結果

問題 No.1574 Swap and Repaint
ユーザー PCTprobabilityPCTprobability
提出日時 2021-04-13 23:49:42
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 2,402 ms / 10,000 ms
コード長 13,090 bytes
コンパイル時間 4,871 ms
コンパイル使用メモリ 305,976 KB
実行使用メモリ 105,112 KB
最終ジャッジ日時 2024-10-03 12:16:36
合計ジャッジ時間 33,471 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge2
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 3 ms
5,248 KB
testcase_01 AC 3 ms
5,248 KB
testcase_02 AC 3 ms
5,248 KB
testcase_03 AC 3 ms
5,248 KB
testcase_04 AC 3 ms
5,248 KB
testcase_05 AC 3 ms
5,248 KB
testcase_06 AC 2 ms
5,248 KB
testcase_07 AC 3 ms
5,248 KB
testcase_08 AC 3 ms
5,248 KB
testcase_09 AC 15 ms
5,632 KB
testcase_10 AC 9 ms
5,248 KB
testcase_11 AC 9 ms
5,248 KB
testcase_12 AC 13 ms
5,248 KB
testcase_13 AC 10 ms
5,248 KB
testcase_14 AC 11 ms
5,248 KB
testcase_15 AC 15 ms
5,504 KB
testcase_16 AC 5 ms
5,248 KB
testcase_17 AC 7 ms
5,248 KB
testcase_18 AC 545 ms
36,164 KB
testcase_19 AC 2,325 ms
100,164 KB
testcase_20 AC 672 ms
38,524 KB
testcase_21 AC 468 ms
33,032 KB
testcase_22 AC 417 ms
29,796 KB
testcase_23 AC 109 ms
12,800 KB
testcase_24 AC 1,865 ms
84,408 KB
testcase_25 AC 989 ms
55,692 KB
testcase_26 AC 43 ms
7,552 KB
testcase_27 AC 326 ms
24,508 KB
testcase_28 AC 2,379 ms
104,984 KB
testcase_29 AC 2,375 ms
104,988 KB
testcase_30 AC 2,380 ms
105,112 KB
testcase_31 AC 2,382 ms
104,984 KB
testcase_32 AC 2,368 ms
105,112 KB
testcase_33 AC 2,380 ms
105,112 KB
testcase_34 AC 2,394 ms
104,932 KB
testcase_35 AC 2,402 ms
104,984 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <bits/stdc++.h>
using namespace std;
#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
#endif
using ll = long long;
using ld = long double;
using ull = long long;
#define all(s) (s).begin(),(s).end()
#define rep2(i, m, n) for (int i = (m); i < (n); ++i)
#define rep(i, n) rep2(i, 0, n)
#define drep2(i, m, n) for (int i = (m)-1; i >= (n); --i)
#define drep(i, n) drep2(i, n, 0)
#define rever(vec) reverse(vec.begin(), vec.end())
#define sor(vec) sort(vec.begin(), vec.end())
#define fi first
#define se second
#define P pair<ll,ll>
#define REP(i, n) for (int i = 0; i < (n); ++i)
const ll mod = 998244353;
//const ll mod = 1000000007;
const ll inf = 2000000000000000000ll;
static const long double pi = 3.141592653589793;
template<class T>void vcin(vector<T> &n){for(int i=0;i<int(n.size());i++) cin>>n[i];}
template<class T>void vcout(vector<T> &n){for(int i=0;i<int(n.size());i++){cout<<n[i]<<" ";}cout<<endl;}
void YesNo(bool a){if(a){cout<<"Yes"<<endl;}else{cout<<"No"<<endl;}}
void YESNO(bool a){if(a){cout<<"YES"<<endl;}else{cout<<"NO"<<endl;}}
template<class T,class U> void chmax(T& t,const U& u){if(t<u) t=u;}
template<class T,class U> void chmin(T& t,const U& u){if(t>u) t=u;}
template<class T> void ifmin(T t,T u){if(t>u){cout<<-1<<endl;}else{cout<<t<<endl;}}
template<class T> void ifmax(T t,T u){if(t>u){cout<<-1<<endl;}else{cout<<t<<endl;}}
