n! 分解素因子 快速幂
ei=[N/pi^1]+ [N/pi^2]+ …… + [N/pi^n] 其中[]为取整
ei 为数 N！中pi 因子的个数；
1 #include <iostream> 2 #include <cstdio> 3 #include <cstring> 4 #include <algorithm> 5 #include <cmath> 6 using namespace std; 7 8 const int maxn=10005; 9 10 int sign[maxn]; 11 int pri[maxn]; 12 int tot; 13 14 void getpri (){ 15 memset (sign,0,sizeof sign); 16 sign[0]=sign[1]=1; 17 for (int i=2;i<sqrt (maxn+0.5);i++) 18 if (!sign[i]) 19 for (int j=i*i;j<maxn;j+=i) 20 sign[j]=1; 21 tot=0; 22 for (int i=2;i<maxn;i++) 23 if (!sign[i]) 24 pri[tot++]=i; 25 } 26 27 int e[maxn]; 28 29 int power (int a,int b){ 30 int ans=1; 31 while (b){ 32 if (b&1) 33 ans*=a; 34 a*=a; 35 b>>=1; 36 } 37 return ans; 38 } 39 40 int main (){ 41 getpri ();//cout<<tot<<endl; 42 int p,q,r,s; 43 while (~scanf ("%d%d%d%d",&p,&q,&r,&s)/*cin>>p>>q>>r>>s*/){ 44 memset (e,0,sizeof e); 45 int ma=max (p,r); 46 for (int i=0;i<tot;i++){ 47 int temp=pri[i]; 48 while (temp<=ma){ 49 e[i]+=p/temp+s/temp+(r-s)/temp;//if (i==0) cout<<ma<<" "; 50 e[i]-=r/temp+q/temp+(p-q)/temp; 51 temp*=pri[i]; 52 } 53 } 54 double ans=1; 55 for (int i=0;i<tot;i++){ 56 if (e[i]>=0) 57 ans*=1.0*power (pri[i],e[i]); 58 else ans/=1.0*power (pri[i],-e[i]);//cout<<e[i]<<":"<<pri[i]<<"=";//<<ans<<" "; 59 } 60 printf ("%.5f ",ans); 61 } 62 return 0; 63 }