結果

問題 No.2075 GCD Subsequence
ユーザー 👑 tute7627tute7627
提出日時 2022-09-16 22:58:29
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 911 ms / 4,000 ms
コード長 12,858 bytes
コンパイル時間 2,746 ms
コンパイル使用メモリ 227,856 KB
実行使用メモリ 24,400 KB
最終ジャッジ日時 2024-06-01 13:55:30
合計ジャッジ時間 15,962 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge1
このコードへのチャレンジ
（要ログイン）

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 30 ms
22,932 KB
testcase_01 AC 31 ms
22,624 KB
testcase_02 AC 30 ms
22,740 KB
testcase_03 AC 31 ms
22,736 KB
testcase_04 AC 30 ms
22,720 KB
testcase_05 AC 30 ms
22,720 KB
testcase_06 AC 31 ms
22,676 KB
testcase_07 AC 31 ms
22,760 KB
testcase_08 AC 156 ms
23,556 KB
testcase_09 AC 243 ms
24,348 KB
testcase_10 AC 166 ms
23,688 KB
testcase_11 AC 210 ms
23,924 KB
testcase_12 AC 184 ms
23,700 KB
testcase_13 AC 140 ms
23,536 KB
testcase_14 AC 202 ms
24,036 KB
testcase_15 AC 147 ms
23,556 KB
testcase_16 AC 158 ms
23,640 KB
testcase_17 AC 240 ms
24,224 KB
testcase_18 AC 895 ms
24,156 KB
testcase_19 AC 895 ms
24,304 KB
testcase_20 AC 908 ms
24,280 KB
testcase_21 AC 900 ms
24,280 KB
testcase_22 AC 900 ms
24,156 KB
testcase_23 AC 901 ms
24,280 KB
testcase_24 AC 896 ms
24,264 KB
testcase_25 AC 896 ms
24,332 KB
testcase_26 AC 898 ms
24,296 KB
testcase_27 AC 892 ms
24,400 KB
testcase_28 AC 911 ms
24,280 KB
testcase_29 AC 31 ms
22,908 KB
testcase_30 AC 32 ms
22,632 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 # 

//#define _GLIBCXX_DEBUG

#include<bits/stdc++.h>
using namespace std;

