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];
    }
};