[Leetcode Series] [algorithm] different [medium] binary search tree (mathematics to solve)

topic:

Topic links:  https://leetcode-cn.com/problems/unique-binary-search-trees/

 

Problem-solving ideas:

The number of different types of binary search, in line with Cattleya number, also known as Catalan number , general term formula is:

Directly into the formula, you can obtain any of

 

Code:

class Solution:
    def numTrees(self, n: int) -> int:
        res = 1
        for i in range(n):
            res = res * 2 * (2 * i + 1) // (i + 2)
        
        return res