22 Generate Parentheses (生成括号)

Given n pairs of parentheses, write a function to generate all combinations of well-formed parentheses.（给定n对括号，编写一个函数来生成格式正确的括号的所有组合。）

For example, given n = 3, a solution set is:

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

1. 递归方法解决

class Solution {
public:
    void generateParenthesisDFS(int left, int right, string out, vector &vec) {
        if (left > right) return;
        if (left == 0 && right == 0) vec.push_back(out);
        else {
            if (left > 0) generateParenthesisDFS(left - 1, right, out + "(", vec);
            if (right > 0) generateParenthesisDFS(left, right - 1, out + ")", vec);
        }
    }
    
    vector generateParenthesis(int n) {
        vector vec;
        generateParenthesisDFS(n, n, "", vec);
        return vec;
    }
};

2. 另一种巧妙方法

class Solution {
public:
    vector generateParenthesis(int n) {
        set t;
        if (n == 0) t.insert("");
        else {
            vector pre = generateParenthesis(n - 1);
            for (auto a : pre) {
                for (int i = 0; i < a.size(); ++i) {
                    if (a[i] == '(') {
                        a.insert(a.begin() + i + 1, '(');
                        a.insert(a.begin() + i + 2, ')');
                        t.insert(a);
                        a.erase(a.begin() + i + 1, a.begin() + i + 3);
                    }
                }
                t.insert("()" + a);
            }
        }
        return vector(t.begin(), t.end());
    }
};

参考链接：

1. https://leetcode.com/problems/generate-parentheses/description/
2. http://www.cnblogs.com/grandyang/p/4444160.html