各大算法专题-组合数学篇

    #include<cstdio>
    #include<vector>
    #include<cmath>
    #include<cstring>

    using namespace std;
    const int maxn1 = 1000+ 5;
    const int maxn2 = 100000 + 5;
    int prime_factor[maxn1];
    int bad[maxn2];
    int num;// length of prime_factor[maxn]
    void prime_resolve(int n)
    {                             //函数功能：找到n的所有质因子
       int i;
        num = 0;
         for(i = 2;i*i <= n;i++)
           {
              if(n % i == 0)
              {
                prime_factor[num++] = i;
                 while(n % i == 0)
                    n /= i;
              }
           }
           if(n > 1)         //如果没有除尽，说明n的质因子是它本身
           prime_factor[num++] = n;
    }




    int main()
    {
          int n , m;
          while(scanf("%d%d",&n , &m) != EOF)
          {
               memset(bad , 0 , sizeof(bad));

                prime_resolve(m);
                n--;
                for(int i = 0;i < num;i++) //素因子表的一层循环
                {
                    int p = prime_factor[i] , e = 0;
                    int min_e = 0 , x = m;
                    while(x % p == 0)   {min_e++ ; x /= p;}

                    //c(n,k) = (n-k+1)/k * c(n,k-1)

                    for(int k = 1;k  <  n;k++)
                    {

                        x = n - k  + 1;
                        while(x % p == 0)   { x /= p;e++;}
                        x = k;
                        while(x % p == 0)   { x /= p;e--;}


                        if(min_e > e) bad[k] = 1;
                    }
                }



                int temp[maxn2];
                  int index = 0;
                  for(int i = 1;i < n;i++)
                       if(!bad[i])   temp[index++] = i+1;

                       printf("%d\n",index);
                 if(index){
                       printf("%d",temp[0]);
                       for(int i = 1;i < index;i++)
                          printf(" %d" , temp[i]);}

                          printf("\n");
          }
    }