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
#include <iostream>
using namespace std;
int a[105][100];//ans[i][j] i表示第几个卡特兰数，
//j=0表示位数，j从1到ans[i][0]是个位数往上
void ktl()
{
a[1][0]=1; a[1][1]=1;
a[2][0]=1; a[2][1]=2;
int len=1,yu,t,i,j;
for( i=3;i<=104;i++)
{
yu=0;
for(j=1;j<=len;j++)
{
t=a[i-1][j]*(4*i-2)+yu;//注意先乘再加余数
a[i][j]=t%10;//这一位的值是对10取余
yu=t/10;//进位是除以10
}
while(yu)
{
a[i][++len]=yu%10;
yu/=10;
}
for(j=len;j>=1;j--)
{
t=a[i][j]+yu*10;//除法先加“余数”再除
a[i][j]=t/(i+1);//留在这一位是除
yu=t%(i+1);//“余数”是取余
//除法和乘法是逆过程，计算时也是反过来
}
while(!a[i][len])
{
len--;
}
a[i][0]=len;
}
}
int main()
{
ktl();
int n;
while(~scanf("%d",&n))
{
for(int i=a[n][0];i>0;i--)
printf("%d",a[n][i]);
printf("\n");
}
return 0;
}