結果
問題 | No.1322 Totient Bound |
ユーザー |
|
提出日時 | 2020-12-19 03:39:37 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
TLE
|
実行時間 | - |
コード長 | 9,944 bytes |
コンパイル時間 | 2,852 ms |
コンパイル使用メモリ | 220,600 KB |
最終ジャッジ日時 | 2025-01-17 03:46:44 |
ジャッジサーバーID (参考情報) |
judge3 / judge3 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 17 RE * 1 TLE * 18 |
ソースコード
#include <bits/stdc++.h>using ll = long long;using uint = unsigned int;using ull = unsigned long long;using ld = long double;template<typename T> using max_heap = std::priority_queue<T>;template<typename T> using min_heap = std::priority_queue<T, std::vector<T>, std::greater<T>>;constexpr int popcount(const ull v) { return v ? __builtin_popcountll(v) : 0; }constexpr int log2p1(const ull v) { return v ? 64 - __builtin_clzll(v) : 0; }constexpr int lsbp1(const ull v) { return __builtin_ffsll(v); }constexpr int clog(const ull v) { return v ? log2p1(v - 1) : 0; }constexpr ull ceil2(const ull v) { return 1ULL << clog(v); }constexpr ull floor2(const ull v) { return v ? (1ULL << (log2p1(v) - 1)) : 0ULL; }constexpr bool btest(const ull mask, const int ind) { return (mask >> ind) & 1ULL; }template<typename T> bool chmin(T& a, const T& b) { return (a > b ? a = b, true : false); }template<typename T> bool chmax(T& a, const T& b) { return (a < b ? a = b, true : false); }template<typename T> constexpr T inf_v = std::numeric_limits<T>::max() / 4;template<typename Real> constexpr Real pi_v = Real{3.141592653589793238462643383279502884};template<typename T> constexpr T TEN(const int n) { return n == 0 ? T{1} : TEN<T>(n - 1) * T{10}; }template<typename F> struct fix : F{fix(F&& f) : F{std::forward<F>(f)} {}template<typename... Args> auto operator()(Args&&... args) const { return F::operator()(*this, std::forward<Args>(args)...); }};template<typename T, int n, int i = 0>auto nd_array(int const (&szs)[n], const T x = T{}){if constexpr (i == n) {return x;} else {return std::vector(szs[i], nd_array<T, n, i + 1>(szs, x));}}class printer{public:printer(std::ostream& os_ = std::cout) : m_os{os_} { m_os << std::fixed << std::setprecision(15); }template<typename... Args> int ln(const Args&... args) { return dump(args...), m_os << '\n', 0; }template<typename... Args> int el(const Args&... args) { return dump(args...), m_os << std::endl, 0; }private:template<typename T> void dump(const T& v) { m_os << v; }template<typename T> void dump(const std::vector<T>& vs){for (int i = 0; i < (int)vs.size(); i++) { m_os << (i ? " " : ""), dump(vs[i]); }}template<typename T> void dump(const std::vector<std::vector<T>>& vss){for (int i = 0; i < (int)vss.size(); i++) { m_os << (0 <= i or i + 1 < (int)vss.size() ? "\n" : ""), dump(vss[i]); }}template<typename T, typename... Args> int dump(const T& v, const Args&... args) { return dump(v), m_os << ' ', dump(args...), 0; }std::ostream& m_os;};printer out;class range{private:struct itr{itr(const int start = 0, const int step = 1) : m_cnt{start}, m_step{step} {}bool operator!=(const itr& it) const { return m_cnt != it.m_cnt; }int& operator*() { return m_cnt; }itr& operator++() { return m_cnt += m_step, *this; }int m_cnt, m_step;};int m_start, m_end, m_step;public:range(const int start, const int end, const int step = 1) : m_start{start}, m_end{end}, m_step{step}{assert(m_step != 0);if (m_step > 0) { m_end = m_start + std::max(m_step - 1, m_end - m_start + m_step - 1) / m_step * m_step; }if (m_step < 0) { m_end = m_start - std::max(-m_step - 1, m_start - m_end - m_step - 1) / (-m_step) * (-m_step); }}itr begin() const { return itr{m_start, m_step}; }itr end() const { return itr{m_end, m_step}; }};range rep(const int end, const int step = 1) { return range(0, end, step); }range per(const int rend, const int step = -1) { return range(rend - 1, -1, step); }class scanner{public:scanner(std::istream& is_ = std::cin) : m_is{is_} { m_is.tie(nullptr), std::ios::sync_with_stdio(false); }template<typename T> T val(){T v;return m_is >> v, v;}template<typename T> T val(const T offset) { return val<T>() - offset; }template<typename T> std::vector<T> vec(const int n){return make_v<T>(n, [this]() { return val<T>(); });}template<typename T> std::vector<T> vec(const int n, const T offset){return make_v<T>(n, [this, offset]() { return val<T>(offset); });}template<typename T> std::vector<std::vector<T>> vvec(const int n0, const int n1){return make_v<std::vector<T>>(n0, [this, n1]() { return vec<T>(n1); });}template<typename T> std::vector<std::vector<T>> vvec(const int n0, const int n1, const T offset){return make_v<std::vector<T>>(n0, [this, n1, offset]() { return vec<T>(n1, offset); });}template<typename... Args> auto tup() { return std::tuple<std::decay_t<Args>...