generateCombinationsOfBraces.js

var cleverBrace = function(prefix, suffix, n, result) {
    if (n % 2 !== 0) return;
    if (n == 2) {
        var val = prefix + "()" + suffix;
        if (result.indexOf(val) === -1) {
            result.push(val);
        }
    } else if (n > 2) {
        cleverBrace(prefix + "(", ")" + suffix, n - 2, result);
        cleverBrace(prefix + "()", suffix, n - 2, result);
        cleverBrace(prefix, "()" + suffix, n - 2, result);
    }
}

//Test cases
for (var i = 2; i < 10; i += 2) {
    console.log("When n = " + i);
    var res = [];
    cleverBrace("", "", i, res);
    console.log(res.toString());
}