結果
問題 | No.1080 Strange Squared Score Sum |
ユーザー |
![]() |
提出日時 | 2020-06-12 23:18:33 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
TLE
|
実行時間 | - |
コード長 | 19,585 bytes |
コンパイル時間 | 4,755 ms |
コンパイル使用メモリ | 241,592 KB |
最終ジャッジ日時 | 2025-01-11 03:06:51 |
ジャッジサーバーID (参考情報) |
judge5 / judge5 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 2 |
other | AC * 6 TLE * 14 |
ソースコード
#include <bits/stdc++.h>using namespace std;using lint = long long int;using pint = pair<int, int>;using plint = pair<lint, lint>;struct fast_ios { fast_ios(){ cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;#define ALL(x) (x).begin(), (x).end()#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)#define REP(i, n) FOR(i,0,n)#define IREP(i, n) IFOR(i,0,n)template<typename T> void ndarray(vector<T> &vec, int len) { vec.resize(len); }template<typename T, typename... Args> void ndarray(vector<T> &vec, int len, Args... args) { vec.resize(len); for (auto &v : vec) ndarray(v, args...); }template<typename T> bool chmax(T &m, const T q) { if (m < q) {m = q; return true;} else return false; }template<typename T> bool chmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; }template<typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }template<typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }template<typename T> istream &operator>>(istream &is, vector<T> &vec){ for (auto &v : vec) is >> v; return is; }template<typename T> ostream &operator<<(ostream &os, const vector<T> &vec){ os << "["; for (auto v : vec) os << v << ","; os << "]"; return os; }template<typename T> ostream &operator<<(ostream &os, const deque<T> &vec){ os << "deq["; for (auto v : vec) os << v << ","; os << "]"; return os; }template<typename T> ostream &operator<<(ostream &os, const set<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }template<typename T> ostream &operator<<(ostream &os, const unordered_set<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; returnos; }template<typename T> ostream &operator<<(ostream &os, const multiset<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }template<typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}";return os; }template<typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa){ os << "(" << pa.first << "," << pa.second << ")"; returnos; }template<typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp){ os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; }template<typename TK, typename TV> ostream &operator<<(ostream &os, const unordered_map<TK, TV> &mp){ os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; }#define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl;/*#include <ext/pb_ds/assoc_container.hpp>#include <ext/pb_ds/tree_policy.hpp>#include <ext/pb_ds/tag_and_trait.hpp>using namespace __gnu_pbds; // find_by_order(), order_of_key()template<typename TK> using pbds_set = tree<TK, null_type, less<TK>, rb_tree_tag, tree_order_statistics_node_update>;template<typename TK, typename TV> using pbds_map = tree<TK, TV, less<TK>, rb_tree_tag, tree_order_statistics_node_update>;*/template <int mod>struct ModInt{using lint = long long;static int get_mod() { return mod; }static int get_primitive_root() {static int primitive_root = 0;if (!primitive_root) {primitive_root = [&](){std::set<int> fac;int v = mod - 1;for (lint i = 2; i * i <= v; i++) while (v % i == 0) fac.insert(i), v /= i;if (v > 1) fac.insert(v);for (int g = 1; g < mod; g++) {bool ok = true;for (auto i : fac) if (ModInt(g).power((mod - 1) / i) == 1) { ok = false; break; }if (ok) return g;}return -1;}();}return primitive_root;}int val;constexpr ModInt() : val(0) {}constexpr ModInt &_setval(lint v) { val = (v >= mod ? v - mod : v); return *this; }constexpr ModInt(lint v) { _setval(v % mod + mod); }explicit operator bool() const { return val != 0; }constexpr ModInt operator+(const ModInt &x) const { return ModInt()._setval((lint)val + x.val); }constexpr ModInt operator-(const ModInt &x) const { return