[Leetcode 22, Medium] Generate Parentheses

Problem:

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:

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

Analysis:

Solutions:

C++:

void Generate_Aux(int left, int right, string seq, vector<string>& col_seq)
    {
        for(int i = left; i > 0;) {
            seq.push_back('(');
            --i;
            string seq_backup(seq);
            for(int j = right; j > i;) {
                seq.push_back(')');
                --j;
                if(!i && !j)
                    col_seq.push_back(seq);
                else
                    Generate_Aux(i, j, seq, col_seq);
            }
            seq = seq_backup;
        }
    }

    vector<string> generateParenthesis(int n) {
        vector<string> col_seq;
        string seq;
        Generate_Aux(n, n, seq, col_seq);
        return col_seq;
    }

Java:

Python: