[LeetCode]Unique Binary Search Trees

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


找规律。
f(0)=0
f(1)=1
f(2)=f(0)*f(1)+f(1)*f(0)
f(3)=f(0)*f(2)+f(1)*f(1)+f(2)*f(0)
递推公式就是
f(i)=Σf(i-j)*f(j-1)

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[i-j]*f[j-1];
            }
        }
        return f[n];
    }
};