結果
| 問題 | No.2876 Infection |
| ユーザー |
 siganai
|
| 提出日時 | 2024-09-06 23:09:23 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 124 ms / 2,000 ms |
| コード長 | 14,531 bytes |
| コンパイル時間 | 2,472 ms |
| コンパイル使用メモリ | 208,416 KB |
| 最終ジャッジ日時 | 2025-02-24 04:54:55 |
|
ジャッジサーバーID （参考情報） |
judge3 / judge4 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 27 |
ソースコード
#line 1 "main.cpp"#include<bits/stdc++.h>using namespace std;// #pragma GCC target("avx,avx2")// #pragma GCC optimize("O3")// #pragma GCC optimize("unroll-loops")#ifdef LOCAL#include <debug.hpp>#define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)#else#define debug(...) (static_cast<void>(0))#endifusing namespace std;using ll = long long;using ull = unsigned long long;using ld = long double;using pll = pair<ll,ll>;using pii = pair<int,int>;using vi = vector<int>;using vvi = vector<vi>;using vvvi = vector<vvi>;using vl = vector<ll>;using vvl = vector<vl>;using vvvl = vector<vvl>;using vul = vector<ull>;using vpii = vector<pii>;using vvpii = vector<vpii>;using vpll = vector<pll>;using vs = vector<string>;template<class T> using pq = priority_queue<T,vector<T>, greater<T>>;#define overload4(_1, _2, _3, _4, name, ...) name#define overload3(a,b,c,name,...) name#define rep1(n) for (ll UNUSED_NUMBER = 0; UNUSED_NUMBER < (n); ++UNUSED_NUMBER)#define rep2(i, n) for (ll i = 0; i < (n); ++i)#define rep3(i, a, b) for (ll i = (a); i < (b); ++i)#define rep4(i, a, b, c) for (ll i = (a); i < (b); i += (c))#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)#define rrep1(n) for(ll i = (n) - 1;i >= 0;i--)#define rrep2(i,n) for(ll i = (n) - 1;i >= 0;i--)#define rrep3(i,a,b) for(ll i = (b) - 1;i >= (a);i--)#define rrep4(i,a,b,c) for(ll i = (a) + ((b)-(a)-1) / (c) * (c);i >= (a);i -= c)#define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__)#define all1(i) begin(i) , end(i)#define all2(i,a) begin(i) , begin(i) + a#define all3(i,a,b) begin(i) + a , begin(i) + b#define all(...) overload3(__VA_ARGS__, all3, all2, all1)(__VA_ARGS__)#define sum(...) accumulate(all(__VA_ARGS__),0LL)template<class T> bool chmin(T &a, const T &b){ if(a > b){ a = b; return 1; } else return 0; }template<class T> bool chmax(T &a, const T &b){ if(a < b){ a = b; return 1; } else return 0; }template<class T> auto min(const T& a){return *min_element(all(a));}template<class T> auto max(const T& a){return *max_element(all(a));}template<class... Ts> void in(Ts&... t);#define INT(...) int __VA_ARGS__; in(__VA_ARGS__)#define LL(...) ll __VA_ARGS__; in(__VA_ARGS__)#define STR(...) string __VA_ARGS__; in(__VA_ARGS__)#define CHR(...) char __VA_ARGS__; in(__VA_ARGS__)#define DBL(...) double __VA_ARGS__; in(__VA_ARGS__)#define LD(...) ld __VA_ARGS__; in(__VA_ARGS__)#define VEC(type, name, size) vector<type> name(size); in(name)#define VV(type, name, h, w) vector<vector<type>> name(h, vector<type>(w)); in(name)ll intpow(ll a, ll b){ll ans = 1; while(b){if(b & 1) ans *= a; a *= a; b /= 