tkmst201's Library
This documentation is automatically generated by online-judge-tools/verification-helper
Test/NumberTheoreticTransform_AnyMod.test.cpp
- View this file on GitHub
- Last update: 2021-06-05 13:56:14+09:00
- Problem: https://judge.yosupo.jp/problem/convolution_mod_1000000007
Depends on
- 数論変換 (NTT)
(Convolution/NumberTheoreticTransform.hpp)
- 任意 mod 数論変換 (任意 mod NTT)
(Convolution/NumberTheoreticTransform_AnyMod.hpp)
- ユークリッドの互除法
(Mathematics/euclid.hpp)
- Garner (連立一次合同式 mod M)
(Mathematics/garner.hpp)
- $\mod{m}$ での冪と逆元
(Mathematics/mod_pow_inv.hpp)
Code
#define PROBLEM "https://judge.yosupo.jp/problem/convolution_mod_1000000007"
#include "Convolution/NumberTheoreticTransform_AnyMod.hpp"
#include <cstdio>
#include <vector>
int main() {
int N, M;
scanf("%d %d", &N, &M);
std::vector<int> A(N), B(M);
for (int i = 0; i < N; ++i) scanf("%d", &A[i]);
for (int i = 0; i < M; ++i) scanf("%d", &B[i]);
auto ans = NumberTheoreticTransform_AnyMod<1'000'000'007>::multiply(A, B);
for (int i = 0; i < N + M - 1; ++i) printf("%d%c", ans[i], i == N + M - 1 ? '\n': ' ');
}#line 1 "Test/NumberTheoreticTransform_AnyMod.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/convolution_mod_1000000007"
#line 1 "Convolution/NumberTheoreticTransform_AnyMod.hpp"
#line 1 "Convolution/NumberTheoreticTransform.hpp"
#line 1 "Mathematics/mod_pow_inv.hpp"
#include <cassert>
#include <type_traits>
/**
* @brief https://tkmst201.github.io/Library/Mathematics/mod_pow_inv.hpp
*/
namespace tk {
template<typename T>
constexpr T mod_pow(T x, T n, T m) noexcept {
static_assert(std::is_integral<T>::value);
assert(m > 0);
assert(n >= 0);
x = x % m + (x >= 0 ? 0 : m);
T res = 1 % m;
while (n > 0) {
if (n & 1) res = res * x % m;
x = x * x % m;
n >>= 1;
}
return res;
}
template<typename T>
constexpr T mod_inv(T x, T m) noexcept {
static_assert(std::is_integral<T>::value);
static_assert(std::is_signed<T>::value);
assert(m > 0);
x = x % m + (x >= 0 ? 0 : m);
T x1 = 1, y = m, y1 = 0;
while (y > 0) {
const T q = x / y;
T tmp = x - q * y; x = y; y = tmp;
tmp = x1 - q * y1; x1 = y1; y1 = tmp;
}
assert(x == 1);
if (x1 == m) x1 = 0;
if (x1 < 0) x1 += m;
return x1;
}
} // namespace tk
#line 5 "Convolution/NumberTheoreticTransform.hpp"
#include <vector>
#include <utility>
#line 9 "Convolution/NumberTheoreticTransform.hpp"
#include <cstdint>
/**
* @brief https://tkmst201.github.io/Library/Convolution/NumberTheoreticTransform.hpp
*/
template<int MOD, int PRIMITIVE_ROOT>
struct NumberTheoreticTransform {
static_assert(MOD > 0);
static_assert(PRIMITIVE_ROOT > 0);
private:
using uint32 = std::uint32_t;
using calc_type = long long;
public:
template<typename T>
static std::vector<T> multiply(const std::vector<T> & a, const std::vector<T> & b) {
static_assert(std::is_integral<T>::value);
if (a.empty() || b.empty()) return {};
const uint32 n_ = a.size() + b.size() - 1;
uint32 n = 1;
while (n < n_) n <<= 1;
{
uint32 two_exp = 0;
int tm = MOD - 1;
