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

方法一：递归（超时）

 1 class Solution {
 2 public:
 3     int numTrees(int n) {
 4         int sum = 0;
 5         if(n<=1) return 1;
 6         for(int i=0;i<n;i++){
 7             sum +=numTrees(i)*numTrees(n-1-i);
 8         }
 9        return sum;
10     }
11 };

方法二：动态规划（AC）

 1 class Solution {
 2 public:
 3     int numTrees(int n) {
 4         int num[n+1];
 5         fill(num,num+n+1,0);
 6         num[0] = 1;
 7         num[1] = 1;
 8         num[2] = 2;
 9         for(int i=3; i<=n; i++){
10             for(int j=1; j<=i; j++)
11                 num[i]+=num[j-1]*num[i-j];
12            
13         }
14         return num[n];
15     }
16 };