*Unique Binary Search Tree

 1 public class Solution {
 2 /*
 3 The case for 3 elements example
 4 Count[3] = Count[0]*Count[2]  (1 as root)
 5               + Count[1]*Count[1]  (2 as root)
 6               + Count[2]*Count[0]  (3 as root)
 7 
 8 Therefore, we can get the equation:
 9 Count[i] = ∑ Count[0...k] * [ k+1....i]     0<=k<i-1  
10 
11 */
12     public int numTrees(int n) {
13         int[] count = new int[n+2];
14         count[0] = 1;
15         count[1] = 1;
16         
17         for(int i=2;  i<= n; i++){
18             for(int j=0; j<i; j++){
19                 count[i] += count[j] * count[i - j - 1];
20             }
21         }
22         return count[n];
23     }
24 }