[leetcode] Unique Binary Search Trees (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

题目的意思是，给定一个节点数n，问可以组合成多少种二叉树。

这里提供两种解法，递归法 和 动态规划法

递归法：

 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

 

动态规划法：

def numTrees(self, n):
        if n ==1 or n ==0:
            return 1
        
        dp =[]
        i =1
        while i <= n+1:
            dp.append(0)
            i = i + 1
        dp[0] =1
        dp[1] =1
        
        i =2
        while i <=n:
            j =1
            sumVal =0
            while j <= i:
                sumVal = sumVal + dp[j-1]*dp[i-j]
                j =j + 1
            dp[i] =sumVal
            i = i + 1
        
        return dp[n]