結果

問題 No.1322 Totient Bound
ユーザー maroon_kurimaroon_kuri
提出日時 2020-12-28 18:07:47
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 359 ms / 5,000 ms
コード長 10,163 bytes
コンパイル時間 2,843 ms
コンパイル使用メモリ 231,268 KB
実行使用メモリ 19,104 KB
最終ジャッジ日時 2024-10-03 08:58:31
合計ジャッジ時間 10,187 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge5
このコードへのチャレンジ
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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
testcase_00 AC 18 ms
13,108 KB
testcase_01 AC 18 ms
13,112 KB
testcase_02 AC 18 ms
13,108 KB
testcase_03 AC 18 ms
13,108 KB
testcase_04 AC 18 ms
13,108 KB
testcase_05 AC 19 ms
13,108 KB
testcase_06 AC 19 ms
13,104 KB
testcase_07 AC 17 ms
13,112 KB
testcase_08 AC 16 ms
13,108 KB
testcase_09 AC 15 ms
13,108 KB
testcase_10 AC 17 ms
13,108 KB
testcase_11 AC 17 ms
13,108 KB
testcase_12 AC 16 ms
13,108 KB
testcase_13 AC 16 ms
13,108 KB
testcase_14 AC 18 ms
13,052 KB
testcase_15 AC 16 ms
13,104 KB
testcase_16 AC 17 ms
13,108 KB
testcase_17 AC 17 ms
13,112 KB
testcase_18 AC 89 ms
14,520 KB
testcase_19 AC 127 ms
15,388 KB
testcase_20 AC 274 ms
17,828 KB
testcase_21 AC 304 ms
18,208 KB
testcase_22 AC 306 ms
18,208 KB
testcase_23 AC 356 ms
18,976 KB
testcase_24 AC 354 ms
19,100 KB
testcase_25 AC 355 ms
19,104 KB
testcase_26 AC 355 ms
18,972 KB
testcase_27 AC 356 ms
18,976 KB
testcase_28 AC 359 ms
19,104 KB
testcase_29 AC 358 ms
19,100 KB
testcase_30 AC 18 ms
13,108 KB
testcase_31 AC 16 ms
13,104 KB
testcase_32 AC 16 ms
13,104 KB
testcase_33 AC 355 ms
19,104 KB
testcase_34 AC 356 ms
18,976 KB
testcase_35 AC 359 ms
19,104 KB
testcase_36 AC 359 ms
18,976 KB
testcase_37 AC 355 ms
18,980 KB
testcase_38 AC 355 ms
19,100 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 # 

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

using ll=long long;
#define int ll

#define rng(i,a,b) for(int i=int(a);i<int(b);i++)
#define rep(i,b) rng(i,0,b)
#define gnr(i,a,b) for(int i=int(b)-1;i>=int(a);i--)
#define per(i,b) gnr(i,0,b)
#define pb push_back
#define eb emplace_back
#define a first
#define b second
#define bg begin()
#define ed end()
#define all(x) x.bg,x.ed
#define si(x) int(x.size())
#ifdef LOCAL
#define dmp(x) cerr<<__LINE__<<" "<<#x<<" "<<x<<endl
#else
#define dmp(x) void(0)
#endif

template<class t,class u> bool chmax(t&a,u b){if(a<b){a=b;return true;}else return false;}
template<class t,class u> bool chmin(t&a,u b){if(b<a){a=b;return true;}else return false;}

template<class t> using vc=vector<t>;
template<class t> using vvc=vc<vc<t>>;

using pi=pair<int,int>;
using vi=vc<int>;

template<class t,class u>
ostream& operator<<(ostream& os,const pair<t,u>& p){
	return os<<"{"<<p.a<<","<<p.b<<"}";
}

template<class t> ostream& operator<<(ostream& os,const vc<t>& v){
	os<<"{";
	for(auto e:v)os<<e<<",";
	return os<<"}";
}

