mmrz's library

This documentation is automatically generated by online-judge-tools/verification-helper

---

Project maintained by mm-rz Hosted on GitHub Pages — Theme by mattgraham

verify/yukicoder/3044.test.cpp

• View this file on GitHub
• Last update: 2025-07-05 17:21:00+09:00
• Problem: https://yukicoder.me/problems/no/3044

Depends on

• 行列ライブラリ (math/matrix.hpp)
• modint (math/modint.hpp)
• template/template.hpp

Code

#define PROBLEM "https://yukicoder.me/problems/no/3044"

#include "./../../template/template.hpp"
#include "./../../math/matrix.hpp"
#include "./../../math/modint.hpp"

using namespace mmrz;

using mint = modint<998244353>;

void SOLVE(){
	int n, t;
	int k, l;
	cin >> n >> t >> k >> l;

	matrix<mint> mat(t);

	mint a = mint(k-1)/mint(6);
	mint b = mint(l-k)/mint(6);
	mint c = mint(7-l)/mint(6);

	mat[0][0] = a;
	mat[0][1] = b;
	mat[0][t-1] = c;
	rep(i, t-1)mat[i+1][i] = 1;

	mat = matrix_power(mat, n-1);

	matrix<mint> iv(t, 1);
	auto f = [&](int x){
		return t-x-1;
	};
	iv[f(0)][0] = 1;
	rep(i, t){
		if(i+1 < t)iv[f(i+1)][0] += iv[f(i)][0]*a;
		if(i+2 < t)iv[f(i+2)][0] += iv[f(i)][0]*b;
	}
	
	matrix<mint> ans = mat*iv;
	cout << ans[f(0)][0] << '\n';
}

void mmrz::solve(){
	int t = 1;
	//cin >> t;
	while(t--)SOLVE();
}

#line 1 "verify/yukicoder/3044.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/3044"

#line 1 "template/template.hpp"
# include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;
const double pi = acos(-1);
template<class T>constexpr T inf() { return ::std::numeric_limits<T>::max(); }
template<class T>constexpr T hinf() { return inf<T>() / 2; }
template <typename T_char>T_char TL(T_char cX) { return tolower(cX); }
template <typename T_char>T_char TU(T_char cX) { return toupper(cX); }
template<class T> bool chmin(T& a,T b) { if(a > b){a = b; return true;} return false; }
template<class T> bool chmax(T& a,T b) { if(a < b){a = b; return true;} return false; }
int popcnt(unsigned long long n) { int cnt = 0; for (int i = 0; i < 64; i++)if ((n >> i) & 1)cnt++; return cnt; }
int d_sum(ll n) { int ret = 0; while (n > 0) { ret += n % 10; n /= 10; }return ret; }
int d_cnt(ll n) { int ret = 0; while (n > 0) { ret++; n /= 10; }return ret; }
ll gcd(ll a, ll b) { if (b == 0)return a; return gcd(b, a%b); };
ll lcm(ll a, ll b) { ll g = gcd(a, b); return a / g*b; };
ll MOD(ll x, ll m){return (x%m+m)%m; }
ll FLOOR(ll x, ll m) {ll r = (x%m+m)%m; return (x-r)/m; }
template<class T> using dijk = priority_queue<T, vector<T>, greater<T>>;
# define all(qpqpq)           (qpqpq).begin(),(qpqpq).end()
# define UNIQUE(wpwpw)        (wpwpw).erase(unique(all((wpwpw))),(wpwpw).end())
# define LOWER(epepe)         transform(all((epepe)),(epepe).begin(),TL<char>)
# define UPPER(rprpr)         transform(all((rprpr)),(rprpr).begin(),TU<char>)
# define rep(i,upupu)         for(ll i = 0, i##_len = (upupu);(i) < (i##_len);(i)++)
# define reps(i,opopo)        for(ll i = 1, i##_len = (opopo);(i) <= (i##_len);(i)++)
# define len(x)                ((ll)(x).size())
# define bit(n)               (1LL << (n))
# define pb push_back
# define eb emplace_back
# define exists(c, e)         ((c).find(e) != (c).end())

struct INIT{
	INIT(){
		std::ios::sync_with_stdio(false);
		std::cin.tie(0);
		cout << fixed << setprecision(20);
	}
}INIT;

namespace mmrz {
	void solve();
}

int main(){
	mmrz::solve();
}
#line 2 "math/matrix.hpp"

