LeetCode--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

思路：動態規劃。

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];
            }
        }
        return f[n];
    }
};