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test/polynomial/Pow_of_Formal_Power_Series_Sparse.test.cpp
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- Last update: 2024-05-23 18:52:03+09:00
- Problem: https://judge.yosupo.jp/problem/pow_of_formal_power_series_sparse
Depends on
- Formal Power Series (Sparse)
(fps/fps_sparse.hpp)
- Mod Inv
(math/mod_inv.hpp)
- modint/base.hpp
- modint/modint.hpp
Code
#define PROBLEM \
"https://judge.yosupo.jp/problem/pow_of_formal_power_series_sparse"
#include <iostream>
#include <vector>
#include "../../fps/fps_sparse.hpp"
#include "../../modint/modint.hpp"
using mint = ebi::modint998244353;
int main() {
int n, k;
long long m;
std::cin >> n >> k >> m;
std::vector<mint> f(n);
for (int i = 0; i < k; i++) {
int idx, a;
std::cin >> idx >> a;
f[idx] = a;
}
auto g = ebi::pow_sparse(f, m, n);
for (int i = 0; i < n; i++) {
std::cout << g[i].val() << " \n"[i == n - 1];
}
}#line 1 "test/polynomial/Pow_of_Formal_Power_Series_Sparse.test.cpp"
#define PROBLEM \
"https://judge.yosupo.jp/problem/pow_of_formal_power_series_sparse"
#include <iostream>
#include <vector>
#line 2 "fps/fps_sparse.hpp"
#include <cassert>
#line 5 "fps/fps_sparse.hpp"
#line 2 "math/mod_inv.hpp"
#line 5 "math/mod_inv.hpp"
#line 2 "modint/base.hpp"
#include <concepts>
#line 5 "modint/base.hpp"
#include <utility>
namespace ebi {
template <class T>
concept Modint = requires(T a, T b) {
a + b;
a - b;
a * b;
a / b;
a.inv();
a.val();
a.pow(std::declval<long long>());
T::mod();
};
template <Modint mint> std::istream &operator>>(std::istream &os, mint &a) {
long long x;
os >> x;
a = x;
return os;
}
template <Modint mint>
std::ostream &operator<<(std::ostream &os, const mint &a) {
return os << a.val();
}
} // namespace ebi
#line 7 "math/mod_inv.hpp"
namespace ebi {
template <Modint mint> mint inv(int n) {
static const int mod = mint::mod();
static std::vector<mint> dat = {0, 1};
assert(0 <= n);
if (n >= mod) n -= mod;
while (int(dat.size()) <= n) {
int num = dat.size();
int q = (mod + num - 1) / num;
dat.emplace_back(dat[num * q - mod] * mint(q));
}
return dat[n];
}
} // namespace ebi
#line 8 "fps/fps_sparse.hpp"
namespace ebi {
template <Modint mint>
std::vector<mint> mul_sparse(const std::vector<mint> &f,
const std::vector<mint> &g) {
int n = f.size();
int m = g.size();
std::vector<std::pair<int, mint>> cf, cg;
for (int i = 0; i < n; i++) {
if (f[i] != 0) cf.emplace_back(i, f[i]);
}
for (int i = 0; i < m; i++) {
if (g[i] != 0) cg.emplace_back(i, g[i]);
}
std::vector<mint> h(n + m - 1);
for (auto [i, p] : cf) {
for (auto [j, q] : cg) {
h[i + j] += p * q;
}
}
return h;
}
template <Modint mint>
std::vector<mint> inv_sparse(const std::vector<mint> &f, int d = -1) {
assert(f[0] != 0);
if (d < 0) {
d = f.size();
}
std::vector<std::pair<int, mint>> ret;
for (int i = 1; i < int(f.size()); i++) {
if (f[i] != 0) {
ret.emplace_back(i, f[i]);
}
}
std::vector<mint> g(d);
g[0] = f[0].inv();
for (int i = 1; i < d; i++) {
for (auto [k, p] : ret) {
if (i - k < 0) break;
g[i] -= g[i - k] * p;
}
g[i] *= g[0];
}
return g;
}
template <Modint mint>
std::vector<mint> exp_sparse(const std::vector<mint> &f, int d = -1) {
int n = f.size();
if (d < 0) d = n;
std::vector<std::pair<int, mint>> ret;
for (int i = 1; i < n; i++) {
if (f[i] != 0) {
ret.emplace_back(i - 1, f[i] * i);
}
}
std::vector<mint> g(d);
g[0] = 1;
for (int i = 0; i < d - 1; i++) {
for (auto [k, p] : ret) {
if (i - k < 0) break;
g[i + 1] += g[i - k] * p;
}
g[i + 1] *= inv<mint>(i + 1);
}
return g;
}
template <Modint mint>
std::vector<mint> log_sparse(const std::vector<mint> &f, int d = -1) {
int n = f.size();
if (d < 0) d = n;
std::vector<mint> df(d);
for (int i = 0; i < std::min(d, n - 1); i++) {
df[i] = f[i + 1] * (i + 1);
}
auto dg = mul_sparse(df, inv_sparse(f));
dg.resize(d);
std::vector<mint> g(d);
for (int i = 0; i < d - 1; i++) {
g[i + 1] = dg[i] * inv<mint>(i + 1);
}
return g;
}
template <Modint mint>
