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  • [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
    题目大意很简单,就是计算有多少个不同的二叉寻找树满足前序遍历是1,2,3...n的条件
    思路:每一棵树都是由根节点,左子树,右子树构成,一旦确定根节点是x的同时,
    左子树只能由1,2,3...x-1构成,同理右子树由x+1,x+2...n构成,可以
    [方法1]跌代求解;
    
    
    class Solution:
        # @return an integer
        def numTrees(self, n):
            dp = [1, 1, 2]
            if n < 3: return dp[n]
            dp += [0 for i in range(n-2)]
            for i in range(3, n+1):
                for j in range(i):
                    dp[i] += dp[j]*dp[i-j-1]
            return dp[n]
    [方法2]递归求解
    class Solution:
        # @return an integer
        def numTrees(self, n):
            dp = [1, 1, 2]
            if n < 3: return dp[n]
            ans = 0  
            for i in range(n):  
                ans += self.numTrees(i)*self.numTrees(n-i-1)  
            return ans
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  • 原文地址:https://www.cnblogs.com/asrman/p/4027651.html
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