卡特兰数

卡塔兰数是组合数学中一个常在各种计数问题中出现的数列。仍存有疑惑，之后再解释；

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. 

InputThe 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. 
OutputFor 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.

#include <algorithm>
#include<iostream>
#include <cstring>
#include<stdio.h>
#define maxn 1000
using namespace std;
int cata[105][maxn];

void op()
{
    cata[1][0] = 1;
    cata[1][1] = 1;
    cata[2][1] = 2;
    cata[2][0] = 1;
    int len = 1, yu;
    int i, j;
    for (i = 3; i<101; i++)
    {
        yu = 0;
        for (j = 1; j <= len; j++)
        {
            int it = cata[i - 1][j] * (4 * i - 2) + yu;
            yu = it / 10;
            cata[i][j] = it % 10;
        }
        while (yu)
        {
            cata[i][++len] = yu % 10;
            yu /= 10;//归零;
        }

        for (j = len; j >= 1; j--)
        {
            int it = cata[i][j] + yu * 10;
            cata[i][j] = it / (i + 1);
            yu = it % (i + 1);
        }
        while (cata[i][len]==0)
        {
            len--;
        }
        cata[i][0] = len;
    }
}

int main()
{
    op();
    int n;
    while (scanf("%d", &n) != EOF)
    {
        for (int i = cata[n][0]; i>0; i--)
            printf("%d", cata[n][i]);
        printf("
");
    }
    return 0;
}