LeetCode--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：动态规划。

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 k=1;k<=i;k++){
f[i]+=f[k-1]*f[i-k];
}
}
return f
;
}
};