#define mp make_pair
#define mt make_tuple
#define one(x) memset(x,-1,sizeof(x))
#define zero(x) memset(x,0,sizeof(x))
#ifdef LOCAL
void dmpr(ostream&os){os<<endl;}
template<class T,class... Args>
void dmpr(ostream&os,const T&t,const Args&... args){
	os<<t<<" ";
	dmpr(os,args...);
}
#define dmp2(...) dmpr(cerr,__LINE__,##__VA_ARGS__)
#else
#define dmp2(...) void(0)
#endif

using uint=unsigned;
using ull=unsigned long long;

template<class t,size_t n>
ostream& operator<<(ostream&os,const array<t,n>&a){
	return os<<vc<t>(all(a));
}

template<int i,class T>
void print_tuple(ostream&,const T&){
}

template<int i,class T,class H,class ...Args>
void print_tuple(ostream&os,const T&t){
	if(i)os<<",";
	os<<get<i>(t);
	print_tuple<i+1,T,Args...>(os,t);
}

template<class ...Args>
ostream& operator<<(ostream&os,const tuple<Args...>&t){
	os<<"{";
	print_tuple<0,tuple<Args...>,Args...>(os,t);
	return os<<"}";
}

template<class t>
void print(t x,int suc=1){
	cout<<x;
	if(suc==1)
		cout<<"\n";
	if(suc==2)
		cout<<" ";
}

ll read(){
	ll i;
	cin>>i;
	return i;
}

vi readvi(int n,int off=0){
	vi v(n);
	rep(i,n)v[i]=read()+off;
	return v;
}

pi readpi(int off=0){
	int a,b;cin>>a>>b;
	return pi(a+off,b+off);
}

template<class t,class u>
void print(const pair<t,u>&p,int suc=1){
	print(p.a,2);
	print(p.b,suc);
}

template<class T>
void print(const vector<T>&v,int suc=1){
	rep(i,v.size())
		print(v[i],i==int(v.size())-1?suc:2);
}

string readString(){
	string s;
	cin>>s;
	return s;
}

template<class T>
T sq(const T& t){
	return t*t;
}

//#define CAPITAL
void yes(bool ex=true){
	#ifdef CAPITAL
	cout<<"YES"<<"\n";
	#else
	cout<<"Yes"<<"\n";
	#endif
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}
void no(bool ex=true){
	#ifdef CAPITAL
	cout<<"NO"<<"\n";
	#else
	cout<<"No"<<"\n";
	#endif
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}
void possible(bool ex=true){
	#ifdef CAPITAL
	cout<<"POSSIBLE"<<"\n";
	#else
	cout<<"Possible"<<"\n";
	#endif
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}
void impossible(bool ex=true){
	#ifdef CAPITAL
	cout<<"IMPOSSIBLE"<<"\n";
	#else
	cout<<"Impossible"<<"\n";
	#endif
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}

constexpr ll ten(int n){
	return n==0?1:ten(n-1)*10;
}

const ll infLL=LLONG_MAX/3;

#ifdef int
const int inf=infLL;
#else
const int inf=INT_MAX/2-100;
#endif

int topbit(signed t){
	return t==0?-1:31-__builtin_clz(t);
}
int topbit(ll t){
	return t==0?-1:63-__builtin_clzll(t);
}
int botbit(signed a){
	return a==0?32:__builtin_ctz(a);
}
int botbit(ll a){
	return a==0?64:__builtin_ctzll(a);
}
int popcount(signed t){
	return __builtin_popcount(t);
}
int popcount(ll t){
	return __builtin_popcountll(t);
}
bool ispow2(int i){
	return i&&(i&-i)==i;
}
ll mask(int i){
	return (ll(1)<<i)-1;
}

bool inc(int a,int b,int c){
	return a<=b&&b<=c;
}

template<class t> void mkuni(vc<t>&v){
	sort(all(v));
	v.erase(unique(all(v)),v.ed);
}

ll rand_int(ll l, ll r) { //[l, r]
	#ifdef LOCAL
	static mt19937_64 gen;
	#else
	static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());
	#endif
	return uniform_int_distribution<ll>(l, r)(gen);
}

template<class t>
void myshuffle(vc<t>&a){
	rep(i,si(a))swap(a[i],a[rand_int(0,i)]);
}

template<class t>
int lwb(const vc<t>&v,const t&a){
	return lower_bound(all(v),a)-v.bg;
}

vvc<int> readGraph(int n,int m){
	vvc<int> g(n);
	rep(i,m){
		int a,b;
		cin>>a>>b;
		//sc.read(a,b);
		a--;b--;
		g[a].pb(b);
		g[b].pb(a);
	}
	return g;
}

