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:

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

题意是给出n对括号，计算出其所有可能的组合。同样的与上题一样画出树形解法，求解有以下几个原则：

• 现有左括号，才能有右括号
• 可以插入右括号“)”的前提是'('的数量大于‘)’
  -括号总数不超过n

void back_tracting(vector<string> &result, int left, int right,string &tmp_result){
    if(left==0&right==0){
        result.push_back(tmp_result);
        return;
    }
    if(left>0){
        tmp_result += '(';
        back_tracting(result,left-1,right,tmp_result);
        tmp_result.pop_back();
    }

    if(right>left){
        tmp_result+=')';
        back_tracting(result,left,right-1,tmp_result);
        tmp_result.pop_back();
    }
}

通过pop_back回到上一个回溯点

代码：
https://github.com/HCMY/UnCategoticalableAlgorithm/blob/master/Leetcode/BackTrack/Medium/GenerateParentheses.cc