Remove the outermost parentheses of every primitive component.

Problem Statement

A valid parentheses string is either empty `""`, `"(" + A + ")"`, or `A + B`, where `A` and `B` are valid parentheses strings, and `+` represents string concatenation. Return `s` after removing the outermost parentheses of every primitive component in the primitive decomposition of `s`.

Examples

Input: s = "(()())(())"

Output: "()()()"

Explanation: Outer parentheses of each primitive block are removed yielding "()()()".

Input: s = "(()())(())(()(()))"

Output: "()()()()(())"

Explanation: Outer parentheses of each primitive block are removed yielding "()()()()(())".

Complexity

Time Complexity: O(N)

Space Complexity: O(N)

Hints

💡 Hint 1: Track the balance of open parentheses with a counter opened. 💡 Hint 2: An opening parenthesis belongs to the inner content if opened > 0 before incrementing. 💡 Hint 3: A closing parenthesis belongs to the inner content if opened > 1 before decrementing.

Editorial & Approach

Problem Overview & Intuition

A primitive valid parenthesis string has balance > 0 inside, and returns to balance 0 only at the outermost closing parenthesis. By maintaining a balance counter opened, we filter out the outermost ( at opened = 0 and outermost ) at opened = 1.

Step-by-Step Approach

Initialize res = "" and opened = 0.
Iterate through each character c in s.
If c === "(", if opened > 0 append to res, then opened++.
If c === ")", if opened > 1 append to res, then opened--.
Return res.

Optimal Implementation (JavaScript)

function removeOuterParentheses(s) {
  let res = '', opened = 0;
  for (let c of s) {
    if (c === '(' && opened++ > 0) res += c;
    if (c === ')' && opened-- > 1) res += c;
  }
  return res;
}

Complexity Analysis

Time Complexity O(N) — single pass over the string.

Space Complexity O(N) — for the resulting string.

Edge Cases & Corner Traps Handled

Single primitive component: returns inner parentheses.
Empty inner component "()()": returns empty string "".
Deeply nested parentheses.

Remove Outermost Parentheses

Easy

Example Scenarios

1Example 1

Input: s = "(()())(())"

Output: "()()()"

Explanation:

Outer parentheses of each primitive block are removed yielding "()()()".

2Example 2

Input: s = "(()())(())(()(()))"

Output: "()()()()(())"

Explanation:

Outer parentheses of each primitive block are removed yielding "()()()()(())".

Editor

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s =

"(()())(())"

Output:Click "Run" above to execute and verify your code here.

()()()