Generate Parentheses

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

答案
The idea is to prevent your backtracking algorithm from generating any invalid strings on the fly.
So then, when your algorithm generates up to n * 2 chars, it has to be valid.

···
class Solution {
public List generateParenthesis(int n) {
List list = new ArrayList<>();
if(n == 0) return list;
recur(n, 0, new StringBuilder(), list, 0, 0);
return list;
}

/*
    Rules
        cannot have more than n
*/
private void recur(int n, int i, StringBuilder curr, List list, int numl, int numr) {
    if(i == n * 2) {
        list.add(curr.toString());
        return;
    }
    
    // let ith char be left paren
    if(numl < n) {
        recur(n, i + 1, curr.append('('), list, numl + 1, numr);
        curr.deleteCharAt(curr.length() - 1);
    }
    
    // let ith char be right paren
    if(numr < numl) {
        recur(n, i + 1, curr.append(')'), list, numl, numr + 1);
        curr.deleteCharAt(curr.length() - 1);
    }
}

}
···