lintcode-medium-Unique Binary Search Trees

Given n, how many structurally unique BSTs (binary search trees) that store values 1...n?

 

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

public class Solution {
    /**
     * @paramn n: An integer
     * @return: An integer
     */
    public int numTrees(int n) {
        // write your code here
        
        if(n <= 1)
            return 1;
        
        int[] dp = new int[n + 1];
        dp[0] = 1;
        dp[1] = 1;
        
        for(int i = 2; i <= n; i++){
            for(int j = 1; j <= i; j++){
                dp[i] += dp[j - 1] * dp[i - j];
            }
        }
        
        
        return dp[n];
    }
}