22. 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:

[

  "((()))",

  "(()())",

  "(())()",

  "()(())",

  "()()()"

] 

做出来了 效率还行 

n parenthesis => n left + n right => 2*n positions.Each time, one left or right should be chosen.

We can always pick left.

If there are more right remained, we can put right.

public ArrayList<String> generateParenthesis(int n) { 
    ArrayList<String> results = new ArrayList<>(); 
    generateParenthesis(results, "", n, n);
    return results;
}
public void generateParenthesis(ArrayList<String> results, String prefix, int left, int right) {
    if (left == 0 && right == 0) { 
        results.add(prefix); 
        return;
    }
    if (left > 0) {
        generateParenthesis(results, prefix+"(", left-1, right); 
    }
    if (left < right) {
        generateParenthesis(results, prefix+")", left, right-1);
    } 
}