#define endl '\n'
#define lfs cout<<fixed<<setprecision(10)
#define ALL(a)  (a).begin(),(a).end()
#define ALLR(a)  (a).rbegin(),(a).rend()
#define UNIQUE(a) (a).erase(unique((a).begin(),(a).end()),(a).end())
#define spa << " " <<
#define fi first
#define se second
#define MP make_pair
#define MT make_tuple
#define PB push_back
#define EB emplace_back
#define rep(i,n,m) for(ll i = (n); i < (ll)(m); i++)
#define rrep(i,n,m) for(ll i = (ll)(m) - 1; i >= (ll)(n); i--)
using ll = long long;
using ld = long double;
const ll MOD1 = 1e9+7;
const ll MOD9 = 998244353;
const ll INF = 1e18;
using P = pair<ll, ll>;
template<typename T> using PQ = priority_queue<T>;
template<typename T> using QP = priority_queue<T,vector<T>,greater<T>>;
template<typename T1, typename T2>bool chmin(T1 &a,T2 b){if(a>b){a=b;return true;}else return false;}
template<typename T1, typename T2>bool chmax(T1 &a,T2 b){if(a<b){a=b;return true;}else return false;}
ll median(ll a,ll b, ll c){return a+b+c-max({a,b,c})-min({a,b,c});}
void ans1(bool x){if(x) cout<<"Yes"<<endl;else cout<<"No"<<endl;}
void ans2(bool x){if(x) cout<<"YES"<<endl;else cout<<"NO"<<endl;}
void ans3(bool x){if(x) cout<<"Yay!"<<endl;else cout<<":("<<endl;}
template<typename T1,typename T2>void ans(bool x,T1 y,T2 z){if(x)cout<<y<<endl;else cout<<z<<endl;}  
template<typename T1,typename T2,typename T3>void anss(T1 x,T2 y,T3 z){ans(x!=y,x,z);};  
template<typename T>void debug(const T &v,ll h,ll w,string sv=" "){for(ll i=0;i<h;i++){cout<<v[i][0];for(ll j=1;j<w;j++)cout<<sv<<v[i][j];cout<<endl;}};
template<typename T>void debug(const T &v,ll n,string sv=" "){if(n!=0)cout<<v[0];for(ll i=1;i<n;i++)cout<<sv<<v[i];cout<<endl;};
template<typename T>void debug(const vector<T>&v){debug(v,v.size());}
template<typename T>void debug(const vector<vector<T>>&v){for(auto &vv:v)debug(vv,vv.size());}
template<typename T>void debug(stack<T> st){while(!st.empty()){cout<<st.top()<<" ";st.pop();}cout<<endl;}
template<typename T>void debug(queue<T> st){while(!st.empty()){cout<<st.front()<<" ";st.pop();}cout<<endl;}
template<typename T>void debug(deque<T> st){while(!st.empty()){cout<<st.front()<<" ";st.pop_front();}cout<<endl;}
template<typename T>void debug(PQ<T> st){while(!st.empty()){cout<<st.top()<<" ";st.pop();}cout<<endl;}
template<typename T>void debug(QP<T> st){while(!st.empty()){cout<<st.top()<<" ";st.pop();}cout<<endl;}
template<typename T>void debug(const set<T>&v){for(auto z:v)cout<<z<<" ";cout<<endl;}
template<typename T>void debug(const multiset<T>&v){for(auto z:v)cout<<z<<" ";cout<<endl;}
template<typename T,size_t size>void debug(const array<T, size> &a){for(auto z:a)cout<<z<<" ";cout<<endl;}
template<typename T,typename V>void debug(const map<T,V>&v){for(auto z:v)cout<<"["<<z.first<<"]="<<z.second<<",";cout<<endl;}
template<typename T>vector<vector<T>>vec(ll x, ll y, T w){vector<vector<T>>v(x,vector<T>(y,w));return v;}
ll gcd(ll x,ll y){ll r;while(y!=0&&(r=x%y)!=0){x=y;y=r;}return y==0?x:y;}
vector<ll>dx={1,-1,0,0,1,1,-1,-1};vector<ll>dy={0,0,1,-1,1,-1,1,-1};
template<typename T>vector<T> make_v(size_t a,T b){return vector<T>(a,b);}
template<typename... Ts>auto make_v(size_t a,Ts... ts){return vector<decltype(make_v(ts...))>(a,make_v(ts...));}
template<typename T1, typename T2>ostream &operator<<(ostream &os, const pair<T1, T2>&p){return os << p.first << " " << p.second;}
template<typename T>ostream &operator<<(ostream &os, const vector<T> &v){for(auto &z:v)os << z << " ";cout<<"|"; return os;}
template<typename T>void rearrange(vector<int>&ord, vector<T>&v){
  auto tmp = v;
  for(int i=0;i<tmp.size();i++)v[i] = tmp[ord[i]];
}
template<typename Head, typename... Tail>void rearrange(vector<int>&ord,Head&& head, Tail&&... tail){
  rearrange(ord, head);
  rearrange(ord, tail...);
}
template<typename T> vector<int> ascend(const vector<T>&v){
  vector<int>ord(v.size());iota(ord.begin(),ord.end(),0);
  sort(ord.begin(),ord.end(),[&](int i,int j){return make_pair(v[i],i)<make_pair(v[j],j);});
  return ord;
}
template<typename T> vector<int> descend(const vector<T>&v){
  vector<int>ord(v.size());iota(ord.begin(),ord.end(),0);
  sort(ord.begin(),ord.end(),[&](int i,int j){return make_pair(v[i],-i)>make_pair(v[j],-j);});
  return ord;
}
template<typename T> vector<T> inv_perm(const vector<T>&ord){
  vector<T>inv(ord.size());
  for(int i=0;i<ord.size();i++)inv[ord[i]] = i;
  return inv;
}
ll FLOOR(ll n,ll div){assert(div>0);return n>=0?n/div:(n-div+1)/div;}
ll CEIL(ll n,ll div){assert(div>0);return n>=0?(n+div-1)/div:n/div;}
ll digitsum(ll n){ll ret=0;while(n){ret+=n%10;n/=10;}return ret;}
ll modulo(ll n,ll d){return (n%d+d)%d;};
template<typename T>T min(const vector<T>&v){return *min_element(v.begin(),v.end());}
template<typename T>T max(const vector<T>&v){return *max_element(v.begin(),v.end());}
template<typename T>T acc(const vector<T>&v){return accumulate(v.begin(),v.end(),T(0));};
template<typename T>T reverse(const T &v){return T(v.rbegin(),v.rend());};
//mt19937 mt(chrono::steady_clock::now().time_since_epoch().count());
int popcount(ll x){return __builtin_popcountll(x);};
int poplow(ll x){return __builtin_ctzll(x);};
int pophigh(ll x){return 63 - __builtin_clzll(x);};
template<typename T>T poll(queue<T> &q){auto ret=q.front();q.pop();return ret;};
template<typename T>T poll(priority_queue<T> &q){auto ret=q.top();q.pop();return ret;};
template<typename T>T poll(QP<T> &q){auto ret=q.top();q.pop();return ret;};
template<typename T>T poll(stack<T> &s){auto ret=s.top();s.pop();return ret;};
ll MULT(ll x,ll y){if(LLONG_MAX/x<=y)return LLONG_MAX;return x*y;}
ll POW2(ll x, ll k){ll ret=1,mul=x;while(k){if(mul==LLONG_MAX)return LLONG_MAX;if(k&1)ret=MULT(ret,mul);mul=MULT(mul,mul);k>>=1;}return ret;}
ll POW(ll x, ll k){ll ret=1;for(int i=0;i<k;i++){if(LLONG_MAX/x<=ret)return LLONG_MAX;ret*=x;}return ret;}
template< typename T = int >
struct edge {
  int to;
  T cost;
  int id;
  edge():id(-1){};
  edge(int to, T cost = 1, int id = -1):to(to), cost(cost), id(id){}
  operator int() const { return to; }
};

