96. Unique Binary Search Trees

Given n, how many structurally unique BST's (binary search trees) that store values 1...n?
For example,Given n = 3, there are a total of 5 unique BST's.
1 3 3 2 1
\ / / / \
3 2 1 1 3 2
/ / \
2 1 2 3

class Solution {
public:
    int numTrees(int n) {
        vector<int> f(n+1,0);
        f[0] = 1;
        f[1] = 1;
        for(int i=2;i<=n;i++)
          for(int k=1;k<=i;k++)
          {
              f[i] += f[k-1] * f[i-k];   // f(i) = f(k-1) X f(i-k)的和，即f(i)为i-1以下的所有元素两两相乘的和
          }
        return f[n];  //主要是求出递推公式
    }
};