Train Problem II

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 2830    Accepted Submission(s): 1562

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       简单的卡特兰数问题。 卡特兰数介绍：
http://www.cnblogs.com/kuangbin/archive/2012/03/21/2410516.html   这个已经可以做为模版了~~~

//ｈ( n ) = ( ( 4*n-2 )/( n+1 )*h( n-1 ) );


#include<stdio.h>

//*******************************
//打表卡特兰数
//第 n个 卡特兰数存在a[n]中，a[n][0]表示长度；
//注意数是倒着存的，个位是 a[n][1] 输出时注意倒过来。 
//*********************************
int a[105][100];
void ktl()
{
    int i,j,yu,len;
    a[2][0]=1;
    a[2][1]=2;
    a[1][0]=1;
    a[1][1]=1;
    len=1;
    for(i=3;i<101;i++)
    {
        yu=0;
        for(j=1;j<=len;j++)
        {
            int t=(a[i-1][j])*(4*i-2)+yu;
            yu=t/10;
            a[i][j]=t%10;
        }    
        while(yu)
        {
            a[i][++len]=yu%10;
            yu/=10;
        }
        for(j=len;j>=1;j--)
        {
            int t=a[i][j]+yu*10;
            a[i][j]=t/(i+1);
            yu = t%(i+1);
        }        
        while(!a[i][len])
        {
            len--;
        }    
        a[i][0]=len;
    }    
    
}    
int main()
{
    ktl();
    int n;
    while(scanf("%d",&n)!=EOF)
    {
        for(int i=a[n][0];i>0;i--)
        {
            printf("%d",a[n][i]);
        }    
        puts("");
    }    
    return 0;
}