template<typename T,typename ...Args>auto make_vector(T x,int arg,Args ...args){if constexpr(sizeof...(args)==0)return vector<T>(arg,x);else return vector(arg,make_vector<T>(x,args...));}
ll modPow(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; }

void gbjsmzmfuuvdf(){
  ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
  cout<< fixed << setprecision(20);
}
using mint = modint998244353;
struct S{
    mint value;
    int size;
};
using F = mint;
S op(S a, S b){ return {a.value+b.value, a.size+b.size}; }
S e(){ return {mint(0),1}; }
S mapping(F f, S x){ return {x.value+x.size*f, x.size}; }
F composition(F f, F g){ return f+g; }
F id(){ return mint(0); }
mint k[200100];
void com(){
  k[0]=1;
  for(int i=1;i<200100;i++){
    k[i]=k[i-1]*i;
  }
}
enum Mode {
	FAST = 1,
	NAIVE = -1,
};
template <class T, Mode mode = FAST>
struct FormalPowerSeries : std::vector<T> {
	using std::vector<T>::vector;
	using std::vector<T>::size;
	using std::vector<T>::resize;
	using F = FormalPowerSeries;
  F &operator+=(const F &g){
    for(int i=0;i<int(min((*this).size(),g.size()));i++){
      (*this)[i]+=g[i];
    }
    return *this;
  }
  F &operator+=(const T &t){
    assert(int((*this).size()));
    (*this)[0]+=t;
    return *this;
  }
  F &operator-=(const F &g) {
    for(int i=0;i<int(min((*this).size(),g.size()));i++){
      (*this)[i]-=g[i];
    }
    return *this;
  }
  F &operator-=(const T &t){
    assert(int((*this).size()));
    (*this)[0]-=t;
    return *this;
  }
  F &operator*=(const T &g) {
    for(int i=0;i<int((*this).size());i++){
      (*this)[i]*=g;
    }
    return *this;
  }
  F &operator/=(const T &g) {
    T div=g.inv();
    for(int i=0;i<int((*this).size());i++){
      (*this)[i]*=div;
    }
    return *this;
  }
  F &operator<<=(const int d) {
    int n=(*this).size();
    (*this).insert((*this).begin(),d,0);
    (*this).resize(n);
    return *this;
  }
  F &operator>>=(const int d) {
    int n=(*this).size();
    (*this).erase((*this).begin(),(*this).begin()+min(n, d));
    (*this).resize(n);
    return *this;
  }
  F &operator=(const std::vector<T> &v) {
    int n = (*this).size();
    for(int i = 0; i < n; ++i) (*this)[i] = v[i];
    return *this;
  }
  F operator-() const {
    F ret = *this;
    return ret * -1;
  }
  F &operator*=(const F &g) {
    if(mode==FAST) {
      int n=(*this).size();
      auto tmp=atcoder::convolution(*this,g);
      for(int i=0;i<n;++i){
        (*this)[i]=tmp[i];
      }
      return *this;
    }
    else{
      int n = (*this).size(), m = g.size();
      for(int i = n - 1; i >= 0; --i) {
        (*this)[i] *= g[0];
        for(int j = 1; j < std::min(i + 1, m); j++)
          (*this)[i] += (*this)[i - j] * g[j];
      }
      return *this;
    }
  }
  F &operator/=(const F &g) {
  if(mode == FAST){
  int n = (*this).size();
  (*this) = atcoder::convolution(*this, g.inv());
  return *this;
  }
  else{
