Hdu-1023 Train Problem II（卡特兰数、大数乘除模拟）

Train Problem II

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 10546    Accepted Submission(s): 5637

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

12310

 

Sample Output

12516796

Hint

The result will be very large, so you may not process it by 32-bit integers.

 

卡特兰数递推公式：  h[n]=h[n-1]*(4*n-2)/(n-1)

#include
using namespace std;
int a[101][101];
//二维数组第i行表示第i个卡特兰数,a[i][0]表示第i个卡特兰数的位数 
void ktl()
{
	int s,c,len=1;
	a[1][0]=1,a[1][1]=1,a[2][0]=1,a[2][1]=2;
	for(int i=3;i<=100;i++)
	{
		c=0;
		for(int j=1;j<=len;j++)//大数相乘 ，从最低位个位开始依次与（4*i-2）相乘 
		{
			s=a[i-1][j]*(4*i-2)+c;
			a[i][j]=s%10;
			c=s/10;
		}
		while(c)//开拓更高位 
		{
			a[i][++len]=c%10;
			c/=10;
		}
		
		for(int j=len;j>0;j--)//大数相除 ，从最高位开始依次与（i+1）相除 
		{
			s=a[i][j]+c*10;
			c=s%(i+1);
			a[i][j]=s/(i+1);
		}
		while(!a[i][len])//确定多少位 
		len--;
		a[i][0]=len;
	}
}
int main()
{
	ktl();
	int n;
	while(scanf("%d",&n)!=EOF)
	{
		for(int i=a[n][0];i>0;i--)
		cout<

Java语言，很6

import java.io.*;
import java.util.*;
import java.math.BigInteger;
public class Main
{
    public static void main(String args[])
    {
        BigInteger[] a=new BigInteger[101];
        a[0]=BigInteger.ZERO;
        a[1]=BigInteger.valueOf(1);
        for(int i=2;i<=100;++i)
            a[i]=a[i-1].multiply(BigInteger.valueOf(4*i-2)).divide(BigInteger.valueOf(i+1));
        Scanner in=new Scanner(System.in);
        int n;
        while(in.hasNext())
        {
            n=in.nextInt();
            System.out.println(a[n]);
        }
    }
}