結果
問題 | No.2512 Mountain Sequences |
ユーザー | suisen |
提出日時 | 2023-10-20 22:45:09 |
言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 1,312 ms / 3,000 ms |
コード長 | 21,995 bytes |
コンパイル時間 | 3,132 ms |
コンパイル使用メモリ | 225,204 KB |
実行使用メモリ | 14,248 KB |
最終ジャッジ日時 | 2024-09-20 20:42:21 |
合計ジャッジ時間 | 23,022 ms |
ジャッジサーバーID (参考情報) |
judge1 / judge3 |
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テストケース
テストケース表示入力 | 結果 | 実行時間 実行使用メモリ |
---|---|---|
testcase_00 | AC | 35 ms
7,936 KB |
testcase_01 | AC | 36 ms
8,064 KB |
testcase_02 | AC | 35 ms
8,064 KB |
testcase_03 | AC | 36 ms
8,064 KB |
testcase_04 | AC | 35 ms
7,936 KB |
testcase_05 | AC | 36 ms
8,064 KB |
testcase_06 | AC | 37 ms
7,936 KB |
testcase_07 | AC | 34 ms
8,064 KB |
testcase_08 | AC | 33 ms
8,064 KB |
testcase_09 | AC | 33 ms
7,936 KB |
testcase_10 | AC | 1,282 ms
13,988 KB |
testcase_11 | AC | 1,310 ms
13,992 KB |
testcase_12 | AC | 1,293 ms
13,864 KB |
testcase_13 | AC | 1,298 ms
13,988 KB |
testcase_14 | AC | 1,286 ms
13,868 KB |
testcase_15 | AC | 1,312 ms
13,864 KB |
testcase_16 | AC | 1,270 ms
13,992 KB |
testcase_17 | AC | 1,281 ms
13,992 KB |
testcase_18 | AC | 1,304 ms
13,992 KB |
testcase_19 | AC | 1,287 ms
13,992 KB |
testcase_20 | AC | 706 ms
14,204 KB |
testcase_21 | AC | 710 ms
14,248 KB |
testcase_22 | AC | 714 ms
14,156 KB |
testcase_23 | AC | 711 ms
14,120 KB |
testcase_24 | AC | 733 ms
14,248 KB |
testcase_25 | AC | 98 ms
14,248 KB |
testcase_26 | AC | 98 ms
14,248 KB |
testcase_27 | AC | 107 ms
14,244 KB |
testcase_28 | AC | 103 ms
12,680 KB |
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 suisen namespace 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::io namespace suisen { using io::read; } // namespace suisen namespace 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::io namespace suisen { using io::print, io::print_all; } // namespace suisen namespace 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 suisen const 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 suisen namespace 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; }