#line 5 "math/matrix.hpp"

template<typename T>
struct matrix {
	std::vector<std::vector<T>> a;

	matrix(){}
	matrix(int n, int m) : a(n, std::vector<T>(m, 0)){}
	matrix(int n) : a(n, std::vector<T>(n, 0)){}

	size_t height() const {return a.size(); }
	size_t width() const {return a[0].size(); }

	const std::vector<T> &operator[](int k) const {return a.at(k); }
	std::vector<T> &operator[](int k) {return a.at(k); }

	static matrix I(size_t n){
		matrix mat(n);
		for(size_t i = 0;i < n;i++){
			mat[i][i] = 1;
		}
		return mat;
	}

	matrix &operator+=(const matrix &b){
		size_t n = height(), m = width();
		assert(n == b.height() && m == b.width());
		for(size_t i = 0;i < n;i++){
			for(size_t j = 0;j < m;j++){
				(*this)[i][j] += b[i][j];
			}
		}
		return *this;
	}

	matrix &operator-=(const matrix &b){
		size_t n = height(), m = width();
		assert(n == b.height() && m == b.width());
		for(size_t i = 0;i < n;i++){
			for(size_t j = 0;j < m;j++){
				(*this)[i][j] -= b[i][j];
			}
		}
		return *this;
	}

	matrix &operator*=(const matrix &b){
		size_t n = height(), m = b.width(), p = width();
		assert(p == b.height());
		matrix c(n, m);
		for(size_t i = 0;i < n;i++){
			for(size_t k = 0;k < p;k++){
				for(size_t j = 0;j < m;j++){
					c[i][j] += (*this)[i][k] * b[k][j];
				}
			}
		}
		a.swap(c.a);
		return *this;
	}

	matrix &operator*=(const T &x){
		size_t n = height(), m = width();
		for(int i = 0;i < n;i++){
			for(int j = 0;j < m;j++){
				(*this)[i][j] *= x;
			}
		}
		return *this;
	}

	matrix operator+(const matrix &b) const {return matrix(*this) += b; }
	matrix operator-(const matrix &b) const {return matrix(*this) -= b; }
	matrix operator*(const matrix &b) const {return matrix(*this) *= b; }
	matrix operator*(const T &x) const {return matrix(*this) *= x; }
};

template<typename T>
matrix<T> matrix_power(matrix<T> a, long long k){
	assert(a.height() == a.width());
	matrix<T> ret = matrix<T>::I(a.height());
	while(k > 0){
		if(k & 1)ret *= a;
		a = a*a;
		k >>= 1;
	}
	return ret;
}
#line 2 "math/modint.hpp"

#line 5 "math/modint.hpp"

template <std::uint_fast64_t Modulus> class modint {
	using u64 = std::uint_fast64_t;
public:
	u64 a;
	constexpr modint(const u64 x = 0) noexcept : a(x % Modulus) {}
	constexpr u64 &value() noexcept { return a; }
	constexpr const u64 &value() const noexcept { return a; }
	constexpr modint operator+(const modint rhs) const noexcept {
		return modint(*this) += rhs;
	}
	constexpr modint operator-(const modint rhs) const noexcept {
		return modint(*this) -= rhs;
	}
	constexpr modint operator*(const modint rhs) const noexcept {
		return modint(*this) *= rhs;
	}
	constexpr modint operator/(const modint rhs) const noexcept {
		return modint(*this) /= rhs;
	}
	constexpr modint &operator+=(const modint rhs) noexcept {
		a += rhs.a;
		if (a >= Modulus) {
			a -= Modulus;
		}
		return *this;
	}
	constexpr modint &operator-=(const modint rhs) noexcept {
		if (a < rhs.a) {
			a += Modulus;
		}
		a -= rhs.a;
		return *this;
	}
	constexpr modint &operator*=(const modint rhs) noexcept {
		a = a * rhs.a % Modulus;
		return *this;
	}
	constexpr modint &operator/=(modint rhs) noexcept {
		u64 exp = Modulus - 2;
		while (exp) {
			if (exp % 2) {
				*this *= rhs;
			}
			rhs *= rhs;
			exp /= 2;
		}
		return *this;
	}

	constexpr modint& operator++() noexcept {
		if (++a == Modulus) a = 0;
		return *this;
	}
	constexpr modint operator++(int) noexcept {
		modint tmp(*this);
		++(*this);
		return tmp;
	}
	constexpr modint& operator--() noexcept {
		if (a == 0) a = Modulus;
		--a;
		return *this;
	}
	constexpr modint operator--(int) noexcept {
		modint tmp(*this);
		--(*this);
		return tmp;
	}

	friend std::ostream& operator<<(std::ostream& os, const modint& rhs) {
		os << rhs.a;
		return os;
	}
};
#line 6 "verify/yukicoder/3044.test.cpp"

using namespace mmrz;

using mint = modint<998244353>;

void SOLVE(){
	int n, t;
	int k, l;
	cin >> n >> t >> k >> l;

	matrix<mint> mat(t);

	mint a = mint(k-1)/mint(6);
	mint b = mint(l-k)/mint(6);
	mint c = mint(7-l)/mint(6);

	mat[0][0] = a;
	mat[0][1] = b;
	mat[0][t-1] = c;
	rep(i, t-1)mat[i+1][i] = 1;

	mat = matrix_power(mat, n-1);

	matrix<mint> iv(t, 1);
	auto f = [&](int x){
		return t-x-1;
	};
	iv[f(0)][0] = 1;
	rep(i, t){
		if(i+1 < t)iv[f(i+1)][0] += iv[f(i)][0]*a;
		if(i+2 < t)iv[f(i+2)][0] += iv[f(i)][0]*b;
	}
	
	matrix<mint> ans = mat*iv;
	cout << ans[f(0)][0] << '\n';
}

void mmrz::solve(){
	int t = 1;
	//cin >> t;
	while(t--)SOLVE();
}

Back to top page