Leetcode 22：括号生成

//这里采用dfs算法
class Solution {
public:
    vector<string> generateParenthesis(int n) {
        vector<string> res;
        func(res, "", 0, 0, n);
        return res;
    }
    void func(vector<string> &res, string str, int l, int r, int n){
        if(l > n || r > n || r > l) return ;
        if(l == n && r == n) {res.push_back(str); return;}
        func(res, str + '(', l+1, r, n);
        func(res, str + ')', l, r+1, n);
        return;
    }
};

//利用动态规划相关知识 dp[i]中的str等于dp[j]与dp[i - j - 1]中str的组合（A)B型。其中j < i
class Solution {
public:
	vector<string> generateParenthesis(int n) {
		if (n == 0) return {};
		if (n == 1) return { "()" };
		vector<vector<string>> dp(n+1);
		dp[0] = { "" };
		dp[1] = { "()" };
		for (int i = 2; i <= n; i++) {
			for (int j = 0; j <i; j++) {
				for (string p : dp[j])
					for (string q : dp[i - j - 1]) {
						string str = "(" + p + ")" + q;
						dp[i].push_back(str);
					}
			}
		}
		return dp[n];
	}
};