結果
問題 | No.3101 Range Eratosthenes Query |
ユーザー |
|
提出日時 | 2025-04-11 21:44:59 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 657 ms / 3,000 ms |
コード長 | 21,408 bytes |
コンパイル時間 | 2,094 ms |
コンパイル使用メモリ | 206,732 KB |
実行使用メモリ | 50,540 KB |
最終ジャッジ日時 | 2025-04-11 21:45:17 |
合計ジャッジ時間 | 12,944 ms |
ジャッジサーバーID (参考情報) |
judge3 / judge2 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 2 |
other | AC * 24 |
ソースコード
/** * author: otera **/ #include<bits/stdc++.h> namespace otera {} using namespace std; using namespace otera; struct io_setup { io_setup(int precision = 20) { ios::sync_with_stdio(false); cin.tie(0); cout << fixed << setprecision(precision); } } io_setup_ {}; #line 1 "library/datastructure/wavelet_matrix.hpp" #include <cassert> #include <array> #include <type_traits> #include <limits> #line 1 "library/datastructure/bit_vector.hpp" #include <cstdint> #include <vector> #line 1 "library/type_traits/type_traits.hpp" #line 5 "library/type_traits/type_traits.hpp" #include <iostream> #line 7 "library/type_traits/type_traits.hpp" namespace suisen { template <typename ...Constraints> using constraints_t = std::enable_if_t<std::conjunction_v<Constraints...>, std::nullptr_t>; template <typename T, typename = std::nullptr_t> struct bitnum { static constexpr int value = 0; }; template <typename T> struct bitnum<T, constraints_t<std::is_integral<T>>> { static constexpr int value = std::numeric_limits<std::make_unsigned_t<T>>::digits; }; template <typename T> static constexpr int bitnum_v = bitnum<T>::value; template <typename T, size_t n> struct is_nbit { static constexpr bool value = bitnum_v<T> == n; }; template <typename T, size_t n> static constexpr bool is_nbit_v = is_nbit<T, n>::value; template <typename T, typename = std::nullptr_t> struct safely_multipliable { using type = T; }; template <typename T> struct safely_multipliable<T, constraints_t<std::is_signed<T>, is_nbit<T, 32>>> { using type = long long; }; template <typename T> struct safely_multipliable<T, constraints_t<std::is_signed<T>, is_nbit<T, 64>>> { using type = __int128_t; }; template <typename T> struct safely_multipliable<T, constraints_t<std::is_unsigned<T>, is_nbit<T, 32>>> { using type = unsigned long long; }; template <typename T> struct safely_multipliable<T, constraints_t<std::is_unsigned<T>, is_nbit<T, 64>>> { using type = __uint128_t; }; template <typename T> using safely_multipliable_t = typename safely_multipliable<T>::type; template <typename T, typename = void> struct rec_value_type { using type = T; }; template <typename T> struct rec_value_type<T, std::void_t<typename T::value_type>> { using type = typename rec_value_type<typename T::value_type>::type; }; template <typename T> using rec_value_type_t = typename rec_value_type<T>::type; template <typename T> class is_iterable { template <typename T_> static auto test(T_ e) -> decltype(e.begin(), e.end(), std::true_type{}); static std::false_type test(...); public: static constexpr bool value = decltype(test(std::declval<T>()))::value; }; template <typename T> static constexpr bool is_iterable_v = is_iterable<T>::value; template <typename T> class is_writable { template <typename T_> static auto test(T_ e) -> decltype(std::declval<std::ostream&>() << e, std::true_type{}); static std::false_type test(...); public: static constexpr bool value = decltype(test(std::declval<T>()))::value; }; template <typename T> static constexpr bool is_writable_v = is_writable<T>::value; template <typename T> class is_readable { template <typename T_> static auto test(T_ e) -> decltype(std::declval<std::istream&>() >> e, std::true_type{}); static std::false_type test(...); public: static constexpr bool value = decltype(test(std::declval<T>()))::value; }; template <typename T> static constexpr bool is_readable_v = is_readable<T>::value; } // namespace suisen #line 8 "library/datastructure/bit_vector.hpp" namespace suisen { struct BitVector { explicit BitVector(int n) : n(n), nl((n >> LOG_BLOCK_L) + 1), ns((n >> LOG_BLOCK_S) + 1), cum_l(nl, 0), cum_s(ns, 0), bits(ns, 0) {} BitVector() : BitVector(0) {} template <typename Gen, constraints_t<std::is_invocable_r<bool, Gen, int>> = nullptr> BitVector(int n, Gen gen) : BitVector(n) { build(gen); } BitVector& operator=(const BitVector& bv) { n = bv.n, nl = bv.nl, ns = bv.ns, cum_l = bv.cum_l, cum_s = bv.cum_s, bits = bv.bits; return *this; } BitVector& operator=(BitVector&& bv) { n = bv.n, nl = bv.nl, ns = bv.ns, cum_l = std::move(bv.cum_l), cum_s = std::move(bv.cum_s), bits = std::move(bv.bits); return *this; } template <typename Gen, constraints_t<std::is_invocable_r<bool, Gen, int>> = nullptr> void build(Gen gen) { int i = 0; for (int index_s = 1; index_s < ns; ++index_s) { int count = cum_s[index_s - 1]; for (; i < index_s << LOG_BLOCK_S; ++i) { bool b = gen(i); bits[index_s - 1] |= b << (i & MASK_S); count += b; } if (index_s & ((1 << (LOG_BLOCK_L - LOG_BLOCK_S)) - 1)) { cum_s[index_s] = count; } else { int index_l = i >> LOG_BLOCK_L; cum_l[index_l] = cum_l[index_l - 1] + count; } } for (; i < n; ++i) bits[ns - 1] |= gen(i) << (i & MASK_S); } bool operator[](int i) const { return (bits[i >> LOG_BLOCK_S] >> (i & MASK_S)) & 1; } // returns the i'th val (i: 0-indexed) bool access(int i) const { return (*this)[i]; } // returns the number of val in [0, i) int rank(bool val, int i) const { int res_1 = cum_l[i >> LOG_BLOCK_L] + cum_s[i >> LOG_BLOCK_S] + popcount8(bits[i >> LOG_BLOCK_S] & ((1 << (i & MASK_S)) - 1)); return val ? res_1 : i - res_1; } // returns the number of val in [l, r) int rank(bool val, int l, int r) const { return rank(val, r) - rank(val, l); } // find the index of num'th val. (num: 1-indexed). if not exists, returns default_value. int select(bool val, int num, int default_value = -1) const { int l = -1, r = n + 1; while (r - l > 1) { int m = (l + r) >> 1; (rank(val, m) >= num ? r : l) = m; } return r == n + 1 ? default_value : r; } private: static constexpr int LOG_BLOCK_L = 8; static constexpr int LOG_BLOCK_S = 3; static constexpr int MASK_S = (1 << LOG_BLOCK_S) - 1; int n, nl, ns; std::vector<int> cum_l; std::vector<std::uint8_t> cum_s, bits; static constexpr std::uint8_t popcount8(std::uint8_t x) { x = (x & 0b01010101) + ((x >> 1) & 0b01010101); x = (x & 0b00110011) + ((x >> 2) & 0b00110011); return (x & 0b00001111) + (x >> 4); } }; } // namespace suisen #line 10 "library/datastructure/wavelet_matrix.hpp" namespace suisen { template <typename T, int bit_num = std::numeric_limits<std::make_unsigned_t<T>>::digits> struct WaveletMatrix { // default constructor WaveletMatrix() noexcept : n(0) {} // builds WaveletMatrix from generating function typed as (int) -> T template <typename Gen, constraints_t<std::is_invocable_r<T, Gen, int>> = nullptr> WaveletMatrix(int n, Gen generator) : n(n) { build(generator); } // builds WaveletMatrix from vector template <typename U, constraints_t<std::is_constructible<T, U>> = nullptr> WaveletMatrix(const std::vector<U>& a) : WaveletMatrix(a.size(), [&a](int i) { return T(a[i]); }) {} // builds WaveletMatrix from generating function typed as (int) -> T template <typename Gen, constraints_t<std::is_invocable_r<T, Gen, int>> = nullptr> void build(Gen generator) { std::vector<T> a(n), l(n), r(n); for (int i = 0; i < n; ++i) a[i] = generator(i); for (int log = bit_num - 1; log >= 0; --log) { bv[log] = BitVector(n, [&a, log](int i) -> bool { return (a[i] >> log) & 1; }); int li = 0, ri = 0; for (int i = 0; i < n; ++i) { ((a[i] >> log) & 1 ? r[ri++] : l[li++]) = a[i]; } a.swap(l); std::copy(r.begin(), r.begin() + ri, a.begin() + li); mid[log] = li; } } // returns