NumberTheory/Enumerate_primes.test.cpp

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• Last update: 2025-06-11 15:37:14+07:00
• Problem: https://judge.yosupo.jp/problem/enumerate_primes

Depends on

• NumberTheory/Math/CheckPrime.h
• NumberTheory/Math/Sieve.h
• template.h

Code

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

#include "../template.h"
#include "Math/CheckPrime.h"
#include "Math/Sieve.h"

void solve() {
    int n, a, b; cin >> n >> a >> b;
    ll cnt_pi = Meissel(n);
    
    int lim = 1e6;
    vector<int> need;
    int i = 0;
    while (a*i + b <= n && (int)need.size() < lim) {
        need.push_back(a*i+b);
        i++;
    }

    vector<int> prime = listPrime(0, lim);
    vector<int> res;
    int cnt = 0, idx = 0;
    for (int l = 2; l <= n; l += lim) {
        int r = min(l + lim - 1, n);
        vector<int> isPrime(r - l + 1, 1);
        for (int p : prime) {
            ll low = max(1ll*p*p, 1ll*(l+p-1)/p*p);
            for (ll j = low; j <= r; j += p) {
                if (j-l >= 0) isPrime[j-l] = 0;
            }
        }
        // vector<int> isPrime = segmentSieve(l, r);

        for (int p = l; p <= min(r, n); p++) {
            if (!isPrime[p-l]) continue;
            if (cnt == need[idx]) {
                res.push_back(p);
                idx++;
            }
            cnt++;
            if (idx == (int)need.size()) break;
        }

        if (idx == (int)need.size()) break;
    }

    cout << cnt_pi << ' ' << res.size() << '\n';
    for (int x : res) cout << x << ' ';
}

#line 1 "NumberTheory/Enumerate_primes.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/enumerate_primes"

#line 2 "template.h"

#include <bits/stdc++.h>
using namespace std;
 
#define ll long long
#define MOD (ll)(1e9+7)
#define all(x) (x).begin(),(x).end()
#define unique(x) x.erase(unique(all(x)), x.end())
#define INF32 ((1ull<<31)-1)
#define INF64 ((1ull<<63)-1)
#define inf (ll)1e18

#define vi vector<int>
#define pii pair<int, int>
#define pll pair<ll, ll>
#define fi first
#define se second

const int mod = 998244353;

void solve();

int main(){
    ios_base::sync_with_stdio(false);cin.tie(NULL);
    // cin.exceptions(cin.failbit);
    // int t; cin >> t;
    // while(t--)
        solve();
    cerr << "\nTime run: " << 1000 * clock() / CLOCKS_PER_SEC << "ms" << '\n';
    return 0;
}
#line 2 "NumberTheory/Math/CheckPrime.h"


bool BruteForce(ll n) {
    if (n == 2 || n == 3) return true;
    if (n <= 1 || n % 2 == 0 || n % 3 == 0) return false;
    for (ll i = 5; i * i <= n; i += 6)
        if (n % i == 0 || n % (i+2) == 0)
            return false;
    return true;
}

// https://codeforces.com/blog/entry/91632
ll Meissel(ll n) {
    vector<ll> v;
    for (ll i = 1; i*i <= n; i++) {
        v.push_back(i);
        v.push_back(n / i);
    }
    sort(all(v));
    unique(v);
    ll sq = sqrt(n);
    auto geti = [&](ll x) {
        if (x <= sq) return x-1;
        return (int)v.size() - n / x;
    };
    vector<ll> dp = v;
    ll a = 0;
    for (ll p = 2; p*p <= n; p++) {
        if (dp[geti(p)] == dp[geti(p-1)]) continue;
        a++;
        for (int i = (int)v.size()-1; i >= 0; i--) {
            if (v[i] < p * p) break;
            dp[i] -= dp[geti(v[i] / p)] - a;
        }
    }
    return dp[geti(n)] - 1;
}
#line 2 "NumberTheory/Math/Sieve.h"

vector<int> sieve(int n) {
    vector<int> nt(n+1, 1);
    nt[0] = nt[1] = 0;
    for (int i = 2; i * i <= n; i++) {
        if (!nt[i]) continue;
        for (int j = i * i; j <= n; j += i)
            nt[j] = 0;
    }
    return nt;
}

vector<int> segmentSieve(int l, int r){
    vector<int> prime(r-l+1, 1);
    for(ll p = 2; p*p <= r; p++){
        ll lim = max(p*p, (l+p-1)/p*p);
        for(ll j = lim; j <= r; j += p)
            if (j-l >= 0) prime[j-l] = 0;
    }
    if (l == 0) prime[0] = 0;
    if (l == 0 && r > l) prime[1] = 0;
    if (l == 1) prime[1-l] = 0;
    return prime;
}

vector<int> listPrime(int l, int r) {
    vector<int> prime = segmentSieve(l, r);
    vector<int> listPi;
    for (int i = l; i <= r; i++) {
        if (prime[i-l]) listPi.push_back(i);
    }
    return listPi;
}
#line 6 "NumberTheory/Enumerate_primes.test.cpp"

void solve() {
    int n, a, b; cin >> n >> a >> b;
    ll cnt_pi = Meissel(n);
    
    int lim = 1e6;
    vector<int> need;
    int i = 0;
    while (a*i + b <= n && (int)need.size() < lim) {
        need.push_back(a*i+b);
        i++;
    }

    vector<int> prime = listPrime(0, lim);
    vector<int> res;
    int cnt = 0, idx = 0;
    for (int l = 2; l <= n; l += lim) {
        int r = min(l + lim - 1, n);
        vector<int> isPrime(r - l + 1, 1);
        for (int p : prime) {
            ll low = max(1ll*p*p, 1ll*(l+p-1)/p*p);
            for (ll j = low; j <= r; j += p) {
                if (j-l >= 0) isPrime[j-l] = 0;
            }
        }
        // vector<int> isPrime = segmentSieve(l, r);

        for (int p = l; p <= min(r, n); p++) {
            if (!isPrime[p-l]) continue;
            if (cnt == need[idx]) {
                res.push_back(p);
                idx++;
            }
            cnt++;
            if (idx == (int)need.size()) break;
        }

        if (idx == (int)need.size()) break;
    }

    cout << cnt_pi << ' ' << res.size() << '\n';
    for (int x : res) cout << x << ' ';
}

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