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#403336#2073. Knowledge-Oriented ProblemqwerasdfzxclCompile Error//C++2013.6kb2024-05-02 08:58:422024-05-02 08:58:43

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  • [2024-05-02 08:58:43]
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  • [2024-05-02 08:58:42]
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answer

#include <bits/stdc++.h>
#include <atcoder/modint>

using namespace std;
using mint = atcoder::modint1000000007;
typedef long long ll;

template<class T>
struct matrix{
	int n, m;
	vector<vector<T>> data;
	vector<T> &operator[](int i){
		assert(0 <= i && i < n);
		return data[i];
	}
	const vector<T> &operator[](int i) const{
		assert(0 <= i && i < n);
		return data[i];
	}
	matrix &inplace_slice(int il, int ir, int jl, int jr){
		assert(0 <= il && il <= ir && ir <= n);
		assert(0 <= jl && jl <= jr && jr <= m);
		n = ir - il, m = jr - jl;
		if(il > 0) for(auto i = 0; i < n; ++ i) swap(data[i], data[il + i]);
		data.resize(n);
		for(auto &row: data){
			row.erase(row.begin(), row.begin() + jl);
			row.resize(m);
		}
		return *this;
	}
	matrix slice(int il, int ir, int jl, int jr) const{
		return matrix(*this).inplace_slice(il, ir, jl, jr);
	}
	matrix &inplace_row_slice(int il, int ir){
		assert(0 <= il && il <= ir && ir <= n);
		n = ir - il;
		if(il > 0) for(auto i = 0; i < n; ++ i) swap(data[i], data[il + i]);
		data.resize(n);
		return *this;
	}
	matrix row_slice(int il, int ir) const{
		return matrix(*this).inplace_row_slice(il, ir);
	}
	matrix &inplace_column_slice(int jl, int jr){
		assert(0 <= jl && jl <= jr && jr <= m);
		m = jr - jl;
		for(auto &row: data){
			row.erase(row.begin(), row.begin() + jl);
			row.resize(m);
		}
		return *this;
	}
	matrix column_slice(int jl, int jr) const{
		return matrix(*this).inplace_column_slice(jl, jr);
	}
	bool operator==(const matrix &a) const{
		assert(n == a.n && m == a.m);
		return data == a.data;
	}
	bool operator!=(const matrix &a) const{
		assert(n == a.n && m == a.m);
		return data != a.data;
	}
	matrix &operator+=(const matrix &a){
		assert(n == a.n && m == a.m);
		for(auto i = 0; i < n; ++ i) for(auto j = 0; j < m; ++ j) data[i][j] += a[i][j];
		return *this;
	}
	matrix operator+(const matrix &a) const{
		return matrix(*this) += a;
	}
	matrix &operator-=(const matrix &a){
		assert(n == a.n && m == a.m);
		for(auto i = 0; i < n; ++ i) for(auto j = 0; j < m; ++ j) data[i][j] -= a[i][j];
		return *this;
	}
	matrix operator-(const matrix &a) const{
		return matrix(*this) -= a;
	}
	matrix operator*=(const matrix &a){
		assert(m == a.n);
		int l = a.m;
		matrix res(n, l);
		for(auto i = 0; i < n; ++ i) for(auto j = 0; j < m; ++ j) for(auto k = 0; k < l; ++ k) res[i][k] += data[i][j] * a[j][k];
		return *this = res;
	}
	matrix operator*(const matrix &a) const{
		return matrix(*this) *= a;
	}
	matrix &operator*=(T c){
		for(auto i = 0; i < n; ++ i) for(auto j = 0; j < m; ++ j) data[i][j] *= c;
		return *this;
	}
	matrix operator*(T c) const{
		return matrix(*this) *= c;
	}
	template<class U, typename enable_if<is_integral<U>::value>::type* = nullptr>
	matrix &inplace_power(U e){
		assert(n == m && e >= 0);
		matrix res(n, n, T{1});
		for(; e; *this *= *this, e >>= 1) if(e & 1) res *= *this;
		return *this = res;
	}
	template<class U>
	matrix power(U e) const{
		return matrix(*this).inplace_power(e);
	}
	matrix &inplace_transpose(){
		assert(n == m);
		for(auto i = 0; i < n; ++ i) for(auto j = i + 1; j < n; ++ j) swap(data[i][j], data[j][i]);
		return *this;
	}
	matrix transpose() const{
		if(n == m) return matrix(*this).inplace_transpose();
		matrix res(m, n);
		for(auto i = 0; i < n; ++ i) for(auto j = 0; j < m; ++ j) res[j][i] = data[i][j];
		return res;
	}
	vector<T> operator*(const vector<T> &v) const{
		assert(m == (int)v.size());
		vector<T> res(n, T{0});
		for(auto i = 0; i < n; ++ i) for(auto j = 0; j < m; ++ j) res[i] += data[i][j] * v[j];
		return res;
