0
1
mirror of https://git.sb/baoshuo/OI-codes.git synced 2024-12-25 08:11:59 +00:00
OI-codes/Luogu/P4725/P4725.cpp

201 lines
4.1 KiB
C++

#include <iostream>
#include <algorithm>
#include <vector>
using std::cin;
using std::cout;
const char endl = '\n';
const int mod = 998244353;
constexpr long long binpow(long long a, long long b) {
a %= mod;
long long res = 1;
while (b) {
if (b & 1) res = res * a % mod;
a = a * a % mod;
b >>= 1;
}
return res;
}
class Poly : public std::vector<long long> {
private:
static void number_theoretic_transform(std::vector<long long> &a) {
if (a.size() == 1) return;
// assert(a.size() == (1 << std::__lg(a.size())));
int k = std::__lg(a.size());
for (int i = 0; i < a.size(); i++) {
int t = 0;
for (int j = 0; j < k; j++) {
if (i & (1 << j)) {
t |= 1 << (k - j - 1);
}
}
if (i < t) std::swap(a[i], a[t]);
}
for (int len = 2; len <= a.size(); len <<= 1) {
int m = len >> 1;
long long wn = binpow(3, (mod - 1) / len);
for (int i = 0; i < a.size(); i += len) {
long long w = 1;
for (int j = 0; j < m; j++) {
long long u = a[i + j],
v = a[i + j + m] * w % mod;
a[i + j] = ((u + v) % mod + mod) % mod;
a[i + j + m] = ((u - v) % mod + mod) % mod;
w = w * wn % mod;
}
}
}
}
static void dft(std::vector<long long> &a) {
number_theoretic_transform(a);
}
static void idft(std::vector<long long> &a) {
number_theoretic_transform(a);
std::reverse(a.begin() + 1, a.end());
long long inv = binpow(a.size(), mod - 2);
std::transform(a.begin(), a.end(), a.begin(), [&](long long x) {
return x * inv % mod;
});
}
static Poly derivative(const Poly &a) {
Poly b{a};
for (int i = 1; i < a.size(); i++) {
b[i - 1] = b[i] * i % mod;
}
b[a.size() - 1] = 0;
return b;
}
static Poly integrate(const Poly &a) {
Poly b{a};
for (int i = a.size() - 1; i >= 1; i--) {
b[i] = b[i - 1] * binpow(i, mod - 2) % mod;
}
b[0] = 0;
return b;
}
public:
using std::vector<long long>::vector;
Poly() = default;
Poly(const std::vector<long long> &__v)
: std::vector<long long>(__v) {}
Poly(std::vector<long long> &&__v)
: std::vector<long long>(std::move(__v)) {}
Poly operator*(const Poly &b) {
int n = size() - 1,
m = b.size() - 1,
k = 1 << (std::__lg(n + m) + 1);
long long inv = binpow(k, mod - 2);
std::vector<long long> f(*this), g(b);
f.resize(k);
dft(f);
g.resize(k);
dft(g);
for (int i = 0; i < k; i++) {
f[i] = f[i] * g[i] % mod;
}
idft(f);
f.resize(n + m + 1);
return Poly(f);
}
Poly operator/(const Poly &b) {
Poly c{inv(b)};
return *this * c;
}
static Poly inv(Poly a) {
if (a.size() == 1) return Poly{binpow(a[0], mod - 2)};
int n = a.size(),
k = 1 << (std::__lg(n << 1) + 1);
Poly b{a};
a.resize(k);
dft(a);
b.resize(n + 1 >> 1);
b = inv(b);
b.resize(k);
dft(b);
for (int i = 0; i < k; i++) {
b[i] = (2 - a[i] * b[i] % mod + mod) % mod * b[i] % mod;
}
idft(b);
b.resize(n);
return b;
}
static Poly ln(Poly f) {
Poly a{derivative(f)},
b{inv(f)},
res{integrate(a * b)};
res.resize(f.size());
return res;
}
} poly;
int main() {
std::ios::sync_with_stdio(false);
cin.tie(nullptr);
int n;
cin >> n;
Poly a(n);
for (int i = 0; i < n; i++) {
cin >> a[i];
}
Poly b = Poly::ln(a);
for (int i = 0; i < n; i++) {
cout << b[i] << ' ';
}
cout << endl;
return 0;
}