Problem D
How Many Trees?
Input: standard input
Output: standard output
Time Limit: 100 seconds
Memory Limit: 32 MB
A binary search tree is a binary tree with root k such that any node v reachable from its left has label (v) <label (k) and any node w reachable from its right has label (w) > label (k). It is a search structure which can find a node with label x in O(n log n) average time, where n is the size of the tree (number of vertices).
Given a number n, can you tell how many different binary search trees may be constructed with a set of numbers of size n such that each element of the set will be associated to the label of exactly one node in a binary search tree?
Input
and Output
The input will contain a number 1 <= i <= 1000 per line representing the number of elements of the set. You have to print a line in the output for each entry with the answer to the previous question.
Sample
Input