	}
	// Assumes T is either a floating, integral, or a modular type.
	// If T is a floating type, O(up_to) divisions with O(n * m * up_to) additions, subtractions, and multiplications.
	// Otherwise, O(n * up_to * log(size)) divisions with O(n * m * up_to) additions, subtractions, and multiplications.
	// Returns {REF matrix, determinant, rank}
	tuple<matrix &, T, int> inplace_REF(int up_to = -1){
		if(n == 0) return {*this, T{1}, 0};
		if(!~up_to) up_to = m;
		T det = 1;
		int rank = 0;
		for(auto j = 0; j < up_to; ++ j){
			if constexpr(is_floating_point_v<T>){
				static const T eps = 1e-9;
				int pivot = rank;
				for(auto i = rank + 1; i < n; ++ i) if(abs(data[pivot][j]) < abs(data[i][j])) pivot = i;
				if(rank != pivot){
					swap(data[rank], data[pivot]);
					det *= -1;
				}
				if(abs(data[rank][j]) <= eps) continue;
				det *= data[rank][j];
				T inv = 1 / data[rank][j];
				for(auto i = rank + 1; i < n; ++ i) if(abs(data[i][j]) > eps){
					T coef = data[i][j] * inv;
					for(auto k = j; k < m; ++ k) data[i][k] -= coef * data[rank][k];
				}
				++ rank;
			}
			else{
				for(auto i = rank + 1; i < n; ++ i) while(data[i][j]!=0){
					T q;
					if constexpr(is_integral_v<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>) q = data[rank][j] / data[i][j];
					else q = data[rank][j].val() / data[i][j].val();
					if(q!=0) for(auto k = j; k < m; ++ k) data[rank][k] -= q * data[i][k];
					swap(data[rank], data[i]);
					det *= -1;
				}
				if(rank == j) det *= data[rank][j];
				else det = T{0};
				if(data[rank][j]!=0) ++ rank;
			}
			if(rank == n) break;
		}
		return {*this, det, rank};
	}
	// Assumes T is either a floating, integral, or a modular type.
	// If T is a floating type, O(up_to) divisions with O(n * m * up_to) additions, subtractions, and multiplications.
	// Otherwise, O(n * up_to * log(size)) divisions with O(n * m * up_to) additions, subtractions, and multiplications.
	// Returns {REF matrix, determinant, rank}
	tuple<matrix, T, int> REF(int up_to = -1) const{
		return matrix(*this).inplace_REF(up_to);
	}
	// Assumes T is a field.
	// O(up_to) divisions with O(n * m * up_to) additions, subtractions, and multiplications.
	// Returns {REF matrix, determinant, rank}
	tuple<matrix &, T, int> inplace_REF_field(int up_to = -1){
		if(n == 0) return {*this, T{1}, 0};
		if(!~up_to) up_to = m;
		T det = T{1};
		int rank = 0;
		for(auto j = 0; j < up_to; ++ j){
			int pivot = -1;
			for(auto i = rank; i < n; ++ i) if(data[i][j] != T{0}){
				pivot = i;
				break;
			}
			if(!~pivot){
				det = T{0};
				continue;
			}
			if(rank != pivot){
				swap(data[rank], data[pivot]);
				det *= -1;
			}
			det *= data[rank][j];
			T inv = 1 / data[rank][j];
			for(auto i = rank + 1; i < n; ++ i) if(data[i][j] != T{0}){
				T coef = data[i][j] * inv;
				for(auto k = j; k < m; ++ k) data[i][k] -= coef * data[rank][k];
			}
			++ rank;
			if(rank == n) break;
		}
		return {*this, det, rank};
	}
	// Assumes T is a field.
	// O(up_to) divisions with O(n * m * up_to) additions, subtractions, and multiplications.
	// Returns {REF matrix, determinant, rank}
	tuple<matrix, T, int> REF_field(int up_to = -1) const{
		return matrix(*this).inplace_REF_field(up_to);
	}
	// Assumes T is a field.
	// O(n) divisions with O(n^3) additions, subtractions, and multiplications.
	optional<matrix> inverse() const{
		assert(n == m);
		if(n == 0) return *this;
		auto a = data;
		auto res = multiplicative_identity();
		for(auto j = 0; j < n; ++ j){
			int rank = j, pivot = -1;
			if constexpr(is_floating_point_v<T>){
				static const T eps = 1e-9;
				pivot = rank;
				for(auto i = rank + 1; i < n; ++ i) if(abs(a[pivot][j]) < abs(a[i][j])) pivot = i;
				if(abs(a[pivot][j]) <= eps) return {};
			}
			else{
				for(auto i = rank; i < n; ++ i) if(a[i][j] != T{0}){
					pivot = i;
					break;
				}
				if(!~pivot) return {};
			}
			swap(a[rank], a[pivot]), swap(res[rank], res[pivot]);
			T inv = 1 / a[rank][j];
