96. Unique Binary Search Trees

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

Solution

public class Solution {
      public int numTrees(int n) {
             if (n == 1) return 1;
        int[] arr = new int[n + 1];

        arr[0] = 1;
        arr[1] = 1;
        arr[2] = 2;
        for (int i = 3; i <= n; i++) {
            for (int j = 1; j <= i; j++) {
                arr[i] += arr[j - 1] * arr[i - j];
            }
        }

        return arr[n];
    }
}