22. Generate Parentheses

https://leetcode.com/problems/generate-parentheses/

Problem

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

1. Naive

class Solution {
public:
    vector<string> generateParenthesis(int n) {
        if (n == 0) return vector<string>{""};
        vector<string> paren;
        for (int i = 0; i < n; ++i) {
            for (const auto &p: generateParenthesis(i)) {
                string left = "(" + p + ")";
                for (const auto &right: generateParenthesis(n - 1- i)) {
                    paren.push_back(left + right);
                }
            }
        }
        return paren;
    }
};

2. Optimized using shared variable

class Solution {
public:
    vector<string> generateParenthesis(int n) {
        static vector<vector<string>> paren{{""}};
        if (paren.size() - 1 >= n) return paren[n];
        while (paren.size() - 1 < n) {
            vector<string> par;
            int num_pairs = paren.size();
            for (int i = 0; i < num_pairs; ++i) {
                for (const auto &p: paren[i]) {
                    string left = "(" + p + ")";
                    for (const auto &right: paren[num_pairs - 1- i]) {
                        par.push_back(left + right);
                    }
                }
            }
            paren.push_back(par);
        }
        
        return paren.back();
    }
};

• #recursion

• #dp