結果
| 問題 | No.2446 完全列 |
| ユーザー |
 Aeren
|
| 提出日時 | 2023-08-26 04:48:05 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 3 ms / 2,000 ms |
| コード長 | 10,480 bytes |
| コンパイル時間 | 4,672 ms |
| コンパイル使用メモリ | 376,284 KB |
| 実行使用メモリ | 6,820 KB |
| 最終ジャッジ日時 | 2024-12-24 19:05:22 |
| 合計ジャッジ時間 | 5,396 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge4 |
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| ファイルパターン | 結果 |
|---|---|
| other | AC * 30 |
ソースコード
#include <x86intrin.h>#include <bits/stdc++.h>using namespace std;#if __cplusplus > 201703L#include <ranges>using namespace numbers;#endif// T must support +=, -=, *, *=, ==, and !=template<class T>struct matrix{using ring_t = T;using domain_t = vector<T>;using range_t = vector<T>;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];}T &operator()(int i, int j){assert(0 <= i && i < n && 0 <= j && j < m);return data[i][j];}const T &operator()(int i, int j) const{assert(0 <= i && i < n && 0 <= j && j < m);return data[i][j];}operator vector<vector<T>>() const{return data;}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;}range_t operator*(const domain_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(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.// Returns {REF matrix, determinant, rank}tuple<matrix &, T, int> inplace_REF(){if(n == 0) return {*this, T(1), 0};T det = 1;int rank = 0;for(auto j = 0; j < m; ++ 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]){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].data / data[i][j].data;if(q) 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]) ++ 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(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.// Returns {REF matrix, determinant, rank}tuple<matrix, T, int> REF() const{return matrix(*this).inplace_REF();}// Assumes T is a field.// O(n) divisions with O(n^3) additions, subtractions, and multiplications.// Returns {REF matrix, determinant, rank}tuple<matrix &, T, int> inplace_REF_field(){if(n == 0) return {*this, T(1), 0};T det = T(1);int rank = 0;for(auto j = 0; j < m; ++ 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[j][k];}++ rank;if(rank == n) break;}return {*this, det, rank};}// Assumes T is a field.// O(n) divisions with O(n^3) additions, subtractions, and multiplications.// Returns {REF matrix, determinant, rank}tuple<matrix, T, int> REF_field() const{return matrix(*this).inplace_REF_field();}// Assumes T is a field.// O(n) divisions with O(n^3) additions, subtractions, and multiplications.optional<matrix> inverse(auto find_inverse) const{assert(n == m);if(n == 0) return *this;auto a = data;vector<vector<T>> res(n, vector<T>(n, T(0)));for(auto i = 0; i < n; ++ i) res[i][i] = T(1);for(auto j = 0; j < n; ++ j){int rank = j, pivot = -1;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 = j; k < n; ++ k) a[rank][k] *= inv, res[rank][k] *= inv;for(auto i = 0; i < n; ++ i) if(i != j && a[i][j] != T(0)){T d = a[i][j];for(auto k = j; k < n; ++ k) a[i][k] -= d * a[j][k], res[i][k] -= d * res[j][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());}// 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) << " ";}out << "\n";}return out;}matrix(int n, int m, T init_diagonal = T(0), T init_off_diagonal = T(0)): n(n), m(m){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(const vector<vector<T>> &arr, int _n = -1, int _m = -1): n(~_n ? _n : (int)arr.size()), m(~_m ? _m : (int)arr[0].size()), data(arr){ }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 lefttemplate<class T>typename matrix<T>::domain_t operator*(const typename matrix<T>::range_t &v, const matrix<T> &a){assert(a.n == (int)size(v));typename matrix<T>::domain_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;}int main(){cin.tie(0)->sync_with_stdio(0);cin.exceptions(ios::badbit | ios::failbit);int l, m, n;cin >> l >> m >> n;matrix<int> a(l, m), b(m, n);for(auto i = 0; i < l; ++ i){for(auto j = 0; j < m; ++ j){cin >> a(i, j);}}for(auto i = 0; i < m; ++ i){for(auto j = 0; j < n; ++ j){cin >> b(i, j);}}if(a * b == matrix<int>::additive_identity(l, n) && a.rank() + b.rank() == m){cout << "Yes\n";}else{cout << "No\n";}return 0;}/**/////////////////////////////////////////////////////////////////////////////////////////// //// Coded by Aeren //// //////////////////////////////////////////////////////////////////////////////////////////