Remove outermost parentheses

Time: O(N); Space: O(1); easy

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: s = “(()())(())”

Output: “()()()”

Explanation:

  • The input string is “(()())(())”, with primitive decomposition “(()())” + “(())”.

  • After removing outer parentheses of each part, this is “()()” + “()” = “()()()”.

Example 2:

Input: s = “(()())(())(()(()))”

Output: “()()()()(())”

Explanation:

  • The input string is “(()())(())(()(()))”, with primitive decomposition “(()())” + “(())” + “(()(()))”.

  • After removing outer parentheses of each part, this is “()()” + “()” + “()(())” = “()()()()(())”.

Example 3:

Input: s = “()()”

Output: “”

Explanation:

  • The input string is “()()”, with primitive decomposition “()” + “()”.

  • After removing outer parentheses of each part, this is “” + “” = “”.

Constraints:

  1. len(S) <= 10000

  2. S[i] is “(” or “)”

  3. S is a valid parentheses string

[1]:
class Solution1(object):
    def removeOuterParentheses(self, S):
        """
        :type S: str
        :rtype: str
        """
        deep = 1
        result, cnt = [], 0
        for c in S:
            if c == '(' and cnt >= deep:
                result.append(c)
            if c == ')' and cnt > deep:
                result.append(c)
            cnt += 1 if c == '(' else -1
        return "".join(result)
[2]:
sol = Solution1()
s = "(()())(())"
assert sol.removeOuterParentheses(s) == "()()()"
s = "(()())(())(()(()))"
assert sol.removeOuterParentheses(s) == "()()()()(())"
s = "()()"
assert sol.removeOuterParentheses(s) == ""