Unique Binary Search Trees
Created: September 16, 2018 by [lek-tin]
Last updated: September 16, 2018
Given n, how many structurally unique BST's (binary search trees) that store values 1 … n?
Example
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
Exaplanation
n = 3
root: 1 left: 0 right: 2 f(0)*f(2);
root: 2 left: 1 right: 1 f(1)*f(1);
root: 3 left: 2 right: 0 f(2)*f(0);
Solution
class Solution:
def numTrees(self, n):
"""
:type n: int
:rtype: int
"""
res = [1]
for i in range(1, n+1):
for j in range(i):
res.append(0)
res[i] += res[j] * res[i - j - 1]
return res[n]