compro-library
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test/convolution/DivisorZetaMoebiusTransform-lcm-convolution.test.cpp
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- Last update: 2023-06-18 05:25:18+09:00
- Problem: https://judge.yosupo.jp/problem/lcm_convolution
Depends on
FastIO
(lib/00-util/FastIO.cpp)
- ModInt
(lib/00-util/ModInt.cpp)
- Eratosthenes - エラトステネスの篩
(lib/30-math/Eratosthenes.cpp)
- DivisorZetaMoebiusTransform - 約数のゼータ・メビウス変換 (gcd/lcm畳み込み)
(lib/31-convolution/DivisorZetaMoebiusTransform.cpp)
Code
#define PROBLEM "https://judge.yosupo.jp/problem/lcm_convolution"
#include <vector>
#include <iostream>
#include <cassert>
using namespace std;
#include "../../lib/00-util/ModInt.cpp"
#include "../../lib/00-util/FastIO.cpp"
#include "../../lib/30-math/Eratosthenes.cpp"
#include "../../lib/31-convolution/DivisorZetaMoebiusTransform.cpp"
int main() {
cin.tie(0);ios::sync_with_stdio(false);
using Mint = ModInt<MOD_998244353>;
int N; read(N);
vector<Mint> a(N+1,0),b(N+1,0);
auto e = Eratosthenes(N);
for(int i=1;i<=N;++i) {
int t; read(t); a[i]=t;
}
for(int i=1;i<=N;++i) {
int t; read(t); b[i]=t;
}
auto c = DivisorZetaMoebiusTransform::lcm_convolution(a,b,e);
for(int i=1;i<=N;++i) {
cout << c[i] << " \n"[i==N];
}
return 0;
}#line 1 "test/convolution/DivisorZetaMoebiusTransform-lcm-convolution.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/lcm_convolution"
#include <vector>
#include <iostream>
#include <cassert>
using namespace std;
#line 1 "lib/00-util/ModInt.cpp"
/*
* @title ModInt
* @docs md/util/ModInt.md
*/
template<long long mod> class ModInt {
public:
long long x;
constexpr ModInt():x(0) {}
constexpr ModInt(long long y) : x(y>=0?(y%mod): (mod - (-y)%mod)%mod) {}
constexpr ModInt &operator+=(const ModInt &p) {if((x += p.x) >= mod) x -= mod;return *this;}
constexpr ModInt &operator+=(const long long y) {ModInt p(y);if((x += p.x) >= mod) x -= mod;return *this;}
constexpr ModInt &operator+=(const int y) {ModInt p(y);if((x += p.x) >= mod) x -= mod;return *this;}
constexpr ModInt &operator-=(const ModInt &p) {if((x += mod - p.x) >= mod) x -= mod;return *this;}
constexpr ModInt &operator-=(const long long y) {ModInt p(y);if((x += mod - p.x) >= mod) x -= mod;return *this;}
constexpr ModInt &operator-=(const int y) {ModInt p(y);if((x += mod - p.x) >= mod) x -= mod;return *this;}
constexpr ModInt &operator*=(const ModInt &p) {x = (x * p.x % mod);return *this;}
constexpr ModInt &operator*=(const long long y) {ModInt p(y);x = (x * p.x % mod);return *this;}
constexpr ModInt &operator*=(const int y) {ModInt p(y);x = (x * p.x % mod);return *this;}
constexpr ModInt &operator^=(const ModInt &p) {x = (x ^ p.x) % mod;return *this;}
constexpr ModInt &operator^=(const long long y) {ModInt p(y);x = (x ^ p.x) % mod;return *this;}
constexpr ModInt &operator^=(const int y) {ModInt p(y);x = (x ^ p.x) % mod;return *this;}
constexpr ModInt &operator/=(const ModInt &p) {*this *= p.inv();return *this;}
constexpr ModInt &operator/=(const long long y) {ModInt p(y);*this *= p.inv();return *this;}
constexpr ModInt &operator/=(const int y) {ModInt p(y);*this *= p.inv();return *this;}
