POJ 1286

Burnside定理。

可以用Euler函数优化。

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#define LL __int64

using namespace std;

LL Power(int a,int b){
	LL ret=1; LL p=(LL)a;
	while(b){
		if(b&1) ret=ret*p;
		p=p*p;
		b>>=1;
	}
	return ret;
}

LL Euler(int s){
	LL ret=(LL)s;
	int l=(int)sqrt(s*1.0);
	for(int i=2;i<=l;i++){
		if(s%i==0){
			ret=ret-ret/(LL)i;
			while(s%i==0)
			s/=i;
		}
	}
	if(s>1)
	ret=ret-ret/s;
	return ret;
}

LL Burnside(int n){
	LL res=0;
	for(int i=1;i<=n;i++){
		if(n%i==0)
		res=res+Power(3,i)*Euler(n/i);
	}
	if(n&1){
		res=res+n*Power(3,n/2+1);
	}
	else{
		res=res+n/2*Power(3,n/2)+n/2*Power(3,n/2+1);
	}
	return res;
}

int main(){
	int n;
	while(scanf("%d",&n)!=EOF){
		if(n==-1) break;
		if(n==0) printf("0\n");
		else{
			LL ans=Burnside(n);
			ans=ans/2/n;
			printf("%I64d\n",ans);
		}
	}
	return 0;
}