結果

問題 No.931 Multiplicative Convolution
ユーザー tatyam
提出日時 2019-11-23 07:48:21
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 134 ms / 2,000 ms
コード長 16,273 bytes
コンパイル時間 2,925 ms
コンパイル使用メモリ 218,564 KB
最終ジャッジ日時 2025-01-08 05:27:23
ジャッジサーバーID
(参考情報)
judge3 / judge3
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
コンパイルメッセージ
main.cpp: In function ‘void scan(long long int&)’:
main.cpp:80:38: warning: ignoring return value of ‘int scanf(const char*, ...)’ declared with attribute ‘warn_unused_result’ [-Wunused-result]
   80 | inline void scan(long long &a){ scanf("%lld", &a); }
      |                                 ~~~~~^~~~~~~~~~~~

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;
using ll=long long;
using ld=long double;
using ull=unsigned long long;
using uint=unsigned int;
using pcc=pair<char,char>;
using pii=pair<int,int>;
using pll=pair<ll,ll>;
using pdd=pair<double,double>;
using tuplis=pair<ll,pll>;
using tuplis2=pair<pll,ll>;
template<class T> using pq=priority_queue<T,vector<T>,greater<T>>;
const ll LINF=0x1fffffffffffffff;
const ll MINF=0x7fffffffffff;
const int INF=0x3fffffff;
const ll MOD=1000000007;
const ll MODD=998244353;
const ld DINF=numeric_limits<ld>::infinity();
const ld EPS=1e-9;
const ld PI=3.141592653589793238462643383279;
const vector<ll>four{0,1,0,-1,0};
#define _overload4(_1,_2,_3,_4,name,...) name
#define _overload3(_1,_2,_3,name,...) name
#define _rep1(n) for(ll i=0;i<n;++i)
#define _rep2(i,n) for(ll i=0;i<n;++i)
#define _rep3(i,a,b) for(ll i=a;i<b;++i)
#define _rep4(i,a,b,c) for(ll i=a;i<b;i+=c)
#define rep(...) _overload4(__VA_ARGS__,_rep4,_rep3,_rep2,_rep1)(__VA_ARGS__)
#define _rrep1(n) for(ll i=(n)-1;i>=0;i--)
#define _rrep2(i,n) for(ll i=(n)-1;i>=0;i--)
#define _rrep3(i,a,b) for(ll i=(b)-1;i>=(a);i--)
#define _rrep4(i,a,b,c) for(ll i=a+(b-a-1)/c*c;i>=a;i-=c)
#define rrep(...) _overload4(__VA_ARGS__,_rrep4,_rrep3,_rrep2,_rrep1)(__VA_ARGS__)
#define each(i,a) for(auto &i:a)
#define sum(...) accumulate(range(__VA_ARGS__),0LL)
#define dsum(...) accumulate(range(__VA_ARGS__),double(0))
#define _range(i) (i).begin(),(i).end()
#define _range2(i,k) (i).begin(),(i).begin()+k
#define _range3(i,a,b) (i).begin()+a,(i).begin()+b
#define range(...) _overload3(__VA_ARGS__,_range3,_range2,_range)(__VA_ARGS__)
#define _rrange(i) (i).rbegin(),(i).rend()
#define _rrange2(i,k) (i).rbegin(),(i).rbegin()+k
#define _rrange3(i,a,b) (i).rbegin()+a,(i).rbegin()+b
#define rrange(...) _overload3(__VA_ARGS__,_rrange3,_rrange2,_rrange)(__VA_ARGS__)
#define elif else if
#define unless(a) if(!(a))
#define mp make_pair
#define mt make_tuple
#define INT(...) int __VA_ARGS__;in(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__;in(__VA_ARGS__)
#define ULL(...) ull __VA_ARGS__;in(__VA_ARGS__)
#define STR(...) string __VA_ARGS__;in(__VA_ARGS__)
#define CHR(...) char __VA_ARGS__;in(__VA_ARGS__)
#define DBL(...) double __VA_ARGS__;in(__VA_ARGS__)
#define LD(...) ld __VA_ARGS__;in(__VA_ARGS__)
#define vec(type,name,...) vector<type> name(__VA_ARGS__)
#define VEC(type,name,size) vector<type> name(size);in(name)
#define vv(type,name,h,...) vector<vector<type>>name(h,vector<type>(__VA_ARGS__))
#define VV(type,name,h,...) vector<vector<type>>name(h,vector<type>(__VA_ARGS__));in(name)
