Create primes.cpp

Changes

1 changed files (+89/-0)

• Math/primes.cpp (new)
  • @@ -0,0 +1,89 @@
    + constexpr int sieve_size = 1e7; + bitset<sieve_size + 1> bs; + vector<int> pr; + + void sieve() { + bs.set(); bs[0] = bs[1] = 0; + for (ll i = 2; i < _sieve_size; ++i) if (bs[i]) { + for (ll j = i * i; j < _sieve_size; j += i) bs[j] = 0; + pr.push_back(i); + } + } + + bool is_prime(ll N) { + if (N < sieve_size) return bs[N]; + for (int i = 0; i < pr.size() && pr[i] * pr[i] <= N; ++i) if (N % pr[i] == 0) return false; + return true; + } + + vector<int> pf(ll N) { + vector<int> factors; + ll idx = 0, pf = pr[idx]; + while (N != 1 && pf * pf <= N) { + while (N % pf == 0) { N /= pf; factors.push_back(pf); } + pf = pr[++idx]; + } + if (N != 1) factors.push_back(N); + return factors; + } + + ll num_pf(ll N) { + ll idx = 0, pf = pr[idx], ans = 0; + while (N != 1 && pf * pf <= N)) { + while (N % pf == 0) { N /= pf; ans++; } + pf = pr[++idx]; + } + return ans + (N != 1); + } + + ll num_diff_pf(ll N) { + ll idx = 0, pf = pr[idx], ans = 0; + while (N != 1 && pf * pf <= N) { + if (N % pf == 0) ans++; + while (N % pf == 0) N /= pf; + pf = pr[++idx]; + } + return ans + (N != 1); + } + + ll sum_pf(ll N) { + ll idx = 0, pf = pr[idx], ans = 0; + while (N != 1 && pf * pf <= N)) { + while (N % pf == 0) { N /= pf; ans += pf; } + pf = pr[++idx]; + } + return ans + (N != 1) * N; + } + + ll num_div(ll N) { + ll idx = 0, pf = pr[idx], ans = 1; + while (N != 1 && pf * pf <= N)) { + ll power = 0; + while (N % pf == 0) { N /= pf; ++power; } + ans *= (power + 1); + pf = pr[++idx]; + } + return (N != 1) ? 2 * ans : ans; + } + + ll sum_div(ll N) { + ll idx = 0, pf = pr[idx], ans = 1; + while (N != 1 && pf * pf <= N) { + ll power = 0; + while (N % pf == 0) { N /= pf; ++power; } + ans *= ((ll)pow((double)pf, power + 1.0) - 1) / (pf - 1); + pf = pr[++idx]; + } + if (N != 1) ans *= ((ll)pow((double)N, 2.0) - 1) / (N - 1); + return ans; + } + + ll phi(ll N) { + ll idx = 0, pf = pr[idx], ans = N; + while (N != 1 && pf * pf <= N) { + if (N % pf == 0) ans -= ans / pf; + while (N % pf == 0) N /= pf; + pf = pr[++idx]; + } + return N != 1 ? ans - ans / N : ans; + }