結果

問題 No.2405 Minimal Matrix Decomposition
ユーザー ecotteaecottea
提出日時 2023-08-04 22:36:45
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
AC  
実行時間 777 ms / 2,000 ms
コード長 14,459 bytes
コンパイル時間 4,571 ms
コンパイル使用メモリ 277,132 KB
実行使用メモリ 8,320 KB
最終ジャッジ日時 2024-10-14 20:38:12
合計ジャッジ時間 14,466 ms
ジャッジサーバーID
(参考情報)
judge4 / judge2
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
5,248 KB
testcase_01 AC 2 ms
5,248 KB
testcase_02 AC 2 ms
5,248 KB
testcase_03 AC 2 ms
5,248 KB
testcase_04 AC 463 ms
8,192 KB
testcase_05 AC 777 ms
8,320 KB
testcase_06 AC 2 ms
5,248 KB
testcase_07 AC 2 ms
5,248 KB
testcase_08 AC 2 ms
5,248 KB
testcase_09 AC 2 ms
5,248 KB
testcase_10 AC 209 ms
6,656 KB
testcase_11 AC 563 ms
7,424 KB
testcase_12 AC 4 ms
5,248 KB
testcase_13 AC 146 ms
5,504 KB
testcase_14 AC 53 ms
5,248 KB
testcase_15 AC 164 ms
5,888 KB
testcase_16 AC 74 ms
5,248 KB
testcase_17 AC 186 ms
5,248 KB
testcase_18 AC 74 ms
5,248 KB
testcase_19 AC 74 ms
5,760 KB
testcase_20 AC 83 ms
5,248 KB
testcase_21 AC 35 ms
5,248 KB
testcase_22 AC 443 ms
7,040 KB
testcase_23 AC 2 ms
5,248 KB
testcase_24 AC 109 ms
5,376 KB
testcase_25 AC 11 ms
5,248 KB
testcase_26 AC 152 ms
5,760 KB
testcase_27 AC 73 ms
5,248 KB
testcase_28 AC 147 ms
6,016 KB
testcase_29 AC 37 ms
5,504 KB
testcase_30 AC 167 ms
6,144 KB
testcase_31 AC 51 ms
5,248 KB
testcase_32 AC 159 ms
5,760 KB
testcase_33 AC 270 ms
6,016 KB
testcase_34 AC 37 ms
5,248 KB
testcase_35 AC 2 ms
5,248 KB
testcase_36 AC 172 ms
5,760 KB
testcase_37 AC 136 ms
5,248 KB
testcase_38 AC 106 ms
5,632 KB
testcase_39 AC 176 ms
6,016 KB
testcase_40 AC 276 ms
6,820 KB
testcase_41 AC 15 ms
5,248 KB
testcase_42 AC 357 ms
6,400 KB
testcase_43 AC 127 ms
5,248 KB
testcase_44 AC 30 ms
5,248 KB
testcase_45 AC 9 ms
5,248 KB
testcase_46 AC 29 ms
5,248 KB
testcase_47 AC 41 ms
5,248 KB
testcase_48 AC 23 ms
5,248 KB
testcase_49 AC 52 ms
5,248 KB
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 #
プレゼンテーションモードにする

#ifndef HIDDEN_IN_VS //
//
#define _CRT_SECURE_NO_WARNINGS
//
#include <bits/stdc++.h>
using namespace std;
//
using ll = long long; // -2^63 2^63 = 9 * 10^18int -2^31 2^31 = 2 * 10^9
using pii = pair<int, int>; using pll = pair<ll, ll>; using pil = pair<int, ll>; using pli = pair<ll, int>;
using vi = vector<int>; using vvi = vector<vi>; using vvvi = vector<vvi>; using vvvvi = vector<vvvi>;
using vl = vector<ll>; using vvl = vector<vl>; using vvvl = vector<vvl>; using vvvvl = vector<vvvl>;
using vb = vector<bool>; using vvb = vector<vb>; using vvvb = vector<vvb>;
using vc = vector<char>; using vvc = vector<vc>; using vvvc = vector<vvc>;
using vd = vector<double>; using vvd = vector<vd>; using vvvd = vector<vvd>;
template <class T> using priority_queue_rev = priority_queue<T, vector<T>, greater<T>>;
using Graph = vvi;
//
const double PI = acos(-1);
const vi DX = { 1, 0, -1, 0 }; // 4
const vi DY = { 0, 1, 0, -1 };
int INF = 1001001001; ll INFL = 4004004003104004004LL; // (int)INFL = 1010931620;