			for(auto k = 0; k < n; ++ k) a[rank][k] *= inv, res[rank][k] *= inv;
			for(auto i = 0; i < n; ++ i){
				if constexpr(is_floating_point_v<T>){
					static const T eps = 1e-9;
					if(i != rank && abs(a[i][j]) > eps){
						T d = a[i][j];
						for(auto k = 0; k < n; ++ k) a[i][k] -= d * a[rank][k], res[i][k] -= d * res[rank][k];
					}
				}
				else if(i != rank && a[i][j] != T{0}){
					T d = a[i][j];
					for(auto k = 0; k < n; ++ k) a[i][k] -= d * a[rank][k], res[i][k] -= d * res[rank][k];
				}
			}
		}
		return res;
	}
	// Assumes T is either a floating, integral, or a modular type.
	// If T is a floating type, O(n) divisions with O(n^3) additions, subtractions, and multiplications.
	// Otherwise, O(n^2 * log(size)) divisions with O(n^3) additions, subtractions, and multiplications.
	T determinant() const{
		assert(n == m);
		return get<1>(REF());
	}
	// Assumes T is a field.
	// O(n) divisions with O(n^3) additions, subtractions, and multiplications.
	T determinant_field() const{
		assert(n == m);
		return get<1>(REF_field());
	}
	// Assumes T is either a floating, integral, or a modular type.
	// If T is a floating type, O(n) divisions with O(n^3) additions, subtractions, and multiplications.
	// Otherwise, O(n^2 * log(size)) divisions with O(n^3) additions, subtractions, and multiplications.
	int rank() const{
		return get<2>(REF());
	}
	// Assumes T is a field.
	// O(n) divisions with O(n^3) additions, subtractions, and multiplications.
	int rank_field() const{
		return get<2>(REF_field());
	}
	// Regarding the matrix as a system of linear equations by separating first m-1 columns, find a solution of the linear equation.
	// Assumes T is a field
	// O(n * m^2)
	optional<vector<T>> find_a_solution() const{
		assert(m >= 1);
		auto [ref, _, rank] = REF_field(m - 1);
		for(auto i = rank; i < n; ++ i) if(ref[i][m - 1] != T{0}) return {};
		vector<T> res(m - 1);
		for(auto i = rank - 1; i >= 0; -- i){
			int pivot = 0;
			while(pivot < m - 1 && ref[i][pivot] == T{0}) ++ pivot;
			assert(pivot < m - 1);
			res[pivot] = ref[i][m - 1];
			for(auto j = pivot + 1; j < m - 1; ++ j) res[pivot] -= ref[i][j] * res[j];
			res[pivot] /= ref[i][pivot];
		}
		return res;
	}
	// O(n * 2^n)
	T permanent() const{
		assert(n <= 30 && n == m);
		T perm = n ? 0 : 1;
		vector<T> sum(n);
		for(auto order = 1; order < 1 << n; ++ order){
			int j = __lg(order ^ order >> 1 ^ order - 1 ^ order - 1 >> 1), sign = (order ^ order >> 1) & 1 << j ? 1 : -1;
			T prod = order & 1 ? -1 : 1;
			if((order ^ order >> 1) & 1 << j) for(auto i = 0; i < n; ++ i) prod *= sum[i] += data[i][j];
			else for(auto i = 0; i < n; ++ i) prod *= sum[i] -= data[i][j];
			perm += prod;
		}
		return perm * (n & 1 ? -1 : 1);
	}
	template<class output_stream>
	friend output_stream &operator<<(output_stream &out, const matrix &a){
		out << "\n";
		for(auto i = 0; i < a.n; ++ i){
			for(auto j = 0; j < a.m; ++ j) out << a[i][j].val() << " ";
			out << "\n";
		}
		return out;
	}
	matrix(int n, int m, T init_diagonal = T{0}, T init_off_diagonal = T{0}): n(n), m(m){
		assert(n >= 0 && m >= 0);
		data.assign(n, vector<T>(m, T{0}));
		for(auto i = 0; i < n; ++ i) for(auto j = 0; j < m; ++ j) data[i][j] = i == j ? init_diagonal : init_off_diagonal;
	}
	matrix(int n, int m, const vector<vector<T>> &a): n(n), m(m), data(a){ }
	static matrix additive_identity(int n, int m){
		return matrix(n, m, T{0}, T{0});
	}
	static matrix multiplicative_identity(int n, int m){
		return matrix(n, m, T{1}, T{0});
	}
};
template<class T>
matrix<T> operator*(T c, matrix<T> a){
	for(auto i = 0; i < a.n; ++ i) for(auto j = 0; j < a.m; ++ j) a[i][j] = c * a[i][j];
	return a;
}
// Multiply a row vector v on the left
template<class T>
vector<T> operator*(const vector<T> &v, const matrix<T> &a){
	assert(a.n == (int)size(v));
	vector<T> res(a.m, T{0});
	for(auto i = 0; i < a.n; ++ i) for(auto j = 0; j < a.m; ++ j) res[j] += v[i] * a[i][j];
	return res;
}

