#757636 (C++17) No.1964 sum = length

提出ソース
結果

問題	No.1964 sum = length
ユーザー	MtSaka
提出日時	2022-05-01 22:37:26
言語	C++17 (gcc 13.3.0 + boost 1.87.0)
結果	AC
実行時間	4 ms / 2,000 ms
コード長	15,846 bytes
コンパイル時間	3,093 ms
コンパイル使用メモリ	214,352 KB
最終ジャッジ日時	2025-01-29 01:25:28
ジャッジサーバーID （参考情報）	judge1 / judge5
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 * 40
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

raw source code
#line 1 "library/template/template.hpp"
//#pragma GCC target("avx")
//#pragma GCC optimize("O3")
//#pragma GCC optimize("unroll-loops")
#include<bits/stdc++.h>
#define overload4(a,b,c,d,e,...) e
#define overload3(a,b,c,d,...) d
#define rep1(a) for(ll i=0;i<(ll)(a);i++)
#define rep2(i,a) for(ll i=0;i<(ll)(a);i++)
#define rep3(i,a,b) for(ll i=(ll)(a);i<(ll)(b);i++)
#define rep4(i,a,b,c) for(ll i=(ll)(a);i<(ll)(b);i+=(ll)(c))
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define rrep1(a) for(ll i=(ll)(a)-1;i>=0;i--)
#define rrep2(i,a) for(ll i=(ll)(a)-1;i>=0;i--)
#define rrep3(i,a,b) for(ll i=(ll)(b)-1;i>=(ll)(a);i--)
#define rrep(...) overload3(__VA_ARGS__,rrep3,rrep2,rrep1)(__VA_ARGS__)
#define fore(...) for (auto&& __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 rall(n) (n).rbegin(),(n).rend()
#define INT(...) int __VA_ARGS__;scan(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__;scan(__VA_ARGS__)
#define STR(...) string __VA_ARGS__;scan(__VA_ARGS__)
#define CHR(...) char __VA_ARGS__;scan(__VA_ARGS__)
#define DBL(...) double __VA_ARGS__;scan(__VA_ARGS__)
#define LD(...) ld __VA_ARGS__;scan(__VA_ARGS__)
#define pb push_back
#define eb emplace_back
#define END(...) {print(__VA_ARGS__);return;}
using namespace std;
using ll=long long;
using ull=unsigned long long;
using ld=long double;
using vl=vector<ll>;
using vi=vector<int>;
using vs=vector<string>;
using vc=vector<char>;
using vvl=vector<vl>;
using pi=pair<int,int>;
using pl=pair<ll,ll>;
using vvc=vector<vc>;
using vd=vector<double>;
using vp=vector<pl>;
using vb=vector<bool>;
const int dx[8]={1,0,-1,0,1,-1,-1,1};
const int dy[8]={0,1,0,-1,1,1,-1,-1};
const ll MOD=1000000007;
const ll mod=998244353;
const ld EPS=1e-8;
const ld PI=3.1415926535897932384626;
template<typename T,typename U>
ostream &operator<<(ostream&os,const pair<T,U>&p){os<<p.first<<" "<<p.second;return os;}
template<typename T,typename U>
istream &operator>>(istream&is,pair<T,U>&p){is>>p.first>>p.second;return is;}
template<typename T>
ostream &operator<<(ostream&os,const vector<T>&v){for(auto it=v.begin();it!=v.end();){os<<*it<<((++it)!=v.end()?" ":"");}return os;}
template<typename T>
istream &operator>>(istream&is,vector<T>&v){for(T &in:v){is>>in;}return is;}
void scan(){}
template<class Head,class... Tail>
void scan(Head&head,Tail&... tail){cin>>head;scan(tail...);}
template<class T>
void print(const T &t){cout<<t<<'\n';}
template<class Head, class... Tail>
void print(const Head &head, const Tail &... tail){cout<<head<<' ';print(tail...);}
template<class... T>
void fin(const T &... a){print(a...);exit(0);}
template<typename T,typename U>
inline bool chmax(T&a,U b){return a<b&&(a=b,true);}
template<typename T,typename U>
inline bool chmin(T&a,U b){return a>b&&(a=b,true);}
