[LeetCode] 032: 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]

class Solution {
public:
    vector<string> generateParenthesis(int left, int right, stack<char> myStack){
        vector<string> res;
        if(left == 0 && right == 0){
            return res;
        }
        // insert '(' only
        if(myStack.empty()){
            myStack.push('(');
            vector<string> nextResult = generateParenthesis(left-1, right, myStack);
            for(int i = 0; i < nextResult.size(); ++i){
                res.push_back("(" + nextResult[i]);
            }
        }
        else{
            if(myStack.top() == '('){
                // 1. insert '('
                if(left > 0){
                    myStack.push('(');
                    vector<string> nextResult = generateParenthesis(left-1, right, myStack);
                    for(int i = 0; i < nextResult.size(); ++i){
                        res.push_back("(" + nextResult[i]);
                    }
                    
                    // remove the '(' inserted just now
                    myStack.pop();
                }
                
                // 2. insert ')'
                myStack.pop();
                if(right == 1){
                    res.push_back(")");
                }
                else{
                    vector<string> nextResult = generateParenthesis(left, right-1, myStack);
                    for(int i = 0; i < nextResult.size(); ++i){
                        res.push_back(")" + nextResult[i]);
                    }
                }
            }
        }
        return res;
    }
    vector<string> generateParenthesis(int n) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        stack<char> myStack;
        return generateParenthesis(n, n, myStack);
    }
};

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