#define vvv(type,name,h,w,...) vector<vector<vector<type>>>name(h,vector<vector<type>>(w,vector<type>(__VA_ARGS__)))
inline ll gcd(ll a, ll b){ while(b){ ll c = b; b = a % b; a = c; } return a; }
inline ll lcm(ll a, ll b){ if(!a || !b) return 0; return a * b / gcd(a, b); }
template<class T> inline T min(const vector<T> &v){ return *min_element(range(v)); }
inline char min(const string &v){ return *min_element(range(v)); }
template<class T> inline T max(const vector<T> &v){ return *max_element(range(v)); }
inline char max(const string &v){ return *max_element(range(v)); }
inline ll intpow(ll a, ll b){ ll ans = 1; while(b){ if(b & 1) ans *= a; a *= a; b /= 2; } return ans; }
inline ll modpow(ll a, ll b, ll p){ ll ans = 1; while(b){ if(b & 1) (ans *= a) %= p; (a *= a) %= p; b /= 2; } return ans; }
template<class T> inline bool chmin(T &a, const T &b){ if(a > b){ a = b; return 1; } return 0; }
template<class T> inline bool chmax(T &a, const T &b){ if(a < b){ a = b; return 1; } return 0; }
map<ll, ll> factor(ull x){ map<ll, ll> ans; for(ll i = 2; i * i <= x; i++) while(x % i == 0){ ans[i]++; x /= i; } if(x != 1) ans[x]++; return ans; }
set<ll> divisor(ull x){ set<ll> ans; for(ll i = 1; i * i <= x; i++) if(x % i == 0){ ans.insert(i); ans.insert(x / i); } return ans; }
template<class T> unordered_map<T, ll> press(vector<T> &a){ auto b = a; sort(range(b)); b.erase(unique(range(b)), b.end()); unordered_map<T,ll> ans;
    rep(b.size()) ans[b[i]] = i; each(i, a) i = ans[i]; return ans; }
template<class T> map<T, ll> press_map(vector<T> &a){ auto b = a; sort(range(b)); b.erase(unique(range(b)), b.end()); map<T,ll> ans; rep(b.size())
    ans[b[i]] = i; each(i, a) i = ans[i]; return ans; }
inline int scan(){ return getchar(); }
inline void scan(int &a){ scanf("%d", &a); }
inline void scan(unsigned &a){ scanf("%u", &a); }
inline void scan(long &a){ scanf("%ld", &a); }
inline void scan(long long &a){ scanf("%lld", &a); }
inline void scan(unsigned long long &a){ scanf("%llu", &a); }
inline void scan(char &a){ cin >> a; }
inline void scan(float &a){ scanf("%f", &a); }
inline void scan(double &a){ scanf("%lf", &a); }
inline void scan(long double &a){ scanf("%Lf", &a); }
inline void scan(vector<bool> &vec){ for(unsigned i = 0; i < vec.size(); i++) { int a; scan(a); vec[i] = a; } }
inline void scan(char a[]){ scanf("%s", a); }
inline void scan(string &a){ cin >> a; }
template<class T> inline void scan(vector<T> &vec);
template<class T, size_t size> inline void scan(array<T, size> &vec);
template<class T, class L> inline void scan(pair<T, L> &p);
template<class T, size_t size> inline void scan(T (&vec)[size]);
template<class T> inline void scan(vector<T> &vec){ for(auto &i : vec) scan(i); }
template<class T> inline void scan(deque<T> &vec){ for(auto &i : vec) scan(i); }
template<class T, size_t size> inline void scan(array<T, size> &vec){ for(auto &i : vec) scan(i); }
template<class T, class L> inline void scan(pair<T, L> &p){ scan(p.first); scan(p.second); }
template<class T, size_t size> inline void scan(T (&vec)[size]){ for(auto &i : vec) scan(i); }
template<class T> inline void scan(T &a){ cin >> a; }
inline void in(){}
template <class Head, class... Tail> inline void in(Head &head, Tail&... tail){ scan(head); in(tail...); }
