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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#322339 | #5743. Palindromic Polynomial | do_while_true | RE | 0ms | 0kb | C++20 | 4.8kb | 2024-02-06 21:20:42 | 2024-02-06 21:20:42 |
answer
#include<cstdio>
#include<vector>
#include<queue>
#include<cstring>
#include<map>
#include<iostream>
#include<algorithm>
#include<ctime>
#include<random>
#include<assert.h>
#define pb emplace_back
#define mp make_pair
#define fi first
#define se second
#define dbg(x) cerr<<"In Line "<< __LINE__<<" the "<<#x<<" = "<<x<<'\n'
#define dpi(x,y) cerr<<"In Line "<<__LINE__<<" the "<<#x<<" = "<<x<<" ; "<<"the "<<#y<<" = "<<y<<'\n'
#define DE(fmt,...) fprintf(stderr, "Line %d : " fmt "\n",__LINE__,##__VA_ARGS__)
#define mem(a) memset(a,0,sizeof(a))
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int>pii;
typedef pair<ll,int>pli;
typedef pair<ll,ll>pll;
typedef pair<int,ll>pil;
typedef vector<int>vi;
typedef vector<ll>vll;
typedef vector<pii>vpii;
typedef vector<pll>vpll;
template<typename T>T cmax(T &x, T y){return x=x>y?x:y;}
template<typename T>T cmin(T &x, T y){return x=x<y?x:y;}
template<typename T>
T &read(T &r){
r=0;bool w=0;char ch=getchar();
while(ch<'0'||ch>'9')w=ch=='-'?1:0,ch=getchar();
while(ch>='0'&&ch<='9')r=r*10+(ch^48),ch=getchar();
return r=w?-r:r;
}
template<typename T1,typename... T2>
void read(T1 &x,T2& ...y){read(x);read(y...);}
const int mod=1000000009;
const int inv2=(mod+1)/2;
inline void cadd(int &x,int y){x=(x+y>=mod)?(x+y-mod):(x+y);}
inline void cdel(int &x,int y){x=(x-y<0)?(x-y+mod):(x-y);}
inline int add(int x,int y){return (x+y>=mod)?(x+y-mod):(x+y);}
inline int del(int x,int y){return (x-y<0)?(x-y+mod):(x-y);}
int qpow(int x,int y){
int s=1;
while(y){
if(y&1)s=1ll*s*x%mod;
x=1ll*x*x%mod;
y>>=1;
}
return s;
}
const int N=10010;
struct Lag{
int n;
int a[N],b[N];
int f[N],g[N];
void clear(int d){n=0;mem(a);mem(b);mem(f);mem(g);}
void ins(int x,int y){++n;a[n]=x;b[n]=y;}
void solve(){
for(int i=0;i<=n;i++)f[i]=g[i]=0;
f[0]=1;
for(int i=1;i<=n;i++){
for(int j=n;j>=1;j--)
f[j]=del(f[j-1],1ll*a[i]*f[j]%mod);
f[0]=1ll*del(0,a[i])*f[0]%mod;
}
for(int i=1;i<=n;i++){
int t=qpow(del(0,a[i]),mod-2);
f[0]=1ll*t*f[0]%mod;
for(int j=1;j<=n;j++){
cdel(f[j],f[j-1]);
f[j]=1ll*t*f[j]%mod;
}
int s=b[i];
for(int j=1;j<=n;j++)if(i!=j)s=1ll*s*qpow(del(a[i],a[j]),mod-2)%mod;
for(int j=0;j<=n;j++)cadd(g[j],1ll*f[j]*s%mod);
for(int j=n;j>=1;j--)
f[j]=del(f[j-1],1ll*a[i]*f[j]%mod);
f[0]=1ll*del(0,a[i])*f[0]%mod;
}
}
}lag;
int n;
int a[N],b[N],ok[N];
int ta[N],tb[N];