>{val<Args>()...}; }template<typename... Args> auto tup(const Args&... offsets) { return std::tuple<std::decay_t<Args>...>{val<Args>(offsets)...}; }private:template<typename T, typename F>std::vector<T> make_v(const int n, F f){std::vector<T> ans;for (int i = 0; i < n; i++) { ans.push_back(f()); }return ans;}std::istream& m_is;};scanner in;template<typename T, typename ST = T>class prime_accum{public:prime_accum(const T N) : N{N}, SQRT{sqrt(N)}, isp(SQRT + 1, true){assert(N >= 2);init();init_smalls();init_larges();for (int i = 0; i < pn; i++) {const int p = ps[i];for (int j = nn; (j--) > 0;) {const T n = ns[j];if (n < (T)p * (T)p) { break; }const T pn = n / (T)p;const int pj = rev(pn);assert(C_smalls[p - 1] == i);Cs[j] -= Cs[pj] - C_smalls[p - 1];Ss[j] -= (ST)p * (Ss[pj] - S_smalls[p - 1]);}}}T count(const T n) const{const int i = rev(n);assert(ns[i] == n);return Cs[i];}ST sum(const T n) const{const int i = rev(n);assert(ns[i] == n);return Ss[i];}private:static int sqrt(const T n){int ans = std::sqrt(n);for (; (T)(ans + 1) * (T)(ans + 1) <= n; ans++) {}return ans;}void init(){isp[0] = false, isp[1] = false;for (int p = 2; p <= SQRT; p++) {if (not isp[p]) { continue; }ps.push_back(p);for (int q = p * 2; q <= SQRT; q += p) { isp[q] = false; }}for (T p = 1; p * p <= N; p++) { ns.push_back(p), ns.push_back(N / p); }std::sort(ns.begin(), ns.end());ns.erase(std::unique(ns.begin(), ns.end()), ns.end());pn = ps.size(), nn = ns.size();}void init_smalls(){C_smalls.resize(SQRT + 1, 0), S_smalls.resize(SQRT + 1, 0);for (int n = 1; n <= SQRT; n++) {if (not isp[n]) { continue; }C_smalls[n] = isp[n] ? (T)1 : (T)0;S_smalls[n] = isp[n] ? (ST)n : (ST)0;}for (int n = 1; n <= SQRT; n++) { C_smalls[n] += C_smalls[n - 1], S_smalls[n] += S_smalls[n - 1]; }}void init_larges(){Cs.resize(nn, 0), Ss.resize(nn, 0);for (int i = 0; i < nn; i++) {const T n = ns[i];Cs[i] = (T)n - (T)1;Ss[i] = (ST)n * (ST)(n + 1) / (ST)2 - (ST)2;}}int rev(const T n) const { return n <= SQRT ? (int)(n - 1) : nn - (int)(N / n); }T N = 0;const int SQRT;int pn, nn;std::vector<bool> isp;std::vector<int> ps;std::vector<T> ns;std::vector<T> Cs;std::vector<ST> Ss;std::vector<T> C_smalls;std::vector<ST> S_smalls;};template<typename T, typename V>inline bool miller_rabin(const T& n, const std::vector<T>& as){auto pow = [&](auto&& self, const V& a, const T k) -> V {if (k == 0) { return 1; }if (k % 2 == 0) {return self(self, (a * a) % V(n), k / 2);} else {return (self(self, a, k - 1) * a) % V(n);}};T d = n - 1;for (; (d & 1) == 0; d >>= 1) {}for (const T& a : as) {if (n <= a) { break; }T s = d;V x = pow(pow, a, s);while (x != 1 and x != n - 1 and s != n - 1) {(x *= x) %= V(n);s *= 2;}if (x != n - 1 and s % 2 == 0) { return false; }}return true;}inline bool is_prime(const ull n){if (n % 2 == 0) { return n == 2; }if (n < (1ULL << 32)) {return miller_rabin<uint, ull>((uint)n, std::vector<uint>{2, 7, 61});} else {return miller_rabin<ull, __uint128_t>(n, std::vector<ull>{2, 325, 9375, 28178, 450775, 9780504});}}constexpr int B = 100001;bool isp[B];std::vector<ll> ps;int main(){std::fill(isp + 2, isp + B, true);for (const int p : range(2, B)) {if (not isp[p]) { continue; }ps.push_back(p);for (const int q : range(p + p, B, p)) { isp[q] = false; }}const auto N = in.val<ll>();auto solve = [&](const ll N) {std::map<ll, ll> cands;cands[1] = 1;std::map<ll, ll> adds;int i = 0;for (const ll p : ps) {adds.clear();for (const auto& [prod, num] : cands) {if (prod * (p - 1) > N) { break; }for (ll pr = prod * (p - 1); pr <= N; pr *= p) { adds[pr] += num; }}for (const auto& [p, n] : adds) { cands[p] += n; }if (adds.empty()) { break; }}prime_accum<ll, ll> pi(N);ll ans = 0;for (const auto& [p, n] : cands) {ans += n;const ll pmax = N / p + 1;if (pmax < B) { continue; }const ll P = pi.count(pmax - 1) + is_prime(pmax) - (ll)ps.size();ans += n * P;}return ans;};out.ln(solve(N));return 0;}