WaveletMatrix[i] T operator[](int i) const { T res = 0; for (int log = bit_num - 1; log >= 0; --log) { bool b = bv[log][i]; res |= T(b) << log; i = b * mid[log] + bv[log].rank(b, i); } return res; } // returns WaveletMatrix[i] T access(int i) const { return (*this)[i]; } // returns the number of `val` in WaveletMatrix[0, i). int rank(T val, int i) const { check_value_bounds(val); int l = 0, r = i; for (int log = bit_num - 1; log >= 0; --log) succ(l, r, (val >> log) & 1, log); return r - l; } // returns the k'th smallest value in the multiset {| x ^ WaveletMatrix[i] : i in [l, r) |} (k : 0-indexed) T range_xor_kth_smallest(int l, int r, int k, T x, T default_value = T(-1)) const { if (k < 0 or k >= r - l) return default_value; T res = 0; check_value_bounds(x); for (int log = bit_num - 1; log >= 0; --log) { bool z = (x >> log) & 1; int cnt_z = bv[log].rank(z, l, r); bool skip_z = k >= cnt_z, bit = z ^ skip_z; succ(l, r, bit, log); res |= T(bit) << log; k -= skip_z * cnt_z; } return res; } // returns the k'th largest value in the multiset {| x ^ WaveletMatrix[i] : i in [l, r) |} (k : 0-indexed) T range_xor_kth_largest(int l, int r, int k, T x, T default_value = T(-1)) const { return range_xor_kth_smallest(l, r, r - l - 1 - k, x, default_value); } // returns the minimum value in the set { x ^ WaveletMatrix[i] : i in [l, r) } T range_xor_min(int l, int r, T x) const { assert(l < r); return range_xor_kth_smallest(l, r, 0, x); } // returns the maximum value in the set { x ^ WaveletMatrix[i] : i in [l, r) } T range_xor_max(int l, int r, T x) const { assert(l < r); return range_xor_kth_largest(l, r, 0, x); } // returns the number of v in WaveletMatrix[l, r) s.t. v ^ x < upper int range_xor_freq(int l, int r, T x, T upper) const { if (r <= l) return 0; if (upper > MAX) return r - l; check_value_bounds(x); int res = 0; for (int log = bit_num - 1; log >= 0; --log) { bool z = (x >> log) & 1, u = (upper >> log) & 1; if (u) res += bv[log].rank(z, l, r); succ(l, r, z ^ u, log); } return res; } // returns the number of v in WaveletMatrix[l, r) s.t. lower <= x ^ v < upper int range_xor_freq(int l, int r, T x, T lower, T upper) const { if (lower >= upper) return 0; return range_xor_freq(l, r, x, upper) - range_xor_freq(l, r, x, lower); } // returns the minimum value v in WaveletMatrix[l, r) s.t. lower <= x ^ v T range_xor_min_geq(int l, int r, T x, T lower, T default_value = T(-1)) const { int cnt = range_xor_freq(l, r, x, lower); return cnt >= r - l ? default_value : range_xor_kth_smallest(l, r, cnt, x); } // returns the minimum value v in WaveletMatrix[l, r) s.t. lower < x ^ v T range_xor_min_gt(int l, int r, T x, T lower, T default_value = T(-1)) const { return lower == MAX ? default_value : range_xor_min_geq(l, r, x, lower + 1, default_value); } // returns the maximum value v in WaveletMatrix[l, r) s.t. x ^ v < upper T range_xor_max_lt(int l, int r, T x, T upper, T default_value = T(-1)) const { int cnt = range_xor_freq(l, r, x, upper); return cnt == 0 ? default_value : range_xor_kth_smallest(l, r, cnt - 1, x, default_value); } // returns the maximum value v in WaveletMatrix[l, r) s.t. x ^ v <= upper T range_xor_max_leq(int l, int r, T x, T upper, T default_value = T(-1)) const { if (l >= r) return default_value; return upper == MAX ? range_xor_max(l, r, x) : range_xor_max_lt(l, r, x, upper + 1, default_value); } // returns the k'th smallest value in WaveletMatrix[l, r) (k : 0-indexed) T range_kth_smallest(int l, int r, int k, T default_value = T(-1)) const { return range_xor_kth_smallest(l, r, k, 0, default_value); } // returns the k'th largest value in WaveletMatrix[l, r) (k : 0-indexed) T range_kth_largest(int l, int r, int k, T default_value = T(-1)) const { return range_xor_kth_largest(l, r, k, 0, default_value); } // returns