Submit Info #1297

Problem Lang User Status Time Memory
Partition Function cpp (anonymous) AC 2287 ms 77.07 MiB

ケース詳細
Name Status Time Memory
0_00 AC 1 ms 0.73 MiB
100000_00 AC 415 ms 18.95 MiB
10000_00 AC 39 ms 2.82 MiB
1000_00 AC 5 ms 0.88 MiB
100_00 AC 0 ms 0.67 MiB
1_00 AC 1 ms 0.72 MiB
200000_00 AC 986 ms 37.07 MiB
300000_00 AC 2282 ms 68.21 MiB
400000_00 AC 2272 ms 73.82 MiB
500000_00 AC 2287 ms 77.07 MiB
example_00 AC 2 ms 0.67 MiB

//https://codeforces.com/contest/438/problem/E #include<bits/stdc++.h> #define rep(i,a,b) for(int i=a;i<b;i++) #define rrep(i,a,b) for(int i=a;i>=b;i--) #define fore(i,a) for(auto &i:a) #define all(x) (x).begin(),(x).end() //#pragma GCC optimize ("-O3") using namespace std; void _main(); int main() { cin.tie(0); ios::sync_with_stdio(false); _main(); } typedef long long ll; const int inf = INT_MAX / 2; const ll infl = 1LL << 60; template<class T>bool chmax(T& a, const T& b) { if (a < b) { a = b; return 1; } return 0; } template<class T>bool chmin(T& a, const T& b) { if (b < a) { a = b; return 1; } return 0; } //--------------------------------------------------------------------------------------------------- #ifdef _MSC_VER #pragma push_macro("long") #undef long #ifdef _WIN32 inline unsigned int __builtin_ctz(unsigned int x) { unsigned long r; _BitScanForward(&r, x); return r; } inline unsigned int __builtin_clz(unsigned int x) { unsigned long r; _BitScanReverse(&r, x); return 31 - r; } inline unsigned int __builtin_ffs(unsigned int x) { unsigned long r; return _BitScanForward(&r, x) ? r + 1 : 0; } inline unsigned int __builtin_popcount(unsigned int x) { return __popcnt(x); } #ifdef _WIN64 inline unsigned long long __builtin_ctzll(unsigned long long x) { unsigned long r; _BitScanForward64(&r, x); return r; } inline unsigned long long __builtin_clzll(unsigned long long x) { unsigned long r; _BitScanReverse64(&r, x); return 63 - r; } inline unsigned long long __builtin_ffsll(unsigned long long x) { unsigned long r; return _BitScanForward64(&r, x) ? r + 1 : 0; } inline unsigned long long __builtin_popcountll(unsigned long long x) { return __popcnt64(x); } #else inline unsigned int hidword(unsigned long long x) { return static_cast<unsigned int>(x >> 32); } inline unsigned int lodword(unsigned long long x) { return static_cast<unsigned int>(x & 0xFFFFFFFF); } inline unsigned long long __builtin_ctzll(unsigned long long x) { return lodword(x) ? __builtin_ctz(lodword(x)) : __builtin_ctz(hidword(x)) + 32; } inline unsigned long long __builtin_clzll(unsigned long long x) { return hidword(x) ? __builtin_clz(hidword(x)) : __builtin_clz(lodword(x)) + 32; } inline unsigned long long __builtin_ffsll(unsigned long long x) { return lodword(x) ? __builtin_ffs(lodword(x)) : hidword(x) ? __builtin_ffs(hidword(x)) + 32 : 0; } inline unsigned long long __builtin_popcountll(unsigned long long x) { return __builtin_popcount(lodword(x)) + __builtin_popcount(hidword(x)); } #endif // _WIN64 #endif // _WIN32 #pragma pop_macro("long") #endif // _MSC_VER template<int MOD> struct ModInt { static const int Mod = MOD; unsigned x; ModInt() : x(0) { } ModInt(signed sig) { x = sig < 0 ? sig % MOD + MOD : sig % MOD; } ModInt(signed long long sig) { x = sig < 0 ? sig % MOD + MOD : sig % MOD; } int get() const { return (int)x; } ModInt& operator+=(ModInt