結果
| 問題 |
No.1618 Convolution?
|
| コンテスト | |
| ユーザー |
 kaichou243
|
| 提出日時 | 2022-05-14 23:56:49 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 546 ms / 2,000 ms |
| コード長 | 24,138 bytes |
| コンパイル時間 | 3,132 ms |
| コンパイル使用メモリ | 230,988 KB |
| 最終ジャッジ日時 | 2025-01-29 08:12:43 |
|
ジャッジサーバーID （参考情報） |
judge2 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 15 |
ソースコード
#include<bits/stdc++.h>
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#define FOR(i,n) for(int i = 0; i < (n); i++)
#define sz(c) ((int)(c).size())
#define ten(x) ((int)1e##x)
#define all(v) (v).begin(), (v).end()
using namespace std;
using ll=long long;
using P = pair<ll,ll>;
const long double PI=acos(-1);
const ll INF=1e18;
const int inf=1e9;
struct Edge {
ll to;
ll cost;
};
using Graph=vector<vector<Edge>>;
template <typename T>
bool chmax(T &a,const T& b){
if (a<b){
a=b;
return true;
}
return false;
}
template <typename T>
bool chmin(T &a,const T& b){
if (a>b){
a=b;
return true;
}
return false;
}
template<int MOD> struct Fp{
ll val;
constexpr Fp(long long v = 0) noexcept : val(v % MOD) {
if (val < 0) val += MOD;
}
static constexpr int getmod() { return MOD; }
constexpr Fp operator - () const noexcept {
return val ? MOD - val : 0;
}
constexpr Fp operator + (const Fp& r) const noexcept { return Fp(*this) += r; }
constexpr Fp operator - (const Fp& r) const noexcept { return Fp(*this) -= r; }
constexpr Fp operator * (const Fp& r) const noexcept { return Fp(*this) *= r; }
constexpr Fp operator / (const Fp& r) const noexcept { return Fp(*this) /= r; }
constexpr Fp& operator += (const Fp& r) noexcept {
val += r.val;
if (val >= MOD) val -= MOD;
return *this;
}
constexpr Fp& operator -= (const Fp& r) noexcept {
val -= r.val;
if (val < 0) val += MOD;
return *this;
}
constexpr Fp& operator *= (const Fp& r) noexcept {
val = val * r.val % MOD;
return *this;
}
constexpr Fp& operator /= (const Fp& r) noexcept {
ll a = r.val, b = MOD, u = 1, v = 0;
while (b) {
ll t = a / b;
a -= t * b, swap(a, b);
u -= t * v, swap(u, v);
}
val = val * u % MOD;
if (val < 0) val += MOD;
return *this;
}
constexpr bool operator == (const Fp& r) const noexcept {
return this->val == r.val;
}
constexpr bool operator != (const Fp& r) const noexcept {
return this->val != r.val;
}
constexpr bool operator < (const Fp& r) const noexcept {
return this->val < r.val;
}
friend constexpr istream& operator >> (istream& is, Fp<MOD>& x) noexcept {
is >> x.val;
x.val %= MOD;
if (x.val < 0) x.val += MOD;
return is;
}
friend constexpr ostream& operator << (ostream& os, const Fp<MOD>& x) noexcept {
return os << x.val;
}
friend constexpr Fp<MOD> modpow(const Fp<MOD>& a, long long n) noexcept {
Fp<MOD> res=1,r=a;
while(n){
if(n&1) res*=r;
r*=r;
n>>=1;
}
return res;
}
friend constexpr Fp<MOD> modinv(const Fp<MOD>& r) noexcept {
long long a = r.val, b = MOD, u = 1, v = 0;
while (b) {
long long t = a / b;
a -= t * b, swap(a, b);
u -= t * v, swap(u, v);
}
return Fp<MOD>(u);
}
explicit operator bool()const{
return val;
}
};
ll mod(ll a, ll mod) {
