結果

問題 No.3228 Very Large Fibonacci Sum
ユーザー mihhiael
提出日時 2025-08-08 23:45:07
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 2 ms / 2,000 ms
コード長 8,295 bytes
コンパイル時間 1,728 ms
コンパイル使用メモリ 162,068 KB
実行使用メモリ 6,272 KB
最終ジャッジ日時 2025-08-08 23:45:10
合計ジャッジ時間 3,123 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 23
権限があれば一括ダウンロードができます

ソースコード

diff # 

// #define MOD_IS_998 1
#include <array>
#if __has_include("template.hpp") && false
#include "template.hpp"
#else
// template start
#include <algorithm>
#include <concepts>
#include <cstdint>
#include <iostream>
#include <istream>
#include <limits>
#include <ostream>
#include <queue>
#include <random>
#include <ranges>
#include <set>
#include <stdexcept>
#include <string>
#include <type_traits>
#include <utility>
#include <vector>

#include <atcoder/modint.hpp>
// often use
#include <cassert>
#include <ios>
#include <map>

using namespace std;
using ll = long long;
using pall = pair<ll, ll>;
template<class T>
using vec = vector<T>;
template<class T>
using veve = vec<vec<T>>;
using vell = vec<ll>;
using vest = vec<string>;
using vebo = basic_string<bool>;
using vevell = veve<ll>;
template<class T>
using mset = multiset<T>;
template<class T>
using priority_queue_ascend = priority_queue<T, vec<T>, greater<T>>;
const ll inf = numeric_limits<ll>::max();
const string sp = " ";
const string lf = "\n";
const auto &npos = string::npos;
#ifdef MOD_IS_998
constexpr ll MOD = 998244353;
#else
constexpr ll MOD = 1e9 + 7;
#endif
const vec<pall> grid_move4 = {{0, 1}, {-1, 0}, {0, -1}, {1, 0}};
const vec<pall> grid_move8 = [] {
	auto ret = grid_move4;
	ret.insert(ret.end(), {{-1, 1}, {-1, -1}, {1, -1}, {1, 1}});
	return ret;
}();

#define cont continue
#define br break
#define whlie while
#define foR for
#define auot auto
#define uato auto
#define cosnt const
#define conts const
#define ocnst const
auto &ciN = cin;
auto &icn = cin;
auto &icN = cin;
constexpr bool ture = true;
constexpr bool flase = false;

using namespace atcoder;
using mint = static_modint<MOD>;

#define times(N) \
	static_assert(is_integral_v<decltype((N) + 0)>, \
	              "times(): N must be integral"); \
	for(typedef decltype((N) + 0) _int; \
	    [[maybe_unused]] const _int _i : views::iota((_int)0, (N)))
#define tiems times
#define itmes times

template<int M>
decltype(auto) operator<<(ostream &out, const static_modint<M> &i) {
	return out << i.val();
}

struct debug_stream {
	template<class T>
	debug_stream &operator<<([[maybe_unused]] const T &x) {
#ifndef ONLINE_JUDGE
		clog << x;
#endif
		return *this;
	}

	debug_stream &operator<<([[maybe_unused]] ostream &(*f)(ostream &)) {
#ifndef ONLINE_JUDGE
		clog << f;
#endif
		return *this;
	}
};
template<class T>
concept out_stream = same_as<ostream, T> || same_as<debug_stream, T>;

debug_stream clog_;
#define clog clog_

template<int M>
istream &operator>>(istream &in, static_modint<M> &i) {
	intmax_t tmp;
	in >> tmp;
	tmp = (tmp % M + M) % M;
	i = tmp;
	return in;
}

template<class T, class U>
istream &operator>>(istream &in, pair<T, U> &p) {
	return in >> p.first >> p.second;
}

template<class T, class U>
decltype(auto) operator<<(out_stream auto &out, const pair<T, U> &p) {
	return out << p.first << sp << p.second;
}

template<class T>
istream &operator>>(istream &in, vec<T> &v) {
	for(auto &&e : v) {
		in >> e;
	}
	return in;
}

namespace myinput {
template<class... Ts>
istream &in(Ts &...vecs) {
	static_assert(sizeof...(vecs) != 0,
	              "myfunc::in(): At least one vector must be provided");
	const set sizes = {vecs.size()...};
	if(sizes.size() > 1) {
		throw invalid_argument("myfunc::in(): All vectors must have the same size");
	}
	times(*sizes.begin()) {
		((cin >> vecs[_i]), ...);
	}
	return cin;
}
}  // namespace myinput

using myinput::in;

void out(ranges::range auto v, const string delim, out_stream auto &out) {
	for(auto &&e : v) {
		out << e << delim;
	}
}

void out(ranges::range auto v, const string delim) {
	out(v, delim, cout);
}

[[nodiscard]] const string &yesno(const bool cond, const string &yes = "Yes",
                                  const string &no = "No") noexcept {
	if(cond) return yes;
	return no;
}

