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 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
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ファイルパターン 結果
other AC * 29
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ソースコード

diff #
プレゼンテーションモードにする

#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;
}
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0