[LintCode] Generate Parentheses 生成括号

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

Have you met this question in a real interview?

Example

Given n = 3, a solution set is:

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

LeetCode上的原题，请参见我之前的博客Generate Parentheses。

解法一：

class Solution {
public:
    /**
     * @param n n pairs
     * @return All combinations of well-formed parentheses
     */
    vector<string> generateParenthesis(int n) {
        if (n == ) return {};
        vector<string> res;
        helper(n, n, "", res);
        return res;
    }
    void helper(int left, int right, string out, vector<string>& res) {
        if (left <  || right <  || left > right) return;
        if (left ==  && right == ) {
            res.push_back(out);
            return;
        }
        helper(left - , right, out + "(", res);
        helper(left, right - , out + ")", res);
    }
};

解法二：

class Solution {
public:
    /**
     * @param n n pairs
     * @return All combinations of well-formed parentheses
     */
    vector<string> generateParenthesis(int n) {
        set<string> res;
        if (n == ) {
            res.insert("");
        } else {
            vector<string> pre = generateParenthesis(n - );
            for (auto a : pre) {
                for (int i = ; i < a.size(); ++i) {
                    if (a[i] == '(') {
                        a.insert(a.begin() + i + , '(');
                        a.insert(a.begin() + i + , ')');
                        res.insert(a);
                        a.erase(a.begin() + i + , a.begin() + i + );
                    }
                }
                res.insert("()" + a);
            }
        }
        return vector<string>(res.begin(), res.end());
    }
};