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

【思路】划为一维动态规划，见http://blog.csdn.net/sunnyyoona/article/details/42177001

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 j = 1;j <= i;j++)            {                f[i] += f[j-1] * f[i-j];            }        }        return f[n];    }};