[数论 CRT] BZOJ 2976 [Poi2002]出圈游戏

#include<cstdio>
#include<cstdlib>
#include<algorithm>
#include<cstring>
#define cl(x) memset(x,0,sizeof(x))
using namespace std;
typedef long long ll;
typedef pair<ll,ll> abcd;

inline char nc()
{
static char buf[100000],*p1=buf,*p2=buf;
if (p1==p2) { p2=(p1=buf)+fread(buf,1,100000,stdin); if (p1==p2) return EOF; }
return *p1++;
}

inline void read(ll &x){
char c=nc(),b=1;
for (;!(c>='0' && c<='9');c=nc()) if (c=='-') b=-1;
for (x=0;c>='0' && c<='9';x=x*10+c-'0',c=nc()); x*=b;
}

int pnum=8;
int prime[10]={0,2,3,5,7,11,13,17,19};
int cnt;
ll NN;
ll A[25],N[25],C[25];
ll p[25],q[25],tp[25];

inline abcd EXGCD(ll x,ll y){
abcd ret;
if (x<y) { ret=EXGCD(y,x); return abcd(ret.second,ret.first); }
if (y==0) return abcd(1,0);
ret=EXGCD(y,x%y);
return abcd(ret.second,ret.first-x/y*ret.second);
}

inline ll inv(ll a,ll p){
return ((EXGCD(a,p).first)%p+p)%p;
}

inline ll CRT(){
ll ret;
cnt=0;
for (int i=1;i<=8;i++)
{
ll itmp=1;
for (int j=1;j<=q[i];j++)
itmp*=prime[i];
if (itmp!=1)
A[++cnt]=p[i],N[cnt]=itmp;
}
NN=1;
for (int i=1;i<=cnt;i++)
NN*=N[i];
for (int i=1;i<=cnt;i++)
{
C[i]=1;
for (int j=1;j<=cnt;j++)
if (i!=j)
{
(C[i]*=N[j])%=NN;
(C[i]*=inv(N[j],N[i]))%=NN;
}
}
ret=0;
for (int i=1;i<=cnt;i++)
(ret+=A[i]*C[i]%NN)%=NN;
if (ret==0) ret=NN;
return ret;
}

ll mod[25];

inline bool Add(ll ia,ll in){
mod[in]=ia%in;
for (int i=1;i<=pnum;i++)
if (in%prime[i]==0)
{
ll itmp=0,ip=1;
while (in%prime[i]==0) itmp++,in/=prime[i],ip*=prime[i];
if (q[i]<itmp)
{
q[i]=itmp; p[i]=ia%ip;
}
}
return 1;
}

ll n;
ll a[25];
ll flag[25];

inline bool Check(){
for (int i=n;i;i--)
for (int j=1;j<=i;j++)
if (i%j==0 && mod[i]%j!=mod[j])
return 0;
return 1;
}

int main()
{
ll ix;
freopen("t.in","r",stdin);
freopen("t.out","w",stdout);
memset(tp,-1,sizeof(tp));
read(n);
for (int i=1;i<=n;i++)
read(ix),a[ix]=i;
int s=0;
for (int i=1;i<=n;i++)
{
int icnt=0;
for (;s!=a[i];s=(s==n)?1:s+1) if (!flag[(s==n)?1:s+1]) icnt++;
Add(icnt,n-i+1);
flag[a[i]]=1;
}
if (!Check())
printf("NIE\n");
else
printf("%lld\n",CRT());
return 0;
}