結果
問題 | No.2877 Gunegune Hyperion |
ユーザー |
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提出日時 | 2024-09-06 23:27:49 |
言語 | C++17(gcc12) (gcc 12.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 317 ms / 6,000 ms |
コード長 | 9,475 bytes |
コンパイル時間 | 4,282 ms |
コンパイル使用メモリ | 256,512 KB |
実行使用メモリ | 17,100 KB |
最終ジャッジ日時 | 2024-09-06 23:28:35 |
合計ジャッジ時間 | 8,608 ms |
ジャッジサーバーID (参考情報) |
judge1 / judge5 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 30 |
ソースコード
/** [x ^ {a - 1}]f(x) := 最初に真横になるのが a 日目である確率* [x ^ {a}]g(x) := 真横になった日から次に真横になるまで a 日間かかる確率* 以上の二つがもとまっているとき、* 「fg^{N - H} の (N - 1) 次までの係数の和」* は* 「高さが H 未満になる確率」* と同じになるので、1 からそれを引くと答えが求まる。* K = 3 として、* f, g (mod x ^{N}) は O(NK^2)* fg^{N - H} (mod x^{N}) は log-exp を用いて O(N log(N)) で求まる*/#line 1 "a.cpp"#include <bits/stdc++.h>using namespace std;using std::cout;using std::cin;using std::endl;using ll=long long;using ld=long double;const ll ILL=2167167167167167167;const int INF=2100000000;#define rep(i,a,b) for (int i=(int)(a);i<(int)(b);i++)#define all(p) p.begin(),p.end()template<class T> using _pq = priority_queue<T, vector<T>, greater<T>>;template<class T> ll LB(vector<T> &v,T a){return lower_bound(v.begin(),v.end(),a)-v.begin();}template<class T> ll UB(vector<T> &v,T a){return upper_bound(v.begin(),v.end(),a)-v.begin();}template<class T> bool chmin(T &a,T b){if(a>b){a=b;return 1;}else return 0;}template<class T> bool chmax(T &a,T b){if(a<b){a=b;return 1;}else return 0;}template<class T> void So(vector<T> &v) {sort(v.begin(),v.end());}template<class T> void Sore(vector<T> &v) {sort(v.begin(),v.end(),[](T x,T y){return x>y;});}bool yneos(bool a,bool upp=0){if(a){cout<<(upp?"YES\n":"Yes\n");}else{cout<<(upp?"NO\n":"No\n");}return a;}template<class T> void vec_out(vector<T> &p,int ty=0){if(ty==2){cout<<'{';for(int i=0;i<(int)p.size();i++){if(i){cout<<",";}cout<<'"'<<p[i]<<'"';}cout<<"}\n";}else{if(ty==1){cout<<p.size()<<"\n";}for(int i=0;i<(int)(p.size());i++){if(i) cout<<" ";cout<<p[i];}cout<<"\n";}}template<class T> T vec_min(vector<T> &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmin(ans,x);return ans;}template<class T> T vec_max(vector<T> &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmax(ans,x);return ans;}template<class T> T vec_sum(vector<T> &a){T ans=T(0);for(auto &x:a) ans+=x;return ans;}int pop_count(long long a){int res=0;while(a){res+=(a&1),a>>=1;}return res;}template<class T> bool inside(T l,T x,T r){return l<=x&&x<r;}#include <atcoder/modint>using mint = atcoder::modint998244353;#line 2 "/Users/Shared/po167_library/fps/FPS_pow.hpp"#line 4 "/Users/Shared/po167_library/fps/FPS_pow.hpp"#include <atcoder/convolution>#line 4 "/Users/Shared/po167_library/fps/FPS_cyclic_convolution.hpp"namespace po167{// |f| = |g| = 2 ^ ntemplate<class T>std::vector<T> FPS_cyclic_convolution(std::vector<T> f, std::vector<T> g){atcoder::internal::butterfly(f);atcoder::internal::butterfly(g);for (int i = 0; i < (int)f.size(); i++) f[i] *= g[i];atcoder::internal::butterfly_inv(f);T iz = (T)(1) / (T)(f.size());for (int i = 0; i < (int)f.size(); i++) f[i] *= iz;return f;}}#line 3 "/Users/Shared/po167_library/fps/FPS_differetial.hpp"namespace po167{// return f'template <class T>std::vector<T> FPS_differential(std::vector<T> f){if (f.empty()) return f;for (int i = 0; i < (int)f.size() - 1; i++){f[i] = f[i + 1] * (T)(i + 1);}f.pop_back();return f;}}#line 3 "/Users/Shared/po167_library/fps/FPS_integral.hpp"namespace po167{template <class T>std::vector<T> FPS_integral(std::vector<T> f){if (f.empty()) return f;std::vector<T> num_inv((int)f.size() + 1);num_inv[0] = 1;num_inv[1] = 1;auto m = T::mod();for (int i = 2; i <= (int)f.size(); i++){num_inv[i] = (0 - num_inv[m % i]) * (T)(m / i);}f.reserve((int)f.size() + 1);f.push_back(0);for (int i = (int)f.size() - 1; i > 0; i--){f[i] = f[i - 