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.    1         3     3      2      1
  2.     \       /     /      / \      \
  3.      3     2     1      1   3      2
  4.     /     /       \                 \
  5.    2     1         2                 3

Solution:

  1. public class Solution {
  2.   public int numTrees(int n) {
  3.     if (n == 0)
  4.       return 0;
  6.     int[] dp = new int[n + 1];
  7.     dp[0] = 1;
  9.     for (int i = 1; i <= n; i++) {
  10.       for (int j = 1; j <= i; j++) {
  11.         dp[i] += dp[j - 1] * dp[i - j];
  12.       }
  13.     }
  15.     return dp[n];
  16.   }
  17. }