HDU How Many Trees

How Many Trees?

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)

Total Submission(s): 163 Accepted Submission(s): 102

Problem Description

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

The input will contain a number 1 <= i <= 100 per line representing the number of elements of the set.

 

Output

You have to print a line in the output for each entry with the answer to the previous question.

 

Sample Input

1
2
3

 

Sample Output

1
2
5

 

卡特兰数

 

import java.math.BigDecimal;
import java.util.*;
public class Main {
  public static void main(String[] args){
  BigDecimal []t = new BigDecimal[101];
  BigDecimal n,b;
  int k;
  Scanner cin = new Scanner(System.in);
  t[1] = BigDecimal.valueOf(1);
  for(int i = 2;i< 101;i++){
  n = BigDecimal.valueOf(i);
  b = BigDecimal.valueOf(4).multiply(n);
  b = b.subtract(BigDecimal.valueOf(2));
  n = n.add(BigDecimal.valueOf(1));
  b = b.multiply(t[i-1]);
  t[i] = b.divide(n);
  //System.out.println(t[i]);
  }
  while(cin.hasNext()){
  k = cin.nextInt();
  System.out.println(t[k]);
  }
  }
}