Unique Binary Search Trees

1. Title

Unique Binary Search Trees

2.   Http address

https://leetcode.com/problems/unique-binary-search-trees/

3. The question

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

4 My code (AC)

public class UniqueBinarySearchTrees {

    public static void main(String[] args) {
        // TODO Auto-generated method stub
        System.out.println(numTrees(50));
    }
    
    // Accepted
      public static int numTrees(int n) {
          
          if ( n == 0)
              return 0;
          if ( n == 1)
              return 1;
          if ( n == 2)
              return 2;
          if ( n == 3)
               return 5;
          int sum;
          int opt[] = new int[n+1];
          opt[1] = 1;
          opt[2] = 2;        // n == 2;
          opt[3] = 5;        // n == 3;
          for( int i = 4; i <= n; i++)
          {
              // sum =  [opt(1) * opt(n-2) +   opt(3) * opt ( n-3)  ..... + opt（n-1) * opt(1)]  n = i -2;
              sum = 0;
              for( int j = 1; j <= i - 2; j++)
              {
                  sum += opt[j] * opt[i-j-1];
              }
             opt[i] = 2 * opt[i-1] + sum;
          }
          return opt[n];
        }

}