[POJ] 2084 -> Game of Connections

Game of Connections

Time Limit: 1000MS Memory Limit: 30000KTotal Submissions: 7709 Accepted: 3891

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

解题思路：卡特兰数的应用 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, ...有递归式 h(n)=((4*n-2)/(n+1))*h(n-1);

Code:

import java.math.BigInteger;import java.util.Scanner;public class Main {static BigInteger fun(int n){if(n==0 || n==1) return new BigInteger("1");return fun(n-1).multiply(new BigInteger(String.format("%d", 4*n-2))).divide(new BigInteger(String.format("%d", n + 1)));}public static void main(String[] args){Scanner cin=new Scanner(System.in);while(cin.hasNext()){int n = cin.nextInt();if(n == -1) break;System.out.println(fun(n));}}}