that) { if ((x += that.x) >= MOD) x -= MOD; return *this; } ModInt& operator-=(ModInt that) { if ((x += MOD - that.x) >= MOD) x -= MOD; return *this; } ModInt& operator*=(ModInt that) { x = (unsigned long long)x * that.x % MOD; return *this; } ModInt& operator/=(ModInt that) { return *this *= that.inverse(); } ModInt operator+(ModInt that) const { return ModInt(*this) += that; } ModInt operator-(ModInt that) const { return ModInt(*this) -= that; } ModInt operator*(ModInt that) const { return ModInt(*this) *= that; } ModInt operator/(ModInt that) const { return ModInt(*this) /= that; } ModInt inverse() const { long long a = x, b = MOD, 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); } return ModInt(u); } bool operator==(ModInt that) const { return x == that.x; } bool operator!=(ModInt that) const { return x != that.x; } ModInt operator-() const { ModInt t; t.x = x == 0 ? 0 : Mod - x; return t; } }; template<int MOD> ostream& operator<<(ostream& st, const ModInt<MOD> a) { st << a.get(); return st; }; template<int MOD> ModInt<MOD> operator^(ModInt<MOD> a, unsigned long long k) { ModInt<MOD> r = 1; while (k) { if (k & 1) r *= a; a *= a; k >>= 1; } return r; } typedef ModInt<998244353> mint; template<typename T> struct FormalPowerSeries { using Poly = vector<T>; using Conv = function<Poly(Poly, Poly)>; Conv conv; FormalPowerSeries(Conv conv) :conv(conv) {} Poly pre(const Poly& as, int deg) { return Poly(as.begin(), as.begin() + min((int)as.size(), deg)); } Poly add(Poly as, Poly bs) { int sz = max(as.size(), bs.size()); Poly cs(sz, T(0)); for (int i = 0; i < (int)as.size(); i++) cs[i] += as[i]; for (int i = 0; i < (int)bs.size(); i++) cs[i] += bs[i]; return cs; } Poly sub(Poly as, Poly bs) { int sz = max(as.size(), bs.size()); Poly cs(sz, T(0)); for (int i = 0; i < (int)as.size(); i++) cs[i] += as[i]; for (int i = 0; i < (int)bs.size(); i++) cs[i] -= bs[i]; return cs; } Poly mul(Poly as, Poly bs) { return conv(as, bs); } Poly mul(Poly as, T k) { Poly res(all(as)); for (auto& a : res) a *= k; return res; } // F(0) must not be 0 Poly inv(Poly as, int deg) { assert(as[0] != T(0)); Poly rs({ T(1) / as[0] }); for (int i = 1; i < deg; i <<= 1) rs = pre(sub(add(rs, rs), mul(mul(rs, rs), pre(as, i << 1))), i << 1); return rs; } // not zero Poly div(Poly as, Poly bs) { while (as.back() == T(0)) as.pop_back(); while (bs.back() == T(0)) bs.pop_back(); if (bs.size() > as.size()) return Poly(); reverse(as.begin(), as.end()); reverse(bs.begin(), bs.end()); int need = as.size() - bs.size() + 1; Poly ds = pre(mul(as, inv(bs, need)), need); reverse(ds.begin(), ds.end()); return ds; } // F(0) must be 1 Poly sqrt(Poly as, int deg) { assert(as[0] == T(1)); T inv2 = T(1) / T(2); Poly ss({ T(1) }); for (int i = 1; i < deg; i <<= 1) { ss = pre(add(ss, mul(pre(as, i << 1), inv(ss, i << 1))), i << 1); for (T& x : ss) x *= inv2; } return ss; } Poly diff(Poly as) { int n = as.size(); Poly res(n - 1); for (int i = 1; i < n; i++) res[i - 1] = as[i] * T(i); return res; } Poly integral(Poly as) { int n = as.size(); Poly res(n + 1); res[0] = T(0); for (int i = 0; i < n; i++) res[i + 1] = as[i] / T(i + 1); return res; } // F(0) must be 1 Poly log(Poly as, int deg) { return pre(integral(mul(diff(as), inv(as, deg))), deg); } // F(0) must be 0 Poly exp(Poly as, int deg) { Poly f({ T(1) }); as[0] += T(1); for (int i = 1; i < deg; i <<= 1) f = pre(mul(f, sub(pre(as, i << 1), log(f, i << 1))), i << 1); return f; } Poly partition(int n) { Poly rs(n + 1); rs[0] = T(1); for (int k = 1; k <= n; k++) { if (1LL * k * (3 * k + 1) / 2 <= n) rs[k * (3 * k + 1) / 2] += T(k % 2 ? -1LL : 1LL); if (1LL * k * (3 * k - 1) / 2 <= n) rs[k * (3 * k - 1) / 2] += T(k % 2 ? -1LL : 1LL); } return inv(rs, n + 1); } int getrandmax() { static uint32_t y = time(NULL); y ^= (y << 13); y ^= (y >> 17); y ^= (y << 5); return abs((int)y); } template<typename T2> int jacobi(T2 a, T2 mod) { int s = 1; if (a < 0) a = a % mod + mod; while (mod > 1) { a %= mod; if (a == 0) return 0; int r = __builtin_ctz(a); if ((r & 1) && ((mod + 2) & 4)) s = -s; a >>= r; if (a & mod & 2) s = -s; swap(a, mod); } return s; } template<typename T2> vector<T2> mod_sqrt(T2 a, T2 mod) { if (mod == 2) return { a & 1 }; int j = jacobi(a, mod); if (j == 0) return { 0 }; if (j == -1) return {}; ll b, d; while (1) { b = getrandmax() % mod; d = (b * b - a) % mod; if (d < 0) d += mod; if (jacobi<ll>(d, mod) == -1) break; } ll f0 = b, f1 = 1, g0 = 1, g1 = 0; for (ll e = (mod + 1) >> 1; e; e >>= 1) { if (e & 1) { ll tmp = (g0 * f0 + d * ((g1 * f1) % mod)) % mod; g1 = (g0 * f1 + g1 * f0) % mod; g0 = tmp; } ll tmp = (f0 * f0 + d * ((f1 * f1) % mod)) % mod; f1 = (2 * f0 * f1) % mod; f0 = tmp; } if (g0 > mod - g0) g0 = mod - g0; return { T2(g0),T2(mod - g0) }; } Poly super_sqrt(Poly from, int deg) { deque<int> as(deg); for (int i = 0; i < deg; i++) as[i] = from[i].get(); while (!as.empty() && as.front() == 0) as.pop_front(); if (as.empty()) { Poly res(deg, 0); return res; } int m = as.size(); if ((deg - m) & 1) { return Poly(); } auto ss = mod_sqrt(as[0], 998244353); if (ss.empty()) return Poly(); vector<T> ps(deg, T(0)); for (int i = 0; i < m; i++) ps[i] = T(as[i]) / T(as[0]); auto bs = sqrt(ps, deg); bs.insert(bs.begin(), (deg - m) / 2, T(0)); Poly res(deg); for (int i = 0; i < deg; i++) { res[i] = bs[i] * ss[0]; } return res; } }; #define FOR(i,n) for(int i = 0; i < (n); i++) #define sz(c) ((int)(c).size()) #define ten(x) ((int)1e##x) template<class T> T extgcd(T a, T b, T& x, T& y) { for (T u = y = 1, v = x = 0; a;) { T q = b / a; swap(x -= q * u, u); swap(y -= q * v, v); swap(b -= q * a, a); } return b; } template<class T> T mod_inv(T a, T m) { T x, y; extgcd(a, m, x, y); return (m + x % m) % m; } ll mod_pow(ll a, ll n, ll mod) { ll ret = 1; ll p = a % mod; while (n) { if (n & 1) ret = ret * p % mod; p = p * p % mod; n >>= 1; } return ret; } struct MathsNTTModAny { template<int mod, int primitive_root> class NTT { public: int get_mod() const { return mod; } void _ntt(vector<ll>& a, int sign) { const int n = sz(a); assert((n ^ (n & -n)) == 0); //n = 2^k const int g = 3; //g is primitive root of mod int h = (int)mod_pow(g, (mod - 1) / n, mod); // h^n = 1 if (sign == -1) h = (int)mod_inv(h, mod); //h = h^-1 % mod //bit reverse 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) { const int m2 = 2 * m; const ll base = mod_pow(h, n / m2, mod); ll w = 1; FOR(x, m) { for (int s = x; s < n; s += m2) { ll u = a[s]; ll d = a[s + m] * w % mod; a[s] = u + d; if (a[s] >= mod) a[s] -= mod; a[s + m] = u - d; if (a[s + m] < 0) a[s + m] += mod; } w = w * base % mod; } } for (auto& x : a) if (x < 0) x += mod; } void