This documentation is automatically generated by online-judge-tools/verification-helper
View the Project on GitHub tkmst201/Library
#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/challenges/sources/JAG/Summer/2446?year=2012" #define ERROR "1e-7" #include "Mathematics/zeta_moebius_transform.hpp" #include "Mathematics/euclid.hpp" #include <vector> #include <iostream> #include <cmath> int main() { using ll = long long; int N; ll M; std::cin >> N >> M; std::vector<ll> A(N); std::vector<int> P(N); for (int i = 0; i < N; ++i) std::cin >> A[i]; for (int i = 0; i < N; ++i) std::cin >> P[i]; auto solve1 = [&]() { std::vector<ll> v((1 << N)); for (int s = 1; s < 1 << N; ++s) { ll l = 1; bool ng = false; for (int i = 0; i < N; ++i) { if (~s >> i & 1) continue; ll g = tk::gcd<ll>(l, A[i]); l /= g; if (l > M / A[i]) { ng = true; break; } // l A[i] <= M else l *= A[i]; } if (ng) continue; v[s] = M / l; } tk::moebius_transform_set_lower(v); double ans = 0; for (int s = 0; s < 1 << N; ++s) { double p = 1; for (int i = 0; i < N; ++i) { if (s >> i & 1) p *= P[i] * 0.01; else p *= (100 - P[i]) * 0.01; } ans += std::abs(v[s]) * p; } return ans; }; auto solve2 = [&]() { std::vector<ll> v((1 << N)); for (int s = 0; s < 1 << N; ++s) { ll l = 1; bool ng = false; for (int i = 0; i < N; ++i) { if (~s >> i & 1) continue; ll g = tk::gcd<ll>(l, A[i]); l /= g; if (l > M / A[i]) { ng = true; break; } // l A[i] <= M else l *= A[i]; } if (ng) continue; v[s] = M / l; } tk::moebius_transform_set_upper(v); tk::zeta_tranform_set_lower(v); double ans = 0; for (int s = 0; s < 1 << N; ++s) { double p = 1; for (int i = 0; i < N; ++i) { if (s >> i & 1) p *= P[i] * 0.01; else p *= (100 - P[i]) * 0.01; } ans += (M - v[(1 << N) - 1 - s]) * p; } return ans; }; double ans1 = solve1(); double ans2 = solve2(); printf("%.16f\n", (ans1 + ans2) / 2.0); }
#line 1 "Test/zeta_moebius_transform.set.1.test.cpp" #define PROBLEM "https://onlinejudge.u-aizu.ac.jp/challenges/sources/JAG/Summer/2446?year=2012" #define ERROR "1e-7" #line 1 "Mathematics/zeta_moebius_transform.hpp" /* last-updated: 2020/11/19 TODO: AOJ, yukicoder から verify 問題を探す # 仕様 ## 集合 void zeta_tranform_set_lower(std::vector<T> & v) 時間計算量: Θ(|v|log|v|) 配列 v を配列 v' に書き換える(i の下位集合について総和を取る) v'[i] := \Sum_{j \subset i} v[j] void moebius_transform_set_lower(std::vector<T> & v) 時間計算量: Θ(|v|log|v|) 配列 v を次の式を満たす配列 v' に書き換える(i の下位集合について総和を取る前に戻す) v[i] = \Sum_{j \subset i} v'[j] void zeta_tranform_set_upper(std::vector<T> & v) 時間計算量: Θ(|v|log|v|) 配列 v を配列 v' に書き換える(i の上位集合について総和を取る) v'[i] := \Sum_{i \subset j} v[j] void moebius_transform_set_upper(std::vector<T> & v) 時間計算量: Θ(|v|log|v|) 配列 v を次の式を満たす配列 v' に書き換える(i の上位集合について総和を取る前に戻す) v[i] = \Sum_{i \subset j} v'[j] ## 約数倍数 void zeta_tranform_divisor_lower(std::vector<T> & v) 時間計算量: O(|v|loglog|v|) 配列 v を配列 v' に書き換える(i の約数について総和を取る) v'[i] := \Sum_{j|i} v[j] void moebius_tranform_divisor_lower(std::vector<T> & v) 時間計算量: O(|v|loglog|v|) 配列 v を次の式を満たす配列 v' に書き換える(i の約数について総和を取る前に戻す) v[i] = \Sum_{j|i} v'[j] void zeta_tranform_divisor_upper(std::vector<T> & v) 時間計算量: O(|v|loglog|v|) 配列 v を配列 v' に書き換える(i