mint calc(vector<vector<mint>> &G, int t){
	int n = G.size();
	vector<vector<mint>> fuck(n*t, vector<mint>(n*t, 0));

	for (int z=0;z<t;z++){
		for (int i=0;i<n;i++){
			for (int j=0;j<n;j++){
				fuck[z*n + i][z*n + j] = G[i][j];
			}
		}

		for (int i=0;i<n;i++) if (z<t-1) fuck[z*n+i][(z+1)*n+i] = -1;
		for (int i=0;i<n;i++) if (z<t-1) fuck[(z+1)*n+i][z*n+i] = -1;
	}

	fuck.pop_back();
	for (auto &x:fuck) x.pop_back();

	// cout << matrix<mint>(n*t-1, n*t-1, fuck);

	return matrix<mint>(n*t-1, n*t-1, fuck).determinant();

}

mint guess(vector<vector<mint>> G, ll t){
	int n = G.size();
	vector<matrix<mint>> F(t+1, matrix<mint>(n, n));
	F[0] = matrix<mint>(n, n, mint(1));
	F[1] = matrix<mint>(n, n, G);

	// cout << F[0];
	
	for (int i=2;i<=t;i++) F[i] = F[i-1]*F[1] - F[i-2];
	// return F[t].determinant();

	for (auto &x:G) x.back() = 0;
	for (auto &x:G.back()) x = 0;
	G.back().back() = 1;
	auto G2 = matrix<mint>(n, n, G);
	auto I2 = matrix<mint>(n, n, mint(1));
	I2[n-1][n-1] = 0;

	// cout << "ok " << t << '\n';
	// cout << F[t-1].n << F[t-1].m << G2.n << G2.m << F[t-2].n << F[t-2].m << I2.n << I2.m << '\n';

	if (t==1) return G2.determinant();
	if (t==2) return (F[t-1]*G2 - F[t-2]*I2).determinant();

	auto FUCK = F[1];
	for (int i=0;i<n;i++) FUCK[i][i] -= 1;
	auto H1 = F[t-2]*FUCK - F[t-3];
	auto H2 = F[t-3]*FUCK;
	if (t>3) H2 -= F[t-4];

	auto FUCK2 = FUCK;
	for (int i=0;i<n;i++) FUCK2[i][n-1] = 0;
	for (int j=0;j<n;j++) FUCK2[n-1][j] = 0;
	FUCK2[n-1][n-1] = 1;
	// cout << FUCK2 << "Hello\n";
	// cout << FUCK2[n-1][n-1].val() << '\n';
	return (H1*FUCK - H2*I2).determinant();
}

int main(){
	int n, m;
	ll t;
	scanf("%d %d %lld", &n, &m, &t);

	vector<vector<mint>> G(n, vector<mint>(n));
	for (int i=1;i<=m;i++){
		int x, y;
		scanf("%d %d", &x, &y);
		--x, --y;
		G[x][y] -= 1;
		G[y][x] -= 1;
		G[x][x] += 1;
		G[y][y] += 1;
	}

	for (int i=0;i<n;i++){
		if (t==2) G[i][i] += 1;
		else if (t>2) G[i][i] += 2;
	} 

	cout << guess(G, t).val() << '\n';

}

詳細信息

answer.code:2:10: fatal error: atcoder/modint: No such file or directory
    2 | #include <atcoder/modint>
      |          ^~~~~~~~~~~~~~~~
compilation terminated.