ntt(vector<ll>& input) { _ntt(input, 1); } void intt(vector<ll>& input) { _ntt(input, -1); const int n_inv = mod_inv(sz(input), mod); for (auto& x : input) x = x * n_inv % mod; } vector<ll> convolution(const vector<ll>& a, const vector<ll>& b) { int ntt_size = 1; while (ntt_size < sz(a) + sz(b)) ntt_size *= 2; vector<ll> _a = a, _b = b; _a.resize(ntt_size); _b.resize(ntt_size); ntt(_a); ntt(_b); FOR(i, ntt_size) { (_a[i] *= _b[i]) %= mod; } intt(_a); return _a; } }; ll garner(vector<pair<int, int>> mr, int mod) { mr.emplace_back(mod, 0); vector<ll> coffs(sz(mr), 1); vector<ll> constants(sz(mr), 0); FOR(i, sz(mr) - 1) { // coffs[i] * v + constants[i] == mr[i].second (mod mr[i].first) ll v = (mr[i].second - constants[i]) * mod_inv<ll>(coffs[i], mr[i].first) % mr[i].first; if (v < 0) v += mr[i].first; for (int j = i + 1; j < sz(mr); j++) { (constants[j] += coffs[j] * v) %= mr[j].first; (coffs[j] *= mr[i].first) %= mr[j].first; } } return constants[sz(mr) - 1]; } typedef NTT<167772161, 3> NTT_1; typedef NTT<469762049, 3> NTT_2; typedef NTT<1224736769, 3> NTT_3; vector<ll> solve(vector<ll> a, vector<ll> b, int mod = 1000000007) { for (auto& x : a) x %= mod; for (auto& x : b) x %= mod; NTT_1 ntt1; NTT_2 ntt2; NTT_3 ntt3; assert(ntt1.get_mod() < ntt2.get_mod() && ntt2.get_mod() < ntt3.get_mod()); auto x = ntt1.convolution(a, b); auto y = ntt2.convolution(a, b); auto z = ntt3.convolution(a, b); const ll m1 = ntt1.get_mod(), m2 = ntt2.get_mod(), m3 = ntt3.get_mod(); const ll m1_inv_m2 = mod_inv<ll>(m1, m2); const ll m12_inv_m3 = mod_inv<ll>(m1 * m2, m3); const ll m12_mod = m1 * m2 % mod; vector<ll> ret(sz(x)); FOR(i, sz(x)) { ll v1 = (y[i] - x[i]) * m1_inv_m2 % m2; if (v1 < 0) v1 += m2; ll v2 = (z[i] - (x[i] + m1 * v1) % m3) * m12_inv_m3 % m3; if (v2 < 0) v2 += m3; ll constants3 = (x[i] + m1 * v1 + m12_mod * v2) % mod; if (constants3 < 0) constants3 += mod; ret[i] = constants3; } return ret; } vector<int> solve(vector<int> a, vector<int> b, int mod = 1000000007) { vector<ll> x(all(a)); vector<ll> y(all(b)); auto z = solve(x, y, mod); vector<int> res; fore(aa, z) res.push_back(aa % mod); return res; } vector<mint> solve(vector<mint> a, vector<mint> b, int mod = 998244353) { int n = a.size(); vector<ll> x(n); rep(i, 0, n) x[i] = a[i].get(); n = b.size(); vector<ll> y(n); rep(i, 0, n) y[i] = b[i].get(); auto z = solve(x, y, mod); vector<mint> res; fore(aa, z) res.push_back(aa); return res; } }; /*---------------------------------------------------------------------------------------------------             ∧_∧       ∧_∧  (´<_` )  Welcome to My Coding Space!      ( ´_ゝ`) /  ⌒i @hamayanhamayan     /   \    | |     /   / ̄ ̄ ̄ ̄/  |   __(__ニつ/  _/ .| .|____      \/____/ (u ⊃ ---------------------------------------------------------------------------------------------------*/ int N; //--------------------------------------------------------------------------------------------------- void _main() { using T = mint; MathsNTTModAny ntt; FormalPowerSeries<T> FPS([&](auto a, auto b) { return ntt.solve(a, b, 998244353); }); cin >> N; auto ans = FPS.partition(N); rep(i, 0, N + 1) { if(i) printf(" "); printf("%d", ans[i].get()); } printf("\n"); } /* ///////////////////////// writeup1 start ///////////////////////// writeup2 start ///////////////////////// writeup2 end */