結果

問題 No.1574 Swap and Repaint
ユーザー KoD
提出日時 2021-06-20 15:33:09
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 6,633 ms / 10,000 ms
コード長 13,940 bytes
コンパイル時間 4,702 ms
コンパイル使用メモリ 293,060 KB
最終ジャッジ日時 2025-01-22 10:30:00
ジャッジサーバーID
(参考情報)
judge5 / judge1
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 3
other AC * 33
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 #
プレゼンテーションモードにする

#include <bits/stdc++.h>
#include <unistd.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 REP3(i, m, n) for (int i = (m); (i) < int(n); ++ (i))
#define ALL(x) begin(x), end(x)
#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)
#define in scanner.read_int()
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);
}
class Scanner {
vector<char> buffer;
ssize_t n_written;
ssize_t n_read;
public:
Scanner(): buffer(1024*1024) { do_read(); }
int64_t read_int() {
int64_t ret = 0, sgn = 1;
int ch = current_char();
while (isspace(ch)) { ch = next_char(); }
if (ch == '-') { sgn = -1; ch = next_char(); }
for (; isdigit(ch); ch = next_char())
ret = (ret * 10) + (ch - '0');
return sgn * ret;
}
private:
void do_read() {
ssize_t r = read(0, &buffer[0], buffer.size());
if (r < 0) {
throw runtime_error(strerror(errno));
}
n_written = r;
n_read = 0;
}
inline int next_char() {
++n_read;
if (n_read == n_written) { do_read(); }
return current_char();
}
inline int current_char() {
return (n_read == n_written) ? EOF : buffer[n_read];
}
};
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() {
Scanner scanner;
gbjsmzmfuuvdf();
com();
int n;
n=in;
assert(2<=n&&n<=100000);
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++){
int x;
x=in;
assert(0<=x&&x<=2);
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()<<"\n";
int k=min(int(sqrt(n)*log(n)),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){
unordered_map<int,mint> M;
for(int j=0;j<int(F[i-1].size());j++){
M[F[i-1][j].fi]+=(n/2-3)*F[i-1][j].se;
M[(F[i-1][j].fi-1+n)%n]+=F[i-1][j].se;
M[(F[i-1][j].fi+1)%n]+=F[i-1][j].se;
}
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()<<"\n";
}
if(i%k==k-1){
if(int(p.size())==0){
unordered_map<int,mint> M;
for(int j=0;j<int(F[k-1].size());j++){
M [F[k-1][j].fi]+=(n/2-3)*F[k-1][j].se;
M[(F[k-1][j].fi-1+n)%n]+=F[k-1][j].se;
M[(F[k-1][j].fi+1)%n]+=F[k-1][j].se;
}
vector<pair<int,int>> S(int(M.size()));
int now=0;
for(auto e:M){
if(e.fi>=n/2){
S[now]={e.fi-n,e.se.val()};
}
else{
S[now]={e.fi,e.se.val()};
}
now++;
}
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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