結果

問題 No.3277 Forever Monotonic Number
ユーザー Taiki0715
提出日時 2025-09-19 22:09:45
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 603 ms / 4,000 ms
コード長 7,861 bytes
コンパイル時間 3,364 ms
コンパイル使用メモリ 281,716 KB
実行使用メモリ 9,064 KB
最終ジャッジ日時 2025-09-19 22:10:00
合計ジャッジ時間 7,884 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 1
other AC * 9
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;
using ll=long long;
using ull=unsigned long long;
using P=pair<ll,ll>;
template<typename T>using minque=priority_queue<T,vector<T>,greater<T>>;
template<typename T>bool chmax(T &a,const T &b){return (a<b?(a=b,true):false);}
template<typename T>bool chmin(T &a,const T &b){return (a>b?(a=b,true):false);}
template<typename T1,typename T2>istream &operator>>(istream &is,pair<T1,T2>&p){is>>p.first>>p.second;return is;}
template<typename T1,typename T2,typename T3>istream &operator>>(istream &is,tuple<T1,T2,T3>&a){is>>std::get<0>(a)>>std::get<1>(a)>>std::get<2>(a);return is;}
template<typename T,size_t n>istream &operator>>(istream &is,array<T,n>&a){for(auto&i:a)is>>i;return is;}
template<typename T>istream &operator>>(istream &is,vector<T> &a){for(auto &i:a)is>>i;return is;}
template<typename T1,typename T2>void operator++(pair<T1,T2>&a,int n){a.first++,a.second++;}
template<typename T1,typename T2>void operator--(pair<T1,T2>&a,int n){a.first--,a.second--;}
template<typename T>void operator++(vector<T>&a,int n){for(auto &i:a)i++;}
template<typename T>void operator--(vector<T>&a,int n){for(auto &i:a)i--;}
#define overload3(_1,_2,_3,name,...) name
#define rep1(i,n) for(int i=0;i<(int)(n);i++)
#define rep2(i,l,r) for(int i=(int)(l);i<(int)(r);i++)
#define rep(...) overload3(__VA_ARGS__,rep2,rep1)(__VA_ARGS__)
#define reps(i,l,r) rep2(i,l,r)
#define all(x) x.begin(),x.end()
#define pcnt(x) __builtin_popcountll(x)
#define fin(x) return cout<<(x)<<'\n',static_cast<void>(0)
#define yn(x) cout<<((x)?"Yes\n":"No\n")
#define uniq(x) sort(all(x)),x.erase(unique(all(x)),x.end())
template<typename T>
inline int fkey(vector<T>&z,T key){return lower_bound(z.begin(),z.end(),key)-z.begin();}
ll myceil(ll a,ll b){return (a+b-1)/b;}
template<typename T,size_t n,size_t id=0>
auto vec(const int (&d)[n],const T &init=T()){
  if constexpr (id<n)return vector(d[id],vec<T,n,id+1>(d,init));
  else return init;
}
#ifdef LOCAL
#include<debug.h>
#define SWITCH(a,b) (a)
#else
#define debug(...) static_cast<void>(0)
#define debugg(...) static_cast<void>(0)
#define SWITCH(a,b) (b)
template<typename T1,typename T2>ostream &operator<<(ostream &os,const pair<T1,T2>&p){os<<p.first<<' '<<p.second;return os;}
#endif
struct Timer{
  clock_t start;
  Timer(){
    start=clock();
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout<<fixed<<setprecision(16);
  }
  inline double now(){return (double)(clock()-start)/1000;}
  #ifdef LOCAL
  ~Timer(){
    cerr<<"time:";
    cerr<<now();
    cerr<<"ms\n";
  }
  #endif
}timer;
void SOLVE();
int main(){
  int testcase=1;
  // cin>>testcase;
  for(int i=0;i<testcase;i++){
    SOLVE();
  }
}
#include<type_traits>
#include<optional>
constexpr int carmichael_constexpr(int n){
  if(n==998244353)return 998244352;
  if(n==1000000007)return 1000000006;
  if(n<=1)return n;
  int res=1;
  int t=0;
  while(n%2==0){
    n/=2;
    t++;
  }
  if(t==2)res=2;
  else if(t>=3)res=1<<(t-2);
  for(int i=3;i*i<=n;i++)if(n%i==0){
    int c=0;
    while(n%i==0){
      n/=i;
      c++;
    }
    int prod=i-1;
    for(int j=0;j<c-1;j++)prod*=i;
    res=std::lcm(res,prod);
  }
  if(n!=1)res=std::lcm(res,n-1);
  return res;
}
template<int m>
struct mod_int{
private:
  static constexpr unsigned int umod=static_cast<unsigned int>(m);
  static constexpr unsigned int car=carmichael_constexpr(m);
  using uint=unsigned int;
  using mint=mod_int;
  uint v;
  static_assert(m<uint(1)<<31);
  mint sqrt_impl()const{
    if(this->val()<=1)return *this;
    if constexpr(m%8==1){
      mint b=2;
      while(b.pow((m-1)/2).val()==1)b++;
      int m2=m-1,e=0;
      while(m2%2==0)m2>>=1,e++;
      mint x=this->pow((m2-1)/2);
      mint y=(*this)*x*x;
      x*=*this;
      mint z=b.pow(m2);
      while(y.val()!=1){
