LeetCode-in-All
96. Unique Binary Search Trees
Medium
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
-spec num_trees(N :: integer()) -> integer().
num_trees(N) ->
Result = calculate_num_trees(N, 0, 1),
Result div (N + 1).
-spec calculate_num_trees(N :: integer(), I :: integer(), Acc :: integer()) -> integer().
calculate_num_trees(N, I, Acc) when I >= N ->
Acc;
calculate_num_trees(N, I, Acc) ->
calculate_num_trees(
N,
I + 1,
(Acc * (2 * N - I)) div (I + 1)
).