QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#319722 | #7612. Matrix Inverse | nhuang685 | TL | 1409ms | 66012kb | C++20 | 8.7kb | 2024-02-03 04:58:48 | 2024-02-03 04:58:49 |
Judging History
answer
/**
* @file qoj7612-1.cpp
* @author n685
* @brief
* @date 2024-01-29
*
*
*/
// #ifndef LOCAL
// #pragma GCC optimize("O3,unroll-loops")
// #pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
// #endif
#include <bits/stdc++.h>
#ifdef LOCAL
#include "dd/debug.h"
#else
#define dbg(...) 42
#define dbgR(...) 4242
#define dbgP(...) 420
#define dbgRP(...) 420420
void nline() {}
#endif
template <class T> std::pair<T, T> exEucl(T a, T b) {
if (a < b) {
// auto [x, y] = exEucl(b, a);
T x, y;
std::tie(x, y) = exEucl(b, a);
return {y, x};
}
if (b == 0) {
assert(a == 1);
return {1, 0};
}
// auto [x, y] = exEucl(b, a % b);
T x, y;
std::tie(x, y) = exEucl(b, a % b);
return {y, x - (a / b) * y};
}
template <
class T, class U,
typename std::enable_if<std::is_integral<U>::value, bool>::type = true>
T binpow(T a, U b) {
// 0^0 = 1
T res = 1;
while (b > 0) {
if (b % 2 == 1) {
res *= a;
}
a *= a;
b /= 2;
}
return res;
}
template <class Md, class V = int64_t> struct Mod {
using T = typename std::decay<decltype(Md::value)>::type;
T val = 0;
template <class U> static T normalize(U val) {
if (val <= -Md::value || Md::value <= val) {
val %= Md::value;
}
if (val < 0) {
val += Md::value;
}
return static_cast<T>(val);
}
Mod() : val(0) {}
template <class U, typename std::enable_if<std::is_integral<U>::value,
bool>::type = true>
Mod(U _val) {
val = normalize(_val);
}
// addition
Mod &operator+=(Mod b) {
val += b.val;
if (val >= Md::value) {
val -= Md::value;
}
return *this;
}
friend Mod operator+(Mod a, Mod b) { return (a += b); }
Mod &operator++() { return (*this += 1); }
Mod operator++(int) {
Mod res = *this;
++(*this);
return res;
}
// subtraction
Mod &operator-=(Mod b) {
val -= b.val;
if (val < 0) {
val += Md::value;
}
return *this;
}
friend Mod operator-(Mod a, Mod b) { return (a -= b); }
Mod &operator--() { return (*this -= 1); }
Mod operator--(int) {
Mod res = *this;
--(*this);
return res;
}
// multiplication
Mod &operator*=(Mod b) {
val = static_cast<T>(static_cast<V>(val) * b.val % Md::value);
return *this;
}
friend Mod operator*(Mod a, Mod b) { return (a *= b); }
template <class U> Mod binpow(U b) const { return ::binpow(*this, b); }
Mod inv() const {
return Mod(exEucl(static_cast<V>(val), static_cast<V>(Md::value)).first);
// return binpow(Md::value - 2);
}
// comparison
bool operator==(Mod b) const { return (val == b.val); }
// auto operator<=>(const Mod &b) const = default;
bool operator!=(Mod b) const { return (val != b.val); }
bool operator<(Mod b) const { return (val < b.val); }
bool operator>(Mod b) const { return (val > b.val); }
bool operator<=(Mod b) const { return (val <= b.val); }
bool operator>=(Mod b) const { return (val >= b.val); }
// io
friend std::istream &operator>>(std::istream &in, Mod &a) {
V v;
in >> v;
a = Mod(v);
return in;
}
friend std::ostream &operator<<(std::ostream &out, const Mod &a) {
out << a.val;
return out;
}
// conversion
explicit operator T() const { return val; }
const T &operator()() const { return val; }
