96. Unique Binary Search Trees

n, how many structurally unique BST's (binary search trees) that store values 1...n?

For example,

Given n

1 3 3 2 1 \ / / / \ \ 3 2 1 1 3 2 / / \ \ 2 1 2 3

用卡特兰数的递推公式；

class Solution {
public:
  int numTrees(int n) {
    vector<int> num(n + 1, 0);
    num[0] = 1;
    num[1] = 1;
    for (int i = 2; i <= n; i++){
      for (int j = 0; j < i; j++){
        num[i] += num[j] * num[i - 1 - j];
      }
    }
    return num[n];
  }
};