HDU 1023 Train Problem II

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

12310

Sample Output

12516796          

Hint

The result will be very large, so you may not process it by 32-bit integers.

#include<iostream>#include<string.h>#include<stdio.h>using namespace std;#define MAX 100#define BASE 10000void multiply(int a[],int Max,int b) //大数乘法,注意参数的传递{    int i,array=0;    for (i = Max-1; i >= 0; i--)    {        array += b * a[i];        a[i] = array % BASE; // 数组每一位存放大数的四位数字        array /= BASE;    }}void divide(int a[], int Max, int b) //模拟大数除法{    int i, div = 0;    for (i = 0; i < Max; i++)    {        div = div * BASE + a[i];        a[i] = div / b;        div %= b;    }}int main(){    int a[101][MAX],i, n;    memset(a[1],0,MAX*sizeof(int));    for (i=2, a[1][MAX-1] = 1; i < 101; i++) // 高坐标存放大数低位    {        memcpy(a[i], a[i-1], MAX * sizeof(int));      //h[i] = h[i-1];        multiply(a[i], MAX, 4 * i - 2);               //h[i] *= (4*i-2);        divide(a[i], MAX, i + 1);                  //h[i] /= （i+1）;    }    while (cin >> n)    {        for (i = 0; i < MAX && a[n][i] == 0; i++); //去掉数组前为0的数字。        cout << a[n][i++];             //输出第一个非0数        for (; i < MAX; i++)        {            printf("%04d",a[n][i]);       //输出后面的数，并每位都保持4位长度!(32767)        }        cout << endl;    }    return 0;}

自己并不会写这道题，参考了大佬们的博客，专门讲卡特兰数的点击打开链接