[Leetcode 49] 22 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:

"((()))", "(()())", "(())()", "()(())", "()()()"

 

Analysis:

Also a backtracking problem. Each time either put a '(' or ')' into the current stack.

There's a optimization we can do, a well-formed parentheses must have the same number of '(' and ')', either one exceeds half of the n*2, it won't become a valid solution. So we can prune it as early as possible.

 

Code:

class Solution {
public:
    vector<string> res;
    int total;
    
    vector<string> generateParenthesis(int n) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        //res.clear();
        total = n*2;
        res.clear();
        bc("(", 1, 0);
        
        return res;
    }
    
    void bc(string path, int left, int right) {
        if (left > total/2 || right > total/2)
            return ;
        
        if (path.size()==total && valid(path)) {
            res.push_back(path);
            return ;
        }
        
        bc(path+")", left, right+1);
        bc(path+"(", left+1, right);
        return ;
    }
    
    bool valid(string s) {
        int cnt = 1;
        for (int i=1; i<s.size(); i++) {
            if (s[i] == '(') cnt++;
            if (s[i] == ')') cnt--;
            
            if (cnt < 0) return false;
        }
        
        return true;
    }
};