結果
| 問題 |
No.754 畳み込みの和
|
| コンテスト | |
| ユーザー |
 KoD
|
| 提出日時 | 2020-06-06 12:17:58 |
| 言語 | C++17(gcc12) (gcc 12.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 192 ms / 5,000 ms |
| コード長 | 10,420 bytes |
| コンパイル時間 | 5,473 ms |
| コンパイル使用メモリ | 132,828 KB |
| 最終ジャッジ日時 | 2025-01-10 23:19:15 |
|
ジャッジサーバーID （参考情報） |
judge4 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 3 |
ソースコード
#include <iostream>
#include <algorithm>
#include <utility>
#include <numeric>
#include <vector>
#include <array>
template <class T, class U>
inline bool chmin(T &lhs, const U &rhs) {
if (lhs > rhs) { lhs = rhs; return true; }
return false;
}
template <class T, class U>
inline bool chmax(T &lhs, const U &rhs) {
if (lhs < rhs) { lhs = rhs; return true; }
return false;
}
struct range {
using itr = int64_t;
struct iterator {
itr i;
constexpr iterator(itr i_): i(i_) { }
constexpr void operator ++ () { ++i; }
constexpr itr operator * () const { return i; }
constexpr bool operator != (iterator x) const { return i != x.i; }
};
const iterator l, r;
constexpr range(itr l_, itr r_): l(l_), r(std::max(l_, r_)) { }
constexpr iterator begin() const { return l; }
constexpr iterator end() const { return r; }
};
struct revrange {
using itr = int64_t;
struct iterator {
itr i;
constexpr iterator(itr i_): i(i_) { }
constexpr void operator ++ () { --i; }
constexpr itr operator * () const { return i; }
constexpr bool operator != (iterator x) const { return i != x.i; }
};
const iterator l, r;
constexpr revrange(itr l_, itr r_): l(l_ - 1), r(std::max(l_, r_) - 1) { }
constexpr iterator begin() const { return r; }
constexpr iterator end() const { return l; }
};
using i32 = int32_t;
using i64 = int64_t;
using u32 = uint32_t;
using u64 = uint64_t;
constexpr i32 inf32 = (i32(1) << 30) - 1;
constexpr i64 inf64 = (i64(1) << 62) - 1;
template <uint32_t Modulus>
class modular {
public:
using value_type = uint32_t;
using max_type = uint64_t;
static constexpr value_type mod = Modulus;
static constexpr value_type get_mod() { return mod; }
static_assert(mod >= 2, "invalid mod :: smaller than 2");
static_assert(mod < (value_type(1) << 31), "invalid mod :: over 2^31");
template <class T>
static constexpr value_type normalize(T value_) {
if (value_ < 0) {
value_ = -value_;
value_ %= mod;
if (value_ == 0) return 0;
return mod - value_;
}
return value_ % mod;
}
private:
value_type value;
public:
constexpr modular(): value(0) { }
template <class T>
explicit constexpr modular(T value_): value(normalize(value_)) { }
template <class T>
explicit constexpr operator T() { return static_cast<T>(value); }
constexpr value_type get() const { return value; }
constexpr modular operator - () const { return modular(mod - value); }
constexpr modular operator ~ () const { return inverse(); }
constexpr value_type &extract() { return value; }
constexpr modular inverse() const { return power(mod - 2); }
constexpr modular power(max_type exp) const {
modular res(1), mult(*this);
while (exp > 0) {
if (exp & 1) res *= mult;
mult *= mult;
exp >>= 1;
}
return res;
}
constexpr modular operator + (const modular &rhs) const { return modular(*this) += rhs; }
constexpr modular& operator += (const modular &rhs) {
if ((value += rhs.value) >= mod) value -= mod;
