結果
| 問題 |
No.3172 三角関数べき乗のフーリエ級数展開
|
| ユーザー |
 dyktr_06
|
| 提出日時 | 2025-06-06 21:58:05 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 544 ms / 2,000 ms |
| コード長 | 18,594 bytes |
| コンパイル時間 | 4,498 ms |
| コンパイル使用メモリ | 263,596 KB |
| 実行使用メモリ | 13,972 KB |
| 最終ジャッジ日時 | 2025-06-06 21:58:14 |
| 合計ジャッジ時間 | 7,641 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 4 |
| other | AC * 15 |
ソースコード
#include <bits/stdc++.h>
#include <atcoder/all>
using namespace std;
using namespace atcoder;
#define overload4(_1, _2, _3, _4, name, ...) name
#define rep1(n) for(int i = 0; i < (int)(n); ++i)
#define rep2(i, n) for(int i = 0; i < (int)(n); ++i)
#define rep3(i, a, b) for(int i = (a); i < (int)(b); ++i)
#define rep4(i, a, b, c) for(int i = (a); i < (int)(b); i += (c))
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; --i)
#define ALL(a) (a).begin(), (a).end()
#define Sort(a) (sort((a).begin(), (a).end()))
#define RSort(a) (sort((a).rbegin(), (a).rend()))
#define UNIQUE(a) (a.erase(unique((a).begin(), (a).end()), (a).end()))
using i64 = int64_t;
using i128 = __int128_t;
using ll = long long;
using ul = unsigned long long;
using ull = unsigned long long;
using ld = long double;
using vi = vector<int>;
using vll = vector<long long>;
using vull = vector<unsigned long long>;
using vc = vector<char>;
using vst = vector<string>;
using vd = vector<double>;
using vld = vector<long double>;
using P = pair<long long, long long>;
template<class T> long long sum(const T &a){ return accumulate(a.begin(), a.end(), 0LL); }
template<class T> auto min(const T &a){ return *min_element(a.begin(), a.end()); }
template<class T> auto max(const T &a){ return *max_element(a.begin(), a.end()); }
const long long MINF = 0x7fffffffffff;
const long long INF = 0x1fffffffffffffff;
const long long MOD = 998244353;
const long double EPS = 1e-9;
const long double PI = acos(-1);
template<class T> inline bool chmax(T &a, T b) { if(a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T &a, T b) { if(a > b) { a = b; return 1; } return 0; }
template<typename T1, typename T2> istream &operator>>(istream &is, pair<T1, T2> &p){ is >> p.first >> p.second; return is; }
template<typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &p){ os << "(" << p.first << ", " << p.second << ")"; return os; }
template<typename T> istream &operator>>(istream &is, vector<T> &v){ for(T &in : v) is >> in; return is; }
template<typename T> ostream &operator<<(ostream &os, const vector<T> &v){ for(int i = 0; i < (int) v.size(); ++i){ os << v[i] << (i + 1 != (int) v.size() ? " " : ""); } return os; }
template <typename T, typename S> ostream &operator<<(ostream &os, const map<T, S> &mp){ for(auto &[key, val] : mp){ os << key << ":" << val << " "; } return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &st){ auto itr = st.begin(); for(int i = 0; i < (int) st.size(); ++i){ os << *itr << (i + 1 != (int) st.size() ? " " : ""); itr++; } return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &st){ auto itr = st.begin(); for(int i = 0; i < (int) st.size(); ++i){ os << *itr << (i + 1 != (int) st.size() ? " " : ""); itr++; } return os; }
template <typename T> ostream &operator<<(ostream &os, queue<T> q){ while(q.size()){ os << q.front() << " "; q.pop(); } return os; }
template <typename T> ostream &operator<<(ostream &os, deque<T> q){ while(q.size()){ os << q.front() << " "; q.pop_front(); } return os; }
template <typename T> ostream &operator<<(ostream &os, stack<T> st){ while(st.size()){ os << st.top() << " "; st.pop(); } return os; }
template <class T, class Container, class Compare> ostream &operator<<(ostream &os, priority_queue<T, Container, Compare> pq){ while(pq.size()){ os << pq.top() << " "; pq.pop(); } return os; }