ModInt()._setval((lint)val - x.val + mod); }constexpr ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val * x.val % mod); }constexpr ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val * x.inv() % mod); }constexpr ModInt operator-() const { return ModInt()._setval(mod - val); }constexpr ModInt &operator+=(const ModInt &x) { return *this = *this + x; }constexpr ModInt &operator-=(const ModInt &x) { return *this = *this - x; }constexpr ModInt &operator*=(const ModInt &x) { return *this = *this * x; }constexpr ModInt &operator/=(const ModInt &x) { return *this = *this / x; }friend constexpr ModInt operator+(lint a, const ModInt &x) { return ModInt()._setval(a % mod + x.val); }friend constexpr ModInt operator-(lint a, const ModInt &x) { return ModInt()._setval(a % mod - x.val + mod); }friend constexpr ModInt operator*(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.val % mod); }friend constexpr ModInt operator/(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.inv() % mod); }constexpr bool operator==(const ModInt &x) const { return val == x.val; }constexpr bool operator!=(const ModInt &x) const { return val != x.val; }bool operator<(const ModInt &x) const { return val < x.val; } // To use std::map<ModInt, T>friend std::istream &operator>>(std::istream &is, ModInt &x) { lint t; is >> t; x = ModInt(t); return is; }friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { os << x.val; return os; }constexpr lint power(lint n) const {lint ans = 1, tmp = this->val;while (n) {if (n & 1) ans = ans * tmp % mod;tmp = tmp * tmp % mod;n /= 2;}return ans;}constexpr lint inv() const { return this->power(mod - 2); }constexpr ModInt operator^(lint n) const { return ModInt(this->power(n)); }constexpr ModInt &operator^=(lint n) { return *this = *this ^ n; }inline ModInt fac() const {static std::vector<ModInt> facs;int l0 = facs.size();if (l0 > this->val) return facs[this->val];facs.resize(this->val + 1);for (int i = l0; i <= this->val; i++) facs[i] = (i == 0 ? ModInt(1) : facs[i - 1] * ModInt(i));return facs[this->val];}ModInt doublefac() const {lint k = (this->val + 1) / 2;if (this->val & 1) return ModInt(k * 2).fac() / ModInt(2).power(k) / ModInt(k).fac();else return ModInt(k).fac() * ModInt(2).power(k);}ModInt nCr(const ModInt &r) const {if (this->val < r.val) return ModInt(0);return this->fac() / ((*this - r).fac() * r.fac());}ModInt sqrt() const {if (val == 0) return 0;if (mod == 2) return val;if (power((mod - 1) / 2) != 1) return 0;ModInt b = 1;while (b.power((mod - 1) / 2) == 1) b += 1;int e = 0, m = mod - 1;while (m % 2 == 0) m >>= 1, e++;ModInt x = power((m - 1) / 2), y = (*this) * x * x;x *= (*this);ModInt z = b.power(m);while (y != 1) {int j = 0;ModInt t = y;while (t != 1) j++, t *= t;z = z.power(1LL << (e - j - 1));x *= z, z *= z, y *= z;e = j;}return ModInt(std::min(x.val, mod - x.val));}};using mint = ModInt<1000000009>;// Integer convolution for arbitrary mod// with NTT (and Garner's algorithm) for ModInt / ModIntRuntime class.// We skip Garner's algorithm if `skip_garner` is true or mod is in `nttprimes`.// input: a (size: n), b (size: m)// return: vector (size: n + m - 1)template <typename MODINT>vector<MODINT> nttconv(vector<MODINT> a, vector<MODINT> b, bool skip_garner = false);constexpr int nttprimes[3] = {998244353, 167772161, 469762049};// Integer FFT (Fast Fourier Transform) for ModInt class// (Also known as Number Theoretic Transform, NTT)// is_inverse: inverse transform// ** Input size must be 2^n **template <typename MODINT>void ntt(vector<MODINT> &a, bool is_inverse = false){int n = a.size();assert(__builtin_popcount(n) == 1);MODINT h = MODINT(MODINT::get_primitive_root()).power((MODINT::get_mod() - 1) / n);if (is_inverse) h = 1 / h;int i = 0;for (int j = 1; j < n - 1; j++) {for (int k = n >> 1; k > (i ^= k); k >>= 1);if (j < i) swap(a[i], a[j]);}for (int m = 1; m < n; m *= 2) {int m2 = 2 * m;MODINT base = h.power(n / m2), w = 1;for (int x = 0; x < m; x++) {for (int s = x; s < n; s += m2) {MODINT u = a[s], d = a[s + m] * w;a[s] = u + d, a[s + m] = u - d;}w *= base;}}if (is_inverse) {long long int n_inv = MODINT(n).inv();for (auto &v : a) v *= n_inv;}}template<int MOD>vector<ModInt<MOD>> nttconv_(const vector<int> &a, const vector<int> &b) {int sz = a.size();assert(a.size() == b.size() and __builtin_popcount(sz) == 1);vector<ModInt<MOD>> ap(sz), bp(sz);for (int i = 0; i < sz; i++) ap[i] = a[i], bp[i] = b[i];if (a == b) {ntt(ap, false);bp = ap;}else {ntt(ap, false);ntt(bp, false);}for (int i = 0; i < sz; i++) ap[i] *= bp[i];ntt(ap, true);return ap;}long long int extgcd_ntt_(long long int a, long long int b, long long int &x, long long int &y){long long int d = a;if (b != 0) d = extgcd_ntt_(b, a % b, y, x), y -= (a / b) * x;else x = 1, y = 0;return d;}long long int modinv_ntt_(long long int a, long long int m){long long int x, y;extgcd_ntt_(a, m, x, y);return (m + x % m) % m;}long long int garner_ntt_(int r0, int r1, int r2, int mod){array<long long int, 4> rs = {r0, r1, r2, 0};vector<long long int> coffs(4, 1), constants(4, 0);for (int i = 0; i < 3; i++) {long long int v = (rs[i] - constants[i]) * modinv_ntt_(coffs[i], nttprimes[i]) % nttprimes[i];if (v < 0) v += nttprimes[i];for (int j = i + 1; j < 4; j++) {(constants[j] += coffs[j] * v) %= (j < 3 ? nttprimes[j] : mod);(coffs[j] *= nttprimes[i]) %= (j < 3 ? nttprimes[j] : mod);}}return constants.back();}template <typename MODINT>vector<MODINT> nttconv(vector<MODINT> a, vector<MODINT> b, bool skip_garner){int sz = 1, n = a.size(), m = b.size();while (sz < n + m) sz <<= 1;if (sz <= 16) {vector<MODINT> ret(n + m - 1);for (int i = 0; i < n; i++) {for (int j = 0; j < m; j++) ret[i + j] += a[i] * b[j];}return ret;}int mod = MODINT::get_mod();if (skip_garner or find(begin(nttprimes), end(nttprimes), mod) != end(nttprimes)) {a.resize(sz), b.resize(sz);if (a == b) { ntt(a, false); b = a; }else ntt(a, false), ntt(b, false);for (int i = 0; i < sz; i++) a[i] *= b[i];ntt(a, true);a.resize(n + m - 1);}else {vector<int> ai(sz), bi(sz);for (int i = 0; i < n; i++) ai[i] = a[i].val;for (int i = 0; i < m; i++) bi[i] = b[i].val;auto ntt0 = nttconv_<nttprimes[0]>(ai, bi);auto ntt1 = nttconv_<nttprimes[1]>(ai, bi);auto ntt2 = nttconv_<nttprimes[2]>(ai, bi);a.resize(n + m - 1);for (int i = 0; i < n + m - 1; i++) {a[i] = garner_ntt_(ntt0[i].val, ntt1[i].val, ntt2[i].val, mod);}}return a;}// Formal Power Series (形式的冪級数) based on ModInt<mod> / ModIntRuntime// Reference: <https://ei1333.github.io/luzhiled/snippets/math/formal-power-series.html>template<typename T>struct FormalPowerSeries : vector<T>{using vector<T>::vector;using P = FormalPowerSeries;void shrink() { while (this->size() and this->back() == T(0)) this->pop_back(); }P operator+(const P &r) const { return P(*this) += r; }P operator+(const T &v) const { return P(*this) += v; }P operator-(const P &r) const { return P(*this) -= r; }P operator-(const T &v) const { return P(*this) -= v; }P operator*(const P &r) const { return P(*this) *= r; }P operator*(const T &v) const { return P(*this) *= v; }P operator/(const P &r) const { return P(*this) /= r; }P operator/(const T &v) const { return P(*this) /= v; }P operator%(const P &r) const { return P(*this) %= r; }P &operator+=(const P &r) {if (r.size() > this->size()) this->resize(r.size());for (int i = 0; i < (int)r.size(); i++) (*this)[i] += r[i];shrink();return *this;}P &operator+=(const T &v) {if (this->empty()) this->resize(1);(*this)[0] += v;shrink();return *this;}P &operator-=(const P &r) {if (r.size() > this->size()) this->resize(r.size());for (int i = 0; i < (int)r.size(); i++) (*this)[i] -= r[i];shrink();return *this;}P &operator-=(const T &v) {if (this->empty()) this->resize(1);(*this)[0] -= v;shrink();return *this;}P &operator*=(const T &v) {for (auto &x : (*this)) x *= v;shrink();return *this;}P &operator*=(const P &r) {if (this->empty() || r.empty()) this->clear();else {auto ret = nttconv(*this, r);*this = P(ret.begin(), ret.end());}return *this;}P &operator%=(const P &r) {*this -= *this / r * r;shrink();return *this;}P operator-() const {P ret = *this;for (auto &v : ret) v = -v;return ret;}P &operator/=(const T &v) {assert(v != T(0));for (auto &x : (*this)) x /= v;return *this;}P &operator/=(const P &r) {if (this->size() < r.size()) {this->clear();return *this;}int n = (int)this->size() - r.size() + 1;return *this = (reversed().pre(n) * r.reversed().inv(n)).pre(n).reversed(n);}P pre(int sz) const {P ret(this->begin(), this->begin() + min((int)this->size(), sz));ret.shrink();return ret;}P operator>>(int sz) const {if ((int)this->size() <= sz) return {};return P(this->begin() + sz, this->end());}P operator<<(int sz) const {if (this->empty()) return {};P ret(*this);ret.insert(ret.begin(), sz, T(0));return ret;}P reversed(int deg = -1) const {assert(deg >= -1);P ret(*this);if (deg != -1) ret.resize(deg, T(0));reverse(ret.begin(), ret.end());ret.shrink();return ret;}P differential() const { // formal derivative (differential) of f.p.s.const int n = (int)this->size();P ret(max(0, n - 1));for (int i = 1; i < n; i++) ret[i - 1] = (*this)[i] * T(i);return ret;}P integral() const {const int n = (int)this->size();P ret(n + 1);ret[0] = T(0);for (int i = 0; i < n; i++) ret[i + 1] = (*this)[i] / T(i + 1);return ret;}P inv(int deg) const {assert(deg >= -1);assert(this->size() and ((*this)[0]) != T(0)); // Requirement: F(0) != 0const int n = this->size();if (deg == -1) deg = n;P ret({T(1) / (*this)[0]});for (int i = 1; i < deg; i <<= 1) {ret = (ret + ret - ret * ret * pre(i << 1)).pre(i << 1);}ret = ret.pre(deg);ret.shrink();return ret;}P log(int deg = -1) const {assert(deg >= -1);assert(this->size() and ((*this)[0]) == T(1)); // Requirement: F(0) = 1const int n = (int)this->size();if (deg == 0) return {};if (deg == -1) deg = n;return (this->differential() * this->inv(deg)).pre(deg - 1).integral();}P sqrt(int deg = -1) const {assert(deg >= -1);const int n = (int)this->size();if (deg == -1) deg = n;if (this->empty()) return {};if ((*this)[0] == T(0)) {for (int i = 1; i < n; i++) if ((*this)[i] != T(0)) {if ((i & 1) or deg - i / 2 <= 0) return {};return (*this >> i).sqrt(deg - i / 2) << (i / 2);}return {};}T sqrtf0 = (*this)[0].sqrt();if (sqrtf0 == T(0)) return {};P y = (*this) / (*this)[0], ret({T(1)});T inv2 = T(1) / T(2);for (int i = 1; i < deg; i <<= 1) {ret = (ret + y.pre(i << 1) * ret.inv(i << 1)) * inv2;}return ret.pre(deg) * sqrtf0;}P exp(int deg = -1) const {assert(deg >= -1);assert(this->empty() or ((*this)[0]) == T(0)); // Requirement: F(0) = 0const int n = (int)this->size();if (deg == -1) deg = n;P ret({T(1)});for (int i = 1; i < deg; i <<= 1) {ret = (ret * (pre(i << 1) + T(1) - ret.log(i << 1))).pre(i << 1);}return ret.pre(deg);}P pow(long long int k, int deg = -1) const {assert(deg >= -1);const int n = (int)this->size();if (deg == -1) deg = n;for (int i = 0; i < n; i++) {if ((*this)[i] != T(0)) {T rev = T(1) / (*this)[i];P C(*this * rev);P D(n - i);for (int j = i; j < n; j++) D[j - i] = C[j];D = (D.log(deg) * T(k)).exp(deg) * (*this)[i].power(k);P E(deg);if (k * (i > 0) > deg or k * i > deg) return {};long long int S = i * k;for (int j = 0; j + S < deg and j < (int)D.size(); j++) E[j + S] = D[j];E.shrink();return E;}}return *this;}T coeff(int i) const {if ((int)this->size() <= i) return T(0);return (*this)[i];}T eval(T x) const {T ret = 0, w = 1;for (auto &v : *this) ret += w * v, w *= x;return ret;}};using fps = FormalPowerSeries<mint>;fps sin(fps f, int n, mint j){REP(i, n) f[i] *= j;fps ret = (f.exp() - (-f).exp());dbg(ret);ret /= (2 * j);return ret;}fps cos(fps f, int n, mint j){REP(i, n) f[i] *= j;fps ret = (f.exp() + (-f).exp());dbg(ret);ret /= (2);return ret;}int main(){mint j = mint(-1).sqrt();dbg(j * j + 1);int N;cin >> N;fps f(N + 10);FOR(i, 1, f.size()) f[i] = mint(i + 1) * (i + 1);// dbg(f);fps ret = sin(f, N + 5, j) + cos(f, N + 5, j);// ret = ret + ret.differential();ret *= mint(N).fac();FOR(K, 1, N + 1) cout << ret.coeff(K) << '\n';}