結果

問題 No.906 Y字グラフ
コンテスト
ユーザー ゆにぽけ
提出日時 2024-01-04 22:37:24
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 2 ms / 2,000 ms
コード長 3,956 bytes
コンパイル時間 1,091 ms
コンパイル使用メモリ 80,472 KB
最終ジャッジ日時 2025-02-18 16:13:40
ジャッジサーバーID
（参考情報） 		judge3 / 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 * 4
other AC * 28
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 # 

#include<iostream>
#include<vector>
#include<cassert>
using namespace std;
template<class T> struct Matrix
{
	private:
	vector<vector<T>> M;
	int H,W;

	public:
	static const Matrix e(int N)
	{
		Matrix ret(N,N);
		for(int i = 0;i < N;i++) ret[i][i] = 1;
		return ret;
	};
	constexpr Matrix(int h,int w,T x = 0) noexcept
	{
		H = h,W = w;
		M.assign(H,vector<T>(W,x));
	}

	constexpr vector<T> &operator[](const int i) noexcept
	{
		assert(0 <= i && i < H);
		return M[i];
	}

	constexpr vector<T> operator[](const int i) const
	{
		assert(0 <= i && i < H);
		return M[i];
	}

	constexpr Matrix &operator*=(const Matrix &rhs) noexcept
	{
		assert(W == rhs.H);
		Matrix tmp(H,rhs.W);
		for(int i = 0;i < H;i++)
		{
			for(int j = 0;j < rhs.W;j++)
			{
				for(int k = 0;k < W;k++)
				{
					tmp[i][j] += M[i][k] * rhs.M[k][j];
				}
			}
		}
		swap(*this,tmp);
		return *this;
	}

	constexpr Matrix power(long long N) noexcept
	{
		assert(H == W);
		assert(N >= 0);
		Matrix res = e(H),P = *this;
		while(N)
		{
			if(N & 1) res *= P;
			P *= P;
			N >>= 1;
		}
		return res;
	};

	friend Matrix operator*(const Matrix &lhs,const Matrix &rhs)
	{
		return Matrix(lhs) *= rhs;
	}

	friend ostream &operator<<(ostream &os,const Matrix &x)
	{
		for(int i = 0;i < x.H;i++)
		{
			for(int j = 0;j < x.W;j++)
			{
				os << x.M[i][j] << (i + 1 < x.H && j + 1 == x.W ? "\n":" ");
			}
		}
		return os;
	}
};
template<int m> struct modint
{
	private:
	unsigned int value;
	static constexpr int mod() {return m;}

	public:
	constexpr modint(const long long x = 0) noexcept
	{
		long long y = x;
		if(y < 0 || y >= mod())
		{
			y %= mod();
			if(y < 0) y += mod();
		}
		value = (unsigned int)y;
	}
	constexpr unsigned int val() noexcept {return value;}
	constexpr modint &operator+=(const modint &other) noexcept
	{
		value += other.value;
		if(value >= mod()) value -= mod();
		return *this;
	}
	constexpr modint &operator-=(const modint &other) noexcept
	{
		unsigned int x = value;
		if(x < other.value) x += mod();
		x -= other.value;
		value = x;
		return *this;
	}
	constexpr modint &operator*=(const modint &other) noexcept
	{
		unsigned long long x = value;
		x *= other.value;
		value = (unsigned int) (x % mod());
		return *this;
	}
	constexpr modint &operator/=(const modint &other) noexcept
	{
		return *this *= other.inverse();
	}
	constexpr modint inverse() const noexcept
	{
		assert(value);
		long long a = value,b = mod(),x = 1,y = 0;
		while(b)
		{
			long long q = a/b;
			a -= q*b; swap(a,b);
			x -= q*y; swap(x,y);
		}
		return modint(x);
	}
	constexpr modint power(long long N) const noexcept
	{
		assert(N >= 0);
		modint p = *this,ret = 1;
		while(N)
		{
			if(N & 1) ret *= p;
			p *= p;
			N >>= 1;
		}
		return ret;
	}
	constexpr modint operator+() {return *this;}
	constexpr modint operator-() {return modint() - *this;}
	constexpr modint &operator++(int) noexcept {return *this += 1;}
	constexpr modint &operator--(int) noexcept {return *this -= 1;}
	friend modint operator+(const modint& lhs, const modint& rhs) {return modint(lhs) += rhs;}
	friend modint operator-(const modint& lhs, const modint& rhs) {return modint(lhs) -= rhs;}
	friend modint operator*(const modint& lhs, const modint& rhs) {return modint(lhs) *= rhs;}
	friend modint operator/(const modint& lhs, const modint& rhs) {return modint(lhs) /= rhs;}
	friend ostream &operator<<(ostream &os,const modint &x) {return os << x.value;}
};
/* using mint = modint<998244353>; */
using mint = modint<1000000007>;

using mat = Matrix<mint>;
int main()
{	long long N;
	cin >> N;
	mint ans = 0;
	N -= 4;
	//x + y + z = N 0 <= x <= y <= z
	
	mat dp(6,6);
	dp[0][1] = 1,dp[0][2] = 1,dp[0][4] = -1,dp[0][5] = 1;
	for(int i = 1;i < 5;i++) dp[i][i-1] = 1;
	dp[5][5] = 1;
	mat S(6,1);
	S[0][0] = 4;
	S[1][0] = 3;
	S[2][0] = 2;
	S[3][0] = 1;
	S[4][0] = 1;
	S[5][0] = 1;
	if(N >= 4)
	{
		S = dp.power(N-4) * S;
		cout << S[0][0] << "\n";
	}
	else
	{
		cout << S[4 - N][0] << "\n";
	}
}
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