template<class T, class U>
void inGraph(vector<vector<T>> &G, U n, U m, bool directed = true, bool zero_index = true){
G.resize(n);
for(int i = 0; i < m; i++){
int a, b;
cin >> a >> b;
if(!zero_index) a--, b--;
G[a].push_back(b);
if(!directed) G[b].push_back(a);
}
}
template <typename T>
long long binary_search(long long ok, long long ng, T check){
while(abs(ok - ng) > 1){
long long mid = (ok + ng) / 2;
if(check(mid)) ok = mid;
else ng = mid;
}
return ok;
}
template <typename T>
long double binary_search_real(long double ok, long double ng, T check, int iter = 100){
for(int i = 0; i < iter; ++i){
long double mid = (ok + ng) / 2;
if(check(mid)) ok = mid;
else ng = mid;
}
return ok;
}
long long trisum(long long a, long long b){
if(a > b) return 0;
long long res = ((b - a + 1) * (a + b)) / 2;
return res;
}
template <typename T>
T intpow(T x, int n){
T ret = 1;
while(n > 0) {
if(n & 1) (ret *= x);
(x *= x);
n >>= 1;
}
return ret;
}
template <typename T>
T getDivision(T a, T b){
if(b == 0) return -1;
if(a >= 0 && b > 0){
return a / b;
} else if(a < 0 && b > 0){
return a / b - (a % b != 0);
} else if(a >= 0 && b < 0){
return a / b;
} else{
return a / b + (a % b != 0);
}
}
template <typename T>
T getReminder(T a, T b){
if(b == 0) return -1;
if(a >= 0 && b > 0){
return a % b;
} else if(a < 0 && b > 0){
return ((a % b) + b) % b;
} else if(a >= 0 && b < 0){
return a % b;
} else{
return (abs(b) - abs(a % b)) % b;
}
}
template<class T, class U> inline T vin(T &vec, U n) { vec.resize(n); for(int i = 0; i < (int) n; ++i) cin >> vec[i]; return vec; }
template<class T> inline void vout(T vec, string s = "\n"){ for(auto x : vec) cout << x << s; }
template<class... T> void in(T&... a){ (cin >> ... >> a); }
void out(){ cout << '\n'; }
template<class T, class... Ts> void out(const T &a, const Ts&... b){ cout << a; (cout << ... << (cout << ' ', b)); cout << '\n'; }
void fout(){ cout << endl; }
template<class T, class... Ts> void fout(const T &a, const Ts&... b){ cout << a; (cout << ... << (cout << ' ', b)); cout << endl; }
void debug(){ cerr << '\n'; }
template<class T, class... Ts> void debug(const T &a, const Ts&... b){ cerr << a; (cerr << ... << (cerr << ' ', b)); cerr << '\n'; }
template <long long Modulus>
struct ModInt{
long long val;
static constexpr int mod() { return Modulus; }
constexpr ModInt(const long long _val = 0) noexcept : val(_val) {
normalize();
}
void normalize(){
val = (val % Modulus + Modulus) % Modulus;
}
inline ModInt &operator+=(const ModInt &rhs) noexcept {
if(val += rhs.val, val >= Modulus) val -= Modulus;
return *this;
}
inline ModInt &operator-=(const ModInt &rhs) noexcept {
if(val -= rhs.val, val < 0) val += Modulus;
return *this;
}
inline ModInt &operator*=(const ModInt &rhs) noexcept {
val = val * rhs.val % Modulus;
return *this;
}
inline ModInt &operator/=(const ModInt &rhs) noexcept {
val = val * inv(rhs.val).val % Modulus;
return *this;
}
inline ModInt &operator++() noexcept {
if(++val >= Modulus) val -= Modulus;
return *this;
}
inline ModInt operator++(int) noexcept {
ModInt t = val;
if(++val >= Modulus) val -= Modulus;
return t;
}
inline ModInt &operator--() noexcept {
if(--val < 0) val += Modulus;
return *this;
}
inline ModInt operator--(int) noexcept {
ModInt t = val;
if(--val < 0) val += Modulus;
return t;
}
inline ModInt operator-() const noexcept { return (Modulus - val) % Modulus; }
inline ModInt inv(void) const { return inv(val); }
ModInt pow(long long n) const {
assert(0 <= n);
ModInt x = *this, r = 1;
while(n){
if(n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
ModInt inv(const long long n) const {
long long a = n, b = Modulus, u = 1, v = 0;
while(b){
long long t = a / b;
a -= t * b; std::swap(a, b);
u -= t * v; std::swap(u, v);
}
u %= Modulus;
