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：动态规划。

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];    }};