Leetcode-Generate Parentheses

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:

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

Have you met this question in a real interview?

 

Analysis:

We define the subproblem as if we now have n left parenthese and m right parenthese, how to generate all legal output.

1. We can always put a left parenthese, and then solve the subproblem with n-1 and m.

2. We can put a right parenthese here only if m>n, otherwise, the output violate the mathcing rule. If we put a right parenthese, we then solve the subproblem with n and m-1.

 

Solution:

public class Solution {
    public List<String> generateParenthesis(int n) {
        List<String> resSet = new ArrayList<String>();
        if (n==0) return resSet;
        String curStr = "";
        parenthesisRecur(curStr,n,n,resSet);
        return resSet;
    }

    public void parenthesisRecur(String curStr, int n, int m, List<String> resSet){
        if (n==0 && m==0){
            resSet.add(curStr);
            return;
        }

        if (n>0){
            curStr = curStr+"(";
            parenthesisRecur(curStr,n-1,m,resSet);
            curStr = curStr.substring(0,curStr.length()-1);
        }

        if (m>n){
            curStr=curStr+")";
            parenthesisRecur(curStr,n,m-1,resSet);
            curStr = curStr.substring(0,curStr.length()-1);
        }

    }
}