vvc<int> readTree(int n){
	return readGraph(n,n-1);
}

int gcd(int a,int b){return b?gcd(b,a%b):a;}

template<class t>
t pow_mod(t x,t n,t m){
	t r=1;
	while(n){
		if(n&1)r=(r*x)%m;
		x=(x*x)%m;
		n>>=1;
	}
    return r;
}

bool is_prime(ll n) {
    if (n <= 1) return false;
    if (n == 2) return true;
    if (n % 2 == 0) return false;
    ll d = n - 1;
    while (d % 2 == 0) d /= 2;
    for (ll a : {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}) {
        if (n <= a) break;
        ll t = d;
        ll y = pow_mod<__int128_t>(a, t, n);  // over
        while (t != n - 1 && y != 1 && y != n - 1) {
            y = __int128_t(y) * y % n;  // flow
            t <<= 1;
        }
        if (y != n - 1 && t % 2 == 0) {
            return false;
        }
    }
    return true;
}

ll pollard_single(ll n) {
    auto f = [&](ll x) { return (__int128_t(x) * x + 1) % n; };
    if (is_prime(n)) return n;
    if (n % 2 == 0) return 2;
    ll st = 0;
    while (true) {
        st++;
        ll x = st, y = f(x);
        while (true) {
            ll p = gcd((y - x + n), n);
            if (p == 0 || p == n) break;
            if (p != 1) return p;
            x = f(x);
            y = f(f(y));
        }
    }
}

vc<ll> pollard(ll n) {
    if (n == 1) return {};
    ll x = pollard_single(n);
    if (x == n) return {x};
    vc<ll> le = pollard(x);
    vc<ll> ri = pollard(n / x);
    le.insert(le.end(), ri.begin(), ri.end());
    return le;
}

ll primitive_root(ll p) {
    auto v = pollard(p - 1);
    //while (true) {
    //    ll g = rand_int(1, p - 1);  //[1, p-1]
    rng(g,4,p){
        bool ok = true;
        for (auto d : v) {
            ll f = (p - 1) / d;
            if (pow_mod<__int128_t>(g, f, p) == 1) {
                ok = false;
                break;
            }
        }
        if (ok) return g;
    }
    assert(0);
}

vc<pi> to_freq(vi a){
	sort(all(a));
	vc<pi> res;
	for(auto v:a){
		if(res.empty()||res.back().a!=v)res.eb(v,0);
		res.back().b++;
	}
	return res;
}

vi enum_divs(int n){
	auto f=to_freq(pollard(n));
	dmp(f);
	
	vi res;
	auto rec=[&](auto self,int i,int d)->void{
		if(i==si(f))res.pb(d);
		else{
			rep(_,f[i].b+1){
				self(self,i+1,d);
				d*=f[i].a;
			}
		}
	};
	rec(rec,0,1);
	
	return res;
}

const int vmax=ten(6)+10;
bool pri[vmax];
vi ps;
int sf[vmax]; //smallest factor, sf[1] is undefined(0)
void linear_sieve(){
	rng(i,2,vmax)
		pri[i]=1;
	rng(i,2,vmax){
		if(pri[i]){
			ps.pb(i);
			sf[i]=i;
		}
		for(int j=0;i*ps[j]<vmax;j++){
			pri[i*ps[j]]=0;
			sf[i*ps[j]]=ps[j];
			if(i%ps[j]==0)break;
		}
	}
}

//手元でテストしたら 10^18 まで大丈夫そうだった
ll isqrt(ll n){
	return sqrtl(n);
}
ll icbrt(ll n){
	return cbrtl(n);
}

const ull mask64=-1;

pair<ull,bool> pow_cap(ull a,int n){
	if(a==0)return make_pair(0,0);
	bool over=false;
	auto mult=[&](ull x,ull y){
		if(x<=mask64/y)return x*y;
		else{
			over=true;
			return mask64;
		}
	};
	ull res=1;
	while(n){
		if(n&1)res=mult(res,a);
		n>>=1;
		if(n)a=mult(a,a);
	}
	return make_pair(res,over);
}