return (a%mod+mod)%mod;
}
ll modpow(ll a,ll n,ll mod){
ll res=1;
a%=mod;
while (n>0){
if (n & 1) res*=a;
a *= a;
a%=mod;
n >>= 1;
res%=mod;
}
return res;
}
ll modinv(ll a, ll mod) {
ll b = mod, u = 1, v = 0;
while (b) {
ll t = a/b;
a -= t * b, swap(a, b);
u -= t * v, swap(u, v);
}
u %= mod;
if (u < 0) u += mod;
return u;
}
namespace NTT {
int calc_primitive_root(int mod) {
if (mod == 2) return 1;
if (mod == 167772161) return 3;
if (mod == 469762049) return 3;
if (mod == 754974721) return 11;
if (mod == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
long long x = (mod - 1) / 2;
while (x % 2 == 0) x /= 2;
for (long long i = 3; i * i <= x; i += 2) {
if (x % i == 0) {
divs[cnt++] = i;
while (x % i == 0) x /= i;
}
}
if (x > 1) divs[cnt++] = x;
for (int g = 2;; g++) {
bool ok = true;
for (int i = 0; i < cnt; i++) {
if (modpow(g, (mod - 1) / divs[i], mod) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
int get_fft_size(int N, int M) {
int size_a = 1, size_b = 1;
while (size_a < N) size_a <<= 1;
while (size_b < M) size_b <<= 1;
return max(size_a, size_b) << 1;
}
constexpr int bsf_constexpr(unsigned int n) {
int x = 0;
while (!(n & (1 << x))) x++;
return x;
}
int bsf(unsigned int n) {
#ifdef _MSC_VER
unsigned long index;
_BitScanForward(&index, n);
return index;
#else
return __builtin_ctz(n);
#endif
}
template <class mint>
struct fft_info{
static constexpr int rank2 = bsf_constexpr(mint::getmod() - 1);
std::array<mint, rank2 + 1> root; // root[i]^(2^i) == 1
std::array<mint, rank2 + 1> iroot; // root[i] * iroot[i] == 1
std::array<mint, std::max(0, rank2 - 2 + 1)> rate2;
std::array<mint, std::max(0, rank2 - 2 + 1)> irate2;
std::array<mint, std::max(0, rank2 - 3 + 1)> rate3;
std::array<mint, std::max(0, rank2 - 3 + 1)> irate3;
int g;
fft_info(){
int MOD=mint::getmod();
g=calc_primitive_root(MOD);
root[rank2] = modpow(mint(g),(MOD - 1) >> rank2);
iroot[rank2] = modinv(root[rank2]);
for (int i = rank2 - 1; i >= 0; i--) {
root[i] = root[i + 1] * root[i + 1];
iroot[i] = iroot[i + 1] * iroot[i + 1];
}
{
mint prod = 1, iprod = 1;
for (int i = 0; i <= rank2 - 2; i++) {
rate2[i] = root[i + 2] * prod;
irate2[i] = iroot[i + 2] * iprod;
prod *= iroot[i + 2];
iprod *= root[i + 2];
}
}
{
mint prod = 1, iprod = 1;
for (int i = 0; i <= rank2 - 3; i++) {
rate3[i] = root[i + 3] * prod;
irate3[i] = iroot[i + 3] * iprod;
prod *= iroot[i + 3];
iprod *= root[i + 3];
}
}
}
};
int ceil_pow2(int n) {
int x = 0;
while ((1U << x) < (unsigned int)(n)) x++;
return x;
}
// number-theoretic transform
template <class mint>
void trans(std::vector<mint>& a) {
int n = int(a.size());
int h = ceil_pow2(n);
int MOD=a[0].getmod();
static const fft_info<mint> info;
int len = 0; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
while (len < h) {
if (h - len == 1) {
int p = 1 << (h - len - 1);
mint rot = 1;
for (int s = 0; s < (1 << len); s++) {
int offset = s << (h - len);
for (int i = 0; i < p; i++) {
auto l = a[i + offset];
auto r = a[i + offset + p] * rot;
a[i + offset] = l + r;