inline void print(){ putchar(' '); }
inline void print(const bool &a){ printf("%d", a); }
inline void print(const int &a){ printf("%d", a); }
inline void print(const unsigned &a){ printf("%u", a); }
inline void print(const long &a){ printf("%ld", a); }
inline void print(const long long &a){ printf("%lld", a); }
inline void print(const unsigned long long &a){ printf("%llu", a); }
inline void print(const char &a){ printf("%c", a); }
inline void print(const char a[]){ printf("%s", a); }
inline void print(const float &a){ printf("%.15f", a); }
inline void print(const double &a){ printf("%.15f", a); }
inline void print(const long double &a){ printf("%.15Lf", a); }
inline void print(const string &a){ for(auto&& i : a) print(i); }
template<class T> inline void print(const vector<T> &vec);
template<class T, size_t size> inline void print(const array<T, size> &vec);
template<class T, class L> inline void print(const pair<T, L> &p);
template<class T, size_t size> inline void print(const T (&vec)[size]);
template<class T> inline void print(const vector<T> &vec){ if(vec.empty()) return; print(vec[0]); for(auto i = vec.begin(); ++i != vec.end(); ){
    putchar(' '); print(*i); } }
template<class T> inline void print(const deque<T> &vec){ if(vec.empty()) return; print(vec[0]); for(auto i = vec.begin(); ++i != vec.end(); ){
    putchar(' '); print(*i); } }
template<class T, size_t size> inline void print(const array<T, size> &vec){ print(vec[0]); for(auto i = vec.begin(); ++i != vec.end(); ){ putchar('
    '); print(*i); } }
template<class T, class L> inline void print(const pair<T, L> &p){ print(p.first); putchar(' '); print(p.second); }
template<class T, size_t size> inline void print(const T (&vec)[size]){ print(vec[0]); for(auto i = vec; ++i != end(vec); ){ putchar(' '); print(*i);
    } }
template<class T> inline void print(const T &a){ cout << a; }
inline int out(){ putchar('\n'); return 0; }
template<class T> inline int out(const T &t){ print(t); putchar('\n'); return 0; }
template<class Head, class... Tail> inline int out(const Head &head, const Tail&... tail){ print(head); putchar(' '); out(tail...); return 0; }
#ifdef DEBUG
inline void err(){ putchar('\n'); }
template<class T> inline void err(const T &t){ print(t); putchar('\n'); }
template<class Head, class... Tail> inline void err(const Head &head, const Tail&... tail){ print(head); putchar(' '); out(tail...); }
#else
template<class... T> inline void err(const T&...){}
#endif
inline int first(bool i = true){ return out(i?"first":"second"); }
inline int yes(bool i = true){ return out(i?"yes":"no"); }
inline int Yes(bool i = true){ return out(i?"Yes":"No"); }
inline int No(){ return out("No"); }
inline int YES(bool i = true){ return out(i?"YES":"NO"); }
inline int NO(){ return out("NO"); }
inline int Yay(bool i = true){ return out(i?"Yay!":":("); }
inline int Possible(bool i = true){ return out(i?"Possible":"Impossible"); }
inline int POSSIBLE(bool i = true){ return out(i?"POSSIBLE":"IMPOSSIBLE"); }
inline void Case(ll i){ printf("Case #%lld: ", i); }
constexpr ll mod = MODD;
inline constexpr ll extgcd(ll a, ll b, ll &x, ll &y){ ll g = a; x = 1; y = 0; if(b){ g = extgcd(b, a % b, y, x); y -= a / b * x; } return g; }
inline constexpr ll invmod(ll a, ll m = mod){ ll x = 0, y = 0; extgcd(a, m, x, y); return (x + m) % m; }
struct Modint{
ll num;
constexpr Modint() : num() { num = 0; }
constexpr Modint(ll x) : num() { num = x % mod; if(num < 0) num += mod; }
inline constexpr Modint& operator= (int x){ num = x % mod; if(num < 0) num += mod; return *this; }
inline constexpr Modint& operator= (ll x){ num = x % mod; if(num < 0) num += mod; return *this; }
inline constexpr Modint& operator= (Modint x){ num = x.num; return *this; }
inline constexpr Modint operator+ (int x) const { return Modint(num + x); }
inline constexpr Modint operator+ (ll x) const { return Modint(num + x); }
inline constexpr Modint operator+ (Modint x) const { ll a = num + x.num; if(a >= mod) a -= mod; return Modint{a}; }
inline constexpr Modint& operator+=(int x){ num += x; num %= mod; if(num < 0) num += mod; return *this; }
inline constexpr Modint& operator+=(ll x){ num += x; num %= mod; if(num < 0) num += mod; return *this; }
inline constexpr Modint& operator+=(Modint x){ num += x.num; if(num >= mod) num -= mod; return *this; }
inline constexpr Modint& operator++(){ if(num == mod - 1) num = 0; else num++; return *this; }
inline constexpr Modint operator++(int){ Modint ans = *this; if(num == mod - 1) num = 0; else num++; return ans; }
inline constexpr Modint operator- () const { if(num == 0) return 0; return Modint(mod - num); }
inline constexpr Modint operator- (int x) const { return Modint(num - x); }
inline constexpr Modint operator- (ll x) const { return Modint(num - x); }
inline constexpr Modint operator- (Modint x) const { ll a = num - x.num; if(a < 0) a += mod; return Modint{a}; }
inline constexpr Modint& operator-=(int x){ num -= x; num %= mod; if(num < 0) num += mod; return *this; }
inline constexpr Modint& operator-=(ll x){ num -= x; num %= mod; if(num < 0) num += mod; return *this; }
inline constexpr Modint& operator-=(Modint x){ num -= x.num; if(num < 0) num += mod; return *this; }
inline constexpr Modint& operator--(){ if(num == 0) num = mod - 1; else num--; return *this; }
inline constexpr Modint operator--(int){ Modint ans = *this; if(num == 0) num = mod - 1; else num--; return ans; }
inline constexpr Modint operator* (int x) const { return Modint(num * (x % mod)); }
inline constexpr Modint operator* (ll x) const { return Modint(num * (x % mod)); }
inline constexpr Modint operator* (Modint x) const { return Modint{num * x.num % mod}; }
inline constexpr Modint& operator*=(int x){ num *= Modint(x); num %= mod; return *this; }
inline constexpr Modint& operator*=(ll x){ num *= Modint(x); num %= mod; return *this; }
inline constexpr Modint& operator*=(Modint x){ num *= x.num; num %= mod; return *this; }
inline constexpr Modint operator/ (int x) const { return Modint(num * invmod(Modint(x), mod)); }
inline constexpr Modint operator/ (ll x) const { return Modint(num * invmod(Modint(x), mod)); }
inline constexpr Modint operator/ (Modint x) const { return Modint{num * invmod(x.num, mod) % mod}; }
inline constexpr Modint& operator/=(int x){ num *= invmod(Modint(x), mod); num %= mod; return *this; }
inline constexpr Modint& operator/=(ll x){ num *= invmod(Modint(x), mod); num %= mod; return *this; }
