暑假集训Day1 B(拓展欧拉定理)

Posted 2022-09-16 MichaelZona

 

这题公式其实非常好推，主要是在幂的指数上取模的时候，应该用欧拉定理，指数上模的应该是MOD对应的欧拉函数值

1 #include "bits/stdc++.h"
 2 using namespace std;
 3 typedef long long LL;
 4 const int MOD=1e9+7;
 5 const int MAX=2e5+5;
 6 LL ans,n,a[MAX],b[MAX],c[MAX];
 7 LL ksm(LL x,LL y)
 8     LL an=1ll;
 9     while (y)
10         if (y%2==1ll) an=(an*x)%MOD;
11         x=(x*x)%MOD;
12         y/=2ll;
13     
14     return an;
15 
16 LL ksm2(LL x,LL y)
17     LL an=1ll;
18     while (y)
19         if (y%2==1ll) an=(an*x)%(MOD-1);
20         x=(x*x)%(MOD-1);
21         y/=2ll;
22     
23     return an;
24 
25 inline LL read()
26     LL an(0ll),x=1ll;char c=getchar();
27     while (c<0 || c>9) if (c==-) x=-1;c=getchar();
28     while (c>=0 && c<=9) an=an*10+c-0;c=getchar();
29     return an*x;
30 
31 bool cmp(LL x,LL y)
32     return x<y;
33 
34 int main()
35     freopen ("b.in","r",stdin);
36     freopen ("b.out","w",stdout);
37     int i,j;
38     LL x,y,z,mul=1ll;
39     n=read();
40     for (i=1;i<=n;i++) a[i]=read();
41     sort(a+1,a+n+1,cmp);
42     memset(b,0,sizeof(b));
43     memset(c,0,sizeof(c));
44     for (i=1;i<=n;i++)
45         if (a[i]!=a[i-1])
46             b[++b[0]]=a[i];
47             c[++c[0]]=1;
48         
49         else c[c[0]]++;
50     ans=1ll;bool flag=true;
51     for (i=1;i<=c[0];i++)
52         mul=(mul*(c[i]+1))%(MOD-1);
53         if ((c[i]+1)%2==0 && flag)
54             flag=false;
55             mul/=2;
56         
57     
58     for (i=1;i<=b[0];i++)
59         x=c[i];
60         if (flag) x/=2ll;
61         z=(x*mul%(MOD-1))%(MOD-1);
62         ans=(ans*ksm(b[i],z))%MOD;
63     
64     printf("%lld",ans);
65     return 0;
66