a[i + offset + p] = l - r;
}
if (s + 1 != (1 << len))
rot *= info.rate2[bsf(~(unsigned int)(s))];
}
len++;
} else {
// 4-base
int p = 1 << (h - len - 2);
mint rot = 1, imag = info.root[2];
for (int s = 0; s < (1 << len); s++) {
mint rot2 = rot * rot;
mint rot3 = rot2 * rot;
int offset = s << (h - len);
for (int i = 0; i < p; i++) {
auto mod2 = 1ULL * MOD * MOD;
auto a0 = 1ULL * a[i + offset].val;
auto a1 = 1ULL * a[i + offset + p].val * rot.val;
auto a2 = 1ULL * a[i + offset + 2 * p].val * rot2.val;
auto a3 = 1ULL * a[i + offset + 3 * p].val * rot3.val;
auto a1na3imag =
1ULL * mint(a1 + mod2 - a3).val * imag.val;
auto na2 = mod2 - a2;
a[i + offset] = a0 + a2 + a1 + a3;
a[i + offset + 1 * p] = a0 + a2 + (2 * mod2 - (a1 + a3));
a[i + offset + 2 * p] = a0 + na2 + a1na3imag;
a[i + offset + 3 * p] = a0 + na2 + (mod2 - a1na3imag);
}
if (s + 1 != (1 << len))
rot *= info.rate3[bsf(~(unsigned int)(s))];
}
len += 2;
}
}
}
template <class mint>
void trans_inv(std::vector<mint>& a) {
int n = int(a.size());
int h = ceil_pow2(n);
static const fft_info<mint> info;
int MOD=a[0].getmod();
int len = h; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
while (len) {
if (len == 1) {
int p = 1 << (h - len);
mint irot = 1;
for (int s = 0; s < (1 << (len - 1)); s++) {
int offset = s << (h - len + 1);
for (int i = 0; i < p; i++) {
auto l = a[i + offset];
auto r = a[i + offset + p];
a[i + offset] = l + r;
a[i + offset + p] =
(unsigned long long)(MOD + l.val - r.val) *
irot.val;
;
}
if (s + 1 != (1 << (len - 1)))
irot *= info.irate2[bsf(~(unsigned int)(s))];
}
len--;
} else {
// 4-base
int p = 1 << (h - len);
mint irot = 1, iimag = info.iroot[2];
for (int s = 0; s < (1 << (len - 2)); s++) {
mint irot2 = irot * irot;
mint irot3 = irot2 * irot;
int offset = s << (h - len + 2);
for (int i = 0; i < p; i++) {
auto a0 = 1ULL * a[i + offset + 0 * p].val;
auto a1 = 1ULL * a[i + offset + 1 * p].val;
auto a2 = 1ULL * a[i + offset + 2 * p].val;
auto a3 = 1ULL * a[i + offset + 3 * p].val;
auto a2na3iimag =
1ULL *
mint((MOD + a2 - a3) * iimag.val).val;
a[i + offset] = a0 + a1 + a2 + a3;
a[i + offset + 1 * p] =
(a0 + (MOD - a1) + a2na3iimag) * irot.val;
a[i + offset + 2 * p] =
(a0 + a1 + (MOD - a2) + (MOD - a3)) *
irot2.val;
a[i + offset + 3 * p] =
(a0 + (MOD - a1) + (MOD - a2na3iimag)) *
irot3.val;
}
if (s + 1 != (1 << (len - 2)))
irot *= info.irate3[bsf(~(unsigned int)(s))];
}
len -= 2;
}
}
}
// for garner
static constexpr int MOD0 = 754974721;
static constexpr int MOD1 = 167772161;
static constexpr int MOD2 = 469762049;
using mint0 = Fp<MOD0>;
using mint1 = Fp<MOD1>;
using mint2 = Fp<MOD2>;
static const mint1 imod0 = 95869806; // modinv(MOD0, MOD1);
static const mint2 imod1 = 104391568; // modinv(MOD1, MOD2);
static const mint2 imod01 = 187290749; // imod1 / MOD0;
// small case (T = mint, long long)
template<class T> vector<T> naive_mul
(const vector<T> &A, const vector<T> &B) {
if (A.empty() || B.empty()) return {};
int N = (int)A.size(), M = (int)B.size();
vector<T> res(N + M - 1);
