結果

問題 No.3182 recurrence relation’s intersection sum
ユーザー sgfc
提出日時 2025-06-13 22:48:37
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 518 ms / 2,000 ms
コード長 5,714 bytes
コンパイル時間 9,136 ms
コンパイル使用メモリ 542,856 KB
実行使用メモリ 39,072 KB
最終ジャッジ日時 2025-06-13 22:49:00
合計ジャッジ時間 17,987 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 * 40
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 # 

#pragma GCC optimize("O3")

#include "bits/stdc++.h"
#include <stdio.h>
#include "atcoder/all"
#include <boost/multiprecision/cpp_int.hpp>
using namespace boost::multiprecision;

using namespace std;
using namespace atcoder;

using ll = long long;
using ull = unsigned long long;
using mint = modint998244353;
using mint2 = modint1000000007;
const double eps = 1e-9;

#define OVERLOAD3(_1, _2, _3, call,...) call
#define REP0(n) for (ll i = 0; i < ll(n); ++i)
#define REP1(i, n) for (ll i = 0; i < ll(n); ++i)
#define REP2(i, a, b) for (ll i = ll(a); i < ll(b); ++i)
#define REP(...) OVERLOAD3(__VA_ARGS__, REP2, REP1, REP0)(__VA_ARGS__)
#define RREP0(n) for (ll i = ll(n) - 1; i >= 0; --i)
#define RREP1(i, n) for (ll i = ll(n) - 1; i >= 0; --i)
#define RREP2(i, a, b) for (ll i = ll(a) - 1; i >= b; --i)
#define RREP(...) OVERLOAD3(__VA_ARGS__, RREP2, RREP1, RREP0)(__VA_ARGS__)
#define REPE(i, c) for (auto&& i : c)
#define TCASE() ll _ttt; cin >> _ttt; while(_ttt--)

template<class... T> void COMMON_IN(T&... a) { (cin >> ... >> a); }
#define LI(...) ll __VA_ARGS__; COMMON_IN(__VA_ARGS__);
#define SI(...) string __VA_ARGS__; COMMON_IN(__VA_ARGS__);

using vl = vector<ll>; using vvl = vector<vl>; using vvvl = vector<vvl>;
#define VLI(a, n) vector<ll> a; a.assign(n, 0); for(auto& x : a) cin >> x;
#define DLI(a, n) deque<ll> a; a.assign(n, 0); for(auto& x : a) cin >> x;
#define VSI(a, n) vector<string> a; a.assign(n, ""); for(auto& x : a) cin >> x;
#define VVLI(a, n, m) vector<vector<ll>> a(n, vector<ll>(m)); for(auto& x : a) for(auto& y : x) cin >> y;
using vd = vector<double>; using pl = pair<ll, ll>; using vpl = vector<pl>; using vvpl = vector<vpl>;

struct uv { ll u; ll v; };
struct uvc { ll u; ll v; ll c = 1; };
#define VUVI(a, n) vector<uv> a; a.assign(n, {0, 0}); for(auto& x : a) {cin >> x.u >> x.v; x.u--; x.v--;}
#define VUVCI(a, n) vector<uvc> a; a.assign(n, {0, 0, 0}); for(auto& x : a) {cin >> x.u >> x.v >> x.c; x.u--; x.v--;}
vvl to_edge(const ll n, const vector<uv>& v) { vvl ret(n); for (auto& x : v) ret[x.u].emplace_back(x.v); return ret; }
vvl to_edge_d(const ll n, const vector<uv>& v) { vvl ret(n); for (auto& x : v) { ret[x.u].emplace_back(x.v); ret[x.v].emplace_back(x.u); } return ret; }
vvpl to_edge_d(const ll n, const vector<uvc>& v) { vvpl ret(n); for (auto& x : v) { ret[x.u].emplace_back(x.v, x.c); ret[x.v].emplace_back(x.u, x.c); } return ret; }

template <class T = long long> using pql = priority_queue<T>;
template <class T = long long> using pqg = priority_queue<T, vector<T>, greater<T>>;
using vm = vector<mint>; using vvm = vector<vm>;

