LeetCode in Racket
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
(define/contract (num-trees n)
(-> exact-integer? exact-integer?)
(let loop ((i 0) (result 1))
(if (= i n)
(quotient result (+ n 1))
(loop (+ i 1)
(quotient (* result (- (* 2 n) i)) (+ i 1))))))