while (tm > 0 && (~tm & 1)) ++two_exp, tm >>= 1;
assert((1u << two_exp) >= n);
}
std::vector<T> c(n, 0);
for (uint32 i = 0; i < a.size(); ++i) c[i] = a[i] % MOD + (a[i] >= 0 ? 0 : MOD);
ntt(c);
std::vector<T> d(n, 0);
for (uint32 i = 0; i < b.size(); ++i) d[i] = b[i] % MOD + (b[i] >= 0 ? 0 : MOD);
ntt(d);
const int ninv = tk::mod_inv<int>(n, MOD);
for (uint32 i = 0; i < n; ++i) c[i] = static_cast<calc_type>(c[i]) * d[i] % MOD * ninv % MOD;
d.clear();
ntt(c, true);
c.resize(a.size() + b.size() - 1);
return c;
}
private:
template<typename T>
static void ntt(std::vector<T> & a, bool inv = false) {
const uint32 n = a.size();
int nroot = tk::mod_pow<calc_type>(PRIMITIVE_ROOT, (MOD - 1) / n, MOD);
if (inv) nroot = tk::mod_inv(nroot, MOD);
for (uint32 w = n; w > 1; w >>= 1) {
const uint32 m = w >> 1;
std::vector<int> omega(m, 0);
omega[0] = 1;
for (uint32 i = 1; i < m; ++i) omega[i] = static_cast<calc_type>(omega[i - 1]) * nroot % MOD;
const int half = static_cast<calc_type>(omega.back()) * nroot % MOD;
for (uint32 p = 0; p < n; p += w) {
for (uint32 i = p; i < p + m; ++i) {
const calc_type x = a[i], y = a[i + m];
a[i] = (x + y) % MOD;
a[i + m] = (x + y * half % MOD) % MOD * omega[i - p] % MOD;
}
}
nroot = static_cast<calc_type>(nroot) * nroot % MOD;
}
bit_reverse(a);
}
template<typename T>
static void bit_reverse(std::vector<T> & a) noexcept {
const uint32 n = a.size();
for (uint32 i = 1, j = 0; i < n - 1; ++i) {
for (uint32 k = n >> 1; k > (j ^= k); k >>= 1);
if (i < j) std::swap(a[i], a[j]);
}
}
};
#line 1 "Mathematics/garner.hpp"
#line 7 "Mathematics/garner.hpp"
#line 1 "Mathematics/euclid.hpp"
#line 6 "Mathematics/euclid.hpp"
#include <tuple>
#line 8 "Mathematics/euclid.hpp"
#include <cmath>
/**
* @brief https://tkmst201.github.io/Library/Mathematics/euclid.hpp
*/
namespace tk {
template<typename T>
constexpr T gcd(T a, T b) noexcept {
static_assert(std::is_integral<T>::value);
assert(a >= 0);
assert(b >= 0);
while (b != 0) {
const T t = a % b;
a = b; b = t;
}
return a;
}
template<typename T>
constexpr T lcm(T a, T b) noexcept {
static_assert(std::is_integral<T>::value);
assert(a >= 0);
assert(b >= 0);
if (a == 0 || b == 0) return 0;
return a / gcd(a, b) * b;
}
template<typename T>
constexpr std::tuple<T, T, T> ext_gcd(T a, T b) noexcept {
static_assert(std::is_integral<T>::value);
static_assert(std::is_signed<T>::value);
assert(a != 0);
assert(b != 0);
T a1 = (a > 0) * 2 - 1, a2 = 0, b1 = 0, b2 = (b > 0) * 2 - 1;
a = std::abs(a);
b = std::abs(b);
while (b > 0) {
const T q = a / b;
T tmp = a - q * b; a = b; b = tmp;
tmp = a1 - q * b1; a1 = b1; b1 = tmp;
tmp = a2 - q * b2; a2 = b2; b2 = tmp;
}
return {a, a1, a2};
}
} // namespace tk
#line 10 "Mathematics/garner.hpp"
/**
* @brief https://tkmst201.github.io/Library/Mathematics/garner.hpp
*/
namespace tk {
template<typename T>
bool pre_garner(std::vector<T> & b, std::vector<T> & m) noexcept {
static_assert(std::is_integral<T>::value);
static_assert(std::is_signed<T>::value);