for (int i = 0; i < N; ++i)
for (int j = 0; j < M; ++j)
res[i + j] += A[i] * B[j];
return res;
}
// mint
template<class mint>
vector<mint> mul(vector<mint> A,vector<mint> B) {
if (A.empty() || B.empty()) return {};
int n = int(A.size()), m = int(B.size());
if (min(n, m) < 30) return naive_mul(A, B);
int MOD = A[0].getmod();
int z = 1 << ceil_pow2(n + m - 1);
if (MOD == 998244353) {
A.resize(z);
trans(A);
B.resize(z);
trans(B);
for (int i = 0; i < z; i++) {
A[i] *= B[i];
}
trans_inv(A);
A.resize(n + m - 1);
mint iz = modinv(mint(z));
for (int i = 0; i < n + m - 1; i++) A[i] *= iz;
return A;
}
vector<mint0> a0(z, 0), b0(z, 0);
vector<mint1> a1(z, 0), b1(z, 0);
vector<mint2> a2(z, 0), b2(z, 0);
for (int i = 0; i < n; ++i)
a0[i] = A[i].val, a1[i] = A[i].val, a2[i] = A[i].val;
for (int i = 0; i < m; ++i)
b0[i] = B[i].val, b1[i] = B[i].val, b2[i] = B[i].val;
trans(a0), trans(a1), trans(a2), trans(b0), trans(b1), trans(b2);
for (int i = 0; i < z; ++i) {
a0[i] *= b0[i];
a1[i] *= b1[i];
a2[i] *= b2[i];
}
trans_inv(a0), trans_inv(a1), trans_inv(a2);
static const mint mod0 = MOD0, mod01 = mod0 * MOD1;
mint0 i0=modinv(mint0(z));
mint1 i1=modinv(mint1(z));
mint2 i2=modinv(mint2(z));
vector<mint> res(n + m - 1);
for (int i = 0; i < n + m - 1; ++i) {
a0[i]*=i0;
a1[i]*=i1;
a2[i]*=i2;
int y0 = a0[i].val;
int y1 = (imod0 * (a1[i] - y0)).val;
int y2 = (imod01 * (a2[i] - y0) - imod1 * y1).val;
res[i] = mod01 * y2 + mod0 * y1 + y0;
}
return res;
}
vector<ll> mul_ll(vector<ll> A,vector<ll> B) {
if (A.empty() || B.empty()) return {};
int n = int(A.size()), m = int(B.size());
if (min(n, m) < 30) return naive_mul(A, B);
int z = 1 << ceil_pow2(n + m - 1);
vector<mint0> a0(z, 0), b0(z, 0);
vector<mint1> a1(z, 0), b1(z, 0);
vector<mint2> a2(z, 0), b2(z, 0);
for (int i = 0; i < n; ++i)
a0[i] = A[i], a1[i] = A[i], a2[i] = A[i];
for (int i = 0; i < m; ++i)
b0[i] = B[i], b1[i] = B[i], b2[i] = B[i];
trans(a0), trans(a1), trans(a2), trans(b0), trans(b1), trans(b2);
for (int i = 0; i < z; ++i) {
a0[i] *= b0[i];
a1[i] *= b1[i];
a2[i] *= b2[i];
}
trans_inv(a0), trans_inv(a1), trans_inv(a2);
static const ll mod0 = MOD0, mod01 = mod0 * MOD1;
mint0 i0=modinv(mint0(z));
mint1 i1=modinv(mint1(z));
mint2 i2=modinv(mint2(z));
vector<ll> res(n + m - 1);
for (int i = 0; i < n + m - 1; ++i) {
a0[i]*=i0;
a1[i]*=i1;
a2[i]*=i2;
int y0 = a0[i].val;
int y1 = (imod0 * (a1[i] - y0)).val;
int y2 = (imod01 * (a2[i] - y0) - imod1 * y1).val;
res[i] = mod01 * y2 + mod0 * y1 + y0;
}
return res;
}
};
#include <unistd.h>
#include <algorithm>
#include <array>
#include <cassert>
#include <cctype>
#include <cstring>
#include <sstream>
#include <string>
#include <type_traits>
#include <vector>
namespace fastio{
/*
quote from yosupo's submission in Library Checker
*/
int bsr(unsigned int n) {
return 8 * (int)sizeof(unsigned int) - 1 - __builtin_clz(n);
}
// @param n `1 <= n`
// @return maximum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsr(unsigned long n) {
return 8 * (int)sizeof(unsigned long) - 1 - __builtin_clzl(n);