ostream& operator<<(ostream& os, const mint& v) { os << v.val(); return os; }
void yn(bool f) { std::cout << (f ? "Yes" : "No") << "\n"; };
template<class T> void ov(const T& v) { for (auto it = v.begin(); it != v.end(); it++) { if (it != v.begin()) cout << " "; cout << *it; } };
template<> void ov(const vm& v) { for (auto it = v.begin(); it != v.end(); it++) { if (it != v.begin()) cout << " "; cout << it->val(); } };

const ll llhuge = 1LL << 61; //十分でかいが多少足しても溢れない数値
auto gmax(const auto& a, const auto& b) { return a > b ? a : b; };
auto gmin(const auto& a, const auto& b) { return a < b ? a : b; };
bool chmin(auto& a, const auto& b) { const auto olda = a; a = gmin(a, b); return olda != a; }
bool chmax(auto& a, const auto& b) { const auto olda = a; a = gmax(a, b); return olda != a; }
void sort(auto& v) { std::ranges::sort(v); };
void rev(auto& v) { std::ranges::reverse(v); };
template<class T> auto p_sum(const T& v) { T ret(v.size()); std::partial_sum(begin(v), end(v), ret.begin()); return ret; };
template<class T, class K = T::key_type, class V = T::mapped_type> [[nodiscard]] V myat(const T& mp, const K& key) { return mp.find(key) == mp.end() ? V() : mp.at(key); }
long long ceil(const long long a, const long long b) { return (a + b - 1) / b; }

using _mint = atcoder::modint998244353;

_mint fac[3000001], finv[3000001], inv[3000001];

void setup(int _max = 3000000) {
	constexpr int MOD = _mint::mod();
	fac[0] = fac[1] = 1;
	finv[0] = finv[1] = 1;
	inv[1] = 1;
	for (int i = 2; i <= _max; i++) {
		fac[i] = fac[i - 1] * i;
		inv[i] = (_mint)MOD - inv[MOD % i] * (MOD / i);
		finv[i] = finv[i - 1] * inv[i];
	}
}

_mint binom(int n, int r) {
	if (n < r or n < 0 or r < 0) return _mint::raw(0);
	return fac[n] * finv[r] * finv[n - r];
}

_mint nHr(int n, int r) {
	return binom(n + r - 1, r);
}

using mat_row = vector<mint>;
using mat = vector<mat_row>;
mat make_mat(ll size, mat_row::value_type init = 0) {
	return mat(size, mat_row(size, init));
}

mat operator*(const mat& a, const mat& b) {
	mat c(a.size(), mat_row(b[0].size()));
	for (size_t i = 0; i < c.size(); ++i)
		for (size_t j = 0; j < c[0].size(); ++j)
			for (size_t k = 0; k < a[0].size(); ++k)
				c[i][j] += a[i][k] * b[k][j];
	return c;
}
mat pow(mat a, ll n) {
	mat res(a.size(), mat_row(a[0].size()));
	for (size_t i = 0; i < res.size(); ++i) res[i][i] = 1;
	for (; n; n /= 2) {
		if (n & 1) res = res * a;
		a = a * a;
	}
	return res;
}


int main() {
	cin.tie(nullptr);
	ios::sync_with_stdio(false);

	LI(k, l, r);
	setup(k + 1);

	auto m = make_mat(k + 4, 0);

	REP(i, k + 4) {
		if (i == 0) {
			m[i][0] = k;
			m[i][1] = 1;
			REP(j, 2, 2 + k) {
				m[i][j] = 0;
			}
			m[i][2 + k] = 1;
		}
		if (i > 0 && i < k + 2) {
			ll top = k - (i - 1);
			REP(j, i, 2 + k) {
				m[i][j] = binom(top, k + 1 - j);
			}
		}
		if (i == k + 2) {
			m[i][k + 2] = k;
		}
		if (i == k + 3) {
			m[i][0] = 1;
			m[i][i] = 1;
		}
	}
	
	auto ml = pow(m, l);
	auto mr = pow(m, r + 1);
	cout << (mr[k+3][0] + mr[k+3][k+1] + mr[k+3][k+2] - (ml[k + 3][0] + ml[k+3][k+1] + ml[k + 3][k + 2])).val() << "\n";
}
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