for (int i = 0; i < static_cast<int>(b.size()); ++i) {
b[i] = b[i] % m[i] + (b[i] >= 0 ? 0 : m[i]);
for (int j = 0; j < i; ++j) {
T g = gcd(m[i], m[j]);
if ((b[i] - b[j]) % g != 0) return false;
m[i] /= g; m[j] /= g;
T gi = gcd(g, m[i]), gj = g / gi;
do {
g = gcd(gi, gj);
gi *= g; gj /= g;
} while (g != 1);
m[i] *= gi; m[j] *= gj;
b[i] %= m[i]; b[j] %= m[j];
}
}
return true;
}
template<typename T, typename U>
T garner(const std::vector<T> & b, const std::vector<T> & m, const T M) {
static_assert(std::is_integral<T>::value);
assert(b.size() == m.size());
const int n = b.size();
assert(n > 0);
{
T g = 0;
for (auto v : m) {
assert(v > 0);
g = gcd(g, v);
}
assert(n == 1 || g == 1);
}
assert(M > 0);
std::vector<T> sum(n + 1, 0), ip(n + 1, 1);
for (int i = 0; i < n; ++i) {
if (m[i] == 1) continue;
U t = (b[i] % m[i] + static_cast<U>(2) * m[i] - sum[i]) % m[i] * mod_inv(ip[i], m[i]) % m[i];
for (int j = i + 1; j < n; ++j) {
sum[j] = (sum[j] + ip[j] * t) % m[j];
ip[j] = static_cast<U>(ip[j]) * m[i] % m[j];
}
sum[n] = (sum[n] + ip[n] * t % M) % M;
ip[n] = static_cast<U>(ip[n]) * m[i] % M;
}
return sum.back();
}
} // namespace tk
#line 6 "Convolution/NumberTheoreticTransform_AnyMod.hpp"
#line 11 "Convolution/NumberTheoreticTransform_AnyMod.hpp"
/**
* @brief https://tkmst201.github.io/Library/Convolution/NumberTheoreticTransform_AnyMod.hpp
*/
template<int MOD>
struct NumberTheoreticTransform_AnyMod {
static_assert(MOD > 0);
private:
using calc_type = long long;
using uint32 = std::uint32_t;
public:
template<typename T>
static std::vector<T> multiply(const std::vector<T> & a, const std::vector<T> & b) {
static_assert(std::is_integral<T>::value);
static_assert(std::is_signed<T>::value);
for (uint32 i = 0; i < a.size(); ++i) assert(a[i] >= 0);
for (uint32 i = 0; i < b.size(); ++i) assert(b[i] >= 0);
std::vector<T> m;
auto ntt1_res = NumberTheoreticTransform<1'224'736'769, 3>::multiply(a, b);
m.emplace_back(1'224'736'769);
auto ntt2_res = NumberTheoreticTransform<469'762'049, 3>::multiply(a, b);
m.emplace_back(469'762'049);
auto ntt3_res = NumberTheoreticTransform<167'772'161, 3>::multiply(a, b);
m.emplace_back(167'772'161);
// auto ntt4_res = NumberTheoreticTransform<998'244'353, 3>::multiply(a, b);
// m.emplace_back(998'244'353);
std::vector<T> c(m.size());
std::vector<T> res(ntt1_res.size());
for (uint32 i = 0; i < res.size(); ++i) {
c[0] = ntt1_res[i];
c[1] = ntt2_res[i];
c[2] = ntt3_res[i];
// c[3] = ntt4_res[i];
res[i] = tk::garner<T, calc_type>(c, m, MOD);
}
return res;
}
};
#line 4 "Test/NumberTheoreticTransform_AnyMod.test.cpp"
#include <cstdio>
#line 7 "Test/NumberTheoreticTransform_AnyMod.test.cpp"
int main() {
int N, M;
scanf("%d %d", &N, &M);
std::vector<int> A(N), B(M);
for (int i = 0; i < N; ++i) scanf("%d", &A[i]);
for (int i = 0; i < M; ++i) scanf("%d", &B[i]);
auto ans = NumberTheoreticTransform_AnyMod<1'000'000'007>::multiply(A, B);
for (int i = 0; i < N + M - 1; ++i) printf("%d%c", ans[i], i == N + M - 1 ? '\n': ' ');
}