template<typename T>
using Graph = vector<vector<edge<T>>>;
template<typename T>
Graph<T>revgraph(const Graph<T> &g){
  Graph<T>ret(g.size());
  for(int i=0;i<g.size();i++){
    for(auto e:g[i]){
      int to = e.to;
      e.to = i;
      ret[to].push_back(e);
    }
  }
  return ret;
}
template<typename T>
Graph<T> readGraph(int n,int m,int indexed=1,bool directed=false,bool weighted=false){
  Graph<T> ret(n);
  for(int es = 0; es < m; es++){
    int u,v;
    T w=1;
    cin>>u>>v;u-=indexed,v-=indexed;
    if(weighted)cin>>w;
    ret[u].emplace_back(v,w,es);
    if(!directed)ret[v].emplace_back(u,w,es);
  }
  return ret;
}
template<typename T>
Graph<T> readParent(int n,int indexed=1,bool directed=true){
  Graph<T>ret(n);
  for(int i=1;i<n;i++){
    int p;cin>>p;
    p-=indexed;
    ret[p].emplace_back(i);
    if(!directed)ret[i].emplace_back(p);
  }
  return ret;
}
vector<int>divisor_num(int sz){
  vector<int>ret(sz+1);
  for(int i=1;i<=sz;i++){
    for(int j=i;j<=sz;j+=i){
      ret[j]++;
    }
  }
  return ret;
}

//10^6でも1sくらいかかるので注意、速度が必要ならテーブルを構築せずに処理すべき
vector<vector<int>>divisor_table(int sz){
  vector<vector<int>>ret(sz+1);
  auto dn=divisor_num(sz);
  for(int i=1;i<=sz;i++){
    ret[i].reserve(dn[i]);
  }
  vector<int>idx(sz);
  for(int i=1;i<=sz;i++){
    for(int j=i;j<=sz;j+=i){
      ret[j].push_back(i);
    }
  }
  return ret;
}
template< int mod >
struct ModInt {
  int x;

  ModInt() : x(0) {}

  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

  ModInt &operator+=(const ModInt &p) {
    if((x += p.x) >= mod) x -= mod;
    return *this;
  }

  ModInt &operator-=(const ModInt &p) {
    if((x += mod - p.x) >= mod) x -= mod;
    return *this;
  }

  ModInt &operator*=(const ModInt &p) {
    x = (int) (1LL * x * p.x % mod);
    return *this;
  }

  ModInt &operator/=(const ModInt &p) {
    *this *= p.inverse();
    return *this;
  }

  ModInt operator-() const { return ModInt(-x); }

  friend ModInt operator+(const ModInt& lhs, const ModInt& rhs) {
        return ModInt(lhs) += rhs;
  }
  friend ModInt operator-(const ModInt& lhs, const ModInt& rhs) {
        return ModInt(lhs) -= rhs;
  }
  friend ModInt operator*(const ModInt& lhs, const ModInt& rhs) {
        return ModInt(lhs) *= rhs;
  }
  friend ModInt operator/(const ModInt& lhs, const ModInt& rhs) {
        return ModInt(lhs) /= rhs;
  }

  bool operator==(const ModInt &p) const { return x == p.x; }

  bool operator!=(const ModInt &p) const { return x != p.x; }

  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while(b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }

  ModInt pow(int64_t n) const {
    ModInt ret(1), mul(x);
    while(n > 0) {
      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) {
    int64_t t;
    is >> t;
    a = ModInt< mod >(t);
    return (is);
  }

  static int get_mod() { return mod; }
};

template< typename T >
struct Combination {
  vector< T > _fact, _rfact, _inv;

