96. Unique Binary Search Trees 动态规划

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

分析：

参见leetcode上的分析Leetcode

代码：

class Solution {
public:
    int numTrees(int n) {
        vector<int>G(n+1,0);
        // for(int t=1;t<G.size();++t)
        G[0]=1;
        G[1]=1;

        for(int i=2;i<=n;++i)
        for(int j=0;j<i;++j)
        G[i]=G[i]+G[j]*G[i-j-1];
         
         return G[n];
        
    }
};