输入: 3
输出: 5
解释:
给定 n = 3, 一共有 5 种不同结构的二叉搜索树:
   1         3     3      2      1
    \       /     /      / \      \
     3     2     1      1   3      2
    /     /       \                 \
   2     1         2                 3

import java.util.HashMap;
import java.util.Map;
class Solution {
        Map<Integer, Integer> map = new HashMap<>(16);
    public int numTrees(int n) {
        Integer integer = map.get(n);
        if (null != integer) {
            return integer;
        }
        if (n == 0 || n == 1) {
            return 1;
        } else if (n == 2) {
            return 2;
        } else if (n == 3) {
            return 5;
        } else {
            int max = n / 2;
            //System.out.println(max);
            int sum = 0;
            for (int i = 0; i < max; i++) {
                sum += 2 * numTrees(i) * numTrees(n - 1 - i);
            }
            if (n % 2 == 1) {
                sum += (int) Math.pow(numTrees(n / 2), 2);
            }
            map.put(n, sum);
            return sum;
        }
    }
}