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);
}
};