template<typename T>
class infinity{
  public:
  static const T MAX=numeric_limits<T>::max();
  static const T MIN=numeric_limits<T>::min();
  static const T value=numeric_limits<T>::max()/2;
  static const T mvalue=numeric_limits<T>::min()/2;
};
#if __cplusplus <= 201402L
template<class T>const T infinity<T>::value;
template<class T>const T infinity<T>::mvalue;
template<class T>const T infinity<T>::MAX;
template<class T>const T infinity<T>::MIN;
#endif
template<typename T>const T INF=infinity<T>::value;
const long long inf=INF<ll>;
inline int popcnt(ull x){
#if __cplusplus>=202002L
return popcount(x);
#endif
x=(x&0x5555555555555555)+((x>>1)&0x5555555555555555);x=(x&0x3333333333333333)+((x>>2)&0x3333333333333333);x=(x&0x0f0f0f0f0f0f0f0f)+((x>>4)&0x0f0f0f0f0f0f0f0f);x=(x&0x00ff00ff00ff00ff)+((x>>8)&0x00ff00ff00ff00ff);x=(x&0x0000ffff0000ffff)+((x>>16)&0x0000ffff0000ffff);return (x&0x00000000ffffffff)+((x>>32)&0x00000000ffffffff);
}
template<typename T,typename=void>
struct is_specialize:false_type{};
template<typename T>
struct is_specialize<T,typename conditional<false,typename T::iterator, void>::type>:true_type{};
template<typename T>
struct is_specialize<T,typename conditional<false,decltype(T::first),void>::type>:true_type{};
template<typename T>
struct is_specialize<T,enable_if_t<is_integral<T>::value,void>>:true_type{};
void dump(const char&t){cerr<<t;}
void dump(const string&t){cerr<<t;}
void dump(const bool&t){cerr<<(t?"true":"false");}
template <typename T,enable_if_t<!is_specialize<T>::value,nullptr_t> =nullptr>
void dump(const T&t){cerr<<t;}
template<typename T>
void dump(const T&t,enable_if_t<is_integral<T>::value>* =nullptr){string tmp;if(t==infinity<T>::value||t==infinity<T>::MAX)tmp="inf";if(t==infinity<T>::mvalue||t==infinity<T>::MIN)tmp="-inf";if(tmp.empty())tmp=to_string(t);cerr<<tmp;}
template <typename T>
void dump(const T&t,enable_if_t<!is_void<typename T::iterator>::value>* =nullptr){cerr<<"{";for(auto it=t.begin();it!=t.end();){dump(*it);cerr<<(++it==t.end()?"":",");}cerr<<"}";}
template<typename T,typename U>
void dump(const pair<T,U>&t){cerr<<"(";dump(t.first);cerr<<",";dump(t.second);cerr<<")";}
void trace(){cerr<<endl;}
template<typename Head,typename... Tail>
void trace(Head&&head,Tail&&... tail){dump(head);if(sizeof...(tail))cerr<<",";trace(forward<Tail>(tail)...);}
#ifdef ONLINE_JUDGE
#define debug(...) (void(0))
#else
#define debug(...) do{cerr<<#__VA_ARGS__<<"=";trace(__VA_ARGS__);}while(0)
#endif
struct IOSetup{IOSetup(){cin.tie(nullptr);ios::sync_with_stdio(false);cout.tie(0);cout<<fixed<<setprecision(12);cerr<<fixed<<setprecision(12);}};
/**
 * @brief Template(テンプレート)
*/
#line 2 "library/Math/modular/modint.hpp"
template<long long m>
struct modint{
  long long x;
  constexpr modint():x(0){}
  constexpr modint(long long y):x(y>=0?y%m:(m-(-y)%m)%m){}
  modint inv()const{
    long long a=x,b=m,u=1,v=0,t;
    while(b){
      t=a/b;
      swap(a-=t*b,b);
      swap(u-=t*v,v);
    }
    return modint(u);
  }
  modint &operator+=(const modint&p){if((x+=p.x)>=m)x-=m;return *this;}
  modint &operator-=(const modint&p){if((x+=m-p.x)>=m)x-=m;return *this;}
  modint &operator*=(const modint&p){x=x*p.x;if(x>=m)x%=m;return *this;}
