結果

問題 No.1964 sum = length
ユーザー MtSakaMtSaka
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
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ファイルパターン 結果
sample AC * 3
other AC * 40
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ソースコード

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プレゼンテーションモードにする

#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()
*/
#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()
*/
#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()
*/
#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]);
}
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