  assert(g[0] != T(0));
  T ig0 = g[0].inv();
  int n = (*this).size(), m = g.size();
  for(int i = 0; i < n; ++i) {
  for(int j = 1; j < std::min(i + 1, m); ++j)
  (*this)[i] -= (*this)[i - j] * g[j];
  (*this)[i] *= ig0;
  }
  return *this;
  }
  }
  
  F &operator%=(const F &g) { return *this-=*this/g*g; }
  F operator*(const T &g) const { return F(*this)*=g;}
  F operator-(const T &g) const { return F(*this)-=g;}
  F operator*(const F &g) const { return F(*this)*=g;}
  F operator-(const F &g) const { return F(*this)-=g;}
  F operator+(const F &g) const { return F(*this)+=g;}
  F operator/(const F &g) const { return F(*this)/=g;}
  F operator%(const F &g) const { return F(*this)%=g;}
  F operator<<(const int d) const { return F(*this)<<=d;}
  F operator>>(const int d) const { return F(*this)>>=d;}  
  void onemul(const int d,const T c){
    int n=(*this).size();
    for(int i=n-d-1;i>=0;i--){
      (*this)[i+d]+=(*this)[i]*c;
    }
  }
  void onediv(const int d,const T c){
    int n=(*this).size();
    for(int i=0;i<n-d;i++){
      (*this)[i+d]-=(*this)[i]*c;
    }
  }
  T eval(const T &t) const {
  int n = (*this).size();
  T res = 0, tmp = 1;
  for(int i = 0; i < n; ++i){
  res += (*this)[i] * tmp, tmp *= t;
  }
  return res;
  }
  F inv(int deg = -1) const {
  int n = (*this).size();
  assert(mode == FAST and n and (*this)[0] != 0);
  if(deg == -1) deg = n;
  assert(deg > 0);
  F res{(*this)[0].inv()};
  while(int(res.size()) < deg) {
  int m = res.size();
  F f((*this).begin(), (*this).begin() + std::min(n, m * 2)), r(res);
  f.resize(m * 2), atcoder::internal::butterfly(f);
  r.resize(m * 2), atcoder::internal::butterfly(r);
  for(int i = 0; i < m * 2; ++i) f[i] *= r[i];
  atcoder::internal::butterfly_inv(f);
  f.erase(f.begin(), f.begin() + m);
  f.resize(m * 2), atcoder::internal::butterfly(f);
  for(int i = 0; i < m * 2; ++i) f[i] *= r[i];
  atcoder::internal::butterfly_inv(f);
  T iz = T(m * 2).inv();
  iz *= -iz;
  for(int i = 0; i < m; ++i) f[i] *= iz;
  res.insert(res.end(), f.begin(), f.begin() + m);
  }
  res.resize(deg);
  return res;
  }
  F &diff_inplace() {
  int n = (*this).size();
  for(int i = 1; i < n; ++i) (*this)[i - 1] = (*this)[i] * i;
  (*this)[n - 1] = 0;
  return *this;
  }
  F diff() const { F(*this).diff_inplace();}
  F &integral_inplace() {
  int n = (*this).size(), mod = T::mod();
  std::vector<T> inv(n);
  {
  inv[1] = 1;
  for(int i = 2; i < n; ++i)
  inv[i] = T(mod) - inv[mod % i] * (mod / i);
  }
  for(int i = n - 2; i >= 0; --i) (*this)[i + 1] = (*this)[i] * inv[i + 1];
  (*this)[0] = 0;
  return *this;
  }
  F integral() const { return F(*this).integral_inplace(); }
  F &log_inplace() {
  int n = (*this).size();
  assert(n and (*this)[0] == 1);
  F f_inv = (*this).inv();
  (*this).diff_inplace();
  (*this) *= f_inv;
  (*this).integral_inplace();
  return *this;
  }
  F log() const { return F(*this).log_inplace(); }
  F &deriv_inplace() {