の倍数について総和) v'[i] := \Sum_{i|j} v[j] void moebius_tranform_divisor_upper(std::vector<T> & v) 時間計算量: O(|v|loglog|v|) 配列 v を次の式を満たす配列 v' に書き換える(i の約数について総和を取る前に戻す) v[i] = \Sum_{i|j} v'[j] # 参考 2020/11/12: https://qiita.com/convexineq/items/afc84dfb9ee4ec4a67d5 2020/11/14: https://aprilganmo.hatenablog.com/entry/2020/02/27/170239 2020/11/14: https://noshi91.hatenablog.com/entry/2018/12/27/121649 2020/11/18: https://aprilganmo.hatenablog.com/entry/2020/07/24/190816 # verify void zeta_tranform_set_lower(std::vector<T> & v) void moebius_transform_set_lower(std::vector<T> & v) void zeta_tranform_set_upper(std::vector<T> & v) - OK void moebius_transform_set_upper(std::vector<T> & v) - TODO: メビウス(上位集合) の verify void zeta_tranform_divisor_lower(std::vector<T> & v) - https://atcoder.jp/contests/abc172/submissions/18200046 void moebius_tranform_divisor_lower(std::vector<T> & v) - TODO: メビウス(倍数) の verify void zeta_tranform_divisor_upper(std::vector<T> & v) void moebius_tranform_divisor_upper(std::vector<T> & v) - https://atcoder.jp/contests/abc162/submissions/18200657 */ #include <vector> #include <cassert> namespace tk { template<typename T> void zeta_tranform_set_lower(std::vector<T> & v) { assert(!v.empty()); using size_type = std::size_t; for (size_type i = 1; i < v.size(); i <<= 1) { for (size_type j = 0; j < v.size(); ++j) { if (j & i) v[j] += v[j ^ i]; } } } template<typename T> void moebius_transform_set_lower(std::vector<T> & v) { assert(!v.empty()); using size_type = std::size_t; for (size_type i = 1; i < v.size(); i <<= 1) { for (size_type j = 0; j < v.size(); ++j) { if (j & i) v[j] -= v[j ^ i]; } } } template<typename T> void zeta_tranform_set_upper(std::vector<T> & v) { assert(!v.empty()); using size_type = std::size_t; for (size_type i = 1; i < v.size(); i <<= 1) { for (size_type j = 0; j < v.size(); ++j) { if (~j & i) v[j] += v[j ^ i]; } } } template<typename T> void moebius_transform_set_upper(std::vector<T> & v) { assert(!v.empty()); using size_type = std::size_t; for (size_type i = 1; i < v.size(); i <<= 1) { for (size_type j = 0; j < v.size(); ++j) { if (~j & i) v[j] -= v[j ^ i]; } } } } // namespace tk namespace tk { template<typename T> void zeta_tranform_divisor_lower(std::vector<T> & v) { assert(!v.empty()); using size_type = std::size_t; std::vector<bool> sieve(v.size(), true); for (size_type p = 2; p < v.size(); ++p) { if (!sieve[p]) continue; for (size_type i = 1, t = p; t < v.size(); ++i, t += p) { v[t] += v[i]; sieve[t] = false; } } } template<typename T> void moebius_tranform_divisor_lower(std::vector<T> & v) { assert(!v.empty()); using size_type = std::size_t; std::vector<bool> sieve(v.size(), true); for (size_type p = 2; p < v.size(); ++p) { if (!sieve[p]) continue; for (size_type i = (v.size() - 1) / p, t = i * p; i > 0; --i, t -= p) { v[t] -= v[i]; sieve[t] = false; } } } template<typename T> void zeta_tranform_divisor_upper(std::vector<T> & v) { assert(!v.empty()); using size_type = std::size_t; std::vector<bool> sieve(v.size(), true); for (size_type p = 2; p < v.size(); ++p) { if (!sieve[p]) continue; for (size_type i = (v.size() - 1) / p, t = i * p; i > 0; --i, t -= p) { v[i] += v[t]; sieve[t] = false; } } } template<typename T> void moebius_tranform_divisor_upper(std::vector<T> & v) { assert(!v.empty()); using size_type = std::size_t; std::vector<bool> sieve(v.size(), true); for (size_type p = 2; p < v.size(); ++p) { if (!sieve[p]) continue; for (size_type i = 1, t = p; t < v.size(); ++i, t += p) { v[i] -= v[t]; sieve[t] = false; } } } } // namespace tk #line 1 "Mathematics/euclid.hpp" #line 5 "Mathematics/euclid.hpp" #include <utility> #include <tuple> #include <type_traits> #include <cmath> /** * @brief https://tkmst201.github.io/Library/Mathematics/euclid.hpp */ namespace tk { template<typename T> constexpr T gcd(T a, T b) noexcept { static_assert(std::is_integral<T>::value); assert(a >= 0); assert(b >= 0); while (b != 0) { const T t = a % b; a = b; b = t; } return a; } template<typename T> constexpr T lcm(T a, T b) noexcept { static_assert(std::is_integral<T>::value); assert(a >= 0); assert(b >= 0); if (a == 0 || b == 0) return 0; return a / gcd(a, b) * b; } template<typename T> constexpr std::tuple<T, T, T> ext_gcd(T a, T b) noexcept { static_assert(std::is_integral<T>::value); static_assert(std::is_signed<T>::value); assert(a != 0); assert(b != 0); T a1 = (a > 0) * 2 - 1, a2 = 0, b1 = 0, b2 = (b > 0) * 2 - 1; a = std::abs(a); b = std::abs(b); while (b > 0) { const T q = a / b; T tmp = a - q * b; a = b; b = tmp; tmp = a1 - q * b1; a1 = b1; b1 = tmp; tmp = a2 - q * b2; a2 = b2; b2 = tmp; } return {a, a1, a2}; } } // namespace tk #line 6 "Test/zeta_moebius_transform.set.1.test.cpp" #line 8 "Test/zeta_moebius_transform.set.1.test.cpp" #include <iostream> #line 10 "Test/zeta_moebius_transform.set.1.test.cpp" int main() { using ll = long long; int N; ll M; std::cin >> N >> M; std::vector<ll> A(N); std::vector<int> P(N); for (int i = 0; i < N; ++i) std::cin >> A[i]; for (int i = 0; i < N; ++i) std::cin >> P[i]; auto solve1 = [&]() { std::vector<ll> v((1 << N)); for (int s = 1; s < 1 << N; ++s) { ll l = 1; bool ng = false; for (int i = 0; i < N; ++i) { if (~s >> i & 1) continue; ll g = tk::gcd<ll>(l, A[i]); l /= g; if (l > M / A[i]) { ng = true; break; } // l A[i] <= M else l *= A[i]; } if (ng) continue; v[s] = M / l; } tk::moebius_transform_set_lower(v); double ans = 0; for (int s = 0; s < 1 << N; ++s) { double p = 1; for (int i = 0; i < N; ++i) { if (s >> i & 1) p *= P[i] * 0.01; else p *= (100 - P[i]) * 0.01; } ans += std::abs(v[s]) * p; } return ans; }; auto solve2 = [&]() { std::vector<ll> v((1 << N)); for (int s = 0; s < 1 << N; ++s) { ll l = 1; bool ng = false; for (int i = 0; i < N; ++i) { if (~s >> i & 1) continue; ll g = tk::gcd<ll>(l, A[i]); l /= g; if (l > M / A[i]) { ng = true; break; } // l A[i] <= M else l *= A[i]; } if (ng) continue; v[s] = M / l; } tk::moebius_transform_set_upper(v); tk::zeta_tranform_set_lower(v); double ans = 0; for (int s = 0; s < 1 << N; ++s) { double p = 1; for (int i = 0; i < N; ++i) { if (s >> i & 1) p *= P[i] * 0.01; else p *= (100 - P[i]) * 0.01; } ans += (M - v[(1 << N) - 1 - s]) * p; } return ans; }; double ans1 = solve1(); double ans2 = solve2(); printf("%.16f\n", (ans1 + ans2) / 2.0); }