[LeetCode] 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:

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

利用一个递归函数来产生，用一个参数来记录当前剩下可对应的左扩号数，只有leftNum > 0，才能加入右括号，同时增加一些剪支，例如leftNumTotal > n时说明左括号太多了，不可能产生合理解。

class Solution {
private:
    vector<string> ret;
public:
    void solve(int dep, int maxDep, int leftNum, int leftNumTotal, string s)
    {
        if (leftNumTotal * 2 > maxDep)
            return;
            
        if (dep == maxDep)
        {
            ret.push_back(s);
            return;
        }
        
        for(int i = 0; i < 2; i++)
            if (i == 0)
            {
                solve(dep + 1, maxDep, leftNum + 1, leftNumTotal + 1, s + '(');
            }
            else
            {
                if (leftNum > 0)
                    solve(dep + 1, maxDep, leftNum - 1, leftNumTotal, s + ')');
            }
    }
    
    vector<string> generateParenthesis(int n) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        ret.clear();
        solve(0, 2 * n, 0, 0, "");
        return ret;
    }
};