constexpr ModInt operator=(const int y) {ModInt p(y);*this = p;return *this;}
constexpr ModInt operator=(const long long y) {ModInt p(y);*this = p;return *this;}
constexpr ModInt operator-() const {return ModInt(-x); }
constexpr ModInt operator++() {x++;if(x>=mod) x-=mod;return *this;}
constexpr ModInt operator--() {x--;if(x<0) x+=mod;return *this;}
constexpr ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
constexpr ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
constexpr ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
constexpr ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
constexpr ModInt operator^(const ModInt &p) const { return ModInt(*this) ^= p; }
constexpr bool operator==(const ModInt &p) const { return x == p.x; }
constexpr bool operator!=(const ModInt &p) const { return x != p.x; }
// ModInt inv() const {int a=x,b=mod,u=1,v=0,t;while(b > 0) {t = a / b;swap(a -= t * b, b);swap(u -= t * v, v);} return ModInt(u);}
constexpr ModInt inv() const {int a=x,b=mod,u=1,v=0,t=0,tmp=0;while(b > 0) {t = a / b;a-=t*b;tmp=a;a=b;b=tmp;u-=t*v;tmp=u;u=v;v=tmp;} return ModInt(u);}
constexpr ModInt pow(long long n) const {ModInt ret(1), mul(x);for(;n > 0;mul *= mul,n >>= 1) if(n & 1) ret *= mul;return ret;}
friend ostream &operator<<(ostream &os, const ModInt &p) {return os << p.x;}
friend istream &operator>>(istream &is, ModInt &a) {long long t;is >> t;a = ModInt<mod>(t);return (is);}
};
constexpr long long MOD_998244353 = 998244353;
constexpr long long MOD_1000000007 = 1'000'000'000LL + 7; //'
#line 1 "lib/00-util/FastIO.cpp"
/*
* @title FastIO
* @docs md/util/FastIO.md
*/
class FastIO{
private:
inline static constexpr int ch_0='0';
inline static constexpr int ch_9='9';
inline static constexpr int ch_n='-';
inline static constexpr int ch_s=' ';
inline static constexpr int ch_l='\n';
inline static void endline_skip(char& ch) {
while(ch==ch_l) ch=getchar();
}
template<typename T> inline static void read_integer(T &x) {
int neg=0; char ch; x=0;
ch=getchar();
endline_skip(ch);
if(ch==ch_n) neg=1,ch=getchar();
for(;(ch_0 <= ch && ch <= ch_9); ch = getchar()) x = x*10 + (ch-ch_0);
if(neg) x*=-1;
}
template<typename T> inline static void read_unsigned_integer(T &x) {
char ch; x=0;
ch=getchar();
endline_skip(ch);
for(;(ch_0 <= ch && ch <= ch_9); ch = getchar()) x = x*10 + (ch-ch_0);
}
inline static void read_string(string &x) {
char ch; x="";
ch=getchar();
endline_skip(ch);
for(;(ch != ch_s && ch!=ch_l); ch = getchar()) x.push_back(ch);
}
inline static char ar[40];
inline static char *ch_ar;
template<typename T> inline static void write_integer(T x) {
ch_ar=ar;
if(x< 0) putchar(ch_n), x=-x;
if(x==0) putchar(ch_0);
for(;x;x/=10) *ch_ar++=(ch_0+x%10);
while(ch_ar--!=ar) putchar(*ch_ar);
}
public:
inline static void read(int &x) {read_integer<int>(x);}
inline static void read(long long &x) {read_integer<long long>(x);}
inline static void read(unsigned int &x) {read_unsigned_integer<unsigned int>(x);}
inline static void read(unsigned long long &x) {read_unsigned_integer<unsigned long long>(x);}
inline static void read(string &x) {read_string(x);}