}
// @param n `1 <= n`
// @return maximum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsr(unsigned long long n) {
return 8 * (int)sizeof(unsigned long long) - 1 - __builtin_clzll(n);
}
// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsr(unsigned __int128 n) {
unsigned long long low = (unsigned long long)(n);
unsigned long long high = (unsigned long long)(n >> 64);
return high ? 127 - __builtin_clzll(high) : 63 - __builtin_ctzll(low);
}
namespace internal {
template <class T>
using is_signed_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value ||
std::is_same<T, __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int128 =
typename std::conditional<std::is_same<T, __uint128_t>::value ||
std::is_same<T, unsigned __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using make_unsigned_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value,
__uint128_t,
unsigned __int128>;
template <class T>
using is_integral =
typename std::conditional<std::is_integral<T>::value ||
internal::is_signed_int128<T>::value ||
internal::is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
std::is_signed<T>::value) ||
is_signed_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<(is_integral<T>::value &&
std::is_unsigned<T>::value) ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
is_signed_int128<T>::value,
make_unsigned_int128<T>,
typename std::conditional<std::is_signed<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type>::type;
template <class T>
using is_integral_t = std::enable_if_t<is_integral<T>::value>;
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T> using to_unsigned_t = typename to_unsigned<T>::type;
} // namespace internal
struct Scanner {
public:
Scanner(const Scanner&) = delete;
Scanner& operator=(const Scanner&) = delete;
Scanner(FILE* fp) : fd(fileno(fp)) {}
void read() {}
template <class H, class... T> void read(H& h, T&... t) {
bool f = read_single(h);
assert(f);
read(t...);
}
int read_unsafe() { return 0; }
template <class H, class... T> int read_unsafe(H& h, T&... t) {
bool f = read_single(h);
if (!f) return 0;
return 1 + read_unsafe(t...);
}
int close() { return ::close(fd); }
private:
static constexpr int SIZE = 1 << 15;
int fd = -1;
std::array<char, SIZE + 1> line;
int st = 0, ed = 0;
bool eof = false;
bool read_single(std::string& ref) {
if (!skip_space()) return false;
ref = "";
while (true) {
char c = top();
if (c <= ' ') break;
ref += c;
st++;
}
return true;
}
bool read_single(double& ref) {
std::string s;
if (!read_single(s)) return false;
ref = std::stod(s);
return true;
}
template <class T,
std::enable_if_t<std::is_same<T, char>::value>* = nullptr>
bool read_single(T& ref) {
if (!skip_space<50>()) return false;
ref = top();
st++;
return true;
}
template <class T,
internal::is_signed_int_t<T>* = nullptr,
std::enable_if_t<!std::is_same<T, char>::value>* = nullptr>
bool read_single(T& sref) {
using U = internal::to_unsigned_t<T>;
if (!skip_space<50>()) return false;
bool neg = false;
if (line[st] == '-') {
