Unique Binary Search Trees 三种解法 python

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

递归版，也是AC

class Solution:
    @return an integer
    # 2014年10月9日，需要改为dp，这个是递归的
    def numTrees(self, n):
        if n ==1 or n ==0:
            return 1
        else:
            i=1
            sum=0
            while i<=n:
                sum =sum+self.numTrees(i-1)*self.numTrees(n-i)
                i =i+1
            return sum

dp版，当然也能AC

class Solution:
    # @return an integer
    def numTrees(self, n):
        dp = [0 for i in xrange(n+1)]
        dp[0] = 1
        for nodeNum in xrange(1, n+1):
            for leftSubNum in xrange(nodeNum):
                dp[nodeNum] += dp[leftSubNum] * dp[nodeNum - 1 - leftSubNum]
        return dp[n]

代码是抄http://chaoren.is-programmer.com/posts/42907.html的

最后是利用catalan数来求解

#卡塔兰版
class Solution:
    # @return an integer
    def numTrees(self, n):
        catalan =[1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190]
        return catalan[n]

这个时间复杂度还是o(1)呢，/窃笑