inline static void read(__int128_t &x) {read_integer<__int128_t>(x);}
inline static void write(__int128_t x) {write_integer<__int128_t>(x);}
inline static void write(char x) {putchar(x);}
};
#define read(arg) FastIO::read(arg)
#define write(arg) FastIO::write(arg)
#line 1 "lib/30-math/Eratosthenes.cpp"
/*
* @title Eratosthenes - エラトステネスの篩
* @docs md/math/Eratosthenes.md
*/
class Eratosthenes {
unsigned int sz;
public:
vector<unsigned int> sieve;
vector<long long> prime;
Eratosthenes(unsigned int N):sz(N+1),sieve(N+1, 1) {
sieve[0]=sieve[1]=0;
for(int i=1; i <= N/i; ++i) if(sieve[i]) for(int j=2*i;j<=N;j+=i) sieve[j]=0;
for(int i=1; i <= N ; ++i) if(sieve[i]) prime.push_back(i);
}
size_t size() const {
return sz;
}
};
#line 1 "lib/31-convolution/DivisorZetaMoebiusTransform.cpp"
/*
* @title DivisorZetaMoebiusTransform - 約数のゼータ・メビウス変換 (gcd/lcm畳み込み)
* @docs md/math/DivisorZetaMoebiusTransform.md
*/
class DivisorZetaMoebiusTransform {
template<class T> inline static void zeta_multiple(vector<T>& v, const Eratosthenes& eratosthenes) {
assert(v.size()); int N = v.size();
for(const int& p:eratosthenes.prime) for(int i=(N-1)/p; i; --i) v[i] += v[i*p];
}
template<class T> inline static void mobius_multiple(vector<T>& v, const Eratosthenes& eratosthenes) {
assert(v.size()); int N = v.size();
for(const int& p:eratosthenes.prime) for(int i=1; i*p<N; ++i) v[i] -= v[i*p];
}
template<class T> inline static void zeta_divisor(vector<T>& v, const Eratosthenes& eratosthenes) {
assert(v.size()); int N = v.size();
for(const int& p:eratosthenes.prime) for(int i=1; i*p<N; ++i) {v[i*p] += v[i];}
}
template<class T> inline static void mobius_divisor(vector<T>& v, const Eratosthenes& eratosthenes) {
assert(v.size()); int N = v.size();
for(const int& p:eratosthenes.prime) for(int i=(N-1)/p; i; --i) {v[i*p] -= v[i];}
}
public:
template<class T> inline static vector<T> gcd_convolution(const vector<T>& a,const vector<T>& b, const Eratosthenes& eratosthenes) {
int N = max(a.size(),b.size());
assert(N <= eratosthenes.size());
vector<T> f(N,0),g(N,0);
for(int i=0;i<N;++i) f[i] = a[i];
for(int i=0;i<N;++i) g[i] = b[i];
zeta_multiple(f,eratosthenes);zeta_multiple(g,eratosthenes);
for(int i=0;i<N;++i) f[i] = f[i]*g[i];
mobius_multiple(f,eratosthenes);
return f;
}
template<class T> inline static vector<T> lcm_convolution(const vector<T>& a,const vector<T>& b, const Eratosthenes& eratosthenes) {
int N = max(a.size(),b.size());
assert(N <= eratosthenes.size());
vector<T> f(N,0),g(N,0);
for(int i=0;i<N;++i) f[i] = a[i];
for(int i=0;i<N;++i) g[i] = b[i];
zeta_divisor(f,eratosthenes);zeta_divisor(g,eratosthenes);
for(int i=0;i<N;++i) f[i] = f[i]*g[i];
mobius_divisor(f,eratosthenes);
return f;
}
};
#line 11 "test/convolution/DivisorZetaMoebiusTransform-lcm-convolution.test.cpp"
int main() {
cin.tie(0);ios::sync_with_stdio(false);
using Mint = ModInt<MOD_998244353>;
int N; read(N);
vector<Mint> a(N+1,0),b(N+1,0);
auto e = Eratosthenes(N);
for(int i=1;i<=N;++i) {
int t; read(t); a[i]=t;
}
for(int i=1;i<=N;++i) {
int t; read(t); b[i]=t;
}
auto c = DivisorZetaMoebiusTransform::lcm_convolution(a,b,e);
for(int i=1;i<=N;++i) {
cout << c[i] << " \n"[i==N];
}
return 0;
}