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
class Solution(object):
def _numTrees(self, n):
"""
:type n: int
:rtype: int
"""
dp = [0] * (n + 1)
dp[0] = dp[1] = 1
for i in range(2, n + 1):
for j in range(1, i + 1):
dp[i] += dp[j - 1] * dp[i - j]
return dp[-1]
def numTrees(self, n):
ans = 1
for i in range(1, n + 1):
ans = ans * (n + i) / i
return ans / (n + 1)
