結果
問題 | No.2512 Mountain Sequences |
ユーザー |
|
提出日時 | 2023-10-20 22:45:09 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 1,314 ms / 3,000 ms |
コード長 | 21,995 bytes |
コンパイル時間 | 2,536 ms |
コンパイル使用メモリ | 216,568 KB |
最終ジャッジ日時 | 2025-02-17 10:20:49 |
ジャッジサーバーID (参考情報) |
judge2 / judge3 |
(要ログイン)
ファイルパターン | 結果 |
---|---|
other | AC * 29 |
ソースコード
#include <bits/stdc++.h>namespace suisen {template <class T> bool chmin(T& x, const T& y) { return y >= x ? false : (x = y, true); }template <class T> bool chmax(T& x, const T& y) { return y <= x ? false : (x = y, true); }template <class T> constexpr int pow_m1(T n) { return -(n & 1) | 1; }template <class T> constexpr T fld(const T x, const T y) { T q = x / y, r = x % y; return q - ((x ^ y) < 0 and (r != 0)); }template <class T> constexpr T cld(const T x, const T y) { T q = x / y, r = x % y; return q + ((x ^ y) > 0 and (r != 0)); }}namespace suisen::macro {#define IMPL_REPITER(cond) auto& begin() { return *this; } auto end() { return nullptr; } auto& operator*() { return _val; } auto& operator++() {return _val += _step, *this; } bool operator!=(std::nullptr_t) { return cond; }template <class Int, class IntL = Int, class IntStep = Int, std::enable_if_t<(std::is_signed_v<Int> == std::is_signed_v<IntL>), std::nullptr_t> =nullptr> struct rep_impl {Int _val; const Int _end, _step;rep_impl(Int n) : rep_impl(0, n) {}rep_impl(IntL l, Int r, IntStep step = 1) : _val(l), _end(r), _step(step) {}IMPL_REPITER((_val < _end))};template <class Int, class IntL = Int, class IntStep = Int, std::enable_if_t<(std::is_signed_v<Int> == std::is_signed_v<IntL>), std::nullptr_t> =nullptr> struct rrep_impl {Int _val; const Int _end, _step;rrep_impl(Int n) : rrep_impl(0, n) {}rrep_impl(IntL l, Int r) : _val(r - 1), _end(l), _step(-1) {}rrep_impl(IntL l, Int r, IntStep step) : _val(l + fld<Int>(r - l - 1, step) * step), _end(l), _step(-step) {}IMPL_REPITER((_val >= _end))};template <class Int, class IntStep = Int> struct repinf_impl {Int _val; const Int _step;repinf_impl(Int l, IntStep step = 1) : _val(l), _step(step) {}IMPL_REPITER((true))};#undef IMPL_REPITER}#include <iostream>#include <limits>#include <type_traits>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 suisennamespace suisen::io {template <typename IStream, std::enable_if_t<std::conjunction_v<std::is_base_of<std::istream, std::remove_reference_t<IStream>>, std::negation<std::is_const<std::remove_reference_t<IStream>>>>, std::nullptr_t> = nullptr>struct InputStream {private:using istream_type = std::remove_reference_t<IStream>;IStream is;struct { InputStream* is; template <typename T> operator T() { T e; *is >> e; return e; } } _reader{ this };public:template <typename IStream_> InputStream(IStream_ &&is) : is(std::move(is)) {}template <typename IStream_> InputStream(IStream_ &is) : is(is) {}template <typename T> InputStream& operator>>(T& e) {if constexpr (suisen::is_readable_v<T>) is >> e; else _read(e);return *this;}auto read() { return _reader; }template <typename Head, typename... Tail>void read(Head& head, Tail &...tails) { ((*this >> head) >> ... >> tails); }istream_type& get_stream() { return is; }private:static __uint128_t _stou128(const std::string& s) {__uint128_t ret = 0;for (char c : s) if ('0' <= c and c <= '9') ret = 10 * ret + c - '0';return ret;}static __int128_t _stoi128(const std::string& s) { return (s[0] == '-' ? -1 : +1) * _stou128(s); }void _read(__uint128_t& v) { v = _stou128(std::string(_reader)); }void _read(__int128_t& v) { v = _stoi128(std::string(_reader)); }template <typename T, typename U>void _read(std::pair<T, U>& a) { *this >> a.first >> a.second; }template <size_t N = 0, typename ...Args>void _read(std::tuple<Args...>& a) { if constexpr (N < sizeof...