Mod operator-() const { return Mod(-val); }
};
const int MOD = (int)1e9 + 7;
using Mint = Mod<std::integral_constant<std::decay<decltype(MOD)>::type, MOD>>;
using Row = std::vector<Mint>;
Row operator+=(Row &a, Row b) {
if (a.size() < b.size()) {
a.resize(b.size());
}
for (int i = 0; i < (int)a.size(); ++i) {
a[i] += b[i];
}
return a;
}
Row operator+(Row a, Row b) { return (a += b); }
Row operator-=(Row &a, Row b) {
if (a.size() < b.size()) {
a.resize(b.size());
}
for (int i = 0; i < (int)a.size(); ++i) {
a[i] -= b[i];
}
return a;
}
Row operator-(Row a, Row b) { return (a -= b); }
Row operator*=(Row &a, Mint b) {
for (int i = 0; i < (int)a.size(); ++i) {
a[i] *= b;
}
return a;
}
Row operator*(Row a, Mint b) { return a *= b; }
Row operator*(Mint b, Row a) { return a *= b; }
using Mat = std::vector<Row>;
Row operator*(Mat a, Row b) {
int n = (int)a.size();
Row c(n);
for (int i = 0; i < n; ++i) {
for (int k = 0; k < n; ++k) {
c[i] += a[i][k] * b[k];
}
}
return c;
}
template <class T> auto operator*(std::vector<std::vector<T>> a, Mat b) {
int n = (int)a.size(), m = (int)b[0].size();
// Mat c(n, Row(m));
std::vector c(n, std::vector<T>(m));
for (int i = 0; i < n; ++i) {
for (int j = 0; j < m; ++j) {
for (int k = 0; k < (int)a[0].size(); ++k) {
c[i][j] += a[i][k] * b[k][j];
}
}
}
return c;
}
std::vector<Mint> gauss(std::vector<Row> eq) {
if ((int)eq.size() == 0) {
return {};
}
int n = (int)eq.size();
int m = (int)eq[0].size() - 1;
assert(n >= m);
for (int i = 0; i < m; ++i) {
int ind = i;
while (ind < n && eq[ind][i] == 0) {
++ind;
}
if (ind == n) {
std::exit(-1);
}
std::swap(eq[i], eq[ind]);
eq[i] *= eq[i][i].inv();
for (int j = 0; j < n; ++j) {
if (j != i) {
eq[j] -= eq[j][i] * eq[i];
}
}
}
std::vector<Mint> sol(m);
for (int i = 0; i < m; ++i) {
sol[i] = eq[i].back();
}
return sol;
}
int main() {
#ifdef LOCAL
std::freopen("input.txt", "r", stdin);
std::freopen("output.txt", "w", stdout);
#else
std::cin.tie(nullptr)->sync_with_stdio(false);
#endif
int n;
std::cin >> n;
std::vector a(n, std::vector<Mint>(n)), c(n, std::vector<Mint>(n));
for (int i = 0; i < n; ++i) {
for (int j = 0; j < n; ++j) {
std::cin >> a[i][j];
}
}
for (int i = 0; i < n; ++i) {
for (int j = 0; j < n; ++j) {
std::cin >> c[i][j];
}
}
std::mt19937 rng(std::chrono::steady_clock::now().time_since_epoch().count());
// std::vector<int> r(n);
// std::iota(r.begin(), r.end(), 0);
// std::shuffle(r.begin(), r.end(), rng);
// r.resize(std::min(n, 20));
std::vector<int> row, col;
{
Row rr(n);
for (int i = 0; i < n; ++i) {
rr[i] = (int)(rng() % MOD);
}
Row rr2 = c * (a * rr);
for (int i = 0; i < n; ++i) {
if (rr[i] != rr2[i]) {
row.push_back(i);
}
}
}
{
Mat rr(1, Row(n));
for (int i = 0; i < n; ++i) {
rr[0][i] = (int)(rng() % MOD);
}
Mat rr2 = (rr * a) * c;
for (int i = 0; i < n; ++i) {
if (rr[0][i] != rr2[0][i]) {
col.push_back(i);
}
}
}
const int m = (int)row.size() * (int)col.size();
assert((int)row.size() <= 12 && (int)col.size() <= 12);
// std::vector val(n, std::vector(n, Row(m + 1)));
// for (int i = 0; i < n; ++i) {
// for (int j = 0; j < n; ++j) {
// val[i][j].back() = c[i][j];
// }
// }
// for (int i = 0; i < (int)row.size(); ++i) {
// for (int j = 0; j < (int)col.size(); ++j) {