  modint &operator/=(const modint&p){*this*=p.inv();return *this;}
  friend modint operator+(const modint&l,const modint&r){return modint(l)+=r;}
  friend modint operator-(const modint&l,const modint&r){return modint(l)-=r;}
  friend modint operator*(const modint&l,const modint&r){return modint(l)*=r;}
  friend modint operator/(const modint&l,const modint&r){return modint(l)/=r;}
  modint operator-()const{return modint(-x);}
  modint operator+()const{return *this;}
  modint &operator++(){x++;if(x==m)x=0;return *this;}
  modint &operator--(){if(x==0)x=m;x--;return *this;}
  modint operator++(int){modint ret(*this);++*this;return ret;}
  modint operator--(int){modint ret(*this);--*this;return ret;}
  friend bool operator==(const modint&l,const modint&r){return l.x==r.x;}
  friend bool operator!=(const modint&l,const modint&r){return l.x!=r.x;}
  modint pow(long long n)const{
    modint ret(1),mul(x);
    while(n){
      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<m>(t);
    return (is);
  }
  static long long get_mod(){return m;}
};
/**
 * @brief modint
*/
#line 3 "library/Math/convolution/ntt.hpp"
template<long long m>
struct NTT{
  using mint=modint<m>;
  static modint<m> g;
  static int limit;
  static vector<modint<m>>root,inv_root;
  static mint primitive_root(const long long&mo){
    if(mo==167772161)return mint(3);
    if(mo==469762049)return mint(3);
    if(mo==754974721)return mint(11);
    if(mo==998244353)return mint(3);
    if(mo==1224736769)return mint(3);
    return mint(0);
  }
  static void init(){
    if(root.empty()){
      g=primitive_root(m);
      long long now=m-1;
      while(!(now&1))now>>=1,limit++;
      root.resize(limit+1,1),inv_root.resize(limit+1,1);
      root[limit]=g.pow(now);
      inv_root[limit]/=root[limit];
      for(int i=limit-1;i>=0;i--){
        root[i]=root[i+1]*root[i+1];
        inv_root[i]=inv_root[i+1]*inv_root[i+1];
      }
    }
  }
  NTT(){};
  static void dft(vector<mint>&a,int inv){
    init();
    const int sz=a.size();
    if(sz==1)return;
    const int mask=sz-1;
    vector<mint>b(sz);
    for(int i=sz>>1;i>=1;i>>=1){
      int e=__builtin_ffsll(sz/i)-1;
      mint w=1,z=(inv==1?root[e]:inv_root[e]);
      for(int j=0;j<sz;j+=i){
        for(int k=0;k<i;k++)b[j+k]=a[((j<<1)&mask)+k]+w*a[(((j<<1)+i)&mask)+k];
        w*=z;
      }
      swap(a,b);
    }
  }
  static vector<mint>multiply(vector<mint>a,vector<mint>b){
    int sz=1;
    const int mxsiz=a.size()+b.size()-1;
    while(sz<mxsiz)sz<<=1;
    a.resize(sz),b.resize(sz);
    dft(a,1),dft(b,1);
    for(int i=0;i<sz;i++)a[i]*=b[i];
    dft(a,-1);
    a.resize(mxsiz);
    mint iz=mint(sz).inv();
    for(int i=0;i<mxsiz;i++)a[i]*=iz;
    return a;
  }
  template<typename T,std::enable_if_t<is_integral<T>::value>* = nullptr>
  static vector<T>multiply(const vector<T>&a,const vector<T>&b){
    using mint=modint<m>;
    vector<mint>a2(a.size()),b2(b.size());
    for(int i=0;i<(int)a.size();i++)a2[i]=a[i];
    for(int i=0;i<(int)b.size();i++)b2[i]=b[i];
    auto c2=multiply(a2,b2);
    vector<T>c(c2.size());
    for(int i=0;i<(int)c.size();i++)c[i]=c2[i].x;
    return c;
  }
};