return *this;
}
constexpr modular operator - (const modular &rhs) const { return modular(*this) -= rhs; }
constexpr modular& operator -= (const modular &rhs) {
if ((value += mod - rhs.value) >= mod) value -= mod;
return *this;
}
constexpr modular operator * (const modular &rhs) const { return modular(*this) *= rhs; }
constexpr modular& operator *= (const modular &rhs) {
value = (max_type) value * rhs.value % mod;
return *this;
}
constexpr modular operator / (const modular &rhs) const { return modular(*this) /= rhs; }
constexpr modular& operator /= (const modular &rhs) { return (*this) *= rhs.inverse(); }
constexpr bool zero() const { return value == 0; }
constexpr bool operator == (const modular &rhs) const { return value == rhs.value; }
constexpr bool operator != (const modular &rhs) const { return value != rhs.value; }
friend std::ostream& operator << (std::ostream &stream, const modular &rhs) {
return stream << rhs.value;
}
};
using m32 = modular<1000000007>;
namespace detail {
template <size_t N, class T>
constexpr std::array<T, N> calculate_roots(T omega) {
std::array<T, N> res;
res[N - 1] = omega;
for (size_t i = N - 1; i > 0; --i) {
res[i - 1] = res[i] * res[i];
}
return res;
}
template <class OtherModular, class Modular>
constexpr OtherModular convert_mod(Modular x) {
return OtherModular(x.get());
}
template <class OtherModular, class Modular>
std::vector<OtherModular> convert_mod_vec(const std::vector<Modular> &vec) {
std::vector<OtherModular> res(vec.size());
std::transform(vec.cbegin(), vec.cend(), res.begin(), convert_mod<OtherModular, Modular>);
return res;
}
namespace bit_operation {
constexpr uint32_t b16 = 0b00000000000000001111111111111111;
constexpr uint32_t b8 = 0b00000000111111110000000011111111;
constexpr uint32_t b4 = 0b00001111000011110000111100001111;
constexpr uint32_t b2 = 0b00110011001100110011001100110011;
constexpr uint32_t b1 = 0b01010101010101010101010101010101;
constexpr size_t reverse(size_t x) {
x = ((x >> 16) & b16) | ((x & b16) << 16);
x = ((x >> 8) & b8) | ((x & b8) << 8);
x = ((x >> 4) & b4) | ((x & b4) << 4);
x = ((x >> 2) & b2) | ((x & b2) << 2);
x = ((x >> 1) & b1) | ((x & b1) << 1);
return x;
}
};
namespace garner_mod {
constexpr uint32_t m0 = 998244353;
constexpr uint32_t m1 = 935329793;
constexpr uint32_t m2 = 943718401;
constexpr uint32_t p0 = 3;
constexpr uint32_t p1 = 3;
constexpr uint32_t p2 = 7;
constexpr uint64_t m0m1 = (uint64_t) m0 * m1;
constexpr auto im0_m1 = modular<m1>(m0).inverse();
constexpr auto im0m1_m2 = modular<m2>(m0m1).inverse();
};
/*
prime numbers for ntt
[ 1051721729, 6 ] [ 2^20 ]
[ 1045430273, 3 ] [ 2^20 ]
[ 1007681537, 3 ] [ 2^20 ]
[ 962592769, 7 ] [ 2^21 ]
[ 924844033, 5 ] [ 2^21 ]
[ 985661441, 3 ] [ 2^22 ]
[ 943718401, 7 ] [ 2^22 ]
[ 935329793, 3 ] [ 2^22 ]
[ 998244353, 3 ] [ 2^23 ]
*/
}
template <uint32_t Modulus, uint32_t PrimRoot, class Modular = modular<Modulus>>
class number_theoretic_transform {
public:
using value_type = Modular;
static constexpr uint32_t mod = Modulus;
static constexpr uint32_t prim = PrimRoot;
private:
static constexpr size_t level = __builtin_ctz(mod - 1);
static constexpr value_type unit = value_type(1);
static constexpr value_type omega = value_type(prim).power((mod - 1) >> level);
