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#define PROBLEM "https://judge.yosupo.jp/problem/enumerate_primes" #include <bits/stdc++.h> using namespace std; #include "../Prime/SieveFast.h" int n, a, b, cnt = 0, cnt_mod = 0; vector<int> ps; void newPrime(int p) { if (p > n) { cout << cnt << ' ' << ps.size() << '\n'; for (int x : ps) cout << x << ' '; exit(0); } if (cnt_mod == b) ps.push_back(p); ++cnt; ++cnt_mod; if (cnt_mod == a) cnt_mod = 0; } int32_t main() { cin >> n >> a >> b; sieve(1'000'000'000, newPrime); return 0; }
#line 1 "Math/tests/sieve_fast.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/enumerate_primes" #include <bits/stdc++.h> using namespace std; #line 1 "Math/Prime/SieveFast.h" // Tested: // - (3B+) https://oj.vnoi.info/problem/icpc22_national_c // - (1B, collect into vector of primes) https://www.spoj.com/problems/KPRIMES2/ // - (1B, print) https://www.spoj.com/problems/PRIMES2/ // // Note: // - It's possible to extract code from here to have a fast implementation // of segmented sieve for [L, R] where R is very big (e.g. 10^12) // See: https://www.spoj.com/status/SUMPRIM2,mr_invincible/ // However there are several things that need to be fixed: // 1. Initialization of small primes: // - Need to change 256 -> R^0.25 // - Change 32768 -> R^0.5 // 2. Change N_SMALL_PRIMES // 3. If R^0.5 is around 10^6, p^2 overflow int, so need to check everywhere.. // 4. si[SIEVE_SIZE] may not have enough elements to sieve small_primes.. // 5. update_sieve(offset) assumes offset is a multiple of SIEVE_SPAN. This // is not true if we sieve a segment [L, R] // 6. Maybe more issues.. // Essentially if we need to do this, either use SegmentedSieve or copy from // https://www.spoj.com/status/SUMPRIM2,mr_invincible/ which I spent like an // hour to make it work.. // Segmented sieve with wheel factorization {{{ namespace segmented_sieve_wheel { const int WHEEL = 3 * 5 * 7 * 11 * 13; const int N_SMALL_PRIMES = 6536; // cnt primes less than 2^16 const int SIEVE_SPAN = WHEEL * 64; // one iteration of segmented sieve const int SIEVE_SIZE = SIEVE_SPAN / 128 + 1; uint64_t ONES[64]; // ONES[i] = 1<<i int small_primes[N_SMALL_PRIMES]; // primes less than 2^16 // each element of sieve is a 64-bit bitmask. // Each bit (0/1) stores whether the corresponding element is a prime number. // We only need to store odd numbers // -> 1st bitmask stores 3, 5, 7, 9, ... uint64_t si[SIEVE_SIZE]; // for each 'wheel', we store the sieve pattern (i.e. what numbers cannot // be primes) uint64_t pattern[WHEEL]; inline void mark(uint64_t* s, int o) { s[o >> 6] |= ONES[o & 63]; } inline int test(uint64_t* s, int o) { return (s[o >> 6] & ONES[o & 63]) == 0; } // update_sieve {{{ void update_sieve(uint32_t offset) { // copy each wheel pattern to sieve for (int i = 0, k; i < SIEVE_SIZE; i += k) { k = std::min(WHEEL, SIEVE_SIZE - i); memcpy(si + i, pattern, sizeof(*pattern) * k); } // Correctly mark 1, 3, 5, 7, 11, 13 as not prime / primes if (offset == 0) { si[0] |= ONES[0]; si[0] &= ~(ONES[1] | ONES[2] | ONES[3] | ONES[5] | ONES[6]); } // sieve for primes >= 17 (stored in `small_primes`) for (int i = 0; i < N_SMALL_PRIMES; ++i) { uint32_t j = small_primes[i] * (uint32_t) small_primes[i]; if (j > offset + SIEVE_SPAN - 1) break; if (j > offset) j = (j - offset) >> 1; else { j = small_primes[i] - offset % small_primes[i]; if ((j & 1) == 0) j += small_primes[i]; j >>= 1; } while (j < SIEVE_SPAN / 2) { mark(si, j); j += small_primes[i]; } } } // }}} template<typename F> void sieve(uint32_t MAX, F func) { // init small primes {{{ for (int i = 0; i < 64; ++i) ONES[i] = 1ULL << i; // sieve to find small primes for (int i = 3; i < 256; i += 2) { if (test(si, i >> 1)) { for (int j = i*i / 2; j < 32768; j += i) mark(si, j); } } // store primes >= 17 in `small_primes` (we will sieve differently // for primes 2, 3, 5, 7, 11, 13) { int m = 0; for (int i = 8; i < 32768; ++i) { if (test(si, i)) small_primes[m++] = i*2 + 1; } assert(m == N_SMALL_PRIMES); } // }}} // For primes 3, 5, 7, 11, 13: we initialize wheel pattern.. for (int i = 1; i < WHEEL * 64; i += 3) mark(pattern, i); for (int i = 2; i < WHEEL * 64; i += 5) mark(pattern, i); for (int i = 3; i < WHEEL * 64; i += 7) mark(pattern, i); for (int i = 5; i < WHEEL * 64; i += 11) mark(pattern, i); for (int i = 6; i < WHEEL * 64; i += 13) mark(pattern, i); // Segmented sieve if (2 <= MAX) func(2); for (uint32_t offset = 0; offset < MAX; offset += SIEVE_SPAN) { update_sieve(offset); for (uint32_t j = 0; j < SIEVE_SIZE; j++){ uint64_t x = ~si[j]; while (x){ uint32_t p = offset + (j << 7) + (__builtin_ctzll(x) << 1) + 1; if (p > offset + SIEVE_SPAN - 1) break; if (p <= MAX) { func(p); } x ^= (-x & x); } } } } } using segmented_sieve_wheel::sieve; // }}} #line 7 "Math/tests/sieve_fast.test.cpp" int n, a, b, cnt = 0, cnt_mod = 0; vector<int> ps; void newPrime(int p) { if (p > n) { cout << cnt << ' ' << ps.size() << '\n'; for (int x : ps) cout << x << ' '; exit(0); } if (cnt_mod == b) ps.push_back(p); ++cnt; ++cnt_mod; if (cnt_mod == a) cnt_mod = 0; } int32_t main() { cin >> n >> a >> b; sieve(1'000'000'000, newPrime); return 0; }