結果

問題 No.1653 Squarefree
ユーザー eQeeQe
提出日時 2024-10-21 23:12:10
言語 C++23
(gcc 12.3.0 + boost 1.83.0)
結果
TLE  
実行時間 -
コード長 9,337 bytes
コンパイル時間 7,143 ms
コンパイル使用メモリ 336,952 KB
実行使用メモリ 343,640 KB
最終ジャッジ日時 2024-10-21 23:12:24
合計ジャッジ時間 13,392 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge1
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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
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ソースコード

diff # 

#include<bits/stdc++.h>
#include<atcoder/all>
namespace my{
#define eb emplace_back
#define LL(...) ll __VA_ARGS__;lin(__VA_ARGS__)
#define FO(n) for(ll ij=n;ij--;)
#define FOR(i,...) for(auto[i,i##stop,i##step]=range(0,__VA_ARGS__);i<i##stop;i+=i##step)
#define fo(i,...) FO##__VA_OPT__(R)(i __VA_OPT__(,__VA_ARGS__))
#define of(i,...) for(auto[i,i##stop,i##step]=range(1,__VA_ARGS__);i>=i##stop;i-=i##step)
#define fe(a,i,...) for(auto&&__VA_OPT__([)i __VA_OPT__(,__VA_ARGS__]):a)
#define quotient_range_fe(n,y,l,r) for(ll _n=n,y,l,r=1;(y=_n/(l=r))&&(r=_n/y+1);)
#define single_testcase void solve();}int main(){my::io();my::solve();}namespace my{
using namespace std;
void io(){cin.tie(nullptr)->sync_with_stdio(0);cout<<fixed<<setprecision(15);}
using ll=long long;
using ull=unsigned long long;
using ulll=__uint128_t;
using lll=__int128_t;
istream&operator>>(istream&i,ulll&x){ull t;i>>t;x=t;return i;}
ostream&operator<<(ostream&o,const ulll&x){return(x<10?o:o<<x/10)<<ll(x%10);}
istream&operator>>(istream&i,lll&x){ll t;i>>t;x=t;return i;}
ostream&operator<<(ostream&o,const lll&x){return o<<string(x<0,'-')<<ulll(x>0?x:-x);}
auto range(bool s,ll a,ll b=1e18,ll c=1){if(b==1e18)b=a,(s?b:a)=0;return array{a-s,b,c};}
constexpr char nl=10;
constexpr char sp=32;
lll pw(lll x,ll n,ll m=0){assert(n>=0);lll r=1;while(n)n&1?r*=x:r,x*=x,m?r%=m,x%=m:r,n>>=1;return r;}

template<class A,class B>struct pair{
  A a;B b;
  pair()=default;
  pair(A a,B b):a(a),b(b){}
  pair(const std::pair<A,B>&p):a(p.first),b(p.second){}
  auto operator<=>(const pair&)const=default;
  friend ostream&operator<<(ostream&o,const pair&p){return o<<p.a<<sp<<p.b;}
};

template<class F=less<>>auto&sort(auto&a,const F&f={}){ranges::sort(a,f);return a;}

template<class T,class U>ostream&operator<<(ostream&o,const std::pair<T,U>&p){return o<<p.first<<sp<<p.second;}

template<class V>concept vectorial=is_base_of_v<vector<typename V::value_type>,V>;
template<class T>struct core_type{using type=T;};
template<vectorial V>struct core_type<V>{using type=typename core_type<typename V::value_type>::type;};
template<class T>using core_t=core_type<T>::type;
template<class V>istream&operator>>(istream&i,vector<V>&v){fe(v,e)i>>e;return i;}
template<class V>ostream&operator<<(ostream&o,const vector<V>&v){fe(v,e)o<<e<<string(&e!=&v.back(),vectorial<V>?nl:sp);return o;}

template<class V>struct vec:vector<V>{
  using vector<V>::vector;
  vec(const vector<V>&v){vector<V>::operator=(v);}

  vec&operator^=(const vec&u){this->insert(this->end(),u.begin(),u.end());return*this;}
  vec operator^(const vec&u)const{return vec{*this}^=u;}
  vec&operator++(){fe(*this,e)++e;return*this;}
  vec&operator--(){fe(*this,e)--e;return*this;}

