96. Unique Binary Search Trees

Givenn, how many structurally uniqueBST's(binary search trees) that store values 1...n?

For example,
Givenn= 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

Analysis:

DP approach. a[n] = a[0]*a[n-1] + a[1]*a[n-2] + ... + a[n-1]*a[0]

Complexity:

Time: O(n^2) = n-1 + n-2 + .. + 2 = n^2

Space: O(n)

Code:

public class Solution {
    int[] arr;
    public int numTrees(int n) {
        if(n == 0)
        {
            return 0;
        }
        arr = new int[n+1];
        arr[0] = 1;
        arr[1] = 1;
        for(int i=2; i<=n; i++)
        {
            int treeNum = 0;
            for(int j=0; j<=i-1; j++)
            {
                treeNum += arr[j] * arr[i-1-j];
            }
            arr[i] = treeNum;
        }
        return arr[n];
    }
}