Given n pairs of parentheses, write a function to generate all combinations of well-formed parentheses.

For example, given n = 3, a solution set is:

"((()))", "(()())", "(())()", "()(())", "()()()"

思路：使用遞迴方法，

      規則是:

      a. '('沒加完，就可以加'('，

      b. ')'加入需要滿足兩點：1.')'沒加完；

                            2. 剩餘'('數小於剩餘')'數，加上')'才能保證可能匹配

import java.util.ArrayList;
import java.util.List;

public class Solution {
	public List<String> generateParenthesis(int n) {
		List<String> result = new ArrayList<>();
		String s = "";
		int left = n;
		int right = n;
		generate(left, right, s, result);
		return result;
	}

	private void generate(int left, int right, String s, List<String> result) {
		if (left == 0 && right == 0) {
			result.add(s);
		}
		if (left > 0) {
			generate(left - 1, right, s + "(", result);
		}
		if (right > 0 && left < right) {
			generate(left, right - 1, s + ")", result);
		}
	}
}