std::vector<mint> pow_sparse_1(const std::vector<mint> &f, long long k,
int d = -1) {
int n = f.size();
assert(n == 0 || f[0] == 1);
std::vector<std::pair<int, mint>> ret;
for (int i = 1; i < n; i++) {
if (f[i] != 0) ret.emplace_back(i, f[i]);
}
std::vector<mint> g(d);
g[0] = 1;
for (int i = 0; i < d - 1; i++) {
for (const auto &[j, cf] : ret) {
if (i + 1 - j < 0) break;
g[i + 1] +=
(mint(k) * mint(j) - mint(i - j + 1)) * cf * g[i + 1 - j];
}
g[i + 1] *= inv<mint>(i + 1);
}
return g;
}
template <Modint mint>
std::vector<mint> pow_sparse(const std::vector<mint> &f, long long k,
int d = -1) {
int n = f.size();
if (d < 0) d = n;
assert(k >= 0);
if (k == 0) {
std::vector<mint> g(d);
if (d > 0) g[0] = 1;
return g;
}
for (int i = 0; i < n; i++) {
if (f[i] != 0) {
mint rev = f[i].inv();
std::vector<mint> f2(n - i);
for (int j = i; j < n; j++) {
f2[j - i] = f[j] * rev;
}
f2 = pow_sparse_1(f2, k, d);
mint fk = f[i].pow(k);
std::vector<mint> g(d);
for (int j = 0; j < int(f2.size()); j++) {
if (j + i * k >= d) break;
g[j + i * k] = f2[j] * fk;
}
return g;
}
if (i >= (d + k - 1) / k) break;
}
return std::vector<mint>(d);
}
} // namespace ebi
#line 2 "modint/modint.hpp"
#line 5 "modint/modint.hpp"
#line 7 "modint/modint.hpp"
namespace ebi {
template <int m> struct static_modint {
private:
using modint = static_modint;
public:
static constexpr int mod() {
return m;
}
static constexpr modint raw(int v) {
modint x;
x._v = v;
return x;
}
constexpr static_modint() : _v(0) {}
template <std::signed_integral T> constexpr static_modint(T v) {
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template <std::unsigned_integral T> constexpr static_modint(T v) {
_v = (unsigned int)(v % umod());
}
constexpr unsigned int val() const {
return _v;
}
constexpr unsigned int value() const {
return val();
}
constexpr modint &operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
constexpr modint &operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
constexpr modint operator++(int) {
modint res = *this;
++*this;
return res;
}
constexpr modint operator--(int) {
modint res = *this;
--*this;
return res;
}
constexpr modint &operator+=(const modint &rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
constexpr modint &operator-=(const modint &rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
constexpr modint &operator*=(const modint &rhs) {
unsigned long long x = _v;
x *= rhs._v;
_v = (unsigned int)(x % (unsigned long long)umod());
return *this;
}
constexpr modint &operator/=(const modint &rhs) {
return *this = *this * rhs.inv();
}
constexpr modint operator+() const {
return *this;
}
constexpr modint operator-() const {
return modint() - *this;
}
constexpr modint pow(long long n) const {
assert(0 <= n);
modint x = *this, res = 1;
while (n) {
if (n & 1) res *= x;
x *= x;
n >>= 1;
}
return res;
}
constexpr modint inv() const {
assert(_v);
return pow(umod() - 2);
}
friend modint operator+(const modint &lhs, const modint &rhs) {
return modint(lhs) += rhs;
}
friend modint operator-(const modint &lhs, const modint &rhs) {
return modint(lhs) -= rhs;
}
friend modint operator*(const modint &lhs, const modint &rhs) {
return modint(lhs) *= rhs;
}
friend modint operator/(const modint &lhs, const modint &rhs) {
return modint(lhs) /= rhs;
}
friend bool operator==(const modint &lhs, const modint &rhs) {
return lhs.val() == rhs.val();
}
friend bool operator!=(const modint &lhs, const modint &rhs) {
return !(lhs == rhs);
}
private:
unsigned int _v = 0;
static constexpr unsigned int umod() {
return m;
}
};
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
} // namespace ebi
#line 9 "test/polynomial/Pow_of_Formal_Power_Series_Sparse.test.cpp"
using mint = ebi::modint998244353;
int main() {
int n, k;
long long m;
std::cin >> n >> k >> m;
std::vector<mint> f(n);
for (int i = 0; i < k; i++) {
int idx, a;
std::cin >> idx >> a;
f[idx] = a;
}
auto g = ebi::pow_sparse(f, m, n);
for (int i = 0; i < n; i++) {
std::cout << g[i].val() << " \n"[i == n - 1];
}
}