> For the complete documentation index, see [llms.txt](https://jaywin.gitbook.io/leetcode/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://jaywin.gitbook.io/leetcode/solutions/0096-unique-binary-search-trees.md).

# 0096. Unique Binary Search Trees

<https://leetcode.com/problems/unique-binary-search-trees>

## Description

Given an integer `n`, return \*the number of structurally unique \*\*BST'\**s (binary search trees) which has exactly* `n` *nodes of unique values from* `1` *to* `n`.

**Example 1:**

![](https://assets.leetcode.com/uploads/2021/01/18/uniquebstn3.jpg)

```
**Input:** n = 3
**Output:** 5
```

**Example 2:**

```
**Input:** n = 1
**Output:** 1
```

**Constraints:**

* `1 <= n <= 19`

## ac

```java
class Solution {
    public int numTrees(int n) {
        // edge case
        if (n <= 1) return 1;

        int[] dp = new int[n+1]; // For a number n, how many trees can be constructed.
        dp[0] = 1;

        for (int i = 1; i <= n; i++) {
            for (int j = 0; j < i; j++) { // For an n-length array, e.g. [0,1,2], iterate each element as root node.
                dp[i] += dp[j] * dp[i-j-1];
            }
        }

        return dp[n];
    }
}

/*
this dp is special, like dp + divide&conquer
similar: https://leetcode.com/problems/encode-string-with-shortest-length/description/
*/
```