USACO 3.2 Factorials

PKU已经挂了6天了,一直想验证自己写的logn的计算n!最后一位的算法是否正确,这次USACO告诉我我写对了！

 

USER: A e [chenh193]
TASK: fact4
LANG: C++

Compiling...
Compile: OK

Executing...
   Test 1: TEST OK [0.000 secs, 4000 KB]
   Test 2: TEST OK [0.022 secs, 4000 KB]
   Test 3: TEST OK [0.000 secs, 3996 KB]
   Test 4: TEST OK [0.011 secs, 3996 KB]
   Test 5: TEST OK [0.011 secs, 3996 KB]
   Test 6: TEST OK [0.011 secs, 4000 KB]
   Test 7: TEST OK [0.011 secs, 3996 KB]
   Test 8: TEST OK [0.000 secs, 4000 KB]
   Test 9: TEST OK [0.011 secs, 4000 KB]
   Test 10: TEST OK [0.000 secs, 4000 KB]

All tests OK.

 

int cnt2,cnt5,dir[]={1,1,3,1};
int ODD(int L,int R)
{
    //1,3,5,7,9....
    if(L>=R)return 1;
    int Len=(R-L)/2+1;//长
    int O_R=R,O_L=L,buf=1;
    while(!(O_L%5==0&&O_L%2)&&O_L<=R)O_L++;
    while(!(O_R%5==0&&O_R%2)&&O_R>=L)O_R--;
    if(O_L<=O_R)
    {
        cnt5+=(O_R-O_L)/10+1;
        buf*=ODD(O_L/5,O_R/5);
        Len-=(O_R-O_L)/10+1;
    }
    buf*=((Len/4)&0x1?9:1);
    buf*=dir[Len%4];
    buf%=10;
    return buf;
}
int nozero(int L,int R)//L*(L+1)*...*(R-1)*R的非0最后尾数
{
    //分奇，偶
    if(L>=R)return 1;
    int O_L=L,O_R=R,buf=1,Len=R-L+1;
    O_L+=(O_L&0X1);
    O_R-=(O_R&0X1);
    cnt2+=(O_R-O_L)/2+1;//该序列中的偶数的个数，需要继续讨论...
    Len-=(O_R-O_L)/2+1;
    buf*=nozero(O_L/2,O_R/2);//计算子集...
    buf%=10;
    //剩下的只可能是1,3,5,7,9结尾的数...
    //去掉能被5整除的数...
    O_L=L;O_R=R;
    while(!(O_L%5==0&&O_L%2)&&O_L<=R)O_L++;
    while(!(O_R%5==0&&O_R%2)&&O_R>=L)O_R--;
    if(O_L<=O_R)
    {
        cnt5+=(O_R-O_L)/10+1;
        Len-=(O_R-O_L)/10+1;
        buf*=ODD(O_L/5,O_R/5);
    }
    buf*=((Len/4)&0x1?9:1);
    buf*=dir[Len%4];
    buf%=10;
    return buf;
}
int main()
{
    int N;
    freopen("fact4.out","w",stdout);
    freopen("fact4.in","r",stdin);
    while(scanf("%d",&N)!=EOF)
    {
        cnt2=cnt5=0;
        N=nozero(1,N);
        N*=pmod(2,cnt2-cnt5,10);
        printf("%d/n",N%10);
    }
    return 0;
}