Train Problem II

　　　　　　Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
　　　　　　　　Total Submission(s): 9701    Accepted Submission(s): 5210

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 1131 1134 2067

题意：给你n辆火车，编号从1到n，问你有多少种出站的可能序列。

思路：火车进出站问题，首先考虑卡特兰数（不要忘了高精哦）

代码：

#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<iostream>
#include<algorithm>
#define N 110
using namespace std;
int n,len,sum,tmp,a[N][N],b[N];
int catelan()
{
    len=1;a[1][0]=b[1]=1;
    for(int i=2;i<110;i++)
    {
        for(int j=0;j<len;j++)
         a[i][j]=a[i-1][j]*(4*i-2);
        sum=0;
        for(int j=0;j<len;j++)
        {
            tmp=sum+a[i][j];
            a[i][j]=tmp%10;
            sum=tmp/10;
        }
        while(sum)
        {
            a[i][len++]=sum%10;
            sum/=10;
        }
        for(int j=len-1;j>=0;j--)
        {
            tmp=sum*10+a[i][j];
            a[i][j]=tmp/(i+1);
            sum=tmp%(i+1);
        }
        while(!a[i][len-1])
         len--;
        b[i]=len;
    }
}
int main()
{
    catelan();
    while(~scanf("%d",&n))
    {
        for(int i=b[n]-1;i>=0;i--)
         printf("%d",a[n][i]);
        printf("\n");
    }
}