96. Unique Binary Search Trees

题目

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

从1到n分别作为根节点计算，采用dp方法，参考：DP Solution in 6 lines with explanation. F(i, n) = G(i-1) * G(n-i) 。

class Solution {
public:
    int numTrees(int n) {
        vector G(n+1,0);
        G[0]=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];
    }
};