double EPS = 1e-15;
//
struct fast_io { fast_io() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } fastIOtmp;
//
#define all(a) (a).begin(), (a).end()
#define sz(x) ((int)(x).size())
#define lbpos(a, x) (int)distance((a).begin(), std::lower_bound(all(a), x))
#define ubpos(a, x) (int)distance((a).begin(), std::upper_bound(all(a), x))
#define Yes(b) {cout << ((b) ? "Yes\n" : "No\n");}
#define rep(i, n) for(int i = 0, i##_len = int(n); i < i##_len; ++i) // 0 n-1
#define repi(i, s, t) for(int i = int(s), i##_end = int(t); i <= i##_end; ++i) // s t
#define repir(i, s, t) for(int i = int(s), i##_end = int(t); i >= i##_end; --i) // s t
#define repe(v, a) for(const auto& v : (a)) // a
#define repea(v, a) for(auto& v : (a)) // a
#define repb(set, d) for(int set = 0; set < (1 << int(d)); ++set) // d
#define repp(a) sort(all(a)); for(bool a##_perm = true; a##_perm; a##_perm = next_permutation(all(a))) // a
#define smod(n, m) ((((n) % (m)) + (m)) % (m)) // mod
#define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());} //
#define EXIT(a) {cout << (a) << endl; exit(0);} //
#define inQ(x, y, u, l, d, r) ((u) <= (x) && (l) <= (y) && (x) < (d) && (y) < (r)) //
//
template <class T> inline ll pow(T n, int k) { ll v = 1; rep(i, k) v *= n; return v; }
template <class T> inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; } // true
    
template <class T> inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; } // true
    
template <class T> inline T get(T set, int i) { return (set >> i) & T(1); }
//
template <class T, class U> inline istream& operator>>(istream& is, pair<T, U>& p) { is >> p.first >> p.second; return is; }
template <class T> inline istream& operator>>(istream& is, vector<T>& v) { repea(x, v) is >> x; return is; }
template <class T> inline vector<T>& operator--(vector<T>& v) { repea(x, v) --x; return v; }
template <class T> inline vector<T>& operator++(vector<T>& v) { repea(x, v) ++x; return v; }
#endif //
#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
#ifdef _MSC_VER
#include "localACL.hpp"
#endif
//using mint = modint1000000007;
//using mint = modint998244353;
using mint = modint; // mint::set_mod(m);
namespace atcoder {
inline istream& operator>>(istream& is, mint& x) { ll x_; is >> x_; x = x_; return is; }
inline ostream& operator<<(ostream& os, const mint& x) { os << x.val(); return os; }
}
using vm = vector<mint>; using vvm = vector<vm>; using vvvm = vector<vvm>; using vvvvm = vector<vvvm>;
#endif
#ifdef _MSC_VER // Visual Studio
#include "local.hpp"
#else // gcc
inline int popcount(int n) { return __builtin_popcount(n); }
inline int popcount(ll n) { return __builtin_popcountll(n); }
inline int lsb(int n) { return n != 0 ? __builtin_ctz(n) : -1; }
inline int lsb(ll n) { return n != 0 ? __builtin_ctzll(n) : -1; }
inline int msb(int n) { return n != 0 ? (31 - __builtin_clz(n)) : -1; }
inline int msb(ll n) { return n != 0 ? (63 - __builtin_clzll(n)) : -1; }
#define gcd __gcd
#define dump(...)