int f[N],C[N],D[N];
void solve(){
mem(a);mem(b);mem(ok);
mem(ta);mem(tb);mem(f);mem(C);mem(D);
read(n);
for(int i=1;i<=n;i++)read(a[i]);
for(int i=1;i<=n;i++)read(b[i]);
map<int,int>vis;
int tot=0,a0=1,ok0=0;
for(int i=1;i<=n;i++){
if(vis.count(a[i])){
if(vis[a[i]]!=b[i]){
puts("-1");
return ;
}
}
else{
vis[a[i]]=b[i];
if(a[i]==0){
a0=b[i];ok0=1;
}
else{
++tot;ta[tot]=a[i];tb[tot]=b[i];
}
}
}
if(a0==0){
puts("-1");
return ;
}
n=tot;
for(int i=1;i<=n;i++)a[i]=ta[i],b[i]=tb[i];
for(int i=0;i<=10000;i++)ok[i]=1;
int fl=0;
for(int i=1;i<=n;i++)
for(int j=i+1;j<=n;j++)
if(1ll*a[i]*a[j]%mod==1){
int w=b[j];
for(int k=0;k<=10000;k++){
if(w!=b[i])ok[k]=0;
w=1ll*w*a[i]%mod;
fl=1;
}
}
int d=2*n;
if(fl){
d=-1;
for(int i=2*n;i<=10000;i++)if(ok[i]){d=i;break;}
if(d==-1){
for(int i=2*n-1;i>=0;i--)if(ok[i]){d=i;break;}
}
if(d==-1){
puts("-1");
return ;
}
}
lag.clear(d);
for(int i=1;i<=n;i++){
lag.ins(a[i],b[i]);
int u=qpow(a[i],mod-2);
if(vis.count(u))continue;
lag.ins(u,1ll*b[i]*qpow(qpow(a[i],mod-2),d)%mod);
}
int m=lag.n;
lag.solve();
while(m>=0&&!lag.g[m])--m;
if(m>d){
puts("-1");
return ;
}
for(int i=0;i<=d;i++)f[i]=1ll*add(lag.g[i],lag.g[d-i])*inv2%mod,C[i]=0;
if((ok0&&f[0]!=a0)||(!ok0&&!f[0])){
C[0]=1;
for(int i=1;i<=lag.n;i++){
int x=lag.a[i];
for(int i=d;i>=1;i--)C[i]=del(C[i-1],1ll*C[i]*x%mod);
C[0]=1ll*C[0]*del(0,x)%mod;
}
for(int i=0;i<=d;i++)D[i]=1ll*add(C[i],C[d-i])*inv2%mod;
int t=1ll*del(a0,f[0])*qpow(D[0],mod-2)%mod;
for(int i=0;i<=d;i++)cadd(f[i],1ll*D[i]*t%mod);
}
//check
#define WA do{for(int i=1;i<=n;i++)cerr<<a[i]<<' ';for(int i=1;i<=n;i++)cerr<<b[i]<<' ';assert(0);return ;}while(0)
for(int i=0;i<=d;i++)if(f[i]!=f[d-i])WA;
if(!f[0])WA;
for(int i=1;i<=n;i++){
int s=0;
for(int j=d;j>=0;j--)s=add(1ll*s*a[i]%mod,f[j]);
if(s!=b[i]){
// dbg(i);
WA;
}
}
cout<<d<<'\n';
for(int i=0;i<=d;i++)cout<<f[i]<<' ';
puts("");
}
signed main(){
// #ifdef do_while_true
// assert(freopen("data.in","r",stdin));
// #endif
int T;read(T);
while(T--)solve();
#ifdef do_while_true
// cerr<<'\n'<<"Time:"<<1.0*clock()/CLOCKS_PER_SEC*1000<<" ms"<<'\n';
#endif
return 0;
}
Details
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Test #1:
score: 0
Runtime Error
input:
8 2 0 1 2 4 3 0 1 2 2 10 36 4 0 1 2 3 1 4 9 16 5 0 1 2 3 4 1 25 961 14641 116281 2 2 500000005 5 375000004 2 2 500000005 5 375000004 2 2 500000005 1 2 3 2 500000005 3 5 375000004 10
output:
2 2 0 2 4 2 999999998 28 999999998 2 6 1 1000000005 0 10 0 1000000005 1 8 1 2 3 4 5 4 3 2 1 3 416666670 541666673 541666673 416666670 3 416666670 541666673 541666673 416666670 -1