[LeetCode]Unique Binary Search Trees

题目描述:(链接)

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

解题思路:

http://blog.csdn.net/jiadebin890724/article/details/23305915

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[n];
    }
};