首页 > ACM题库 > HDU-杭电 > HDU 1134 Game of Connections-组合数学-[解题报告] java
2013
11-27

HDU 1134 Game of Connections-组合数学-[解题报告] java

Game of Connections

问题描述 :

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?

输入:

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.

输出:

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

样例输入:

2
3
-1

样例输出:

2
5

题目大意:输入一个整数n,用2n个数围成一个圆圈。然后用n条直线练成n对数(连线不能相交),求有多少种连法?

 

解题思路:大数+卡特兰数

1)

an =C(2n,n)/(n+1)=(4n-2)*(an-1 )/(n+1)


代码如下:

 

package com.njupt.acm;

import java.math.BigInteger;
import java.util.Scanner;

public class HDU_1134 {

	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);

		BigInteger one = new BigInteger("1");
		BigInteger two = new BigInteger("2");
		BigInteger four = new BigInteger("4");

		while(scanner.hasNextInt()){
			int n = scanner.nextInt();
			BigInteger catalan = one;
			BigInteger N;
			if(n == -1){
				break;
			}
			if( n == 1 ){
				System.out.println("1");
				continue;
			}

			for(int i = 1 ; i <= n ; ++i){
				N = new BigInteger(String.valueOf(i));
				catalan = catalan.multiply(four.multiply(N).subtract(two)).divide(N.add(one));
			}

			System.out.println(catalan);
		}
	}
}