the minimum value in WaveletMatrix[l, r) T range_min(int l, int r) const { return range_xor_min(l, r, 0); } // returns the maximum value in WaveletMatrix[l, r) T range_max(int l, int r) const { return range_xor_max(l, r, 0); } // returns the number of v in WaveletMatrix[l, r) s.t. v < upper int range_freq(int l, int r, T upper) const { return range_xor_freq(l, r, 0, upper); } // returns the number of v in WaveletMatrix[l, r) s.t. lower <= v < upper int range_freq(int l, int r, T lower, T upper) const { return range_xor_freq(l, r, 0, lower, upper); } // returns the minimum value v in WaveletMatrix[l, r) s.t. lower <= v T range_min_geq(int l, int r, T lower, T default_value = T(-1)) const { return range_xor_min_geq(l, r, 0, lower, default_value); } // returns the minimum value v in WaveletMatrix[l, r) s.t. lower < v T range_min_gt(int l, int r, T lower, T default_value = T(-1)) const { return range_xor_min_gt(l, r, 0, lower, default_value); } // returns the maximum value v in WaveletMatrix[l, r) s.t. v < upper T range_max_lt(int l, int r, T upper, T default_value = T(-1)) const { return range_xor_max_lt(l, r, 0, upper, default_value); } // returns the maximum value v in WaveletMatrix[l, r) s.t. v <= upper T range_max_leq(int l, int r, T upper, T default_value = T(-1)) const { return range_xor_max_leq(l, r, 0, upper, default_value); } protected: WaveletMatrix(int n) noexcept : n(n) {} private: static_assert(bit_num > 0); static constexpr T MAX = bit_num == std::numeric_limits<T>::digits ? std::numeric_limits<T>::max() : (T(1) << bit_num) - 1; int n; std::array<BitVector, bit_num> bv; std::array<int, bit_num> mid; void succ(int& l, int& r, const bool b, const int log) const { l = b * mid[log] + bv[log].rank(b, l); r = b * mid[log] + bv[log].rank(b, r); } static void check_value_bounds(T val) { assert((val >> bit_num) == 0); } }; } // namespace suisen #define int long long using ll = long long; using ld = long double; using ull = unsigned long long; using i128 = __int128_t; using u128 = __uint128_t; #define repa(i, n) for(int i = 0; i < (n); ++ i) #define repb(i, a, b) for(int i = (a); i < (b); ++ i) #define repc(i, a, b, c) for(int i = (a); i < (b); i += (c)) #define overload4(a, b, c, d, e, ...) e #define overload3(a, b, c, d, ...) d #define rep(...) overload4(__VA_ARGS__, repc, repb, repa)(__VA_ARGS__) #define rep1a(i, n) for(int i = 1; i <= (n); ++ i) #define rep1b(i, a, b) for(int i = (a); i <= (b); ++ i) #define rep1c(i, a, b, c) for(int i = (a); i <= (b); i += (c)) #define rep1(...) overload4(__VA_ARGS__, rep1c, rep1b, rep1a)(__VA_ARGS__) #define rev_repa(i, n) for(int i=(n)-1;i>=0;i--) #define rev_repb(i, a, b) for(int i=(b)-1;i>=(a);i--) #define rev_rep(...) overload3(__VA_ARGS__, rev_repb, rev_repa)(__VA_ARGS__) #define rev_rep1a(i, n) for(int i=(n);i>=1;i--) #define rev_rep1b(i, a, b) for(int i=(b);i>=(a);i--) #define rev_rep1(...) overload3(__VA_ARGS__, rev_rep1b, rev_rep1a)(__VA_ARGS__) #define for_subset(t, s) for(ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s))) typedef pair<int, int> P; typedef pair<ll, ll> LP; #define pb push_back #define pf push_front #define ppb pop_back #define ppf pop_front #define eb emplace_back #define mkp make_pair #define mkt make_tuple #define fr first #define sc second #define all(c) std::begin(c), std::end(c) #define rall(c) std::rbegin(c), std::rend(c) #define lb(c, x) distance(std::begin(c), lower_bound(all(c), (x))) #define ub(c, x) distance(std::begin(c), upper_bound(all(c), (x))) #define Sort(a) sort(all(a)) #define Rev(a) reverse(all(a)) #define Uniq(a) sort(all(a));(a).erase(unique(all(a)),std::end(a)) #define si(c) (int)(c).size() inline ll popcnt(ull a){ return __builtin_popcountll(a); } #define kth_bit(x, k) ((x>>k)&1) #define unless(A) if(!