結果
| 問題 | No.2446 完全列 |
| ユーザー |
 tokusakurai
|
| 提出日時 | 2023-08-25 23:11:47 |
| 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 | 9,327 bytes |
| コンパイル時間 | 2,262 ms |
| コンパイル使用メモリ | 206,508 KB |
| 最終ジャッジ日時 | 2025-02-16 14:21:18 |
|
ジャッジサーバーID （参考情報） |
judge4 / judge2 |
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| ファイルパターン | 結果 |
|---|---|
| other | AC * 30 |
ソースコード
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (n); i++)
#define per(i, n) for (int i = (n)-1; i >= 0; i--)
#define rep2(i, l, r) for (int i = (l); i < (r); i++)
#define per2(i, l, r) for (int i = (r)-1; i >= (l); i--)
#define each(e, v) for (auto &e : v)
#define MM << " " <<
#define pb push_back
#define eb emplace_back
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define sz(x) (int)x.size()
using ll = long long;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;
template <typename T>
using minheap = priority_queue<T, vector<T>, greater<T>>;
template <typename T>
using maxheap = priority_queue<T>;
template <typename T>
bool chmax(T &x, const T &y) {
return (x < y) ? (x = y, true) : false;
}
template <typename T>
bool chmin(T &x, const T &y) {
return (x > y) ? (x = y, true) : false;
}
template <typename T>
int flg(T x, int i) {
return (x >> i) & 1;
}
int pct(int x) { return __builtin_popcount(x); }
int pct(ll x) { return __builtin_popcountll(x); }
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int botbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int botbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
template <typename T>
void print(const vector<T> &v, T x = 0) {
int n = v.size();
for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' ');
if (v.empty()) cout << '\n';
}
template <typename T>
void printn(const vector<T> &v, T x = 0) {
int n = v.size();
for (int i = 0; i < n; i++) cout << v[i] + x << '\n';
}
template <typename T>
int lb(const vector<T> &v, T x) {
return lower_bound(begin(v), end(v), x) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, T x) {
return upper_bound(begin(v), end(v), x) - begin(v);
}
template <typename T>
void rearrange(vector<T> &v) {
sort(begin(v), end(v));
v.erase(unique(begin(v), end(v)), end(v));
}
template <typename T>
vector<int> id_sort(const vector<T> &v, bool greater = false) {
int n = v.size();
vector<int> ret(n);
iota(begin(ret), end(ret), 0);
sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; });
return ret;
}
template <typename T>
void reorder(vector<T> &a, const vector<int> &ord) {
int n = a.size();
vector<T> b(n);
for (int i = 0; i < n; i++) b[i] = a[ord[i]];
swap(a, b);
}
template <typename T>
T floor(T x, T y) {
assert(y != 0);
if (y < 0) x = -x, y = -y;
return (x >= 0 ? x / y : (x - y + 1) / y);
}
template <typename T>
T ceil(T x, T y) {
assert(y != 0);
if (y < 0) x = -x, y = -y;
return (x >= 0 ? (x + y - 1) / y : x / y);
}
template <typename S, typename T>
pair<S, T> operator+(const pair<S, T> &p, const pair<S, T> &q) {
return make_pair(p.first + q.first, p.second + q.second);
}
template <typename S, typename T>
pair<S, T> operator-(const pair<S, T> &p, const pair<S, T> &q) {
return make_pair(p.first - q.first, p.second - q.second);
}
template <typename S, typename T>
istream &operator>>(istream &is, pair<S, T> &p) {
S a;
T b;
is >> a >> b;
p = make_pair(a, b);
return is;
}
template <typename S, typename T>
ostream &operator<<(ostream &os, const pair<S, T> &p) {
return os << p.first << ' ' << p.second;
}
struct io_setup {
io_setup() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout << fixed << setprecision(15);
cerr << fixed << setprecision(15);
}
} io_setup;
constexpr int inf = (1 << 30) - 1;
constexpr ll INF = (1LL << 60) - 1;
// constexpr int MOD = 1000000007;
constexpr int MOD = 998244353;
const long double EPS = 1e-7;
template <typename T>
