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

Solutions:

class Solution {
    public int numTrees(int n) {
        int[] count = new int[n+1];
        count[0] = 1;
        count[1] = 1;
        for (int i = 2; i <=n; i++){
            for (int j = 1; j <= i; j ++){
                count[i] += count[j-1] * count[i-j];
            }
        }
        return count[n];
    }
}

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