template<long long m>
int NTT<m>::limit=0;
template<long long m>
vector<modint<m>>NTT<m>::root=vector<modint<m>>();
template<long long m>
vector<modint<m>>NTT<m>::inv_root=vector<modint<m>>();
template<long long m>
modint<m>NTT<m>::g=modint<m>();
/**
 * @brief Number Theoretic Transform(数論変換)
*/
#line 3 "library/Math/fps/fps.hpp"
template<long long Mod>
struct FPS:vector<modint<Mod>>{
  using mint=modint<Mod>;
  using vector<mint>::vector;
  using vector<mint>::operator=;
  void shrink(){while(!(*this).empty()&&(*this).back()==mint(0))(*this).pop_back();}
  FPS inv(int d=-1)const{
    NTT<Mod>ntt;
    const int n=(*this).size();
    if(d==-1)d=n;
    FPS res{(*this)[0].inv()};
    for(int m=1;m<d;m<<=1){
      FPS f((*this).begin(),(*this).begin()+min(n,2*m));
      FPS g(res);
      f.resize(2*m),g.resize(2*m);
      ntt.dft(f,1),ntt.dft(g,1);
      for(int i=0;i<2*m;i++)f[i]*=g[i];
      ntt.dft(f,-1);
      f.erase(f.begin(),f.begin()+m);
      f.resize(2*m);ntt.dft(f,1);
      for(int i=0;i<2*m;i++)f[i]*=g[i];
      ntt.dft(f,-1);
      mint iz=mint(2*m).inv();iz*=-iz;
      for(int i=0;i<m;i++)f[i]*=iz;
      res.insert(res.end(),f.begin(),f.begin()+m);
    }
    res.resize(d);
    return res;
  }
  FPS operator+(const mint&r)const{return FPS(*this)+=r;}
  FPS operator-(const mint&r)const{return FPS(*this)-=r;}
  FPS operator*(const mint&r)const{return FPS(*this)*=r;}
  FPS operator/(const mint&r)const{return FPS(*this)/=r;}
  FPS operator+(const FPS&r)const{return FPS(*this)+=r;}
  FPS operator-(const FPS&r)const{return FPS(*this)-=r;}
  FPS operator<<(const int&d)const{return FPS(*this)<<=d;}
  FPS operator>>(const int&d)const{return FPS(*this)>>=d;}
  FPS operator*(const FPS&r)const{return FPS(*this)*=r;}
  FPS operator/(const FPS&r)const{return FPS(*this)/=r;}
  FPS operator%(const FPS&r)const{return FPS(*this)%=r;}
  FPS operator-()const{
    FPS ret(*this);
    for(auto &i:ret)i=-i;
    return ret;
  }
  FPS &operator+=(const mint&r){
    if((*this).empty())(*this).resize(1);
    (*this)[0]+=r;
    return *this;
  }
  FPS &operator-=(const mint&r){
    if((*this).empty())(*this).resize(1);
    (*this)[0]-=r;
    return *this;
  }
  FPS &operator*=(const mint&r){
    for(auto &i:*this)i*=r;
    return *this;
  }
  FPS &operator/=(const mint&r){
    (*this)*=r.inv();
    return *this;
  }
  FPS &operator+=(const FPS&r){
    const int n=(*this).size(),m=r.size();
    (*this).resize(max(n,m));
    for(int i=0;i<m;i++)(*this)[i]+=r[i];
    return *this;
  }
  FPS &operator-=(const FPS&r){
    const int n=(*this).size(),m=r.size();
    (*this).resize(max(n,m));
    for(int i=0;i<m;i++)(*this)[i]-=r[i];
    return *this;
  }
  FPS &operator<<=(const long long&d){
    (*this).insert((*this).begin(),d,mint(0));
    return *this;
  }
  FPS &operator>>=(const long long&d){
    (*this).erase((*this).begin(),(*this).begin()+d);
    return *this;
  }
  FPS &operator*=(const FPS&r){
    (*this)=NTT<Mod>::multiply((*this),r);
    return *this;
  }
  FPS &operator/=(FPS r){
    const int n=(*this).size(),m=r.size();
    if(n<m){
      (*this).clear();
      return *this;
    }
    const int sz=n-m+1;
    reverse((*this).begin(),(*this).end());
