/*
 * @lc app=leetcode id=22 lang=java
 *
 * [22] Generate Parentheses
 */

// @lc code=start
class Solution {
    public List<String> generateParenthesis(int n) {
        List<String> r = new ArrayList<String>();
        dfsGenParenthesis(r, "", 0, 0, n);
        return r;
    }

    private void dfsGenParenthesis(List<String> r, String s, int i, int k, int n) {
        if(i == n && k == 0) {
            r.add(s);
            return;
        } else if(i > n) {
            return;
        }
        if(i < n) {
            String t = s + "(";
            dfsGenParenthesis(r, t, i+1, k+1, n);
        }
        if(k > 0) {
            String t = s + ")";
            dfsGenParenthesis(r, t, i, k-1, n);
        }
    }
}
// @lc code=end