結果

問題 No.931 Multiplicative Convolution
ユーザー rniya
提出日時 2020-12-04 11:31:54
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 102 ms / 2,000 ms
コード長 9,551 bytes
コンパイル時間 2,708 ms
コンパイル使用メモリ 209,484 KB
最終ジャッジ日時 2025-01-16 15:40:57
ジャッジサーバーID
(参考情報)
judge5 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 14
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#include <bits/stdc++.h>
using namespace std;
// const long long MOD=1000000007;
const long long MOD=998244353;
#define LOCAL
#pragma region Macros
typedef long long ll;
typedef __int128_t i128;
typedef unsigned int uint;
typedef unsigned long long ull;
#define ALL(x) (x).begin(),(x).end()
const int INF=1e9;
const long long IINF=1e18;
const int dx[4]={1,0,-1,0},dy[4]={0,1,0,-1};
const char dir[4]={'D','R','U','L'};
template<typename T>
istream &operator>>(istream &is,vector<T> &v){
for (T &x:v) is >> x;
return is;
}
template<typename T>
ostream &operator<<(ostream &os,const vector<T> &v){
for (int i=0;i<v.size();++i){
os << v[i] << (i+1==v.size()?"": " ");
}
return os;
}
template<typename T,typename U>
ostream &operator<<(ostream &os,const pair<T,U> &p){
os << '(' << p.first << ',' << p.second << ')';
return os;
}
template<typename T,typename U,typename V>
ostream&operator<<(ostream &os,const tuple<T,U,V> &t){
os << '(' << get<0>(t) << ',' << get<1>(t) << ',' << get<2>(t) << ')';
return os;
}
template<typename T,typename U,typename V,typename W>
ostream&operator<<(ostream &os,const tuple<T,U,V,W> &t){
os << '(' << get<0>(t) << ',' << get<1>(t) << ',' << get<2>(t) << ',' << get<3>(t) << ')';
return os;
}
template<typename T,typename U>
ostream &operator<<(ostream &os,const map<T,U> &m){
os << '{';
for (auto itr=m.begin();itr!=m.end();){
os << '(' << itr->first << ',' << itr->second << ')';
if (++itr!=m.end()) os << ',';
}
os << '}';
return os;
}
template<typename T,typename U>
ostream &operator<<(ostream &os,const unordered_map<T,U> &m){
os << '{';
for (auto itr=m.begin();itr!=m.end();){
os << '(' << itr->first << ',' << itr->second << ')';
if (++itr!=m.end()) os << ',';
}
os << '}';
return os;
}
template<typename T>
ostream &operator<<(ostream &os,const set<T> &s){
os << '{';
for (auto itr=s.begin();itr!=s.end();){
os << *itr;
if (++itr!=s.end()) os << ',';
}
os << '}';
return os;
}
template<typename T>
ostream &operator<<(ostream &os,const multiset<T> &s){
os << '{';
for (auto itr=s.begin();itr!=s.end();){
os << *itr;
if (++itr!=s.end()) os << ',';
}
os << '}';
return os;
}
template<typename T>
ostream &operator<<(ostream &os,const unordered_set<T> &s){
os << '{';
for (auto itr=s.begin();itr!=s.end();){
os << *itr;
if (++itr!=s.end()) os << ',';
}
os << '}';
return os;
}
template<typename T>
ostream &operator<<(ostream &os,const deque<T> &v){
for (int i=0;i<v.size();++i){
os << v[i] << (i+1==v.size()?"": " ");
}
return os;
}
void debug_out(){cerr << '\n';}
template<class Head,class... Tail>
void debug_out(Head&& head,Tail&&... tail){
cerr << head;
if (sizeof...(Tail)>0) cerr << ", ";
debug_out(move(tail)...);
}
#ifdef LOCAL
#define debug(...) cerr << " ";\
cerr << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << '\n';\
cerr << " ";\
debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif
template<typename T> T gcd(T x,T y){return y!=0?gcd(y,x%y):x;}
template<typename T> T lcm(T x,T y){return x/gcd(x,y)*y;}
template<class T1,class T2> inline bool chmin(T1 &a,T2 b){
if (a>b){a=b; return true;} return false;
}
template<class T1,class T2> inline bool chmax(T1 &a,T2 b){
if (a<b){a=b; return true;} return false;
}
#pragma endregion
template<uint32_t mod> class modint{
using i64=int64_t;
using u32=uint32_t;
using u64=uint64_t;
public:
u32 v;
constexpr modint(const i64 x=0) noexcept :v(x<0?mod-1-(-(x+1)%mod):x%mod){}
constexpr u32 &value() noexcept {return v;}
constexpr const u32 &value() const noexcept {return v;}
constexpr modint operator+(const modint &rhs) const noexcept {return modint(*this)+=rhs;}
constexpr modint operator-(const modint &rhs) const noexcept {return modint(*this)-=rhs;}
constexpr modint operator*(const modint &rhs) const noexcept {return modint(*this)*=rhs;}
constexpr modint operator/(const modint &rhs) const noexcept {return modint(*this)/=rhs;}
constexpr modint &operator+=(const modint &rhs) noexcept {