2;} return ans;}ll modpow(ll a, ll b, ll p){ ll ans = 1; a %= p;if(a < 0) a += p;while(b){ if(b & 1) (ans *= a) %= p; (a *= a) %= p; b /= 2; } return ans; }bool is_clamp(ll val,ll low,ll high) {return low <= val && val < high;}void Yes() {cout << "Yes\n";return;}void No() {cout << "No\n";return;}void YES() {cout << "YES\n";return;}void NO() {cout << "NO\n";return;}template <typename T>T floor(T a, T b) {return a / b - (a % b && (a ^ b) < 0);}template <typename T>T ceil(T x, T y) {return floor(x + y - 1, y);}template <typename T>T bmod(T x, T y) {return x - y * floor(x, y);}template <typename T>pair<T, T> divmod(T x, T y) {T q = floor(x, y);return {q, x - q * y};}namespace IO{#define VOID(a) decltype(void(a))struct setting{ setting(){cin.tie(nullptr); ios::sync_with_stdio(false);fixed(cout); cout.precision(15);}} setting;template<int I> struct P : P<I-1>{};template<> struct P<0>{};template<class T> void i(T& t){ i(t, P<3>{}); }void i(vector<bool>::reference t, P<3>){ int a; i(a); t = a; }template<class T> auto i(T& t, P<2>) -> VOID(cin >> t){ cin >> t; }template<class T> auto i(T& t, P<1>) -> VOID(begin(t)){ for(auto&& x : t) i(x); }template<class T, size_t... idx> void ituple(T& t, index_sequence<idx...>){in(get<idx>(t)...);}template<class T> auto i(T& t, P<0>) -> VOID(tuple_size<T>{}){ituple(t, make_index_sequence<tuple_size<T>::value>{});}#undef VOID}#define unpack(a) (void)initializer_list<int>{(a, 0)...}template<class... Ts> void in(Ts&... t){ unpack(IO :: i(t)); }#undef unpackconstexpr long double PI = 3.141592653589793238462643383279L;template <class F> struct REC {F f;REC(F &&f_) : f(forward<F>(f_)) {}template <class... Args> auto operator()(Args &&...args) const { return f(*this, forward<Args>(args)...); }};constexpr int mod = 998244353;//constexpr int mod = 1000000007;#line 2 "library/modint/Modint.hpp"template <int mod>struct Modint{int x;Modint():x(0) {}Modint(long long y): x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}Modint &operator += (const Modint &p) {if((x += p.x) >= mod) x -= mod;return *this;}Modint &operator -= (const Modint &p) {if ((x += mod - p.x) >= mod) x -= mod;return *this;}Modint &operator *= (const Modint &p) {x = (int)(1LL * x * p.x % mod);return *this;}Modint &operator /= (const Modint &p) {*this *= p.inverse();return *this;}Modint operator -() const{return Modint(-x);}Modint operator +(const Modint &p) const {return Modint(*this) += p;}Modint operator -(const Modint &p) const {return Modint(*this) -= p;}Modint operator *(const Modint &p) const {return Modint(*this) *= p;}Modint operator /(const Modint &p) const {return Modint(*this) /= p;}Modint &operator ++() {if(x == mod - 1) x = 0; else x++; return *this;}Modint &operator --() {if(x == 0) x = mod - 1; else x--; return *this;}bool operator == (const Modint &p) const {return x == p.x;}bool operator != (const Modint &p) const {return x != p.x;}Modint inverse() const {int a = x, b = mod, u = 1, v = 0, t;while (b > 0) {t = a / b;swap(a -= t * b, b);swap(u -= t * v, v);}return Modint(u);}Modint pow(long long n) const {Modint ret(1), mul(x);while (n > 0) {if (n & 1) ret *= mul;mul *= mul;n >>= 1;}return ret;}friend ostream &operator<<(ostream &os, const Modint &p) { return os << p.x; }friend istream &operator>>(istream &is, Modint &a) {long long t;is >> t;a = Modint<mod>(t);return (is);}int get() const { return x; }static constexpr int get_mod() {return mod;}};#line 100 "main.cpp"using mint = Modint<mod>;using vm = vector<mint>;using vvm = vector<vm>;using vvvm = vector<vvm>;#line 2 "library/ntt/ntt.hpp"template<typename mint>struct NTT{static constexpr uint32_t get_pr() {uint32_t _mod = mint::get_mod();using u64 = uint64_t;u64 ds[32] = {};int idx = 0;u64 m = _mod - 1;for(u64 i = 2;i * i <= m; ++i) {if(m % i == 0) {ds[idx++] = i;while(m % i == 0) m /= i;}}if (m != 1) ds[idx++] = m;uint32_t _pr = 2;while(1) {int flg = 1;for(int i = 0;i < idx; ++i) {u64 a = _pr, b = (_mod - 1) / ds[i],r = 1;while(b) {if(b & 1) r = r * a % _mod;a = a * a % _mod;b >>= 1;}if(r == 1) {flg = 0;break;}}if (flg == 1) break;++_pr;}return _pr;};static constexpr uint32_t mod = mint::get_mod();static constexpr uint32_t pr = get_pr();static constexpr int level = __builtin_ctzll(mod - 1);mint dw[level], dy[level];void setwy(int k) {mint w[level],y[level];w[k - 1] = mint(pr).pow((mod - 1) / (1 << k));y[k - 1] = w[k - 1].inverse();for(int i = k - 2;i > 0; --i) w[i] = w[i+1] * w[i+1],y[i] = y[i+1] * y[i+1];dw[1] = w[1], dy[1] = y[1], dw[2] = w[2], dy[2] = y[2];for(int i = 3;i < k;++i) {dw[i] = dw[i-1] * y[i-2] * w[i];dy[i] = dy[i-1] * w[i-2] * y[i];}}NTT() {setwy(level);}void fft4(vector<mint> &a,int k) {if((int)a.size() <= 1) return;if(k == 1) {mint a1 = a[1];a[1] = a[0] - a[1];a[0] = a[0] + a1;return;}if (k & 1) {int v = 1 << (k - 1);for(int j = 0;j < v; ++j) {mint ajv = a[j + v];a[j + v] = a[j] - ajv;a[j] += ajv;}}int u = 1 << (2 + (k & 1));int v = 1 << (k - 2 - (k & 1));mint one = mint(1);mint imag = dw[1];while(v) {{int j0 = 0,j1 = v;int j2 = j1 + v;int j3 = j2 + v;for(;j0 < v; ++j0,++j1,++j2,++j3) {mint t0 = a[j0], t1 = a[j1],t2 = a[j2],t3 = a[j3];mint t0p2 = t0 + t2,t1p3 = t1 + t3;mint t0m2 = t0 - t2,t1m3 = (t1 - t3) * imag;a[j0] = t0p2 + t1p3, a[j1] = t0p2 - t1p3;a[j2] = t0m2 + t1m3, a[j3] = t0m2 - t1m3;}}mint ww = one,xx = one * dw[2],wx = one;for(int jh = 4;jh < u;) {ww = xx * xx,wx = ww * xx;int j0 = jh * v;int je = j0 + v;int j2 = je + v;for(;j0 < je;++j0,++j2) {mint t0 = a[j0], t1 = a[j0 + v] * xx, t2 = a[j2] * ww,t3 = a[j2 + v] * wx;mint t0p2 = t0 + t2,t1p3 = t1 + t3;mint t0m2 = t0 - t2,t1m3 = (t1 - t3) * imag;a[j0] = t0p2 + t1p3, a[j0 + v] = t0p2 - t1p3;a[j2] = t0m2 + t1m3, a[j2 + v] = t0m2 - t1m3;}xx *= dw[__builtin_ctzll((jh += 4))];}u <<= 2;v >>= 2;}}void ifft4(vector<mint> &a,int k) {if((int)a.size() <= 1) return;if(k == 1) {mint a1 = a[1];a[1] = a[0] - a[1];a[0] = a[0] + a1;return;}int u = 1 << (k - 2);int v = 1;mint one = mint(1);mint