid parentheses string S, consider its primitive decomposition: S = P_1 + P_2 + … + P_k, where P_i are primitive valid parentheses strings.

Return S after removing the outermost parentheses of every primitive string in the primitive decomposition of S.

Example 1:

Input: "(()())(())"
Output: "()()()"
Explanation: 
The input string is "(()())(())", with primitive decomposition "(()())" + "(())".
After removing outer parentheses of each part, this is "()()" + "()" = "()()()".

Example 2:

Input: "(()())(())(()(()))"
Output: "()()()()(())"
Explanation: 
The input string is "(()())(())(()(()))", with primitive decomposition "(()())" + "(())" + "(()(()))".
After removing outer parentheses of each part, this is "()()" + "()" + "()(())" = "()()()()(())".

Example 3:

Input: "()()"
Output: ""
Explanation: 
The input string is "()()", with primitive decomposition "()" + "()".
After removing outer parentheses of each part, this is "" + "" = "".

Note:

  • S.length <= 10000
  • S[i] is “(” or “)”
  • S is a valid parentheses string
class Solution {
    public String removeOuterParentheses(String S) {
        StringBuilder sb = new StringBuilder();
        int opened = 0;
        for (char c : S.toCharArray()) {
            if (c == '(') {
                // skip first opened
                if (opened != 0) {
                    sb.append(c);
                }
                opened++;
            } else {
                opened--;
                // skip last closed
                if (opened != 0) {
                     sb.append(c);
                }
            }
        }
        return sb.toString();
    }
}