Unique Binary Search Trees (leetcode)

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.

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

此即为卡特兰数C(n),其值为1/(n+1) * A(2*n)/(A(n)*A(n))

class Solution:
    # @return an integer
    def f( self,n ):
        sum = 1
        i = n
        while i > 1:
            sum = sum * i
            i = i - 1
        return sum
    def numTrees(self, n):
        return self.f( 2 * n ) / ( self.f( n ) * self.f( n ) ) / ( n + 1 ) 

这是取巧使用python做的所以没有数据太大超出int或者long long 的限制