  int n = (*this).size();
  assert(n);
  for(int i = 2; i < n; ++i) (*this)[i] *= i;
 (*this).erase((*this).begin());
 (*this).push_back(0);
 return *this;
 }
 F deriv() const { return F(*this).deriv_inplace(); }
 F &exp_inplace() {
 int n = (*this).size();
 assert(n and (*this)[0] == 0);
 F g{1};
 (*this)[0] = 1;
 F h_drv((*this).deriv());
 for(int m = 1; m < n; m *= 2) {	
 F f((*this).begin(), (*this).begin() + m);
 f.resize(2 * m), atcoder::internal::butterfly(f);
 auto mult_f = [&](F &p) {
 p.resize(2 * m);
 atcoder::internal::butterfly(p);
 for(int i = 0; i < 2 * m; ++i) p[i] *= f[i];
 atcoder::internal::butterfly_inv(p);
 p /= 2 * m;
 };
 if(m > 1) {
 F g_(g);
 g_.resize(2 * m), atcoder::internal::butterfly(g_);
 for(int i = 0; i < 2 * m; ++i) g_[i] *= g_[i] * f[i];
 atcoder::internal::butterfly_inv(g_);
 T iz = T(-2 * m).inv();
 g_ *= iz;
 g.insert(g.end(), g_.begin() + m / 2, g_.begin() + m);
 }
 F t((*this).begin(), (*this).begin() + m);
 t.deriv_inplace();
 {
 F r{h_drv.begin(), h_drv.begin() + m - 1};
 mult_f(r);
 for(int i = 0; i < m; ++i) t[i] -= r[i] + r[m + i];
 }
 t.insert(t.begin(), t.back());
 t.pop_back();
 t *= g;
 F v((*this).begin() + m, (*this).begin() + std::min(n, 2 * m));
 v.resize(m);
 t.insert(t.begin(), m - 1, 0);
 t.push_back(0);
 t.integral_inplace();
 for(int i = 0; i < m; ++i) v[i] -= t[m + i];
 mult_f(v);
 for(int i = 0; i < std::min(n - m, m); ++i)
 (*this)[m + i] = v[i];
 }
 return *this;
 }
 F exp() const { return F(*this).exp_inplace(); }
 F &pow_inplace(long long k) {
 int n = (*this).size(), l = 0;
 assert(k >= 0);
 if(!k){
 for(int i = 0; i < n; ++i) (*this)[i] = !i;
 return *this;
 }
 while(l < n and (*this)[l] == 0) ++l;
 if(l > (n - 1) / k or l == n) return *this = F(n);
 T c = (*this)[l];
 (*this).erase((*this).begin(), (*this).begin() + l);
 (*this) /= c;
 (*this).log_inplace();
 (*this).resize(n - l * k);
 (*this) *= k;
 (*this).exp_inplace();
 (*this) *= c.pow(k);
 (*this).insert((*this).begin(), l * k, 0);
 return *this;
 }
 F pow(const long long k) const { return F(*this).pow_inplace(); }
 void spacemul(vector<pair<int, T>> g) {
    int n = (*this).size();
    auto [d, c] = g.front();
    if (d == 0) g.erase(g.begin());
    else c = 0;
    for(int i=n-1;i>=0;i--){
      (*this)[i] *= c;
      for (auto &[j, b] : g) {
        if (j > i) break;
        (*this)[i] += (*this)[i-j] * b;
      }
    }
  }
  void spacediv(vector<pair<int, T>> g) {
    int n = (*this).size();
    auto [d, c] = g.front();
    assert(d == 0 && c != T(0));
    T ic = c.inv();
    g.erase(g.begin());
    for(int i=0;i<n;i++){
      for (auto &[j, b] : g) {
        if (j > i) break;
        (*this)[i] -= (*this)[i-j] * b;
      }
      (*this)[i] *= ic;
    }
  }
};
using fps = FormalPowerSeries<atcoder::modint998244353, FAST>;
mint g(ll a,ll b){
  if(a==1){
    return mint(1);
  }
  if(b==1){
    return mint(1)/mint(2);
  }
  if(a==b){