neg = true;
st++;
}
U ref = 0;
do {
ref = 10 * ref + (line[st++] & 0x0f);
} while (line[st] >= '0');
sref = neg ? -ref : ref;
return true;
}
template <class U,
internal::is_unsigned_int_t<U>* = nullptr,
std::enable_if_t<!std::is_same<U, char>::value>* = nullptr>
bool read_single(U& ref) {
if (!skip_space<50>()) return false;
ref = 0;
do {
ref = 10 * ref + (line[st++] & 0x0f);
} while (line[st] >= '0');
return true;
}
bool reread() {
if (ed - st >= 50) return true;
if (st > SIZE / 2) {
std::memmove(line.data(), line.data() + st, ed - st);
ed -= st;
st = 0;
}
if (eof) return false;
auto u = ::read(fd, line.data() + ed, SIZE - ed);
if (u == 0) {
eof = true;
line[ed] = '\0';
u = 1;
}
ed += int(u);
line[ed] = char(127);
return true;
}
char top() {
if (st == ed) {
bool f = reread();
assert(f);
}
return line[st];
}
template <int TOKEN_LEN = 0>
bool skip_space() {
while (true) {
while (line[st] <= ' ') st++;
if (ed - st > TOKEN_LEN) return true;
if (st > ed) st = ed;
for (auto i = st; i < ed; i++) {
if (line[i] <= ' ') return true;
}
if (!reread()) return false;
}
}
};
//fast Output by ei1333
/**
* @brief Printer(高速出力)
*/
struct Printer {
public:
explicit Printer(FILE *fp) : fp(fp) {}
~Printer() { flush(); }
template< bool f = false, typename T, typename... E >
void write(const T &t, const E &... e) {
if(f) write_single(' ');
write_single(t);
write< true >(e...);
}
template< typename... T >
void writeln(const T &...t) {
write(t...);
write_single('\n');
}
void flush() {
fwrite(line, 1, st - line, fp);
st = line;
}
private:
FILE *fp = nullptr;
static constexpr size_t line_size = 1 << 16;
static constexpr size_t int_digits = 20;
char line[line_size + 1] = {};
char small[32] = {};
char *st = line;
template< bool f = false >
void write() {}
void write_single(const char &t) {
if(st + 1 >= line + line_size) flush();
*st++ = t;
}
template< typename T, enable_if_t< is_integral< T >::value, int > = 0 >
void write_single(T s) {
if(st + int_digits >= line + line_size) flush();
if(s == 0) {
write_single('0');
return;
}
if(s < 0) {
write_single('-');
s = -s;
}
char *mp = small + sizeof(small);
typename make_unsigned< T >::type y = s;
size_t len = 0;
while(y > 0) {
*--mp = y % 10 + '0';
y /= 10;
++len;
}
memmove(st, mp, len);
st += len;
}
void write_single(const string &s) {
for(auto &c : s) write_single(c);
}
void write_single(const char *s) {
while(*s != 0) write_single(*s++);
}
template< typename T >
void write_single(const vector< T > &s) {
for(size_t i = 0; i < s.size(); i++) {
if(i) write_single(' ');
write_single(s[i]);
}
}
};
}; //namespace fastio
using mint=Fp<998244353>;
int main(){
fastio::Scanner sc(stdin);
fastio::Printer pr(stdout);
int n;
sc.read(n);
vector<ll> a(n),b(n);
FOR(i,n) sc.read(a[i]);
FOR(i,n) sc.read(b[i]);
vector<ll> s(n),c(n),d(n);
FOR(i,n){
s[i]=i+1;
c[i]=a[i]+i+1;
d[i]=b[i]+i+1;
}
vector<ll> ans=NTT::mul_ll(c,d);
vector<ll> m1=NTT::mul_ll(s,s),m2=NTT::mul_ll(a,b);
pr.write(0),pr.write(' ');
FOR(i,2*n-1) pr.write(ans[i]-m1[i]-m2[i]),pr.write(' ');
}