if(u < 0) u += Modulus;
return u;
}
friend inline ModInt operator+(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) += rhs; }
friend inline ModInt operator-(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) -= rhs; }
friend inline ModInt operator*(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) *= rhs; }
friend inline ModInt operator/(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) /= rhs; }
friend inline bool operator==(const ModInt &lhs, const ModInt &rhs) noexcept { return lhs.val == rhs.val; }
friend inline bool operator!=(const ModInt &lhs, const ModInt &rhs) noexcept { return lhs.val != rhs.val; }
friend inline std::istream &operator>>(std::istream &is, ModInt &x) noexcept {
is >> x.val;
x.normalize();
return is;
}
friend inline std::ostream &operator<<(std::ostream &os, const ModInt &x) noexcept { return os << x.val; }
};
namespace CRT{
inline long long mod(long long a, long long m){
return (a % m + m) % m;
}
long long extGCD(long long a, long long b, long long &x, long long &y){
if(b == 0){
x = 1;
y = 0;
return a;
}
long long d = extGCD(b, a % b, y, x);
y -= a / b * x;
return d;
}
std::pair<long long, long long> chineseRem(const std::vector<long long> &b, const std::vector<long long> &m) {
long long r = 0, M = 1;
for(int i = 0; i < (int) b.size(); i++){
long long p, q;
long long d = extGCD(M, m[i], p, q);
if((b[i] - r) % d != 0) return {0, -1};
long long tmp = (b[i] - r) / d * p % (m[i] / d);
r += M * tmp;
M *= m[i] / d;
}
r %= M;
if(r < 0) r += M;
return {r, M};
}
// not coprime
long long preGarner(std::vector<long long> &b, std::vector<long long> &m, const long long MOD){
long long res = 1;
int n = b.size();
for(int i = 0; i < n; i++){
for(int j = 0; j < i; j++){
long long g = std::gcd(m[i], m[j]);
if((b[i] - b[j]) % g != 0) return -1;
m[i] /= g, m[j] /= g;
// gcd の分だけ被ってるので振り分ける
long long gi = std::gcd(m[i], g), gj = g / gi;
do{
g = std::gcd(gi, gj);
gi *= g, gj /= g;
}while(g != 1);
m[i] *= gi, m[j] *= gj;
b[i] %= m[i], b[j] %= m[j];
}
}
for(auto x : m) (res *= x) %= MOD;
return res;
}
long long garner(const std::vector<long long> &b, const std::vector<long long> &m, const long long MOD){
std::vector<long long> tm = m;
tm.push_back(MOD);
auto inv = [&](long long a, long long m) -> long long {
long long x, y;
extGCD(a, m, x, y);
return mod(x, m);
};
int n = b.size();
std::vector<long long> coeffs(n + 1, 1), constants(n + 1, 0);
for(int i = 0; i < n; i++){
// solve "coeffs[i] * t[i] + constants[i] = b[i] (mod. m[i])
long long t = mod((b[i] - constants[i]) * inv(coeffs[i], tm[i]), tm[i]);
for(int j = i + 1; j < n + 1; j++){
(constants[j] += t * coeffs[j]) %= tm[j];
(coeffs[j] *= tm[i]) %= tm[j];
}
}
return constants[n];
}
// ax + b ≡ 0 (mod m)
long long modEquation(long long a, long long b, long long m, bool is_positive = false){
a %= m; b %= m;
b = (m - b) % m;
long long g = std::gcd(a, m);
if(b % g != 0) return -1;
a /= g; b /= g; m /= g;
if(is_positive && b == 0){
return m;
}
long long x, y;
extGCD(a, m, x, y);
return (b * x % m + m) % m;
}
}
namespace NTT{
// @param n `0 <= n`
// @return minimum non-negative `x` s.t. `n <= 2**x`
int ceil_pow2(int n) {
int x = 0;
while((1U << x) < (unsigned int) (n)) x++;
return x;
}
// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsf(unsigned int n) {
return __builtin_ctz(n);
}
int primitive_root(int m) {
if(m == 2) return 1;
if(m == 167772161) return 3;
if(m == 469762049) return 3;
if(m == 754974721) return 11;
if(m == 998244353) return 3;
return 1;
}
template <typename T>
void butterfly(std::vector<T> &a){
int g = primitive_root(T::mod());
int n = int(a.size());
int h = ceil_pow2(n);
static bool first = true;
static T sum_e[30]; // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]
if(first){