(Args)) *this >> std::get<N>(a), _read<N + 1>(a); }template <typename Iterable, std::enable_if_t<suisen::is_iterable_v<Iterable>, std::nullptr_t> = nullptr>void _read(Iterable& a) { for (auto& e : a) *this >> e; }};template <typename IStream>InputStream(IStream &&) -> InputStream<IStream>;template <typename IStream>InputStream(IStream &) -> InputStream<IStream&>;InputStream cin{ std::cin };auto read() { return cin.read(); }template <typename Head, typename... Tail>void read(Head& head, Tail &...tails) { cin.read(head, tails...); }} // namespace suisen::ionamespace suisen { using io::read; } // namespace suisennamespace suisen::io {template <typename OStream, std::enable_if_t<std::conjunction_v<std::is_base_of<std::ostream, std::remove_reference_t<OStream>>, std::negation<std::is_const<std::remove_reference_t<OStream>>>>, std::nullptr_t> = nullptr>struct OutputStream {private:using ostream_type = std::remove_reference_t<OStream>;OStream os;public:template <typename OStream_> OutputStream(OStream_ &&os) : os(std::move(os)) {}template <typename OStream_> OutputStream(OStream_ &os) : os(os) {}template <typename T> OutputStream& operator<<(const T& e) {if constexpr (suisen::is_writable_v<T>) os << e; else _print(e);return *this;}void print() { *this << '\n'; }template <typename Head, typename... Tail>void print(const Head& head, const Tail &...tails) { *this << head, ((*this << ' ' << tails), ...), *this << '\n'; }template <typename Iterable, std::enable_if_t<suisen::is_iterable_v<Iterable>, std::nullptr_t> = nullptr>void print_all(const Iterable& v, std::string sep = " ", std::string end = "\n") {for (auto it = v.begin(); it != v.end();) if (*this << *it; ++it != v.end()) *this << sep;*this << end;}ostream_type& get_stream() { return os; }private:void _print(__uint128_t value) {char buffer[41], *d = std::end(buffer);do *--d = '0' + (value % 10), value /= 10; while (value);os.rdbuf()->sputn(d, std::end(buffer) - d);}void _print(__int128_t value) {if (value < 0) *this << '-';_print(__uint128_t(value < 0 ? -value : value));}template <typename T, typename U>void _print(const std::pair<T, U>& a) { *this << a.first << ' ' << a.second; }template <size_t N = 0, typename ...Args>void _print(const std::tuple<Args...>& a) {if constexpr (N < std::tuple_size_v<std::tuple<Args...>>) {if constexpr (N) *this << ' ';*this << std::get<N>(a), _print<N + 1>(a);}}template <typename Iterable, std::enable_if_t<suisen::is_iterable_v<Iterable>, std::nullptr_t> = nullptr>void _print(const Iterable& a) { print_all(a, " ", ""); }};template <typename OStream_>OutputStream(OStream_ &&) -> OutputStream<OStream_>;template <typename OStream_>OutputStream(OStream_ &) -> OutputStream<OStream_&>;OutputStream cout{ std::cout }, cerr{ std::cerr };template <typename... Args>void print(const Args &... args) { cout.print(args...); }template <typename Iterable, std::enable_if_t<suisen::is_iterable_v<Iterable>, std::nullptr_t> = nullptr>void print_all(const Iterable& v, const std::string& sep = " ", const std::string& end = "\n") { cout.print_all(v, sep, end); }} // namespace suisen::ionamespace suisen { using io::print, io::print_all; } // namespace suisennamespace suisen {template <class T, class ToKey, class CompKey = std::less<>, std::enable_if_t<std::conjunction_v<std::is_invocable<ToKey, T>, std::is_invocable_r<bool, CompKey, std::invoke_result_t<ToKey, T>, std::invoke_result_t<ToKey, T>>>, std::nullptr_t> = nullptr>auto comparator(const ToKey& to_key, const CompKey& comp_key = std::less<>()) {return [=](const T& x, const T& y) { return comp_key(to_key(x), to_key(y)); };}template <class Compare, std::enable_if_t<std::is_invocable_r_v<bool, Compare, int, int>, std::nullptr_t> = nullptr>std::vector<int> sorted_indices(int n, const Compare& compare) {std::vector<int> p(n);return std::iota(p.begin(), p.end(), 0), std::sort(p.begin(), p.end(), compare), p;}template <class ToKey, std::enable_if_t<std::is_invocable_v<ToKey, int>, std::nullptr_t> = nullptr>std::vector<int> sorted_indices(int n, const ToKey& to_key) { return sorted_indices(n, comparator<int>(to_key)); }template <class T, class Comparator>auto priority_queue_with_comparator(const Comparator& comparator) { return std::priority_queue<T, std::vector<T>, Comparator>{ comparator }; }template <class Iterable, std::enable_if_t<suisen::is_iterable_v<Iterable>, std::nullptr_t> = nullptr>void sort_unique_erase(Iterable& a) { std::sort(a.begin(), a.end()), a.erase(std::unique(a.begin(), a.end()), a.end()); }template <size_t D> struct Dim : std::array<int, D> {template <typename ...Ints> Dim(const Ints& ...ns) : std::array<int, D>::array{ static_cast<int>(ns)... } {}};template <typename ...Ints> Dim(const Ints& ...) -> Dim<sizeof...