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

 1 class Solution {
 2 public:
 3     vector<int>q;
 4     int _numTrees(int n) {
 5         if (q[n] != -1)return q[n];
 6         int ans = 0;
 7         for (int i = 1; i <= n; i++)
 8             ans += _numTrees(i - 1) * _numTrees(n - i);
 9         q[n] = ans;
10         return ans;
11     }
12     int numTrees(int n) {
13         q=vector<int>(n+1,-1);
14         q[1] = 1; q[0] = 1;
15         return _numTrees(n);
16     }
17 };

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可以用dp