(A)) #define elif else if ll modulo(ll n, ll d){ return (n % d + d) % d; }; ll intpow(ll a, ll b){ ll ans = 1; while(b){ if(b & 1) ans *= a; a *= a; b /= 2; } return ans; } ll intpow(ll a, ll b, ll m) {ll ans = 1; while(b){ if(b & 1) (ans *= a) %= m; (a *= a) %= m; b /= 2; } return ans; } template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; } template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; } template <typename T> constexpr inline int pow_m1(T n) { return -(n & 1) | 1; } template <typename T> constexpr inline T fld(const T x, const T y) { return (x ^ y) >= 0 ? x / y : (x - (y + pow_m1(y >= 0))) / y; } template <typename T> constexpr inline T cld(const T x, const T y) { return (x ^ y) <= 0 ? x / y : (x + (y + pow_m1(y >= 0))) / y; } #define INT(...) int __VA_ARGS__;in(__VA_ARGS__) #define LL(...) ll __VA_ARGS__;in(__VA_ARGS__) #define ULL(...) ull __VA_ARGS__;in(__VA_ARGS__) #define STR(...) string __VA_ARGS__;in(__VA_ARGS__) #define CHR(...) char __VA_ARGS__;in(__VA_ARGS__) #define DBL(...) double __VA_ARGS__;in(__VA_ARGS__) #define LD(...) ld __VA_ARGS__;in(__VA_ARGS__) #define vec(type,name,...) vector<type>name(__VA_ARGS__) #define VEC(type,name,size) vector<type>name(size);in(name) #define vv(type,name,h,...) vector<vector<type>>name(h,vector<type>(__VA_ARGS__)) #define VV(type,name,h,w) vector<vector<type>>name(h,vector<type>(w));in(name) #define vvv(type,name,h,w,...) vector<vector<vector<type>>>name(h,vector<vector<type>>(w,vector<type>(__VA_ARGS__))) template <class T> using vc = vector<T>; template <class T> using vvc = vector<vc<T>>; template <class T> using vvvc = vector<vvc<T>>; template <class T> using vvvvc = vector<vvvc<T>>; template <class T> using pq = priority_queue<T>; template <class T> using pqg = priority_queue<T, vector<T>, greater<T>>; template <class T, class U> using umap = unordered_map<T, U>; template<class T> void scan(T& a){ cin >> a; } template<class T> void scan(vector<T>& a){ for(auto&& i : a) scan(i); } void in(){} template <class Head, class... Tail> void in(Head& head, Tail&... tail){ scan(head); in(tail...); } void print(){ cout << ' '; } template<class T> void print(const T& a){ cout << a; } template<class T> void print(const vector<T>& a){ if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ cout << ' '; print(*i); } } int out(){ cout << '\n'; return 0; } template<class T> int out(const T& t){ print(t); cout << '\n'; return 0; } template<class Head, class... Tail> int out(const Head& head, const Tail&... tail){ print(head); cout << ' '; out(tail...); return 0; } #define CHOOSE(a) CHOOSE2 a #define CHOOSE2(a0,a1,a2,a3,a4,x,...) x #define debug_1(x1) cout<<#x1<<": "<<x1<<endl #define debug_2(x1,x2) cout<<#x1<<": "<<x1<<", "#x2<<": "<<x2<<endl #define debug_3(x1,x2,x3) cout<<#x1<<": "<<x1<<", "#x2<<": "<<x2<<", "#x3<<": "<<x3<<endl #define debug_4(x1,x2,x3,x4) cout<<#x1<<": "<<x1<<", "#x2<<": "<<x2<<", "#x3<<": "<<x3<<", "#x4<<": "<<x4<<endl #define debug_5(x1,x2,x3,x4,x5) cout<<#x1<<": "<<x1<<", "#x2<<": "<<x2<<", "#x3<<": "<<x3<<", "#x4<<": "<<x4<<", "#x5<<": "<<x5<<endl #ifdef DEBUG #define debug(...) CHOOSE((__VA_ARGS__,debug_5,debug_4,debug_3,debug_2,debug_1,~))(__VA_ARGS__) #define dump(...) { print(#__VA_ARGS__); print(":"); out(__VA_ARGS__); } #else #define debug(...) #define dump(...) #endif const int A = 1e6 + 100; void solve() { vc<int> check(A, -1); for(int x = 2; x < A; ++ x) { for(int y = x; y < A; y += x) { if(check[y] == -1) check[y] = x; } } vc<int> a(A, 1); for(int x = 2; x < A; ++ x) { a[x] = x / check[x]; } suisen::WaveletMatrix<int, 32> wm(a); INT(q); rep(_, q) { INT(l, r); ++ r; // [l, r) int len = r - l; if(l == 1) { out(1); } else { int ans = wm.range_freq(l, r, 1, l); out(ans); } } } signed main() { int testcase = 1; // in(testcase); while(testcase--) solve(); return 0; }