    return mint(1)/mint(mint(2).pow(a-1)*k[a-1]);
  }
  return mint(1)/mint(mint(2).pow(b))*(mint(2)/mint(k[b-1])-mint(1)/mint(k[b]));
}
int main()  {
  gbjsmzmfuuvdf();
  com();
  ll n;
  cin>>n;
  mint h=mint(4).pow(n-1);
  for(int i=1;i<=n-1;i++){
    h*=i;
  }
  vector<mint> a(n),b(n);
  lazy_segtree<S, op, e, F, mapping, composition, id> seg(n);
  for(int i=0;i<n;i++){
    seg.apply(i,g(n-i,1));
  }
  for(int i=2;i<n;i++){
    seg.apply(i-1,n-1,g(n,i));
  }
  for(int i=2;i<=n;i++){
    seg.apply(n-1,g(i,i));
  }
  for(int i=0;i<n;i++){
    ll x;
    cin>>x;
    a[i]=x;
  }
  mint ans=0;
  for(int i=0;i<n;i++){
    ans+=a[i]*seg.prod(i,i+1).value;
    b[i]=seg.prod(i,i+1).value;
  }
  for(int i=n-1;i>=0;i--){
    a.push_back(a[i]);
    b.push_back(b[i]);
  }
  n*=2;
  rever(b);
  vector<mint> c=convolution(a,b);
  for(int i=n;i<int(c.size());i++){
    c[i%n]+=c[i];
  }
  c.resize(n);
  rever(c);
  fps f(n);
  f[0]=1;
  cout<<(c[0]*h/mint(2)).val()<<endl;
  ll k=min(int(sqrt(n/2)*6),int(n));
  vector<vector<pair<int,mint>>> F(k+1);
  vector<mint> p;
  F[0]={{0,mint(1)}};
  for(int i=1;i<=n/2;i++){
    ll v=i%k;
    if(v==i){
      for(int j=0;j<int(F[i-1].size());j++){
        F[i].push_back({F[i-1][j].fi,(n/2-3)*F[i-1][j].se});
        F[i].push_back({(F[i-1][j].fi-1+n)%n,F[i-1][j].se});
        F[i].push_back({(F[i-1][j].fi+1)%n,F[i-1][j].se});
      }
      unordered_map<int,mint> M;
      for(int j=0;j<int(F[i].size());j++){
        M[F[i][j].fi]+=F[i][j].se;
      }
      F[i].resize(0);
      for(auto e:M){
        F[i].push_back({e.fi,e.se});
      }
      mint ans=0;
      for(int j=0;j<int(F[i].size());j++){
        ans+=F[i][j].se*c[F[i][j].fi];
      }
      cout<<(ans*h/mint(2)).val()<<endl;
    }
    else{
      mint ans=0;
      for(int j=0;j<int(F[v].size());j++){
        ans+=F[v][j].se*c[F[v][j].fi];
      }
      cout<<(ans*h/mint(2)).val()<<endl;
    }
    if(i%k==k-1){
      if(int(p.size())==0){
        vector<pair<ll,mint>> tmp;
        for(int j=0;j<int(F[k-1].size());j++){
          F[k].push_back({F[k-1][j].fi,(n/2-3)*F[k-1][j].se});
          F[k].push_back({(F[k-1][j].fi-1+n)%n,F[k-1][j].se});
          F[k].push_back({(F[k-1][j].fi+1)%n,F[k-1][j].se});
        }
        unordered_map<int,mint> M;
        for(int j=0;j<int(F[k].size());j++){
          M[F[k][j].fi]+=F[k][j].se;
        }
        vector<pair<int,int>> S;
        for(auto e:M){
          if(e.fi>=n/2){
            S.push_back({e.fi-n,e.se.val()});
          }
          else{
            S.push_back({e.fi,e.se.val()});
          }
        }
        sor(S);
        for(int j=0;j<int(S.size());j++){
          p.push_back(S[j].se);
        }
      }
      auto d=convolution(c,p);
      for(int j=0;j<int(c.size());j++){
        c[j]=0;
      }
      for(int j=0;j<int(d.size());j++){
        c[(j-k+n)%n]+=d[j];
      }
    }
  }
}
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