HDU 1133 Buy the Ticket

公式：(C(m+n, n)-C(m+n, m+1)) * m! * n! 化简即 (m+n)! * (m-n+1) / (m+1)
由公式：C(m, n) = m! / (n!*(m-n)!)推导得来
(C(m+n, n)-C(m+n, m+1)) * m! * n!：总共的排列减去违法的排列，又因为每个人不一样再乘以本身的全排列

#include<stdio.h>
#include<string.h>
# define N 1010
int a[N], m, n;
void Fact()
{
    int i, j, s, r = 0;
    for (i = 2; i <= (m+n); i++)
    {
        for (j = 0; j < N; j++)
        {
            s = a[j] * i + r;
            r = s / 10;
            a[j] = s % 10;
        }
    }
} //求出(m+n)!
void Sum()
{
    int i, j, c = m-n+1, d = m+1, b[N], k = 0, s, r = 0;
    for (i = 0; i < N; i++)
        a[i] *= c;
    for (i = 0; i < N-1; i++)
    {
        if (a[i] > 9)
        {
            a[i+1] += a[i] / 10;
            a[i] %= 10;
        }
    } //求出(m+n)! * (m-n+1)
    i = N-1;
    while (a[i] == 0) i--;
    for (j = i; j >= 0; j--)
        b[k++] = a[j];
    for (i = 0; i < k; i++)
    {
        s = b[i] + 10*r;
        r = s % d;
        b[i] = s / d;
    } //求出(m+n)! * (m-n+1) / (m+1)
    i = 0;
    while (b[i] == 0) i++;
    for (j = i; j < k; j++)
        printf("%d", b[j]);
    printf("\n");
}
int main ()
{
    int k = 0;
    while (scanf("%d %d", &m, &n), m+n)
    {
        k++;
        printf("Test #%d:\n", k);
        if (m < n)
           printf("0\n"); //要是拿100的人比拿50的人还多的话，那么不存在这种排法
        else
        {
            memset(a, 0, sizeof(a));
            a[0] = 1;
            Fact();
            Sum();
        }
    }
    return 0;
}