095 Unique Binary Search Trees II 不同的二叉查找树 II

给出 n，问由 1...n 为节点组成的不同的二叉查找树有多少种？
例如，
给出 n = 3，则有 5 种不同形态的二叉查找树：
   1         3     3      2      1
    \       /     /      / \      \
     3     2     1      1   3      2
    /     /       \                 \
   2     1         2                 3
详见：https://leetcode.com/problems/unique-binary-search-trees-ii/description/

Java实现：

/**

 * Definition for a binary tree node.

 * public class TreeNode {

 *     int val;

 *     TreeNode left;

 *     TreeNode right;

 *     TreeNode(int x) { val = x; }

 * }

 */

class Solution {

    public List<TreeNode> generateTrees(int n) {

        if(n<1){

            return new ArrayList<TreeNode>();

        }

        return generateTrees(1,n);

    }

    private ArrayList<TreeNode> generateTrees(int left, int right){

        ArrayList<TreeNode> res = new ArrayList<TreeNode>();

        if (left > right){

            res.add(null);

            return res;

        }

        for (int i = left; i <= right; i++){

            ArrayList<TreeNode> lefts = generateTrees(left, i-1);//以i作为根节点，左子树由[1,i-1]构成

            ArrayList<TreeNode> rights = generateTrees(i+1, right);//右子树由[i+1, n]构成

            for (int j = 0; j < lefts.size(); j++){

                for (int k = 0; k < rights.size(); k++){

                    TreeNode root = new TreeNode(i);

                    root.left = lefts.get(j);

                    root.right = rights.get(k);

                    res.add(root);//存储所有可能行

                }

            }

        }

        return res;

    }

}