imag = dy[1];while(u) {{int j0 = 0,j1 = v;int j2 = j1 + v;int j3 = j2 + v;for(;j0 < v;++j0,++j1,++j2,++j3) {mint t0 = a[j0],t1 = a[j1],t2 = a[j2],t3 = a[j3];mint t0p1 = t0 + t1, t2p3 = t2 + t3;mint t0m1 = t0 - t1, t2m3 = (t2 - t3) * imag;a[j0] = t0p1 + t2p3, a[j2] = t0p1 - t2p3;a[j1] = t0m1 + t2m3, a[j3] = t0m1 - t2m3;}}mint ww = one,xx = one * dy[2],yy = one;u <<= 2;for(int jh = 4;jh < u;) {ww = xx * xx,yy = xx * imag;int j0 = jh * v;int je = j0 + v;int j2 = je + v;for(;j0 < je;++j0,++j2) {mint t0 = a[j0], t1 = a[j0 + v], t2 = a[j2], t3 = a[j2 + v];mint t0p1 = t0 + t1, t2p3 = t2 + t3;mint t0m1 = (t0 - t1) * xx, t2m3 = (t2 - t3) * yy;a[j0] = t0p1 + t2p3, a[j2] = (t0p1 - t2p3) * ww;a[j0 + v] = t0m1 + t2m3, a[j2 + v] = (t0m1 - t2m3) * ww;}xx *= dy[__builtin_ctzll(jh += 4)];}u >>= 4;v <<= 2;}if(k & 1) {u = 1 << (k - 1);for(int j = 0;j < u;++j) {mint ajv = a[j] - a[j+u];a[j] += a[j+u];a[j+u] = ajv;}}}void ntt(vector<mint> &a) {if((int)a.size() <= 1) return;fft4(a,__builtin_ctz(a.size()));}void intt(vector<mint> &a) {if((int)a.size() <= 1) return;ifft4(a,__builtin_ctz(a.size()));mint iv = mint(a.size()).inverse();for(auto &x:a) x *= iv;}vector<mint> multiply(const vector<mint> &a,const vector<mint> &b) {int l = a.size() + b.size() - 1;if(min<int>(a.size(),b.size()) <= 40) {vector<mint> s(l);for(int i = 0;i < (int)a.size();++i) for(int j = 0;j < (int)b.size();++j) s[i+j] += a[i] * b[j];return s;}int k = 2, M = 4;while(M < l) M <<= 1, ++k;//setwy(k);vector<mint> s(M), t(M);for(int i = 0;i < (int)a.size();++i) s[i] = a[i];for(int i = 0;i < (int)b.size();++i) t[i] = b[i];fft4(s,k);fft4(t,k);for(int i = 0;i < M;++i) s[i] *= t[i];ifft4(s,k);s.resize(l);mint invm = mint(M).inverse();for(int i = 0;i < l;++i) s[i] *= invm;return s;}void ntt_doubling(vector<mint> &a) {int M = (int)a.size();auto b = a;intt(b);mint r = 1, zeta = mint(pr).pow((mint::get_mod() - 1) / (M << 1));for(int i = 0;i < M;++i) b[i] *= r,r *= zeta;ntt(b);copy(begin(b),end(b),back_inserter(a));}};#line 105 "main.cpp"vector<mint> fact, fact_inv;void make_fact(int n){fact.resize(n+1), fact_inv.resize(n+1);fact[0] = mint(1); rep(i,1,n+1) fact[i] = fact[i-1] * mint(i);fact_inv[n] = fact[n].inverse(); rrep(i,0,n) fact_inv[i] = fact_inv[i+1] * mint(i+1);}mint ncr(int n, int r){ if(n < 0 || r < 0 || n < r) return mint(0); return fact[n] * fact_inv[r] * fact_inv[n-r];}mint npr(int n, int r){ if(n < 0 || r < 0 || n < r) return mint(0); return fact[n] * fact_inv[n-r]; }int main() {NTT<mint> ntt;INT(n,x);make_fact(2*n);mint p = mint(x) / 100;vm dp(n+1);vm P(n+1),Q(n+1);P[0] = 1;Q[0] = 1;rep(i,1,n+1) {P[i] = P[i-1] * p;Q[i] = Q[i-1] * (-p + 1);}dp[1] = 1;mint ans;rep(i,n-1) {vm v1(n+1),v2(n+1);rep(j,n+1) v1[j] = fact[n-j] * dp[j];rep(j,n+1) v2[j] = P[j] * fact_inv[j];vm v = ntt.multiply(v1,v2);ans += v[i+1] * Q[n-(i+1)] * fact_inv[n-(i+1)] * (i+1);vm ndp(n+1);rep(j,i+2,n+1) {ndp[j] = v[j] * Q[n-j] * fact_inv[n-j];}swap(dp,ndp);}ans += dp[n] * n;cout << ans << '\n';}