noya2_Library

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:heavy_check_mark: test/math/CountingPrimes.test.cpp

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/counting_primes"

#include"../../template/template.hpp"
#include"../../math/prime_count.hpp"

int main(){
    ll n; in(n);
    out(prime_count(n));
}
#line 1 "test/math/CountingPrimes.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/counting_primes"

#line 2 "template/template.hpp"
using namespace std;

#include<bits/stdc++.h>
#line 1 "template/inout_old.hpp"
namespace noya2 {

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){
    int s = (int)v.size();
    for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
    return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v){
    for (auto &x : v) is >> x;
    return is;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &...u){
    cin >> t;
    in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u){
    cout << t;
    if (sizeof...(u)) cout << sep;
    out(u...);
}

template<typename T>
void out(const vector<vector<T>> &vv){
    int s = (int)vv.size();
    for (int i = 0; i < s; i++) out(vv[i]);
}

struct IoSetup {
    IoSetup(){
        cin.tie(nullptr);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(15);
        cerr << fixed << setprecision(7);
    }
} iosetup_noya2;

} // namespace noya2
#line 1 "template/const.hpp"
namespace noya2{

const int iinf = 1'000'000'007;
const long long linf = 2'000'000'000'000'000'000LL;
const long long mod998 =  998244353;
const long long mod107 = 1000000007;
const long double pi = 3.14159265358979323;
const vector<int> dx = {0,1,0,-1,1,1,-1,-1};
const vector<int> dy = {1,0,-1,0,1,-1,-1,1};
const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const string alp = "abcdefghijklmnopqrstuvwxyz";
const string NUM = "0123456789";

void yes(){ cout << "Yes\n"; }
void no(){ cout << "No\n"; }
void YES(){ cout << "YES\n"; }
void NO(){ cout << "NO\n"; }
void yn(bool t){ t ? yes() : no(); }
void YN(bool t){ t ? YES() : NO(); }

} // namespace noya2
#line 2 "template/utils.hpp"

#line 6 "template/utils.hpp"

namespace noya2{

unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){
    if (a == 0 || b == 0) return a + b;
    int n = __builtin_ctzll(a); a >>= n;
    int m = __builtin_ctzll(b); b >>= m;
    while (a != b) {
        int mm = __builtin_ctzll(a - b);
        bool f = a > b;
        unsigned long long c = f ? a : b;
        b = f ? b : a;
        a = (c - b) >> mm;
    }
    return a << std::min(n, m);
}

template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(std::abs(a),std::abs(b))); }

long long sqrt_fast(long long n) {
    if (n <= 0) return 0;
    long long x = sqrt(n);
    while ((x + 1) * (x + 1) <= n) x++;
    while (x * x > n) x--;
    return x;
}

template<typename T> T floor_div(const T n, const T d) {
    assert(d != 0);
    return n / d - static_cast<T>((n ^ d) < 0 && n % d != 0);
}

template<typename T> T ceil_div(const T n, const T d) {
    assert(d != 0);
    return n / d + static_cast<T>((n ^ d) >= 0 && n % d != 0);
}

template<typename T> void uniq(std::vector<T> &v){
    std::sort(v.begin(),v.end());
    v.erase(unique(v.begin(),v.end()),v.end());
}

template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; }

template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; }

template<typename T> inline bool range(T l, T x, T r){ return l <= x && x < r; }

} // namespace noya2
#line 8 "template/template.hpp"

#define rep(i,n) for (int i = 0; i < (int)(n); i++)
#define repp(i,m,n) for (int i = (m); i < (int)(n); i++)
#define reb(i,n) for (int i = (int)(n-1); i >= 0; i--)
#define all(v) (v).begin(),(v).end()

using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
using pil = pair<int,ll>;
using pli = pair<ll,int>;

namespace noya2{

/*　~ (. _________ . /)　*/

}

using namespace noya2;


#line 2 "math/prime_count.hpp"

#line 5 "math/prime_count.hpp"

namespace noya2 {

// ref : https://judge.yosupo.jp/submission/182619

// #{p : prime | p <= n}. n <= 10^13
long long prime_count(long long n){
    struct S {
        int rough;
        long long large;
        int id;
    };
    if (n <= 1) return 0;
    const int v = static_cast<int>(sqrtl(n));
    int pc = 0;
    std::vector<int> smalls(v + 1);
    for (int i = 2; i <= v; i++){
        smalls[i] = (i + 1) / 2;
    }
    std::vector<int> skip(v + 1, false);
    std::vector<S> z((v + 1) / 2);
    for (int i = 0; i < (v + 1) / 2; i++){
        z[i] = {2 * i + 1, (n / (2 * i + 1) + 1) / 2, i};
    }
    for (int p = 3; p <= v; p++){
        if (smalls[p] <= smalls[p - 1]) continue;
        const int q = p * p;
        pc++;
        if (1LL * q * q > n) break;
        skip[p] = true;
        for (int i = q; i <= v; i += 2 * p){
            skip[i] = true;
        }
        int ns = 0;
        for (auto e : z){
            if (skip[e.rough]) continue;
            long long d = 1LL * e.rough * p;
            e.large += pc - (d <= v ? z[smalls[d] - pc].large : smalls[n / d]);
            e.id = ns;
            z[ns++] = e;
        }
        z.resize(ns);
        for (int j = v / p; j >= p; --j){
            const int c = smalls[j] - pc, e = std::min(j * p + p, v + 1);
            for (int i = j * p; i < e; i++){
                smalls[i] -= c;
            }
        }
    }
    long long ans = z[0].large;
    z.erase(z.begin());
    for (auto &[rough, large, k] : z){
        const long long m = n / rough;
        k--;
        ans -= large - (pc + k);
        for (auto [p, _, l] : z){
            if (l >= k || p * p > m) break;
            ans += smalls[m / p] - (pc + l);
        }
    }
    return ans;
}

} // namespace noya2
#line 5 "test/math/CountingPrimes.test.cpp"

int main(){
    ll n; in(n);
    out(prime_count(n));
}
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