96. Unique Binary Search Trees

96. Unique Binary Search Trees

https://leetcode.com/problems/unique-binary-search-trees/discuss/31666/DP-Solution-in-6-lines-with-explanation.-F(i-n)-G(i-1)-*-G(n-i)


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


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