static constexpr auto roots = detail::calculate_roots<level>(omega);
static constexpr auto inv_roots = detail::calculate_roots<level>(omega.inverse());
void M_transform(std::vector<value_type> &F) const {
size_t size = F.size();
size_t logn = __builtin_ctz(size);
for (size_t i = 0; i < size; ++i) {
size_t j = detail::bit_operation::reverse(i) >> (32 - logn);
if (i < j) {
std::swap(F[i], F[j]);
}
}
value_type coeff = unit;
for (size_t s = 0; s < logn; ++s) {
size_t mh = 1 << s;
size_t m = mh << 1;
for (size_t i = 0; i < size; i += m) {
coeff = unit;
for (size_t j = i; j < i + mh; ++j) {
auto a = F[j];
auto b = F[j + mh] * coeff;
F[j] = a + b;
F[j + mh] = a - b;
coeff *= roots[s];
}
}
}
}
void M_inv_transform(std::vector<value_type> &F) const {
size_t size = F.size();
size_t logn = __builtin_ctz(size);
for (size_t i = 0; i < size; ++i) {
size_t j = detail::bit_operation::reverse(i) >> (32 - logn);
if (i < j) {
std::swap(F[i], F[j]);
}
}
value_type coeff = unit;
for (size_t s = 0; s < logn; ++s) {
size_t mh = 1 << s;
size_t m = mh << 1;
for (size_t i = 0; i < size; i += m) {
coeff = unit;
for (size_t j = i; j < i + mh; ++j) {
auto a = F[j];
auto b = F[j + mh] * coeff;
F[j] = a + b;
F[j + mh] = a - b;
coeff *= inv_roots[s];
}
}
}
coeff = value_type(size).inverse();
for (auto &x: F) {
x *= coeff;
}
}
public:
std::vector<value_type> convolve(std::vector<value_type> A, std::vector<value_type> B) const {
if (A.empty() || B.empty()) return { };
size_t res_size = A.size() + B.size() - 1;
size_t fix_size = 1 << (31 - __builtin_clz(2 * res_size - 1));
if (A == B) {
A.resize(fix_size);
M_transform(A);
for (size_t i = 0; i < fix_size; ++i) {
A[i] *= A[i];
}
M_inv_transform(A);
A.resize(res_size);
return A;
}
else {
A.resize(fix_size);
B.resize(fix_size);
M_transform(A);
M_transform(B);
for (size_t i = 0; i < fix_size; ++i) {
A[i] *= B[i];
}
M_inv_transform(A);
A.resize(res_size);
return A;
}
}
template <class OtherModular>
std::vector<value_type> convolve_convert(const std::vector<OtherModular> &A, const std::vector<OtherModular> &B) const {
return convolve(detail::convert_mod_vec<value_type>(A), detail::convert_mod_vec<value_type>(B));
}
};
template <class Modular>
std::vector<Modular> arbitrary_mod_convolution(const std::vector<Modular> &A, const std::vector<Modular> &B) {
using namespace detail::garner_mod;
number_theoretic_transform<m0, p0> ntt0;
number_theoretic_transform<m1, p1> ntt1;
number_theoretic_transform<m2, p2> ntt2;
auto X = ntt0.convolve_convert(A, B);
auto Y = ntt1.convolve_convert(A, B);
auto Z = ntt2.convolve_convert(A, B);
size_t size = X.size();
std::vector<Modular> res(size);
for (size_t i = 0; i < size; ++i) {
uint32_t s = (uint32_t) X[i];
uint64_t t = (uint64_t) ((Y[i] - modular<m1>(s)) * im0_m1) * m0 + s;
res[i] = Modular((__uint128_t) ((Z[i] - modular<m2>(t)) * im0m1_m2) * m0m1 + t);
}
return res;
}
int main() {
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
size_t N;
std::cin >> N;
++N;
std::vector<m32> A(N), B(N);
for (auto &x: A) {
std::cin >> x.extract();
}
for (auto &x: B) {
std::cin >> x.extract();
}
auto C = arbitrary_mod_convolution(A, B);
m32 ans;
for (auto i: range(0, N)) {
ans += C[i];
}
std::cout << ans << '\n';
return 0;
}