# 22. Generate Parentheses

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:

[
  "((()))",
  "(()())",
  "(())()",
  "()(())",
  "()()()"
]

# Solution

Approach 1: Backtracking.

# Code (Python)

Approach 1:

# Code (C++)

Approach 1:

class Solution {
private:
    void generateParenthesis(vector<string>& strSet, string str, int open, int close) {
        if (open == 0 && close == 0)
        {
            strSet.push_back(str);
            return;
        }
        if (open > 0)
            generateParenthesis(strSet, str + "(", open - 1, close);
        if (open < close)
            generateParenthesis(strSet, str + ")", open, close - 1);
    }
public:
    vector<string> generateParenthesis(int n) {
        vector<string> strSet;
        generateParenthesis(strSet, "", n, n);
        return strSet;
    }
};