#define dumpel(v)
#define dump_list(v)
#define dump_mat(v)
#define input_from_file(f)
#define output_to_file(f)
#define Assert(b) { if (!(b)) while (1) cout << "OLE"; }
#endif
//
/*
* Matrix<T>(int n, int m) : O(n m)
* n×m
*
* Matrix<T>(int n) : O(n^2)
* n×n
*
* Matrix<T>(vvT a) : O(n m)
* a[0..n)[0..m)
*
* bool empty() : O(1)
*
*
* A + B : O(n m)
* n×m A, B += 使
*
* A - B : O(n m)
* n×m A, B -= 使
*
* c * A A * c : O(n m)
* n×m A c *= 使
*
* A * x : O(n m)
* n×m A n x
*
* x * A : O(n m)
* m x n×m A
*
* A * B : O(n m l)
* n×m A m×l B
*
* Mat pow(ll d) : O(n^3 log d)
* d
*/
template <class T>
struct Matrix {
int n, m; // n m
vector<vector<T>> v; //
// n×m
Matrix(int n, int m) : n(n), m(m), v(n, vector<T>(m)) {}
// n×n
Matrix(int n) : n(n), m(n), v(n, vector<T>(n)) { rep(i, n) v[i][i] = T(1); }
// a[0..n)[0..m)
Matrix(const vector<vector<T>>& a) : n(sz(a)), m(sz(a[0])), v(a) {}
Matrix() : n(0), m(0) {}
//
Matrix(const Matrix&) = default;
Matrix& operator=(const Matrix&) = default;
//
inline vector<T> const& operator[](int i) const { return v[i]; }
inline vector<T>& operator[](int i) {
// verify : https://judge.yosupo.jp/problem/matrix_product
// inline [] v[]
return v[i];
}
//
friend istream& operator>>(istream& is, Matrix& a) {
rep(i, a.n) rep(j, a.m) is >> a.v[i][j];
return is;
}
//
bool empty() const { return min(n, m) == 0; }
//
bool operator==(const Matrix& b) const { return n == b.n && m == b.m && v == b.v; }
bool operator!=(const Matrix& b) const { return !(*this == b); }
//
Matrix& operator+=(const Matrix& b) {
rep(i, n) rep(j, m) v[i][j] += b[i][j];
return *this;
}
Matrix& operator-=(const Matrix& b) {
rep(i, n) rep(j, m) v[i][j] -= b[i][j];
return *this;
}
Matrix& operator*=(const T& c) {
rep(i, n) rep(j, m) v[i][j] *= c;
return *this;
}
Matrix operator+(const Matrix& b) const { return Matrix(*this) += b; }
Matrix operator-(const Matrix& b) const { return Matrix(*this) -= b; }
Matrix operator*(const T& c) const { return Matrix(*this) *= c; }
friend Matrix operator*(const T& c, const Matrix<T>& a) { return a * c; }
Matrix operator-() const { return Matrix(*this) *= T(-1); }
// : O(m n)
vector<T> operator*(const vector<T>& x) const {
vector<T> y(n);
rep(i, n) rep(j, m) y[i] += v[i][j] * x[j];
return y;
}
// : O(m n)
friend vector<T> operator*(const vector<T>& x, const Matrix& a) {
vector<T> y(a.m);
rep(i, a.n) rep(j, a.m) y[j] += x[i] * a[i][j];
return y;
}
// O(n^3)
Matrix operator*(const Matrix& b) const {
// verify : https://judge.yosupo.jp/problem/matrix_product
Matrix res(n, b.m);
rep(i, res.n) rep(j, res.m) rep(k, m) res[i][j] += v[i][k] * b[k][j];
return res;
}
Matrix& operator*=(const Matrix& b) { *this = *this * b; return *this; }
// O(n^3 log d)
Matrix pow(ll d) const {
Matrix res(n), pow2 = *this;
while (d > 0) {
if (d & 1) res *= pow2;
pow2 *= pow2;
d /= 2;
}
return res;
}
#ifdef _MSC_VER
friend ostream& operator<<(ostream& os, const Matrix& a) {
rep(i, a.n) {
os << "[";
rep(j, a.m) os << a[i][j] << " ]"[j == a.m - 1];
if (i < a.n - 1) os << "\n";
}
return os;
}
#endif
};
//O(n m (n + m))
/*
* A = a[0..n)[0..m) R_r := [I_r, O; O, O]
* P A Q = R_r r = rank A