1] * num_inv[i];}f[0] = 0;return f;}}#line 4 "/Users/Shared/po167_library/fps/FPS_inv.hpp"namespace po167{// return 1 / ftemplate <class T>std::vector<T> FPS_inv(std::vector<T> f, int len = -1){if (len == -1) len = f.size();assert(f[0] != 0);std::vector<T> g = {1 / f[0]};int s = 1;while(s < len){// g = 2g_s - f(g_s)^2 (mod x ^ (2 * s))// g = g - (fg - 1)g// (fg - 1) = 0 (mod x ^ (s))std::vector<T> n_g(s * 2, 0);std::vector<T> f_s(s * 2, 0);g.resize(s * 2);for (int i = 0; i < s * 2; i++){if (int(f.size()) > i) f_s[i] = f[i];n_g[i] = g[i];}atcoder::internal::butterfly(g);atcoder::internal::butterfly(f_s);for (int i = 0; i < s * 2; i++){f_s[i] *= g[i];}atcoder::internal::butterfly_inv(f_s);T iz = 1 / (T)(s * 2);for (int i = s; i < s * 2; i++){f_s[i] *= iz;}for (int i = 0; i < s; i++){f_s[i] = 0;}atcoder::internal::butterfly(f_s);for (int i = 0; i < s * 2; i++){f_s[i] *= g[i];}atcoder::internal::butterfly_inv(f_s);for (int i = s; i < s * 2; i++){n_g[i] -= f_s[i] * iz;}std::swap(n_g, g);s *= 2;}g.resize(len);return g;}}#line 8 "/Users/Shared/po167_library/fps/FPS_exp.hpp"namespace po167{template<class T>std::vector<T> FPS_exp(std::vector<T> f, int len = -1){if (len == -1) len = f.size();if (len == 0) return {};if (len == 1) return {T(1)};assert(!f.empty() && f[0] == 0);int s = 1;// simplestd::vector<T> g = {T(1)};while (s < len){// g' / g// A * Bstd::vector<T> A = g, B = g;A = FPS_differential(A);B = FPS_inv(B, 2 * s);A.resize(2 * s);A = FPS_cyclic_convolution(A, B);A.pop_back();A = FPS_integral(A);for (int i = 0; i < s; i++) A[i] = 0;for (int i = s; i < s * 2; i++) A[i] = (i < (int)f.size() ? f[i] : 0) - A[i];// g_hat = g (1 - g + f)// g += B = g * Ag.resize(2 * s);B = FPS_cyclic_convolution(A, g);for (int i = s; i < s * 2; i++) g[i] = B[i];s *= 2;}g.resize(len);return g;}}#line 5 "/Users/Shared/po167_library/fps/FPS_log.hpp"namespace po167{template<class T>std::vector<T> FPS_log(std::vector<T> f, int len = -1){if (len == -1) len = f.size();if (len == 0) return {};if (len == 1) return {T(0)};assert(!f.empty() && f[0] == 1);std::vector<T> res = atcoder::convolution(FPS_differential(f), FPS_inv(f, len));res.resize(len - 1);return FPS_integral(res);}}#line 8 "/Users/Shared/po167_library/fps/FPS_pow.hpp"namespace po167{template<class T>std::vector<T> FPS_pow(std::vector<T> f,long long M, int len = -1){if (len == -1) len = f.size();std::vector<T> res(len, 0);if (M == 0){res[0] = 1;return res;}for (int i = 0; i < (int)f.size(); i++){if (f[i] == 0) continue;if (i > (len - 1) / M) break;std::vector<T> g((int)f.size() - i);T v = (T)(1) / (T)(f[i]);for (int j = i; j < (int)f.size(); j++){g[j - i] = f[j] * v;}long long zero = i * M;if (i) len -= i * M;g = FPS_log(g, len);for (T &x : g) x *= M;g = FPS_exp(g, len);v = (T)(1) / v;T c = 1;while (M){if (M & 1) c = c * v;v = v * v;M >>= 1;}for (int i = 0; i < len; i++) res[i + zero] = g[i] * c;return res;}return res;}}#line 32 "a.cpp"void solve();// CYAN / FREDERICint main() {ios::sync_with_stdio(false);cin.tie(nullptr);int t = 1;// cin >> t;rep(i, 0, t) solve();}void solve(){ll N, H;cin >> N >> H;vector base(2, vector<mint>(N));vector<mint> inv(6);rep(i, 1, 6) inv[i] = (mint)(1) / (mint)(i);vector to(3, vector<mint>(3));to[0][0] = inv[2];to[0][1] = inv[2];to[1][0] = inv[3];to[1][1] = inv[3];to[1][2] = inv[3];to[2][1] = inv[3] * 2;to[2][2] = inv[3];rep(i, 0, 2){vector<mint> dp(3);if (i == 0) dp[0] = 1;else dp[1] = 2, dp[2] = 1;rep(j, 0, N - 1){vector<mint> n_dp(3);rep(n, 0, 3) rep(m, 0, 3) n_dp[m] += dp[n] * to[n][m];swap(n_dp, dp);for (int k = 0; k < 3; k += 3){base[i][j + 1] += dp[k];dp[k] = 0;}}}vector<mint> f(N), g = base[0];rep(i, 0, 2){if (i == 0) f[0] += inv[5] * 2;else rep(j, 0, N) f[j] += base[i][j] * inv[5];}auto gp = po167::FPS_pow(g, N - H);f = atcoder::convolution(f, gp);f.resize(N);cout << (1 - vec_sum(f)).val() << "\n";}