  auto scan(const auto&f)const{pair<core_t<V>,bool>r{};fe(*this,e)if constexpr(!vectorial<V>)r.b?f(r.a,e),r:r={e,1};else if(auto s=e.scan(f);s.b)r.b?f(r.a,s.a),r:r=s;return r;}
  auto sum()const{return scan([](auto&a,const auto&b){a+=b;}).a;}
  vec zeta()const{vec v=*this;if constexpr(vectorial<V>)fe(v,e)e=e.zeta();fo(i,v.size()-1)v[i+1]+=v[i];return v;}
  vec mobius()const{vec v=*this;if constexpr(vectorial<V>)fe(v,e)e=e.mobius();of(i,v.size()-1)v[i+1]-=v[i];return v;}
};

template<bool is_negative=false>struct infinity{
  template<integral T>constexpr operator T()const{return numeric_limits<T>::max()*(1-is_negative*2);}
  template<floating_point T>constexpr operator T()const{return static_cast<ll>(*this);}
  template<class T>constexpr bool operator==(T x)const{return static_cast<T>(*this)==x;}
  constexpr auto operator-()const{return infinity<!is_negative>();}
  template<class A,class B>constexpr operator pair<A,B>()const{return pair<A,B>{*this,*this};}
};
constexpr infinity oo;

void lin(auto&...a){(cin>>...>>a);}
template<char c=sp>void pp(const auto&...a){ll n=sizeof...(a);((cout<<a<<string(--n>0,c)),...);cout<<nl;}

template<class T,class U=T>auto rle(const vec<T>&a){vec<pair<T,U>>r;fe(a,e)r.size()&&e==r.back().a?++r.back().b:r.eb(e,1).b;return r;}
template<class T,class U=T>auto rce(vec<T>a){return rle<T,U>(sort(a));}

uint64_t kth_root_floor(uint64_t a,ll k){
  if (k==1)return a;
  auto is_within=[&](uint32_t x){uint64_t t=1;fo(k)if(__builtin_mul_overflow(t,x,&t))return false;return t<=a;};

  uint64_t r=0;
  of(i,sizeof(uint32_t)*CHAR_BIT)if(is_within(r|(1u<<i)))r|=1u<<i;
  return r;
}

ll sqrt_floor(ll x){return kth_root_floor(x,2);}

ll rand(ll l=oo,ll r=oo){if(l!=oo&&r==oo)r=l,l=0;static ll a=495;a^=a<<7,a^=a>>9;ll t=a;return l<r?((t%=(r-l))<0?t+r-l:t)+l:a;}

struct montgomery64{
  using i64=__int64_t;
  using u64=__uint64_t;
  using u128=__uint128_t;

  static inline u64 N=998244353;
  static inline u64 N_inv;
  static inline u64 R2;

  static void set_mod(u64 N){
    assert(N<(1ULL<<63));
    assert(N&1);
    montgomery64::N=N;
    R2=-u128(N)%N;
    N_inv=N;
    fo(5)N_inv*=2-N*N_inv;
    assert(N*N_inv==1);
  }

  static u64 mod(){
    return N;
  }

  u64 a;
  montgomery64(const i64&a=0):a(reduce((u128)(a%(i64)N+N)*R2)){}

  static u64 reduce(const u128&T){
    u128 r=(T+u128(u64(T)*-N_inv)*N)>>64;
    return r>=N?r-N:r;
  }

  auto&operator+=(const montgomery64&b){if((a+=b.a)>=N)a-=N;return*this;}
  auto&operator-=(const montgomery64&b){if(i64(a-=b.a)<0)a+=N;return*this;}
  auto&operator*=(const montgomery64&b){a=reduce(u128(a)*b.a);return*this;}
  auto&operator/=(const montgomery64&b){*this*=b.inv();return*this;}

  auto operator+(const montgomery64&b)const{return montgomery64(*this)+=b;}
  auto operator-(const montgomery64&b)const{return montgomery64(*this)-=b;}
  auto operator*(const montgomery64&b)const{return montgomery64(*this)*=b;}
  auto operator/(const montgomery64&b)const{return montgomery64(*this)/=b;}
  bool operator==(const montgomery64&b)const{return a==b.a;}
  auto operator-()const{return montgomery64()-montgomery64(*this);}

  montgomery64 pow(u128 n)const{
    montgomery64 r{1},x{*this};
    while(n){
      if(n&1)r*=x;
      x*=x;
      n>>=1;
    }
    return r;
  }

  montgomery64 inv()const{
    u64 a=this->a,b=N,u=1,v=0;
    while(b)u-=a/b*v,swap(u,v),a-=a/b*b,swap(a,b);
    return u;
  }

  u64 val()const{
    return reduce(a);
  }

  friend istream&operator>>(istream&i,montgomery64&b){
    ll t;i>>t;b=t;
    return i;
  }

  friend ostream&operator<<(ostream&o,const montgomery64&b){
    return o<<b.val();
  }
};