v+=rhs.v;
if (v>=mod) v-=mod;
return *this;
}
constexpr modint &operator-=(const modint &rhs) noexcept {
if (v<rhs.v) v+=mod;
v-=rhs.v;
return *this;
}
constexpr modint &operator*=(const modint &rhs) noexcept {
v=(u64)v*rhs.v%mod;
return *this;
}
constexpr modint &operator/=(const modint &rhs) noexcept {
return *this*=rhs.pow(mod-2);
}
constexpr modint pow(u64 exp) const noexcept {
modint self(*this),res(1);
while (exp>0){
if (exp&1) res*=self;
self*=self; exp>>=1;
}
return res;
}
constexpr modint &operator++() noexcept {if (++v==mod) v=0; return *this;}
constexpr modint &operator--() noexcept {if (v==0) v=mod; return --v,*this;}
constexpr modint operator++(int) noexcept {modint t=*this; return ++*this,t;}
constexpr modint operator--(int) noexcept {modint t=*this; return --*this,t;}
constexpr modint operator-() const noexcept {return modint(mod-v);}
template<class T> friend constexpr modint operator+(T x,modint y) noexcept {return modint(x)+y;}
template<class T> friend constexpr modint operator-(T x,modint y) noexcept {return modint(x)-y;}
template<class T> friend constexpr modint operator*(T x,modint y) noexcept {return modint(x)*y;}
template<class T> friend constexpr modint operator/(T x,modint y) noexcept {return modint(x)/y;}
constexpr bool operator==(const modint &rhs) const noexcept {return v==rhs.v;}
constexpr bool operator!=(const modint &rhs) const noexcept {return v!=rhs.v;}
constexpr bool operator!() const noexcept {return !v;}
friend istream &operator>>(istream &s,modint &rhs) noexcept {
i64 v; rhs=modint{(s>>v,v)}; return s;
}
friend ostream &operator<<(ostream &s,const modint &rhs) noexcept {
return s<<rhs.v;
}
};
template<int mod>
struct NumberTheoreticTransform{
using Mint=modint<mod>;
vector<Mint> roots;
vector<int> rev;
int base,max_base;
Mint root;
NumberTheoreticTransform():base(1),rev{0,1},roots{Mint(0),Mint(1)}{
int tmp=mod-1;
for (max_base=0;tmp%2==0;++max_base) tmp>>=1;
root=2;
while (root.pow((mod-1)>>1)==1) ++root;
root=root.pow((mod-1)>>max_base);
}
void ensure_base(int nbase){
if (nbase<=base) return;
rev.resize(1<<nbase);
for (int i=0;i<(1<<nbase);++i){
rev[i]=(rev[i>>1]>>1)|((i&1)<<(nbase-1));
}
roots.resize(1<<nbase);
for (;base<nbase;++base){
Mint z=root.pow(1<<(max_base-1-base));
for (int i=1<<(base-1);i<(1<<base);++i){
roots[i<<1]=roots[i];
roots[i<<1|1]=roots[i]*z;
}
}
}
void ntt(vector<Mint> &a){
const int n=a.size();
int zeros=__builtin_ctz(n);
ensure_base(zeros);
int shift=base-zeros;
for (int i=0;i<n;++i){
if (i<(rev[i]>>shift)){
swap(a[i],a[rev[i]>>shift]);
}
}
for (int k=1;k<n;k<<=1){
for (int i=0;i<n;i+=(k<<1)){
for (int j=0;j<k;++j){
Mint z=a[i+j+k]*roots[j+k];
a[i+j+k]=a[i+j]-z;
a[i+j]=a[i+j]+z;
}
}
}
}
vector<Mint> multiply(vector<Mint> a,vector<Mint> b){
int need=a.size()+b.size()-1;
int nbase=1;
while ((1<<nbase)<need) ++nbase;
ensure_base(nbase);
int sz=1<<nbase;
a.resize(sz,Mint(0)); b.resize(sz,Mint(0));
ntt(a); ntt(b);
Mint inv_sz=1/Mint(sz);
for (int i=0;i<sz;++i) a[i]*=b[i]*inv_sz;
reverse(a.begin()+1,a.end());
ntt(a);
a.resize(need);
return a;
}
vector<int> multiply(vector<int> a,vector<int> b){
vector<Mint> A(a.size()),B(b.size());
for (int i=0;i<a.size();++i) A[i]=Mint(a[i]);
for (int i=0;i<b.size();++i) B[i]=Mint(b[i]);
vector<Mint> C=multiply(A,B);
vector<int> res(C.size());
for (int i=0;i<C.size();++i) res[i]=C[i].v;
return res;
}
};
long long modpow(long long x,long long n,long long mod){
long long res=1;
while (n>0){
if (n&1LL) res=res*x%mod;
x=x*x%mod; n>>=1LL;
}
return res;
}
using mint=modint<MOD>;
int main(){
cin.tie(0);
ios::sync_with_stdio(false);
int P; cin >> P;
vector<mint> A(P),B(P);
for (int i=1;i<P;++i) cin >> A[i];
for (int i=1;i<P;++i) cin >> B[i];
auto primitive_root=[](int p)->int{
for (int x=1;;++x){
long long power=1;
for (int i=0;i<p;++i){
(power*=x)%=p;
if (i==p-2) return x;
if (power==1) break;
}
}
};
int r=primitive_root(P);
vector<mint> a(P-1),b(P-1);
vector<long long> power(P,1);
for (int i=0;i<P-1;++i){
a[i]=A[power[i]]; b[i]=B[power[i]];
power[i+1]=power[i]*r%P;
}
NumberTheoreticTransform<MOD> NTT;
vector<mint> c=NTT.multiply(a,b),ans(P);
for (int i=0;i<c.size();++i){
ans[power[i%(P-1)]]+=c[i];
}
for (int i=1;i<P;++i) cout << ans[i] << (i+1==P?'\n':' ');
}
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