inline constexpr Modint& operator/=(Modint x){ num *= invmod(x.num, mod); num %= mod; return *this; }
inline constexpr Modint pow(ll x) const { ll i = 1; Modint ans = 1, cnt = *this; while(i <= x){ if(x & i){ ans *= cnt; x ^= i; } cnt *= cnt; i *=
        2; } return ans; }
inline constexpr operator ll() const { return num; }
};
inline constexpr Modint operator""_M(ull x) { return Modint(x); }
std::vector<Modint> fac(1, 1), inv(1, 1);
inline void reserve(ll a){
if(fac.size() >= a) return;
if(a < fac.size() * 2) a = fac.size() * 2;
if(a >= mod) a = mod;
while(fac.size() < a) fac.push_back(fac.back() * ll(fac.size()));
inv.resize(fac.size());
inv.back() = Modint(1) / fac.back();
for(ll i = inv.size() - 1; !inv[i - 1]; i--) inv[i - 1] = inv[i] * i;
}
inline Modint fact(ll n){ if(n < 0) return 0; reserve(n + 1); return fac[n]; }
inline Modint perm(ll n, ll r){ if(r < 0 || n < r) return 0; reserve(n + 1); return fac[n] * inv[n - r]; }
inline Modint comb(ll n, ll r){ if(r < 0 || n < r) return 0; reserve(n + 1); return fac[n] * inv[r] * inv[n - r]; }
inline Modint Mcomb(ll n, ll r){ return comb(n + r - 1, n - 1); } // rn
istream& operator>>(istream& is, Modint& x) { is >> x.num; x = Modint(x.num); return is; }
struct FFT{
size_t size = 1, size_log2 = 0;
vector<size_t> butterfly;
vector<Modint> zeta;
FFT(size_t n) { // size
while(size < n) {
size *= 2;
size_log2++;
}
butterfly.resize(size);
zeta.resize(size + 1);
zeta[0] = 1;
zeta[1] = 3_M .pow((mod - 1) / size);
rep(i, 2, size + 1) zeta[i] = zeta[i - 1] * zeta[1];
rep(size_log2) rep(j, (1 << i)) {
ll a = (j << (size_log2 - i)) | (1 << (size_log2 - 1 - i)), b = (j + 1) << (size_log2 - i);
rep(k, a, b) butterfly[k] |= 1 << i;
}
}
void transform(vector<Modint>& x) {
vector<Modint> ans = x;
rep(size_log2) rep(j, (1 << i)) {
ll zeta1 = zeta[butterfly[j * 2]], zeta2 = zeta[butterfly[j * 2 + 1]];
ll a = j << (size_log2 - i), b = (j << (size_log2 - i)) | (1 << (size_log2 - 1 - i)), c = 1 << (size_log2 - 1 - i);
rep(k, a, b) {
ll x1 = ans[k], x2 = ans[k | c];
ans[k] = x1 + x2 * zeta1;
ans[k | c] = x1 + x2 * zeta2;
}
}
rep(size) x[butterfly[i]] = ans[i];
}
void reverse(vector<Modint>& x) {
vector<Modint> ans = x;
rep(size_log2) rep(j, (1 << i)) {
ll zeta1 = zeta[size - butterfly[j * 2]], zeta2 = zeta[size - butterfly[j * 2 + 1]];
ll a = j << (size_log2 - i), b = (j << (size_log2 - i)) | (1 << (size_log2 - 1 - i)), c = 1 << (size_log2 - 1 - i);
rep(k, a, b) {
ll x1 = ans[k], x2 = ans[k | c];
ans[k] = x1 + x2 * zeta1;
ans[k | c] = x1 + x2 * zeta2;
}
}
rep(size) x[butterfly[i]] = ans[i] / Modint(size);
}
vector<Modint> multiply(vector<Modint> a, vector<Modint> b) {
a.resize(size);
b.resize(size);
transform(a);
transform(b);
rep(size) a[i] *= b[i];
reverse(a);
return a;
}
};
signed main(){
LL(p);
VEC(ll,a,p-1);
VEC(ll,b,p-1);
auto fac = factor(p - 1);
ll g = 0;
rep(i,2,p){
if(all_of(range(fac),[&i,&p](pll a){return modpow(i,(p-1)/a.first,p)!=1;})){
g=i;
break;
}
}
vec(ll,d,p-1);
d[0]=1;
rep(p-2)d[i+1]=d[i]*g%p;
vec(Modint,A,p-1);
vec(Modint,B,p-1);
rep(p-1){
A[i]=a[d[i]-1];
B[i]=b[d[i]-1];
}
FFT fft(p*2-3);
auto C=fft.multiply(A,B);
vec(Modint,c,p-1);
rep(p*2-3){
c[d[i%(p-1)]-1]+=C[i];
}
out(c);
}
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