Train Problem II（卡特兰数组合数学）

佚名 6年前 (2019-04-17) 随笔 853人围观抢沙发百度已收录

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=1023

Train Problem II

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 12035 Accepted Submission(s): 6422

SRE实战互联网时代守护先锋，助力企业售后服务体系运筹帷幄！一键直达领取阿里云限量特价优惠。 Problem Description As we all know the Train Problem I, the boss of the Ignatius Train Station want to know if all the trains come in strict-increasing order, how many orders that all the trains can get out of the railway.

Input The input contains several test cases. Each test cases consists of a number N(1<=N<=100). The input is terminated by the end of file.

Output For each test case, you should output how many ways that all the trains can get out of the railway.

Sample Input 1 2 3 10

Sample Output 1 2 5 16796 Hint The result will be very large, so you may not process it by 32-bit integers.

Author Ignatius.L

Recommend We have carefully selected several similar problems for you: 1133 1022 1130 1131 1134 题目大意：问你有n辆火车，要求进站顺序是1-n 问你有多少种出站次序思路：要用到大数，所以推荐用java来写，方便很多。这题就是一个卡特兰数的板子看代码：

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

public class Main {
    
    
    
    public static void main(String args[]) {
        
        Scanner cin = new Scanner(System.in);
        
        /*
         * 卡特兰数性质:h[n]=h[n-1]*(4n-2)/(n+1)
         */
        BigInteger dp[] = new BigInteger[150];
        dp[1]=BigInteger.valueOf(1);
        for(int i=2;i<=100;i++) {
            dp[i]=dp[i-1].multiply(BigInteger.valueOf(4*i-2)).divide(BigInteger.valueOf(i+1));
        }
        
        
        while(cin.hasNext()) {
            int n=cin.nextInt();
            System.out.println(dp[n]);
        }
    }
}