(Ints)>;template <class T, size_t D, size_t I = 0>auto ndvec(const Dim<D> &ns, const T& value = {}) {if constexpr (I + 1 < D) {return std::vector(ns[I], ndvec<T, D, I + 1>(ns, value));} else {return std::vector<T>(ns[I], value);}}}namespace suisen {using int128 = __int128_t;using uint128 = __uint128_t;template <class T> using min_priority_queue = std::priority_queue<T, std::vector<T>, std::greater<T>>;template <class T> using max_priority_queue = std::priority_queue<T, std::vector<T>, std::less<T>>;}namespace suisen { const std::string Yes = "Yes", No = "No", YES = "YES", NO = "NO"; }#ifdef LOCAL# define debug(...) debug_impl(#__VA_ARGS__, __VA_ARGS__)template <class H, class... Ts> void debug_impl(const char* s, const H& h, const Ts&... t) {suisen::io::cerr << "[\033[32mDEBUG\033[m] " << s << ": " << h, ((suisen::io::cerr << ", " << t), ..., (suisen::io::cerr << "\n"));}#else# define debug(...) void(0)#endif#define FOR(e, v) for (auto &&e : v)#define CFOR(e, v) for (const auto &e : v)#define REP(i, ...) CFOR(i, suisen::macro::rep_impl(__VA_ARGS__))#define RREP(i, ...) CFOR(i, suisen::macro::rrep_impl(__VA_ARGS__))#define REPINF(i, ...) CFOR(i, suisen::macro::repinf_impl(__VA_ARGS__))#define LOOP(n) for ([[maybe_unused]] const auto& _ : suisen::macro::rep_impl(n))#define ALL(iterable) std::begin(iterable), std::end(iterable)using namespace suisen;using namespace std;struct io_setup {io_setup(int precision = 20) {std::ios::sync_with_stdio(false), std::cin.tie(nullptr);std::cout << std::fixed << std::setprecision(precision);}} io_setup_{};constexpr int iinf = std::numeric_limits<int>::max() / 2;constexpr long long linf = std::numeric_limits<long long>::max() / 2;#include <atcoder/modint>using mint = atcoder::modint998244353;namespace atcoder {std::istream& operator>>(std::istream& in, mint &a) {long long e; in >> e; a = e;return in;}std::ostream& operator<<(std::ostream& out, const mint &a) {out << a.val();return out;}} // namespace atcoder// #include "library/polynomial/formal_power_series.hpp"#include <cassert>#include <vector>namespace suisen {template <typename T, typename U = T>struct factorial {factorial() = default;factorial(int n) { ensure(n); }static void ensure(const int n) {int sz = _fac.size();if (n + 1 <= sz) return;int new_size = std::max(n + 1, sz * 2);_fac.resize(new_size), _fac_inv.resize(new_size);for (int i = sz; i < new_size; ++i) _fac[i] = _fac[i - 1] * i;_fac_inv[new_size - 1] = U(1) / _fac[new_size - 1];for (int i = new_size - 1; i > sz; --i) _fac_inv[i - 1] = _fac_inv[i] * i;}T fac(const int i) {ensure(i);return _fac[i];}T operator()(int i) {return fac(i);}U fac_inv(const int i) {ensure(i);return _fac_inv[i];}U binom(const int n, const int r) {if (n < 0 or r < 0 or n < r) return 0;ensure(n);return _fac[n] * _fac_inv[r] * _fac_inv[n - r];}U perm(const int n, const int r) {if (n < 0 or r < 0 or n < r) return 0;ensure(n);return _fac[n] * _fac_inv[n - r];}private:static std::vector<T> _fac;static std::vector<U> _fac_inv;};template <typename T, typename U>std::vector<T> factorial<T, U>::_fac{ 1 };template <typename T, typename U>std::vector<U> factorial<T, U>::_fac_inv{ 1 };} // namespace suisenconst mint inv2 = mint(2).inv();void solve() {int n, m;read(n, m);factorial<mint> fac(2 * m);mint ans = 0;REP(i, 1, n + 1) {ans += mint(-2).pow(i) * fac.binom(2 * m, i);}print(ans * inv2 * (-inv2).pow(n));}#include <algorithm>#include <cmath>#include <numeric>namespace suisen {struct Mo {Mo() = default;Mo(const int n, const