Unique Binary Search Trees

Desicription

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.

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1         3     3      2      1
 \       /     /      / \      \
  3     2     1      1   3      2
 /     /       \                 \
2     1         2                 3

Solution

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class Solution {
public:
    int numTrees(int n) {
        long long res = 1;
        for(int i = n + 1; i <= 2*n; i++)
            res = res*i/(i-n);
        return res/(n+1);
    }
};