HDU 1023 Train Problem II

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

卡特兰数  大数乘除

Java版本

import java.util.*;
import java.io.*;
import java.math.*;
public class Main
{
    static Scanner cin=new Scanner(System.in);
    static PrintWriter cout=new PrintWriter(System.out,true);
    public static void main(String[] args)
    {
        BigInteger a[]=new BigInteger[110];
        BigInteger b=BigInteger.valueOf(4);
        BigInteger d=BigInteger.valueOf(2);
        a[1]=BigInteger.ONE;
        for(int i=2;i<=100;i++)
        {
            BigInteger c=BigInteger.valueOf(i);
            BigInteger e=BigInteger.valueOf(i+1);
            a[i]=a[i-1].multiply(b.multiply(c).subtract(d)).divide(e);
        }
        while(cin.hasNext())
        {
            int n=cin.nextInt();
            System.out.println(a[n].toString());
        }
    }
}

c++版本

#include <iostream> 
#include <algorithm> 
#include <cstring> 
#include <cstdio>
#include <vector> 
#include <queue> 
#include <cstdlib> 
#include <iomanip>
#include <cmath> 
#include <ctime> 
#include <map> 
#include <set> 
using namespace std; 
#define lowbit(x) (x&(-x)) 
#define max(x,y) (x>y?x:y) 
#define min(x,y) (x<y?x:y) 
#define MAX 100000000000000000 
#define MOD 1000000007
#define pi acos(-1.0) 
#define ei exp(1) 
#define PI 3.141592653589793238462
#define ios() ios::sync_with_stdio(false)
#define INF 1044266558
#define mem(a) (memset(a,0,sizeof(a)))
typedef long long ll;
//f[n]=2*(2*n-1)*f[n-1]/(i+1);
int a[101][101],n;
void multiply(int *a,int k,int b)
{
    int ans=0;
    for(int i=k-1;i>=0;i--)
    {
        ans+=a[i]*b;
        a[i]=ans%10000;
        ans/=10000;
    }
}
void divide(int *a,int k,int b)
{
    int ans=0;
    for(int i=0;i<k;i++)
    {
        ans*=10000;
        ans+=a[i];
        a[i]=ans/b;
        ans%=b;
    }
}
void init()
{
    memset(a,0,sizeof(a));
    a[1][99]=1;
    for(int i=2;i<=100;i++)
    {
        memcpy(a[i],a[i-1],sizeof(a[i-1]));
        multiply(a[i],100,4*i-2);
        divide(a[i],100,i+1);
    }
}
int main()
{
    init();
    int i;
    while(scanf("%d",&n)!=EOF)
    {
        for(i=0;i<100 && !a[n][i];i++);
        printf("%d",a[n][i++]);
        for(;i<100;i++)
            printf("%04d",a[n][i]);
        printf("\n");
    }
    return 0;
}