LeetCode 96. Unique Binary Search Trees

Posted on | In |
Words count in article: 115 | Reading time ≈ 1

题目

Given n, how many structurally unique BST’s (binary search trees) that store values 1 … n?

Example:

1
2
3
4
5
6
7
8
9
10
Input: 3
Output: 5
Explanation:
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

思路

DP.

代码

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
class Solution(object):
    def numTrees(self, n):
        """
        :type n: int
        :rtype: int
        """
        # Catalan Number  (2n)!/((n+1)!*n!)  
        # return math.factorial(2*n)/(math.factorial(n)*math.factorial(n+1))
    
    
        dp = [0] * (n+1)
        dp[0] = 1
        for i in range(1, n+1):
            for j in range(i):
                dp[i] += dp[j] * dp[i-1-j]
        return dp[n]