Given an integer n, return the number of structurally unique BST's (binary search trees) which has exactly n nodes of unique values from 1 to n.
Example 1:
Input: n = 3
Output: 5
Example 2:
Input: n = 1
Output: 1
Constraints:
-
1 <= n <= 19
SOLUTION:
class Solution:
def getTrees(self, beg, end):
if beg > end:
return 1
if (beg, end) in self.cache:
return self.cache[(beg, end)]
ways = 0
for i in range(beg, end + 1):
ways += self.getTrees(beg, i - 1) * self.getTrees(i + 1, end)
self.cache[(beg, end)] = ways
return ways
def numTrees(self, n: int) -> int:
self.cache = {}
return self.getTrees(1, n)
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