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#define PROBLEM "https://judge.yosupo.jp/problem/counting_primes" #include <bits/stdc++.h> using namespace std; #include "../Prime/PrimePi.h" int32_t main() { ios::sync_with_stdio(0); cin.tie(0); long long n; cin >> n; cout << prime_pi(n) << endl; return 0; }
#line 1 "Math/tests/prime_pi.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/counting_primes" #include <bits/stdc++.h> using namespace std; #line 1 "Math/Prime/PrimePi.h" // prime_pi(n) = number of primes <= n // // Copied from https://judge.yosupo.jp/submission/61551 // // Tested: // - https://judge.yosupo.jp/problem/counting_primes // - https://www.spoj.com/problems/NTHPRIME/ (binary search + prime pi) // // Notes: // - There's simpler O(N^0.75) code for prime_pi and prime_sum // Write up: https://www.facebook.com/code.cung.rr/posts/pfbid0eAyeQynkVN9evzy7Bnwx52zLeN7EHDE6H9Uur6KTSK2MTiyxJwCV71Wvujqz75vgl // Implementation: // - prime_sum: https://www.spoj.com/status/SUMPRIM1,mr_invincible/ // - prime_pi: https://www.spoj.com/problems/DIVCNT2/ // This can be modified to implement more complicated things such as // https://www.spoj.com/problems/DIVFACT4/ // prime_pi {{{ using ll = long long; int isqrt(ll n) { return sqrtl(n); } ll prime_pi(const ll N) { if (N <= 1) return 0; if (N == 2) return 1; const int v = isqrt(N); int s = (v + 1) / 2; vector<int> smalls(s); for (int i = 1; i < s; i++) smalls[i] = i; vector<int> roughs(s); for (int i = 0; i < s; i++) roughs[i] = 2 * i + 1; vector<ll> larges(s); for (int i = 0; i < s; i++) larges[i] = (N / (2 * i + 1) - 1) / 2; vector<bool> skip(v + 1); const auto divide = [](ll n, ll d) -> int { return (double)n / d;}; const auto half = [](int n) -> int { return (n - 1) >> 1;}; int pc = 0; for (int p = 3; p <= v; p += 2) if (!skip[p]) { int q = p * p; if ((ll)q * q > N) break; skip[p] = true; for (int i = q; i <= v; i += 2 * p) skip[i] = true; int ns = 0; for (int k = 0; k < s; k++) { int i = roughs[k]; if (skip[i]) continue; ll d = (ll)i * p; larges[ns] = larges[k] - (d <= v ? larges[smalls[d >> 1] - pc] : smalls[half(divide(N, d))]) + pc; roughs[ns++] = i; } s = ns; for (int i = half(v), j = ((v / p) - 1) | 1; j >= p; j -= 2) { int c = smalls[j >> 1] - pc; for (int e = (j * p) >> 1; i >= e; i--) smalls[i] -= c; } pc++; } larges[0] += (ll)(s + 2 * (pc - 1)) * (s - 1) / 2; for (int k = 1; k < s; k++) larges[0] -= larges[k]; for (int l = 1; l < s; l++) { ll q = roughs[l]; ll M = N / q; int e = smalls[half(M / q)] - pc; if (e < l + 1) break; ll t = 0; for (int k = l + 1; k <= e; k++) t += smalls[half(divide(M, roughs[k]))]; larges[0] += t - (ll)(e - l) * (pc + l - 1); } return larges[0] + 1; } // }}} #line 7 "Math/tests/prime_pi.test.cpp" int32_t main() { ios::sync_with_stdio(0); cin.tie(0); long long n; cin >> n; cout << prime_pi(n) << endl; return 0; }