C - Train Problem II——（HDU 1023 Catalan 数）

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## C - Train Problem II——（HDU 1023 Catalan 数）

angel_imp 2016-03-28 20:46:00 浏览1058

# Train Problem II

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 7616    Accepted Submission(s): 4101

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.

1. 组合公式为 Cn = C(2n,n) / (n+1);
2. 递推公式为 h(n ) = h(n-1)*(4*n-2) / (n+1)

My Java Code：

```<span style="font-size:18px;">import java.util.*;
import java.math.BigInteger;
public class Main {
public static void main(String[] args) {
BigInteger a[] = new BigInteger[105];
a[0] = BigInteger.ZERO;
a[1] = BigInteger.ONE;
for(int i=2;i<=102;i++) {
a[i] = a[i-1].multiply(BigInteger.valueOf(4*i-2)).divide(BigInteger.valueOf(i+1));
}

Scanner in = new Scanner(System.in);

while(in.hasNext()) {
int n=in.nextInt();
System.out.println(a[n]);
}
}
}</span>```

My Cpp Code：

```<span style="font-size:18px;">#include <iostream>
#include <cstring>
#include <cstdio>
using namespace std;
const int MAXN = 105;
int a[MAXN][MAXN];
int b[MAXN];
///可以作为模板
void Catalan()
{
int yu,len;
a[1][0] = 1;
a[1][1] = 1;
len = 1;
for(int i=2; i<MAXN; i++)
{
yu = 0;
for(int 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(int 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()
{
Catalan();
int n;
while(cin>>n)
{
for(int i=a[n][0]; i>0; i--)
cout<<a[n][i];
puts("");
}
return 0;
}
</span>```

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