Generate Parentheses

generateParentheses.js

/**
 * @param {number} n
 * @return {string[]}
 */
var generateParenthesis = function(n) {
    let res = [];

    function rec(open, close, string = "") {
        if((open == close) && (open + close == 2*n)) {
            res.push(string);
            return;
        }

        if(open < n) {
            rec(open+1, close, string + "(");
        }

        if(close < open) {
            rec(open, close+1, string + ")");
        }
    }

    rec(0, 0, "");

    return res;
};

// If Open < n ----> add open parentheses
// if close < open and open < n add either open parentheses or closed parentheses
// if close < open and open ! < n add closed parentheses
// if open == close and open == close == n ------> push string into res 

// Time: O(2^n)
// Space: O(n)