template<class modular>bool miller_rabin(ll n,vec<ll>as){
  ll d=n-1;
  while(~d&1)d>>=1;

  if((ll)modular::mod()!=n)modular::set_mod(n);
  modular one=1,minus_one=n-1;
  fe(as,a){
    if(a%n==0)continue;
    ll t=d;
    modular y=modular(a).pow(t);
    while(t!=n-1&&y!=one&&y!=minus_one)y*=y,t<<=1;
    if(y!=minus_one&&~t&1)return 0;
  }
  return 1;
}

bool is_prime(ll n){
  if(~n&1)return n==2;
  if(n<=1)return 0;
  if(n<4759123141LL)return miller_rabin<montgomery64>(n,{2,7,61});
  return miller_rabin<montgomery64>(n,{2,325,9375,28178,450775,9780504,1795265022});
}

template<class modular>ll pollard_rho(ll n){
  if(~n&1)return 2;
  if(is_prime(n))return n;
  if((ll)modular::mod()!=n)modular::set_mod(n);
  modular R,one=1;
  auto f=[&](const modular&x){return x*x+R;};
  while(1){
    modular x,y,ys,q=one;
    R=rand(2,n),y=rand(2,n);
    ll g=1;
    constexpr ll m=128;
    for(ll r=1;g==1;r<<=1){
      x=y;
      fo(r)y=f(y);
      for(ll k=0;g==1&&k<r;k+=m){
        ys=y;
        for(ll i=0;i<m&&i<r-k;++i)q*=x-(y=f(y));
        g=std::gcd(q.val(),n);
      }
    }
    if(g==n)do g=std::gcd((x-(ys=f(ys))).val(),n);while(g==1);
    if(g!=n)return g;
  }
}

auto factorize(ll n){
  auto f=[](auto&f,ll m){
    if(m==1)return vec<ll>{};
    ll d=pollard_rho<montgomery64>(m);
    return d==m?vec<ll>{d}:f(f,d)^f(f,m/d);
  };
  return rce(f(f,n));
}

ll mobius_prime_pow(ll,int8_t k,ll){return-(k==1);}

ll mobius(ll n){ll r=1;fe(factorize(n),p,q)r*=mobius_prime_pow(p,q,pw(p,q));return r;}

struct linear_sieve{
  ll n;
  vec<int>lpf;
  vec<int8_t>lpf_ord;
  vec<int>lpf_pow;
  vec<int>lpf_pow_except;
  vec<int>primes;
  linear_sieve(ll n):n(n){
    lpf.resize(n+1,-1);
    lpf_ord.resize(n+1);
    lpf_pow.resize(n+1);
    lpf_pow_except.resize(n+1);
    lpf[1]=lpf_ord[1]=lpf_pow[1]=lpf_pow_except[1]=1;

    fo(i,2,n+1){
      if(lpf[i]==-1)primes.eb(lpf[i]=i);

      fe(primes,p){
        if(p*i>n||p>lpf[i])break;
        lpf[p*i]=p;
      }

      ll j=i/lpf[i];
      lpf_ord[i]=lpf_ord[j]*(lpf[i]==lpf[j])+1;
      lpf_pow[i]=((lpf_pow[j]-1)*(lpf[i]==lpf[j])+1)*lpf[i];
      lpf_pow_except[i]=i/lpf_pow[i];
    }
  }

  auto multiplicative_function_enumerate(const auto&f)const{
    vec<ll>r(n+1);
    r[1]=1;
    fo(i,2,n+1)r[i]=f(lpf[i],lpf_ord[i],lpf_pow[i])*r[lpf_pow_except[i]];
    return r;
  }

  auto mobius_enumerate()const{return multiplicative_function_enumerate(mobius_prime_pow);}
};

ll square_free_count(ll n){
  ll I=kth_root_floor(n,5);
  ll x_I=sqrt_floor(n/I);

  auto mobius=linear_sieve(x_I).mobius_enumerate();
  auto mertens=mobius.zeta();

  ll S1=0;
  fo(i,1,x_I+1)S1+=mobius[i]*(n/(i*i));

  vec<ll>mertens_x(I);
  of(i,I,1){
    mertens_x[i]=1;
    quotient_range_fe(sqrt_floor(n/i),y,l,r){
      if(l==1)continue;
      mertens_x[i]-=(y<=x_I?mertens[y]:mertens_x[l*l*i])*(r-l);
    }
  }
  ll S2=mertens_x.sum()-(I-1)*mertens[x_I];
  return S1+S2;
}

single_testcase
void solve(){
  LL(L,R);++R;
  pp(square_free_count(R-1)-square_free_count(L-1));
}}
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