* P, Q p[0..n)[0..n), q[0..m)[0..m) r
*/
template <class T>
int rank_normal_form(const Matrix<T>& a, Matrix<T>& p, Matrix<T>& q) {
int n = a.n, m = a.m;
// mat
Matrix<T> v(n + m, n + m);
rep(i, n) rep(j, m) v[i][j] = a[i][j];
rep(i, n) rep(j, n) v[i][m + j] = (i == j ? T(1) : T(0));
rep(i, m) rep(j, m) v[n + i][j] = (i == j ? T(1) : T(0));
//
int pi = -1, pj = -1;
// (i, j)i j
int i = 0, j = 0;
//
while (i < n && j < m) {
// 0
int i2 = i;
while (i2 < n && v[i2][j] == 0) i2++;
//
if (i2 == n) { j++; continue; }
// i
pi = i; pj = j;
if (i != i2) swap(v[i], v[i2]);
// v[i][j] 1 v[i][j]
T vij_inv = T(1) / v[i][j];
repi(j2, j, n + m - 1) v[i][j2] *= vij_inv;
// v[i][j] 0 i
rep(i2, n) {
// i
if (i2 == i) continue;
T mul = v[i2][j];
repi(j2, j, n + m - 1) v[i2][j2] -= v[i][j2] * mul;
}
//
i++; j++;
}
//
pi = -1; pj = -1;
// (i, j)i j
i = 0; j = 0;
//
while (i < n && j < m) {
// 0
int j2 = j;
while (j2 < m && v[i][j2] == 0) j2++;
//
if (j2 == m) { i++; continue; }
// j
pi = i; pj = j;
if (j != j2) rep(i2, n + m) swap(v[i2][j], v[i2][j2]);
// v[i][j] 1 v[i][j]
T div = T(1) / v[i][j];
repi(i2, i, n + m - 1) v[i2][j] *= div;
// v[i][j] 0 j
rep(j2, m) {
// j
if (j2 == j) continue;
T mul = v[i][j2];
repi(i2, 0, n + m - 1) v[i2][j2] -= v[i2][i] * mul;
}
//
i++; j++;
}
// P, Q
p = Matrix<T>(n, n); q = Matrix<T>(m, m);
rep(i, n) rep(j, n) p[i][j] = v[i][m + j];
rep(i, m) rep(j, m) q[i][j] = v[n + i][j];
return pi + 1;
}
//O(n^3)
/*
* n mat
*/
template <class T>
Matrix<T> inverse_matrix(const Matrix<T>& mat) {
// verify : https://judge.yosupo.jp/problem/inverse_matrix
int n = mat.n;
// mat v
vector<vector<T>> v(n, vector<T>(2 * n));
rep(i, n) rep(j, n) {
v[i][j] = mat[i][j];
if (i == j) v[i][n + j] = 1;
}
int m = 2 * n;
// (i, j)i j
int i = 0, j = 0;
//
while (i < n && j < m) {
// 0
int i2 = i;
while (i2 < n && v[i2][j] == T(0)) i2++;
// 0 mat
if (i2 == n) return Matrix<T>();
// i
if (i != i2) swap(v[i], v[i2]);
// v[i][j] 1 v[i][j]
T vij_inv = T(1) / v[i][j];
repi(j2, j, m - 1) v[i][j2] *= vij_inv;
// v[i][j] 0 i
rep(i2, n) {
// i
if (i2 == i) continue;
T mul = v[i2][j];
repi(j2, j, m - 1) v[i2][j2] -= v[i][j2] * mul;
}
//
i++; j++;
}
// mat
Matrix<T> mat_inv(n, n);
rep(i, n) rep(j, n) mat_inv[i][j] = v[i][n + j];
return mat_inv;
}
int main() {
// input_from_file("input.txt");
// output_to_file("output.txt");
int P;
cin >> P;
mint::set_mod(P);
int h, w;
cin >> h >> w;
Matrix<mint> a(h, w);
cin >> a;
// P A Q = R_r r = rank A R_r := [I_r, O; O, O]
Matrix<mint> p, q;
int r = rank_normal_form(a, p, q);
bool r_is_zero = false;
if (r == 0) {
r = 1;
r_is_zero = true;
}
dump(r);
if (h * w <= h * r + r * w) {
cout << 1 << endl;
cout << h << " " << w << endl;
rep(i, h) rep(j, w) cout << a[i][j] << " \n"[j == w - 1];
return 0;
}
auto p_inv = inverse_matrix(p);
auto q_inv = inverse_matrix(q);
if (r_is_zero) {
p_inv = Matrix<mint>(h, h);
q_inv = Matrix<mint>(w, w);
}
cout << 2 << endl;
cout << h << " " << r << endl;
rep(i, h) rep(j, r) cout << p_inv[i][j] << " \n"[j == r - 1];
cout << r << " " << w << endl;
rep(i, r) rep(j, w) cout << q_inv[i][j] << " \n"[j == w - 1];
}
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