This documentation is automatically generated by online-judge-tools/verification-helper
View the Project on GitHub beet-aizu/library
// verification-helper: PROBLEM https://judge.yosupo.jp/problem/find_linear_recurrence #include<bits/stdc++.h> using namespace std; #define call_from_test #include "../../mod/mint.cpp" #include "../../polynomial/berlekampmassey.cpp" #undef call_from_test signed main(){ cin.tie(0); ios::sync_with_stdio(0); int n; cin>>n; using M = Mint<int, 998244353>; vector<M> as(n); for(int i=0;i<n;i++) cin>>as[i].v; auto cs=berlekamp_massey(as); cs.pop_back(); reverse(cs.begin(),cs.end()); cout<<cs.size()<<endl; for(int i=0;i<(int)cs.size();i++){ if(i) cout<<" "; cout<<-cs[i]; } cout<<endl; return 0; }
#line 1 "test/yosupo/find_linear_recurrence.test.cpp" // verification-helper: PROBLEM https://judge.yosupo.jp/problem/find_linear_recurrence #include<bits/stdc++.h> using namespace std; #define call_from_test #line 1 "mod/mint.cpp" #line 3 "mod/mint.cpp" using namespace std; #endif //BEGIN CUT HERE template<typename T, T MOD = 1000000007> struct Mint{ inline static constexpr T mod = MOD; T v; Mint():v(0){} Mint(signed v):v(v){} Mint(long long t){v=t%MOD;if(v<0) v+=MOD;} Mint pow(long long k){ Mint res(1),tmp(v); while(k){ if(k&1) res*=tmp; tmp*=tmp; k>>=1; } return res; } static Mint add_identity(){return Mint(0);} static Mint mul_identity(){return Mint(1);} Mint inv(){return pow(MOD-2);} Mint& operator+=(Mint a){v+=a.v;if(v>=MOD)v-=MOD;return *this;} Mint& operator-=(Mint a){v+=MOD-a.v;if(v>=MOD)v-=MOD;return *this;} Mint& operator*=(Mint a){v=1LL*v*a.v%MOD;return *this;} Mint& operator/=(Mint a){return (*this)*=a.inv();} Mint operator+(Mint a) const{return Mint(v)+=a;} Mint operator-(Mint a) const{return Mint(v)-=a;} Mint operator*(Mint a) const{return Mint(v)*=a;} Mint operator/(Mint a) const{return Mint(v)/=a;} Mint operator+() const{return *this;} Mint operator-() const{return v?Mint(MOD-v):Mint(v);} bool operator==(const Mint a)const{return v==a.v;} bool operator!=(const Mint a)const{return v!=a.v;} static Mint comb(long long n,int k){ Mint num(1),dom(1); for(int i=0;i<k;i++){ num*=Mint(n-i); dom*=Mint(i+1); } return num/dom; } }; template<typename T, T MOD> ostream& operator<<(ostream &os,Mint<T, MOD> m){os<<m.v;return os;} //END CUT HERE #ifndef call_from_test signed main(){ return 0; } #endif #line 1 "polynomial/berlekampmassey.cpp" #line 3 "polynomial/berlekampmassey.cpp" using namespace std; #endif //BEGIN CUT HERE // construct a charasteristic equation from sequence // return a monic polynomial in O(n^2) template<typename T> vector<T> berlekamp_massey(vector<T> &as){ using Poly = vector<T>; int n=as.size(); Poly bs({-T(1)}),cs({-T(1)}); T y(1); for(int ed=1;ed<=n;ed++){ int l=cs.size(),m=bs.size(); T x(0); for(int i=0;i<l;i++) x+=cs[i]*as[ed-l+i]; bs.emplace_back(0); m++; if(x==T(0)) continue; T freq=x/y; if(m<=l){ for(int i=0;i<m;i++) cs[l-1-i]-=freq*bs[m-1-i]; continue; } auto ts=cs; cs.insert(cs.begin(),m-l,T(0)); for(int i=0;i<m;i++) cs[m-1-i]-=freq*bs[m-1-i]; bs=ts; y=x; } for(auto &c:cs) c/=cs.back(); return cs; } //END CUT HERE #ifndef call_from_test signed main(){ return 0; } #endif #line 9 "test/yosupo/find_linear_recurrence.test.cpp" #undef call_from_test signed main(){ cin.tie(0); ios::sync_with_stdio(0); int n; cin>>n; using M = Mint<int, 998244353>; vector<M> as(n); for(int i=0;i<n;i++) cin>>as[i].v; auto cs=berlekamp_massey(as); cs.pop_back(); reverse(cs.begin(),cs.end()); cout<<cs.size()<<endl; for(int i=0;i<(int)cs.size();i++){ if(i) cout<<" "; cout<<-cs[i]; } cout<<endl; return 0; }