    reverse(r.begin(),r.end());
    (*this).resize(sz);
    (*this)*=r.inv(sz);
    (*this).resize(sz);
    reverse((*this).begin(),(*this).end());
    return (*this);
  }
  FPS &operator%=(const FPS&r){
    const int n=(*this).size(),m=r.size();
    if(n<m)return (*this);
    (*this)-=(*this)/r*r;
    (*this).resize(m-1);
    shrink();
    return (*this);
  }
  pair<FPS,FPS>div_mod(const FPS&r){
    FPS p=*this/r,q=*this-p*r;
    q.shrink();
    return {p,q};
  }
  mint operator()(const mint&x)const{
    mint ret(0),w(1);
    for(auto &e:*this){
      ret+=e*w;
      w*=x;
    }
    return ret;
  }
  FPS diff()const{
    const int n=(*this).size();
    FPS ret(max(0,n-1));
    for(int i=1;i<n;i++)ret[i-1]=(*this)[i]*mint(i);
    return ret;
  }
  FPS integral()const{
    const int n=(*this).size();
    vector<mint>inv(n+1);
    inv[1]=mint(1);
    for(int i=2;i<=n;i++)inv[i]=-inv[Mod%i]*mint(Mod/i);
    FPS ret(n+1);
    for(int i=0;i<n;i++)ret[i+1]=(*this)[i]*inv[i+1];
    return ret;
  }
  FPS log(int d=-1)const{
    const int n=(*this).size();
    if(d==-1)d=n;
    FPS res=diff()*inv(d);
    res.resize(d-1);
    return res.integral();
  }
  FPS exp(int d=-1)const{
    const int n=(*this).size();
    if(d==-1)d=n;
    FPS f={mint(1)+(*this)[0],(*this)[1]},res{1,1<n?(*this)[1]:0};
    for(int m=2;m<d;m<<=1){
      f.insert(f.end(),(*this).begin()+min(m,n),(*this).begin()+min(n,2*m));
      if((int)f.size()<2*m)f.resize(2*m);
      res=res*(f-res.log(2*m));
      res.resize(2*m);
    }
    res.resize(d);
    return res;
  }
  FPS pow(long long k,int d=-1)const{
    const int n=(*this).size();
    if(d==-1)d=n;
    for(int i=0;i<n;i++){
      if((*this)[i]!=mint()){
        mint rev=(*this)[i].inv();
        if(i*k>d)return FPS(d,mint(0));
        FPS ret=(((*this*rev)>>i).log(d)*k).exp(d)*((*this)[i].pow(k));
        ret=(ret<<(i*k));
        ret.resize(d);
        return ret;
      }
    }
    return FPS(d,mint(0));
  }
  FPS sqrt(int d=-1,const function<mint(mint)>&get_sqrt=[](mint){return mint(1);})const{
    const int n=(*this).size();
    if(d==-1)d=n;
    if((*this)[0]==mint(0)){
      for(int i=1;i<n;i++){
        if((*this)[i]!=mint(0)){
          if(i&1)return {};
          if(d-i/2<=0)break;
          auto ret=(*this>>i).sqrt(d-i/2,get_sqrt);
          if(ret.empty())return {};
          ret=ret<<(i/2);
          if((int)ret.size()<d)ret.resize(d);
          return ret;
        }
      }
      return FPS(d);
    }
    auto sqr=get_sqrt((*this)[0]);
    if(sqr*sqr!=(*this)[0])return {};
    FPS ret{sqr};
    mint inv2=mint(2).inv();
    FPS f={(*this)[0]};
    for(int i=1;i<d;i<<=1){
      if(i<n)f.insert(f.end(),(*this).begin()+i,(*this).begin()+min(n,i<<1));
      if((int)f.size()<(i<<1))f.resize(i<<1);
      ret=(ret+f*ret.inv(i<<1))*inv2;
    }
    ret.resize(d);
    return ret;
  }
};
/**
 * @brief Formal Power Series(形式的冪級数)
*/
#line 3 "code.cpp"
int main(){
  LL(n);
  FPS<mod>cnt(2*n);
  ll now=1;
  ll tmp=0;
  ll nxt=10;
  while(now-tmp<=2*n-1){
    cnt[now-tmp]+=1;
    now++;
    if(now==nxt){
      tmp++;
      nxt*=10;
    }
  }
  cnt=cnt.pow(n);
  print(cnt[2*n-1]);
}
yukicoder

結果

ソースコード
