[leetcode 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) {
        int f[n+1];
        fill_n(&f[0], n+1, 0);
        f[0] = 1;
        for (int i = 1; i <=n; i++) {
            for (int k = 0; k < i; k++) {
                f[i] += f[k]*f[i-k-1];
            }
        }
        return f[n];
    }
};