first = false;
T es[30], ies[30]; // es[i]^(2^(2+i)) == 1
int cnt2 = bsf(T::mod() - 1);
T e = T(g).pow((T::mod() - 1) >> cnt2), ie = e.inv();
for(int i = cnt2; i >= 2; i--){
// e^(2^i) == 1
es[i - 2] = e;
ies[i - 2] = ie;
e *= e;
ie *= ie;
}
T now = 1;
for(int i = 0; i <= cnt2 - 2; i++){
sum_e[i] = es[i] * now;
now *= ies[i];
}
}
for(int ph = 1; ph <= h; ph++){
int w = 1 << (ph - 1), p = 1 << (h - ph);
T now = 1;
for(int s = 0; s < w; s++){
int offset = s << (h - ph + 1);
for(int i = 0; i < p; i++){
auto l = a[i + offset];
auto r = a[i + offset + p] * now;
a[i + offset] = l + r;
a[i + offset + p] = l - r;
}
now *= sum_e[bsf(~(unsigned int) (s))];
}
}
}
template <typename T>
void butterfly_inv(std::vector<T> &a) {
int g = primitive_root(T::mod());
int n = int(a.size());
int h = ceil_pow2(n);
static bool first = true;
static T sum_ie[30]; // sum_ie[i] = es[0] * ... * es[i - 1] * ies[i]
if(first){
first = false;
T es[30], ies[30]; // es[i]^(2^(2+i)) == 1
int cnt2 = bsf(T::mod() - 1);
T e = T(g).pow((T::mod() - 1) >> cnt2), ie = e.inv();
for(int i = cnt2; i >= 2; i--){
// e^(2^i) == 1
es[i - 2] = e;
ies[i - 2] = ie;
e *= e;
ie *= ie;
}
T now = 1;
for(int i = 0; i <= cnt2 - 2; i++){
sum_ie[i] = ies[i] * now;
now *= es[i];
}
}
for(int ph = h; ph >= 1; ph--){
int w = 1 << (ph - 1), p = 1 << (h - ph);
T inow = 1;
for(int s = 0; s < w; s++){
int offset = s << (h - ph + 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) (T::mod() + l.val - r.val) * inow.val;
}
inow *= sum_ie[bsf(~(unsigned int) (s))];
}
}
}
template <typename T>
std::vector<T> convolution(std::vector<T> a, std::vector<T> b){
int n = int(a.size()), m = int(b.size());
if(!n || !m) return {};
if(std::min(n, m) <= 60) {
if(n < m) {
std::swap(n, m);
std::swap(a, b);
}
std::vector<T> ans(n + m - 1);
for(int i = 0; i < n; i++){
for(int j = 0; j < m; j++){
ans[i + j] += a[i] * b[j];
}
}
return ans;
}
int z = 1 << ceil_pow2(n + m - 1);
a.resize(z);
butterfly(a);
b.resize(z);
butterfly(b);
for(int i = 0; i < z; i++){
a[i] *= b[i];
}
butterfly_inv(a);
a.resize(n + m - 1);
T iz = T(z).inv();
for(int i = 0; i < n + m - 1; i++) a[i] *= iz;
return a;
}
template <typename T>
std::vector<T> convolution_mod(const std::vector<T> &a, const std::vector<T> &b, const long long MOD){
if(MOD == 998244353){
return convolution(a, b);
}
constexpr long long M0 = 167772161;
constexpr long long M1 = 469762049;
constexpr long long M2 = 754974721;
using mint0 = ModInt<M0>;
using mint1 = ModInt<M1>;
using mint2 = ModInt<M2>;
int n = a.size(), m = b.size();
std::vector<mint0> a0(n), b0(m);
std::vector<mint1> a1(n), b1(m);
std::vector<mint2> a2(n), b2(m);
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;
}
auto c0 = convolution(a0, b0);
auto c1 = convolution(a1, b1);
auto c2 = convolution(a2, b2);
std::vector<T> ret(n + m - 1);
for(int i = 0; i < n + m - 1; i++){
ret[i] = CRT::garner({c0[i].val, c1[i].val, c2[i].val}, {M0, M1, M2}, MOD);
}
return ret;
}
};
using mint = ModInt<MOD>;
ll T;
void input(){
in(T);
}
void solve(){
ll n; in(n);
mint two = mint(2).inv();
auto dfs = [&](auto &self, ll k) -> vector<mint> {
if(k == 0){
return {mint(1)};
}else if(k == 1){
return {mint(0), mint(1)};
}
ll a = k / 2, b = k - a;
vector<mint> x = self(self, a);
vector<mint> y = self(self, b);
vector<mint> yr = y;
reverse(ALL(yr));
vector<mint> c1 = NTT::convolution(x, y), c2 = NTT::convolution(x, yr);
vector<mint> ans(k + 1);
rep(i, k + 1){
ans[i] += c1[i];
ans[abs(i - b)] += c2[i];
}
rep(i, k + 1) ans[i] *= two;
return ans;
};
vector<mint> ans = dfs(dfs, n);
mint p = mint(2).pow(n);
rep(i, n + 1){
ans[i] *= p;
}
out(ans);
}
int main(){
ios::sync_with_stdio(false);
cin.tie(nullptr);
cout << fixed << setprecision(20);
T = 1;
// input();
while(T--) solve();
}