HDU 1130 How Many Trees?

最新推荐文章于 2022-01-09 04:15:12 发布

ultimater

最新推荐文章于 2022-01-09 04:15:12 发布

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分类专栏：大数文章标签： search tree structure output import numbers

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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，还是大数，实在恶心，不想用C语言写了，这个以后当大数模板用吧。

LANGUAGE:JAVA

CODE:

import java.util.*;
import java.math.*;
public class Main{
    public static void main(String[] args) 
    {
        int n;
        Scanner in=new Scanner(System.in);
        BigInteger one=BigInteger.ONE;
        BigInteger four=new BigInteger("4");
        BigInteger two=new BigInteger("2");
        BigInteger st=null;
        BigInteger ans=null;
        while(in.hasNextInt())
        {
            n=in.nextInt();
            ans=BigInteger.ONE;
            for(int i=2;i<=n;i++)
            {
                st=new BigInteger(""+i);
                ans=ans.multiply(st.multiply(four).subtract(two)).divide(st.add(one));
            }
            System.out.println(ans);
        }
    }
}