        int j=0;
        mint t=y;
        while(t.val()!=1)t*=t,j++;
        z=z.pow(1<<(e-j-1));
        x*=z;
        z*=z;
        y*=z;e=j;
      }
      return x;
    }
    else if constexpr(m%8==5){
      mint ret=this->pow((m+3)/8);
      if((ret*ret).val()==this->val())return ret;
      else return ret*mint::raw(2).pow((m-1)/4);
    }
    else{
      return this->pow((m+1)/4);
    }
  }
public:
  using value_type=uint;
  mod_int():v(0){}
  template<typename T,std::enable_if_t<std::is_signed_v<T>,std::nullptr_t> =nullptr>
  mod_int(T a){
    a%=m;
    if(a<0)v=a+umod;
    else v=a;
  }
  template<typename T,std::enable_if_t<std::is_unsigned_v<T>,std::nullptr_t> =nullptr>
  mod_int(T a):v(a%umod){}
  static constexpr mint raw(int a){
    mint ret;
    ret.v=a;
    return ret;
  }
  inline uint val()const{return this->v;}
  static constexpr int mod(){return m;}
  inline mint &operator+=(const mint &b){
    this->v+=b.v;
    if(this->v>=umod)this->v-=umod;
    return *this;
  }
  inline mint &operator-=(const mint &b){
    this->v-=b.v;
    if(this->v>=umod)this->v+=umod;
    return *this;
  }
  inline mint &operator*=(const mint &b){
    this->v=((unsigned long long)this->v*b.v)%umod;
    return *this;
  }
  inline mint &operator/=(const mint &b){
    *this*=b.inv();
    return *this;
  }
  inline mint operator+()const{return *this;}
  inline mint operator-()const{return mint()-*this;}
  friend inline mint operator+(const mint &a,const mint &b){return mint(a)+=b;}
  friend inline mint operator-(const mint &a,const mint &b){return mint(a)-=b;}
  friend inline mint operator*(const mint &a,const mint &b){return mint(a)*=b;}
  friend inline mint operator/(const mint &a,const mint &b){return mint(a)/=b;}
  friend inline bool operator==(const mint &a,const mint &b){return a.val()==b.val();}
  friend inline bool operator!=(const mint &a,const mint &b){return !(a==b);}
  inline mint operator++(int){
    mint ret=*this;
    *this+=mint::raw(1);
    return ret;
  }
  inline mint operator--(int){
    mint ret=*this;
    *this-=mint::raw(1);
    return ret;
  }
  mint pow(long long n)const{
    mint ret=mint::raw(1),a(*this);
    while(n){
      if(n&1)ret*=a;
      a*=a;
      n>>=1;
    }
    return ret;
  }
  inline mint inv()const{
    assert(this->v!=0);
    return pow(car-1);
  }
  std::optional<mint>sqrt()const{
    if(this->val()<=1||this->pow((m-1)/2)==1)return std::make_optional(this->sqrt_impl());
    else return std::nullopt;
  }
  static constexpr unsigned int order(){return car;}
  friend std::istream &operator>>(std::istream &is,mint &b){
    long long a;
    is>>a;
    b=mint(a);
    return is;
  }
  friend std::ostream &operator<<(std::ostream &os,const mint &b){
    os<<b.val();
    return os;
  }
};
template<int m>
struct std::hash<mod_int<m>>{
  std::size_t operator()(mod_int<m>x)const{
    return std::hash<unsigned int>()(x.val());
  }
};
using mint998=mod_int<998244353>;
using mint107=mod_int<1000000007>;
using mint=mint998;
constexpr int dig=15;
mint repunit(ll dig){
  //1+10+100+...10^(dig-1)
  return (mint(10).pow(dig)-1)/9;
}
mint calc(ll dig,int num){
  return repunit(dig)*num;
}
ll digitsum(ll x){
  string s=to_string(x);
  ll res=0;
  for(char c:s)res+=c-'0';
  return res;
}
void SOLVE(){
  vector<ll>pre;
  auto dfs=[&](auto self,int pos,int v,ll now)->void {
    if(pos==dig){
      if(now<10)pre.push_back(now);
      else{
        ll d=digitsum(now);
        if(binary_search(all(pre),d))pre.push_back(now);
      }
    }
    else{
      rep(i,v,10){
        self(self,pos+1,i,now*10+i);
      }
    }
  };
  dfs(dfs,0,0,0);
  int t;
  cin>>t;
  while(t--){
    ll n;
    cin>>n;
    n++;
    ll v=*lower_bound(all(pre),n);
    mint ans=0;
    ll pos=0;
    rep(i,1,10){
      ll ok=pos,ng=n+1;
      while(ng-ok>1){
        ll mid=(ok+ng)/2;
        if((mid-pos)*i+9*(n-mid)>=v)ok=mid;
        else ng=mid;
      }
      ans*=mint(10).pow(ok-pos);
      ans+=calc(ok-pos,i);
      v-=i*(ok-pos);
      pos=ok;
    }
    assert(v==0);
    assert(pos==n);
    cout<<ans<<'\n';
  }
}
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