std::vector<std::pair<int, int>> &queries) : n(n), q(queries.size()), b(bucket_size(n, q)), qs(queries), ord(q) {std::iota(ord.begin(), ord.end(), 0);std::sort(ord.begin(), ord.end(),[&, this](int i, int j) {const auto &[li, ri] = qs[i];const auto &[lj, rj] = qs[j];const int bi = li / b, bj = lj / b;if (bi != bj) return bi < bj;if (ri != rj) return bi & 1 ? ri > rj : ri < rj;return li < lj;});}// getter methods used in updating functions: AddL, DelL, etc.auto get_left() const { return l; }auto get_right() const { return r; }auto get_range() const { return std::make_pair(l, r); }auto get_query_id() const { return query_id; }/*** [Parameters]* Eval : () -> T : return the current answer* AddL : int -> any (discarded) : add `l` to the current range [l + 1, r)* DelL : int -> any (discarded) : delete `l` from the current range [l, r)* AddR : int -> any (discarded) : add `r` to the current range [l, r)* DelR : int -> any (discarded) : delete `r` from the current range [l, r + 1)** [Note]* starting from the range [0, 0).*/template <typename Eval, typename AddL, typename DelL, typename AddR, typename DelR>auto solve(Eval eval, AddL add_l, DelL del_l, AddR add_r, DelR del_r) {l = 0, r = 0;std::vector<decltype(eval())> res(q);for (int qi : ord) {const auto &[nl, nr] = qs[query_id = qi];while (r < nr) add_r(r), ++r;while (l > nl) --l, add_l(l);while (r > nr) --r, del_r(r);while (l < nl) del_l(l), ++l;res[qi] = eval();}return res;}/*** [Parameters]* Eval : () -> T : return the current answer* Add : int -> any (discarded) : add `i` to the current range [i + 1, r) or [l, i)* Del : int -> any (discarded) : delete `i` from the current range [i, r) or [l, i + 1)** [Note]* starting from the range [0, 0).*/template <typename Eval, typename Add, typename Del>auto solve(Eval eval, Add add, Del del) {return solve(eval, add, del, add, del);}private:int n, q, b;int query_id = -1;std::vector<std::pair<int, int>> qs;std::vector<int> ord;int l = 0, r = 0;static int bucket_size(int n, int q) {return std::max(1, int(::sqrt(3) * n / ::sqrt(std::max(1, 2 * q))));}};} // namespace suisennamespace suisen {template <int base_as_int, typename mint>struct static_pow_mods {static_pow_mods() = default;static_pow_mods(int n) { ensure(n); }const mint& operator[](int i) const {ensure(i);return pows[i];}static void ensure(int n) {int sz = pows.size();if (sz > n) return;pows.resize(n + 1);for (int i = sz; i <= n; ++i) pows[i] = base * pows[i - 1];}private:static inline std::vector<mint> pows { 1 };static inline mint base = base_as_int;static constexpr int mod = mint::mod();};template <typename mint>struct pow_mods {pow_mods() = default;pow_mods(mint base, int n) : base(base) { ensure(n); }const mint& operator[](int i) const {ensure(i);return pows[i];}void ensure(int n) const {int sz = pows.size();if (sz > n) return;pows.resize(n + 1);for (int i = sz; i <= n; ++i) pows[i] = base * pows[i - 1];}private:mutable std::vector<mint> pows { 1 };mint base;static constexpr int mod = mint::mod();};}constexpr int M = 400010;int main() {int q;read(q);pow_mods<mint> pw(-2, M);factorial<mint> fac(M);vector<mint> ans(q);vector<int> qid;vector<pair<int, int>> qs;REP(i, q) {int n, m;read(n, m);m *= 2;if (n >= m) {ans[i] = 0;} else {qid.push_back(i);qs.emplace_back(n, m);}}mint sum = 1;Mo mo(M, qs);auto ans_q = mo.solve([&]{ return sum; },[&](int n) {int m = mo.get_right();// (n + 1, m) -> (n, m)sum -= pw[n + 1] * fac.binom(m, n + 1);},[&](int n) {int m = mo.get_right();// (n, m) -> (n + 1, m)sum += pw[n + 1] * fac.binom(m, n + 1);},[&](int m) {int n = mo.get_left();// (n, m) -> (n, m + 1)sum = 2 * pw[n] * fac.binom(m, n) - sum;},[&](int m) {int n = mo.get_left();// (n, m + 1) -> (n, m)sum = 2 * pw[n] * fac.binom(m, n) - sum;});REP(i, int(ans_q.size())) {auto [n, m] = qs[i];ans[qid[i]] = (ans_q[i] - 1) * inv2 * (-inv2).pow(n);// mint sum = 0;// REP(k, n + 1) sum += pw[k] * fac.binom(m, k);// ans[qid[i]] = (sum - 1) * inv2 * (-inv2).pow(n);}print_all(ans, "\n");return 0;}