22. Generate Parentheses

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22. Generate Parentheses

Description

Given n pairs of parentheses, write a function to generate all combinations of well-formed parentheses.

Example 1:

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Input: n = 3
Output: ["((()))","(()())","(())()","()(())","()()()"]

Example 2:

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Input: n = 1
Output: ["()"]

Constraints:

  • 1 <= n <= 8

Hints/Notes

Solution

Language: C++

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class Solution {
public:
    int n;
    vector<string> res;
    string path;

    vector<string> generateParenthesis(int n) {
        if (!n) {
            return {};
        }
        this->n = n;
        path = string(n * 2, 0);
        dfs(0, 0);
        return res;
    }

    void dfs(int left, int right) {
        if (left == n && right == n) {
            res.push_back(path);
            return;
        }
        int index = left + right;
        if (left < n) {
            path[index] = '(';
            dfs(left + 1, right);
        }
        if (right < left) {
            path[index] = ')';
            dfs(left, right + 1);
        }
    }
};