POJ 2084 Game of Connections 卡特兰数

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Game of Connections

Time Limit: 1000MS Memory Limit: 30000KTotal Submissions: 7050 Accepted: 3592

Description

This is a small but ancient game. You are supposed to write down the numbers 1, 2, 3, . . . , 2n - 1, 2n consecutively in clockwise order on the ground to form a circle, and then, to draw some straight line segments to connect them into number pairs. Every number must be connected to exactly one another. 
And, no two segments are allowed to intersect. 
It's still a simple game, isn't it? But after you've written down the 2n numbers, can you tell me in how many different ways can you connect the numbers into pairs? Life is harder, right?

Input

Each line of the input file will be a single positive number n, except the last line, which is a number -1. 
You may assume that 1 <= n <= 100.

Output

For each n, print in a single line the number of ways to connect the 2n numbers into pairs.

Sample Input

23-1

Sample Output

25

Source

Shanghai 2004 Preliminary

给你2n个数，让这些数按照顺序围成一个圈，任意两个数可以连接，但是每个数只能连接一次，且连线不能交叉，问你一共有多少种方式。

卡特兰数点击打开链接

但是要求是高精度，于是Java了。

import java.math.*;import java.util.*;public class Main {public static void main(String[] args) {Scanner cin=new Scanner(System.in);BigInteger []p=new BigInteger[107];p[0]=BigInteger.valueOf(1);p[1]=BigInteger.valueOf(1);for(int i=2;i<=100;i++){p[i]=p[i-1].multiply(BigInteger.valueOf(4*i-2)).divide(BigInteger.valueOf(i+1));}int n;while(cin.hasNext()){n=cin.nextInt();if(n==-1)break;System.out.println(p[n]);}}}