// [mi, ma)
[[nodiscard]] uint64_t randint(const uint64_t mi, const uint64_t ma) noexcept {
	static random_device seed;
	static mt19937_64 mt(seed());
	if(mi > ma) [[unlikely]]
		return randint(ma, mi);
	if(mi == ma) [[unlikely]]
		return mi;
	const uint64_t w = ma - mi;
	uint64_t r;
	do {
		r = mt();
	} while(mt.max() - mt.max() % w <= r);
	return r % w + mi;
}

template<class T, class U>
requires common_with<T, U>
[[nodiscard]] constexpr auto min(T &&a, U &&b) noexcept {
	return std::min<common_type_t<T, U>>(std::forward<T>(a), std::forward<U>(b));
}

template<class T, class U>
requires common_with<T, U>
[[nodiscard]] constexpr auto max(T &&a, U &&b) noexcept {
	return std::max<common_type_t<T, U>>(std::forward<T>(a), std::forward<U>(b));
}

template<class T>
[[nodiscard]] const T &min(const vec<T> &v) {
	return *ranges::min_element(v);
}

template<class T>
[[nodiscard]] const T &max(const vec<T> &v) {
	return *ranges::max_element(v);
}

template<class... Args>
[[nodiscard]] auto reduce(const ranges::range auto &v, Args... args) {
	return reduce(v.begin(), v.end(), args...);
}

[[nodiscard]] constexpr ll powll(ll a, ll b, const ll m = inf) {
	if(b < 0) [[unlikely]]
		throw invalid_argument("powll(): exponent less than zero");
	if(m < 1) [[unlikely]]
		throw invalid_argument("powll(): modulo less than one");
	a %= m;
	ll ret = 1;
	while(b) {
		if(b % 2) ret *= a, ret %= m;
		a *= a, a %= m;
		b /= 2;
	}
	return ret;
}

template<class T, class U>
requires assignable_from<T &, U> && totally_ordered_with<T, U>
bool mini(T &var, U &&val) noexcept {
	const bool cmp = var > val;
	if(cmp) var = val;
	return cmp;
}

template<class T, class U>
requires assignable_from<T &, U> && totally_ordered_with<T, U>
bool maxi(T &var, U &&val) noexcept {
	const bool cmp = var < val;
	if(cmp) var = val;
	return cmp;
}

namespace myclass {
class [[nodiscard]] grid_base {
	public:
	grid_base(const ll h, const ll w) noexcept : height(h), width(w) {}

	[[nodiscard]] ll operator()(const ll i, const ll j) const noexcept {
		if(! isvalid(i, j)) return -1;
		return i * width + j;
	}

	[[nodiscard]] ll operator()(const pall &p) const noexcept {
		return (*this)(p.first, p.second);
	}

	protected:
	bool isvalid(const ll i, const ll j) const noexcept {
		return 0 <= i && 0 <= j && i < height && j < width;
	}

	const ll height, width;
};

class [[nodiscard]] grid_seen : public myclass::grid_base {
	public:
	grid_seen(const ll h, const ll w) : grid_base(h, w) {
		visited = vebo(h * w, false);
	}

	[[nodiscard]] bool &seen(const ll i, const ll j) & {
		if(! isvalid(i, j)) [[unlikely]]
			throw out_of_range("grid::seen(): out of range");
		return visited[i * width + j];
	}

	[[nodiscard]] bool &seen(const pall &p) & {
		return seen(p.first, p.second);
	}

	private:
	vebo visited;
};
}  // namespace myclass

using grid_lite = myclass::grid_base;
using myclass::grid_seen;

template<class T>
auto erase_single(mset<T> &mset, T &&v) {
	const auto it = mset.find(v);
	if(it == mset.end()) [[unlikely]]
		throw invalid_argument("erase_single(): why v not in mset!?!?");
	return mset.erase(it);
}

void solve();
// template end
#endif

int main(void) {
	cin.tie(nullptr);
	ios::sync_with_stdio(false);
	ll t = 1;
	// cin >> t;
	times(t) solve();
	return 0;
}

using mat55 = array<array<mint, 5>, 5>;

mat55 matmul(const mat55 &a, const mat55 &b) {
	mat55 res{};
	for(intmax_t i = 0; i < intmax_t(5); i++) {
		ranges::fill(res[i], 0);
	}
	for(intmax_t i = 0; i < intmax_t(5); i++) {
		for(intmax_t j = 0; j < intmax_t(5); j++) {
			for(intmax_t k = 0; k < intmax_t(5); k++) {
				res[i][j] += a[i][k] * b[k][j];
			}
		}
	}
	return res;
}

void solve() {
	mint a, b, c, d, e;
	cin >> a >> b >> c >> d >> e;

	ll n;
	cin >> n;
	if(n == 0) {
		cout << a << lf;
		return;
	}
	mat55 m{};
	for(intmax_t i = 0; i < intmax_t(5); i++) {
		ranges::fill(m[i], 0);
	}
	m[0][0] = m[0][1] = m[1][4] = m[2][1] = m[3][2] = m[4][4] = 1;
	m[1][1] = c;
	m[1][2] = d;
	mat55 mn{};
	for(intmax_t i = 0; i < intmax_t(5); i++) {
		ranges::fill(mn[i], 0);
	}
	for(intmax_t i = 0; i < intmax_t(5); i++) {
		mn[i][i] = 1;
	}
	n -= 1;
	whlie(n) {
		if(n % 2) mn = matmul(mn, m);
		m = matmul(m, m);
		n /= 2;
	}
	array<mint, 5> v;
	v[2] = b;
	v[3] = a;
	v[0] = v[2] + v[3];
	v[1] = c * v[2] + d * v[3] + e;
	v[4] = e;
	mint ans = 0;
	for(intmax_t i = 0; i < intmax_t(5); i++) {
		ans += mn[0][i] * v[i];
	}
	out(mn[0], sp, clog), clog << lf;
	out(v, sp, clog), clog << lf;
	cout << ans << lf;
}
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