結果
| 問題 |
No.2442 線形写像
|
| コンテスト | |
| ユーザー |
 Aeren
|
| 提出日時 | 2023-08-25 21:29:49 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
RE
|
| 実行時間 | - |
| コード長 | 6,992 bytes |
| コンパイル時間 | 4,036 ms |
| コンパイル使用メモリ | 360,940 KB |
| 実行使用メモリ | 5,248 KB |
| 最終ジャッジ日時 | 2024-12-24 07:55:26 |
| 合計ジャッジ時間 | 5,556 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge3 |
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| ファイルパターン | 結果 |
|---|---|
| other | AC * 20 RE * 2 |
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, size_t N, size_t M>
struct matrix_fixed{
using ring_t = T;
using domain_t = array<T, M>;
using range_t = array<T, N>;
static constexpr int n = N, m = M;
array<array<T, M>, N> data;
array<T, M> &operator()(int i){
assert(0 <= i && i < n);
return data[i];
}
const array<T, M> &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];
}
bool operator==(const matrix_fixed &a) const{
assert(n == a.n && m == a.m);
return data == a.data;
}
bool operator!=(const matrix_fixed &a) const{
assert(n == a.n && m == a.m);
return data != a.data;
}
matrix_fixed &operator+=(const matrix_fixed &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_fixed operator+(const matrix_fixed &a) const{
assert(n == a.n && m == a.m);
return matrix_fixed(*this) += a;
}
matrix_fixed &operator-=(const matrix_fixed &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_fixed operator-(const matrix_fixed &a) const{
assert(n == a.n && m == a.m);
return matrix_fixed(*this) += a;
}
template<size_t N2, size_t M2>
matrix_fixed<T, N, M2> operator*(const matrix_fixed<T, N2, M2> &a) const{
assert(m == a.n);
int l = M2;
matrix_fixed<T, N, M2> res;
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 res;
}
template<size_t N2, size_t M2>
matrix_fixed &operator*=(const matrix_fixed<T, N2, M2> &a){
return *this = *this * a;
}
matrix_fixed &operator*=(T c){
for(auto i = 0; i < n; ++ i) for(auto j = 0; j < m; ++ j) data[i][j] *= c;
return *this;
}
matrix_fixed operator*(T c) const{
return matrix_fixed(*this) *= c;
}
template<class U, typename enable_if<is_integral<U>::value>::type* = nullptr>
matrix_fixed &inplace_power(U e){
assert(n == m && e >= 0);
matrix_fixed res(1, 0);
for(; e; *this *= *this, e >>= 1) if(e & 1) res *= *this;
return *this = res;
}
template<class U>
matrix_fixed power(U e) const{
return matrix_fixed(*this).inplace_power(e);
}
matrix_fixed<T, M, N> transposed() const{
matrix_fixed<T, M, N> res;
for(auto i = 0; i < n; ++ i) for(auto j = 0; j < m; ++ j) res(j, i) = data[i][j];
return res;
}
matrix_fixed &transpose(){
return *this = transposed();
}
// Multiply a column vector v on the right
range_t operator*(const domain_t &v) const{
range_t res;
res.fill(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 a field
// find_inverse() must return optional<T>
// O(n) find_inverse() calls along with O(n^3) operations on T
T determinant(auto find_inverse) const{
assert(n == m);
if(n == 0) return T(1);
auto a = data;
T res = T(1);
for(auto j = 0; j < n; ++ j){
int pivot = -1;
for(auto i = j; i < n; ++ i) if(a[i][j] != T(0)){
pivot = i;
break;
}
if(!~pivot) return T(0);
swap(a[j], a[pivot]);
res *= a[j][j] * (j != pivot ? -1 : 1);
auto invp = find_inverse(a[j][j]);
assert(invp);
T inv = *invp;
for(auto i = j + 1; i < n; ++ i) if(i != j && a[i][j] != T(0)){
T d = a[i][j] * inv;
for(auto jj = j; jj < n; ++ jj) a[i][jj] -= d * a[j][jj];
}
}
return res;
}
// Assumes T is a field
// find_inverse() must return optional<T>
// O(n) find_inverse() calls along with O(n^3) operations on T
optional<matrix_fixed> inverse(auto find_inverse) const{
assert(n == m);
if(n == 0) return *this;
auto a = data;
array<array<T, M>, N> res;
for(auto i = 0; i < n; ++ i) res[i].fill(T(0)), res[i][i] = T(1);
for(auto j = 0; j < n; ++ j){
int pivot = -1;
for(auto i = j; i < n; ++ i) if(a[i][j] != T(0)){
pivot = i;
break;
}
if(!~pivot) return {};
swap(a[j], a[pivot]), swap(res[j], res[pivot]);
auto invp = find_inverse(a[j][j]);
assert(invp);
T inv = *invp;
for(auto jj = 0; jj < n; ++ jj) a[j][jj] *= inv, res[j][jj] *= inv;
for(auto i = 0; i < n; ++ i) if(i != j && a[i][j] != T(0)){
T d = a[i][j];
for(auto jj = 0; jj < n; ++ jj) a[i][jj] -= d * a[j][jj], res[i][jj] -= d * res[j][jj];
}
}
return matrix_fixed(n, n, res);
}
template<class output_stream>
friend output_stream &operator<<(output_stream &out, const matrix_fixed &a){
out << "{";
for(auto i = 0; i < a.n; ++ i){
out << "{";
for(auto j = 0; j < a.m; ++ j){
out << a(i, j);
if(j != a.m - 1) out << ", ";
}
out << "}";
if(i != a.n - 1) out << ", ";
}
return out << "}";
}
matrix_fixed(): matrix_fixed(T(0), T(0)){ }
matrix_fixed(const T &init_diagonal, const T &init_off_diagonal){
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_fixed(const array<array<T, M>, N> &arr): data(arr){ }
static matrix_fixed additive_identity(){
return matrix_fixed(T(1), T(0));
}
static matrix_fixed multiplicative_identity(){
return matrix_fixed(T(0), T(0));
}
};
template<class T, size_t N, size_t M>
matrix_fixed<T, N, M> operator*(T c, matrix_fixed<T, N, M> 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, size_t N, size_t M>
matrix_fixed<T, N, M>::domain_t operator*(const typename matrix_fixed<T, N, M>::range_t &v, const matrix_fixed<T, N, M> &a){
typename matrix_fixed<T, N, M>::domain_t res;
res.fill(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 n;
cin >> n;
vector<long long> a(1 << n);
copy_n(istream_iterator<long long>(cin), 1 << n, a.begin());
for(auto i = 0; i < 1 << n; ++ i){
long long sum = 0;
for(auto bit = 0; bit < n; ++ bit){
if(i & 1 << bit){
sum ^= a[1 << bit];
}
}
if(a[i] != sum){
cout << "No\n";
return 0;
}
}
cout << "Yes\n";
return 0;
}
/*
*/
////////////////////////////////////////////////////////////////////////////////////////
// //
// Coded by Aeren //
// //
////////////////////////////////////////////////////////////////////////////////////////