struct Matrix {
vector<vector<T>> A;
int n, m;
Matrix(int n, int m) : A(n, vector<T>(m, 0)), n(n), m(m) {}
inline const vector<T> &operator[](int k) const { return A[k]; }
inline vector<T> &operator[](int k) { return A[k]; }
static Matrix I(int l) {
Matrix ret(l, l);
for (int i = 0; i < l; i++) ret[i][i] = 1;
return ret;
}
Matrix &operator*=(const Matrix &B) {
assert(m == B.n);
Matrix ret(n, B.m);
for (int i = 0; i < n; i++) {
for (int k = 0; k < m; k++) {
for (int j = 0; j < B.m; j++) ret[i][j] += A[i][k] * B[k][j];
}
}
swap(A, ret.A);
m = B.m;
return *this;
}
Matrix operator*(const Matrix &B) const { return Matrix(*this) *= B; }
Matrix pow(long long k) const {
assert(n == m);
Matrix now = *this, ret = I(n);
for (; k > 0; k >>= 1, now *= now) {
if (k & 1) ret *= now;
}
return ret;
}
bool eq(const T &a, const T &b) const {
// return a == b;
return abs(a - b) <= EPS;
}
// 行基本変形を用いて簡約化を行い、(rank, det) の組を返す
pair<int, T> row_reduction(vector<T> &b) {
assert((int)b.size() == n);
if (n == 0) return make_pair(0, m > 0 ? 0 : 1);
int check = 0, rank = 0;
T det = (n == m ? 1 : 0);
for (int j = 0; j < m; j++) {
int pivot = check;
for (int i = check; i < n; i++) {
// if (A[i][j] != 0) pivot = i;
if (abs(A[i][j]) > abs(A[pivot][j])) pivot = i; // T が小数の場合はこちら
}
if (check != pivot) det *= T(-1);
swap(A[check], A[pivot]), swap(b[check], b[pivot]);
if (eq(A[check][j], T(0))) {
det = T(0);
continue;
}
rank++;
det *= A[check][j];
T r = T(1) / A[check][j];
for (int k = j + 1; k < m; k++) A[check][k] *= r;
b[check] *= r;
A[check][j] = T(1);
for (int i = 0; i < n; i++) {
if (i == check) continue;
if (!eq(A[i][j], 0)) {
for (int k = j + 1; k < m; k++) A[i][k] -= A[i][j] * A[check][k];
b[i] -= A[i][j] * b[check];
}
A[i][j] = T(0);
}
if (++check == n) break;
}
return make_pair(rank, det);
}
pair<int, T> row_reduction() {
vector<T> b(n, T(0));
return row_reduction(b);
}
// 行基本変形を行い、逆行列を求める
pair<bool, Matrix> inverse() {
if (n != m) return make_pair(false, Matrix(0, 0));
if (n == 0) return make_pair(true, Matrix(0, 0));
Matrix ret = I(n);
for (int j = 0; j < n; j++) {
int pivot = j;
for (int i = j; i < n; i++) {
// if (A[i][j] != 0) pivot = i;
if (abs(A[i][j]) > abs(A[pivot][j])) pivot = i; // T が小数の場合はこちら
}
swap(A[j], A[pivot]), swap(ret[j], ret[pivot]);
if (eq(A[j][j], T(0))) return make_pair(false, Matrix(0, 0));
T r = T(1) / A[j][j];
for (int k = j + 1; k < n; k++) A[j][k] *= r;
for (int k = 0; k < n; k++) ret[j][k] *= r;
A[j][j] = T(1);
for (int i = 0; i < n; i++) {
if (i == j) continue;
if (!eq(A[i][j], T(0))) {
for (int k = j + 1; k < n; k++) A[i][k] -= A[i][j] * A[j][k];
for (int k = 0; k < n; k++) ret[i][k] -= A[i][j] * ret[j][k];
}
A[i][j] = T(0);
}
}
return make_pair(true, ret);
}
// Ax = b の解の 1 つと解空間の基底の組を返す
vector<vector<T>> Gaussian_elimination(vector<T> b) {
row_reduction(b);
vector<vector<T>> ret;
vector<int> p(n, m);
vector<bool> is_zero(m, true);
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
if (!eq(A[i][j], T(0))) {
p[i] = j;
break;
}
}
if (p[i] < m) {
is_zero[p[i]] = false;
} else if (!eq(b[i], T(0))) {
return {};
}
}
vector<T> x(m, T(0));
for (int i = 0; i < n; i++) {
if (p[i] < m) x[p[i]] = b[i];
}
ret.push_back(x);
for (int j = 0; j < m; j++) {
if (!is_zero[j]) continue;
x[j] = T(1);
for (int i = 0; i < n; i++) {
if (p[i] < m) x[p[i]] = -A[i][j];
}
ret.push_back(x);
x[j] = T(0);
}
return ret;
}
};
using mat = Matrix<long double>;
void solve() {
int L, M, N;
cin >> L >> M >> N;
mat A(L, M), B(M, N);
rep(i, L) rep(j, M) cin >> A[i][j];
rep(i, M) rep(j, N) cin >> B[i][j];
auto C = A * B;
rep(i, L) rep(j, N) {
if (abs(C[i][j]) > EPS) {
cout << "No\n";
return;
}
}
int r1 = M - A.row_reduction().first;
int r2 = B.row_reduction().first;
cout << (r1 == r2 ? "Yes\n" : "No\n");
}
int main() {
int T = 1;
// cin >> T;
while (T--) solve();
}