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# Unique Binary Search Trees

 Given *n*, how many structurally unique **BST's** (binary search trees) that store values 1 ... *n*?

**Example:**

```
Input: 3
Output: 5
Explanation:
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
```

```java
class Solution {
    // when i=k is at root position
    // trees possible = nBST(k-1)*nBST(n-k)
    public int numTrees(int n) {
        if (n == 0)
            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];
    }
}
```