//yosupo kth root integer
//0<=a<2^64
ull kth_root_integer(ull a,int k){
	if(a==0)return 0;
	ull z=min((ull)powl(a,(long double)1/k),mask64);
	while(1){
		auto w=pow_cap(z,k);
		if(w.a>a||w.b)z--;
		else break;
	}
	while(z<mask64){
		auto w=pow_cap(z+1,k);
		if(w.a<=a&&!w.b)z++;
		else break;
	}
	return z;
}

//initprime
//kth_root_integer

//VERIFY:yosupo
//pi(n/i) 列挙
//sum[i] = pi(vs[i])
//O(N^(2/3))
//N=10^11, 297ms on yosupo judge 
//D=int Xmas2019 D
template<class D=int>
struct counting_primes{
	const int n,n2,n3,n6;
	int s;
	vi vs,sum,bit;
	int pre;
	void trans(int i,int p){
		int j=getidx(vs[i]/p);
		sum[i]-=sum[j]-pre;
	}
	void trans2(int i,int p){
		int j=getidx(vs[i]/p);
		int z=sum[j];
		if(j>=n3){
			j-=n3;
			for(;j<si(bit);j+=(j+1)&(-j-1))
				z+=bit[j];
		}
		sum[i]-=z-pre;
	}
	void upd(int i,int cur,bool f){
		if(!f){
			for(int x=getidx(cur)-n3;x>=0;x-=(x+1)&(-x-1))
				bit[x]--;
		}
		for(int j=i;cur*ps[j]<=vs[n3];j++)
			upd(j,cur*ps[j],false);
	}
	counting_primes(int nn):n(nn),n2(isqrt(n)),n3(icbrt(n)),n6(kth_root_integer(n,6)){
		{
			int v=n;
			while(v){
				vs.pb(v);
				v=n/(n/v+1);
			}
		}
		s=vs.size();
		
		sum.resize(s);
		rep(i,s)sum[i]=vs[i]-1;
		
		int idx=0;
		pre=0;
		{
			while(ps[idx]<=n6){
				rep(i,s){
					if(sq(ps[idx])>vs[i])break;
					trans(i,ps[idx]);
				}
				pre++;
				idx++;
			}
		}
		{
			bit.resize(s-n3);
			while(ps[idx]<=n3){
				rep(i,n3){
					if(sq(ps[idx])>vs[i])break;
					trans2(i,ps[idx]);
				}
				assert(ps[idx]<=vs[n3]);
				upd(idx,ps[idx],true);
				pre++;
				idx++;
			}
			per(i,s-n3){
				int j=i+((i+1)&(-i-1));
				if(j<si(bit))
					bit[i]+=bit[j];
			}
			rep(i,s-n3){
				sum[i+n3]+=bit[i];
			}
		}
		{
			while(ps[idx]<=n2){
				rep(i,s){
					if(sq(ps[idx])>vs[i])break;
					trans(i,ps[idx]);
				}
				pre++;
				idx++;
			}
		}
	}
	
	vc<D> buf;
	D ans;
	D multiplicative_sum(){
		buf.resize(s);
		rep(i,s){
			buf[i]=sum[i];
			if(is_prime(vs[i]+1))buf[i]++;
		}
		
		ans=1+buf[0];
		
		rep(i,si(ps))if((ps[i])*(ps[i]-1)<=n)dfs(i,n/(ps[i]-1));else break;
		
		return ans;
	}
	void dfs(int i,int lim){
		//assert(ps[i]<=lim);
		ans++;
		if(lim>=sq(ps[i]))dfs(i,lim/ps[i]);
		ans+=buf[getidx(lim)]-buf[getidx(ps[i]-1)];
		for(int j=i+1;(ps[j])*(ps[j]-1)<=lim;j++)
			dfs(j,lim/(ps[j]-1));
	}
	
	int getidx(int a){
		return a<=n2?s-a:n/a-1;
	}
};

void slv(){
	int n;cin>>n;
	counting_primes<int> cp(n);
	print(cp.multiplicative_sum());
}

signed main(){
	cin.tie(0);
	ios::sync_with_stdio(0);
	cout<<fixed<<setprecision(20);
	
	linear_sieve();
	
	//int t;cin>>t;rep(_,t)
	slv();
}
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