// val[row[i]][col[j]].back() = 0;
// val[row[i]][col[j]][(int)col.size() * i + j] = 1;
// }
// }
std::vector<Mint> sol(m);
for (int i = 0; i < (int)row.size(); ++i) {
std::vector<Row> eq;
std::vector val(n, Row((int)col.size() + 1));
for (int j = 0; j < n; ++j) {
val[j].back() = c[row[i]][j];
}
for (int j = 0; j < (int)col.size(); ++j) {
val[col[j]][j] = 1;
val[col[j]].back() = 0;
}
// std::vector res = (std::vector({val}) * a)[0];
// for (int j : col) {
for (int j = 0; j < n; ++j) {
Row r((int)col.size() + 1);
for (int k = 0; k < n; ++k) {
r += val[k] * a[k][j];
}
r.back() = (int)(row[i] == j) - r.back();
eq.push_back(r);
// if ((int)eq.size() >= (int)col.size()) {
// break;
// }
}
std::shuffle(eq.begin(), eq.end(), rng);
eq.resize(std::min((int)eq.size(), (int)col.size()));
std::vector lsol = gauss(eq);
assert(lsol.size() == col.size());
for (int j = 0; j < (int)col.size(); ++j) {
sol[(int)col.size() * i + j] = lsol[j];
}
}
std::vector<std::pair<std::pair<int, int>, Mint>> ans;
for (int i = 0; i < (int)row.size(); ++i) {
for (int j = 0; j < (int)col.size(); ++j) {
Mint v = sol[(int)col.size() * i + j];
if (c[row[i]][col[j]] != v) {
ans.emplace_back(std::pair{row[i], col[j]}, v);
}
}
}
std::cout << (int)ans.size() << '\n';
for (auto [aa, b] : ans) {
std::cout << aa.first + 1 << ' ' << aa.second + 1 << ' ' << b << '\n';
}
}
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 1ms
memory: 3672kb
input:
1 953176428 107682094
output:
0
result:
ok single line: '0'
Test #2:
score: 0
Accepted
time: 908ms
memory: 65852kb
input:
1995 586309310 548144807 578573993 437893403 641164340 712256053 172321263 108058526 768610920 123320669 762746291 856047593 979279376 29067913 309867338 292286426 45124325 239705174 675003623 213743652 620561338 116308277 695369179 669459894 682522334 846995555 159510341 999359657 645579085 7499563...
output:
2 827 238 84815305 1466 499 206940592
result:
ok 3 lines
Test #3:
score: 0
Accepted
time: 1269ms
memory: 65884kb
input:
1995 436890614 28924575 276129332 63568266 576410175 399540058 591733285 531509939 637241038 596750662 811926780 760228238 317196903 751498201 993802643 102539089 382116597 233386377 974332817 495280100 575832855 616941506 297856263 216480938 638907269 434126707 499611855 764625526 51141033 64624519...
output:
3 315 590 222982023 421 1912 523778307 745 1803 328256562
result:
ok 4 lines
Test #4:
score: 0
Accepted
time: 1409ms
memory: 66012kb
input:
1998 583111238 684686962 60000552 833067795 399706437 80311170 511421309 126675237 578609031 629890589 4721597 505178877 965431576 488092987 110903821 856966035 934194793 831090190 93501498 982251231 221658950 561834845 801921306 125139448 771849922 610370373 625334897 671223646 927123592 441019972 ...
output:
4 21 1273 160152585 700 1573 576757184 1674 1165 958703366 1860 1550 451190886
result:
ok 5 lines
Test #5:
score: -100
Time Limit Exceeded
input:
2000 717395008 183448326 460843970 942614578 540060179 334668801 284127311 635920935 518435676 579369810 852254297 342132392 390366615 141010330 256825376 585810764 253867889 483289117 141421931 467578626 750184736 801127935 917825514 702243210 954747981 910219404 311930180 11494244 915417963 820983...