19.2.27 [LeetCode 96] Unique Binary Search Trees

Given n, how many structurally unique BST's (binary search trees) that store values 1 ... n?

Example:

Input: 3
Output: 5
Explanation:
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

class Solution {
public:
    vector<int>q;
    int _numTrees(int n) {
        if (q[n] != -1)return q[n];
        int ans = 0;
        for (int i = 1; i <= n; i++)
            ans += _numTrees(i - 1) * _numTrees(n - i);
        q[n] = ans;
        return ans;
    }
    int numTrees(int n) {
        q=vector<int>(n+1,-1);
        q[1] = 1; q[0] = 1;
        return _numTrees(n);
    }
};

可以用dp