May 29, 2019

# 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

### Solution

``````/**
* @param {string} S
* @return {string}
* @time complexity: O(n) where n is the length of S
* @space complexity: O(n)
*/
var removeOuterParentheses = function(S) {
let bal = 0;
let res = '';

for (let i = 0; i < S.length; i++) {
if (S.charAt(i) === '(') {
if (bal !== 0) {
res += S.charAt(i);
}
bal++;
} else {
if (bal !== 1) {
res += S.charAt(i);
}
bal--;
}
}

return res;
};
``````

### Test Case

``````const assert = require('chai').assert;

describe('Remove Outermost Parentheses', () => {

it('should return \'()()()\' when \'(()())(())\' is given', () => {
assert.strictEqual(removeOuterParentheses('(()())(())'), '()()()');
});

it('should return \'()()()\' when \'(()())(())(()(()))\' is given', () => {
assert.strictEqual(removeOuterParentheses('(()())(())(()(()))'), '()()()()(())');
});

it('should return \'\' when \'()()\' is given', () => {
assert.strictEqual(removeOuterParentheses('()()'), '');
});

});
``````
``````  Remove Outermost Parentheses
✓ should return '()()()' when '(()())(())' is given
✓ should return '()()()' when '(()())(())(()(()))' is given
✓ should return '' when '()()' is given

3 passing (15ms)
``````