  Combination(ll sz) : _fact(sz + 1), _rfact(sz + 1), _inv(sz + 1) {
    _fact[0] = _rfact[sz] = _inv[0] = 1;
    for(ll i = 1; i <= sz; i++) _fact[i] = _fact[i - 1] * i;
    _rfact[sz] /= _fact[sz];
    for(ll i = sz - 1; i >= 0; i--) _rfact[i] = _rfact[i + 1] * (i + 1);
    for(ll i = 1; i <= sz; i++) _inv[i] = _rfact[i] * _fact[i - 1];
  }

  inline T fact(ll k) const { return _fact[k]; }

  inline T rfact(ll k) const { return _rfact[k]; }

  inline T inv(ll k) const { return _inv[k]; }

  T P(ll n, ll r) const {
    if(r < 0 || n < r) return 0;
    return fact(n) * rfact(n - r);
  }

  T C(ll p, ll q) const {
    if(q < 0 || p < q) return 0;
    return fact(p) * rfact(q) * rfact(p - q);
  }
  
  T RC(ll p, ll q) const {
    if(q < 0 || p < q) return 0;
    return rfact(p) * fact(q) * fact(p - q);
  }

  T H(ll n, ll r) const {
    if(n < 0 || r < 0) return (0);
    return r == 0 ? 1 : C(n + r - 1, r);
  }
  //+1がn個、-1がm個で prefix sumが常にk以上
  T catalan(ll n,ll m,ll k){
    if(n>m-k)return 0;
    else return C(n+m,m)-C(n+m,n+k-1);
  }
};
using modint = ModInt< MOD9 >;modint pow(ll n, ll x){return modint(n).pow(x);}modint pow(modint n, ll x){return n.pow(x);}
//using modint=ld;
using Comb=Combination<modint>;
vector< bool > prime_table(ll n) {
  vector< bool > prime(n + 1, true);
  if(n >= 0) prime[0] = false;
  if(n >= 1) prime[1] = false;
  for(ll i = 2; i * i <= n; i++) {
    if(!prime[i]) continue;
    for(ll j = i + i; j <= n; j += i) {
      prime[j] = false;
    }
  }
  return prime;
}
/**
 * @brief Moebius Table(メビウス関数テーブル)
 */
vector< int > moebius_table(int n) {
  vector< int > mu(n + 1, 1), p(n + 1, 1);
  for(int i = 2; i <= n; i++) {
    if(p[i] == 1) {
      for(int j = i; j <= n; j += i) p[j] = i;
    }
    if((i / p[i]) % p[i] == 0) mu[i] = 0;
    else mu[i] = -mu[i / p[i]];
  }
  return mu;
}
//前処理はmaxa=10^7で150ms,78MB、10^8で1800ms,780MB程度
struct osa_k{
  ll maxa;
  vector<ll>data;//data[i]:iの最小の素因数
  osa_k(ll a):maxa(a){
    data.assign(maxa+1,1LL);
    build();
  }
  void build(){
    for(ll i=0;i<=maxa;i++)data[i] = i;
    for(ll i=2;i*i<=maxa;i++){
      if(data[i] < i)continue;
      for(ll j=i*i;j<=maxa;j+=i){
        if(data[j] == j)data[j] = i;
      }
    }
  }
  bool isPrime(ll x){
    return (x >= 2)&&(data[x] == x);
  }
  map<ll,ll>factoring(ll x){
    map<ll,ll>ret;
    while(x > 1){
      ret[data[x]]++;
      x /= data[x];
    }
    return ret;
  }
  vector<ll>divisor_enum(ll x){
    auto v = factoring(x);
    vector<ll>ret;
    ret.push_back(1);
    for(auto z:v){
      ll sz = ret.size();
      ll tmp = z.fi;
      for(ll i=0;i<z.se;i++){
        for(ll j=0;j<sz;j++){
          ret.push_back(ret[j] * tmp);
        }
        tmp *= z.fi;
      }
    }
    sort(ret.begin(),ret.end());//なくてもok
    return ret;
  }
};
int main(){
  cin.tie(nullptr);
  ios_base::sync_with_stdio(false);
  ll res=0,buf=0;
  bool judge = true;
  ll n;cin>>n;
  vector<ll>a(n);
  rep(i,0,n)cin>>a[i];
  ll sz=1000005;
  osa_k osak(sz);
  vector<modint>dp(sz);
  auto cf=moebius_table(sz);
  modint all=0;
  rep(i,0,n){
    modint ret=0;
    auto d=osak.divisor_enum(a[i]);
    for(auto z:d){
      if(z==1)continue;
      ret+=dp[z]*cf[z];
      //cout<<z spa cf[z] spa dp[z]<<endl;
    }
    ret=-ret;
    //cout<<ret<<endl;
    ret+=1;
    all+=ret;
    for(auto z:d){
      if(z==1)continue;
      dp[z]+=ret;
    }
  }
  cout<<all<<endl;
  return 0;
}
0