lintcode:不同的二叉查詢樹
阿新 • • 發佈:2019-01-28
卡特蘭數
其前幾項為 : 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, …
class Solution:
# @paramn n: An integer
# @return: An integer
def numTrees(self, n) :
# write your code here
if n == 0 or n == 1:
return 1
return self.comb(2*n, n)/(n + 1)
# 階乘
def factorial(self, n):
a = 1
for i in range(1, n + 1):
a = a * i
return a
# 組合
def comb(self, downnum, upnum):
fenzi = self.factorial(downnum)
fenmu_1 = self.factorial(upnum)
fenmu_2 = self.factorial(downnum - upnum)
return fenzi/(fenmu_1 * fenmu_2)