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




动态规划：

 

 

class Solution {
    public int numTrees(int n) {
        int[] G = new int[n+1];
        G[0] = 1;G[1] = 1;
        for(int i = 2;i <= n ;i++)
            for(int j = 1;j<= i; j++)
                G[i] +=G[j-1]*G[i-j];
        return G[n];
    }
}