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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#311818 | #7612. Matrix Inverse | PlentyOfPenalty | TL | 1446ms | 98432kb | C++17 | 4.3kb | 2024-01-22 20:31:12 | 2024-01-22 20:31:14 |
Judging History
answer
#include <bits/stdc++.h>
using namespace std;
typedef std::pair<int, int> pii;
typedef long long ll;
const int MAXN = 2011, mod = 1e9 + 7;
void Add(int &a, int t) {
a += t;
if (a >= mod) a -= mod;
}
ll Qpow(ll a, ll p) {
ll res = 1;
while (p) {
if (p & 1) res = res * a % mod;
a = a * a % mod, p >>= 1;
}
return res;
}
int a[MAXN][MAXN], ra[MAXN][MAXN], b[MAXN][MAXN], rb[MAXN][MAXN], res[MAXN][MAXN];
int f[MAXN][MAXN];
int row[MAXN], col[MAXN], cr, cc;
bool type[MAXN];
void gauss(int a[MAXN][15], int n,int m) {//rank = m , n>m
for (int i = 1; i <= m; ++i) {
for (int j = i; j <= n; ++j)
if (a[j][i]) {
std::swap(a[i], a[j]);
break;
}
int inv = Qpow(a[i][i], mod - 2);
for (int k = 1; k <= m + 1; ++k)
a[i][k] = ll(a[i][k]) * inv % mod;
for (int j = 1; j <= n; ++j)
if (i != j && a[j][i]) {
int r = a[j][i];
for (int k = i; k <= m + 1; ++k)
a[j][k] = ((a[j][k] - ll(r) * a[i][k]) % mod + mod) % mod;
}
}
}
int eq[MAXN][15];
struct one {
int x, y, v;
bool operator< (const one& you)const{return x<you.x||(x==you.x&&y<you.y);}
};
std::vector<one> ans;
vector<pii> seq;
int main() {
#ifdef popteam
// freopen("I.in", "r", stdin);
#endif
mt19937 rd(std::chrono::steady_clock::now().time_since_epoch().count());
cin.tie(0)->sync_with_stdio(0);
int n;
cin >> n;
for (int i = 1; i <= n; ++i)
for (int j = 1; j <= n; ++j)
cin >> a[i][j], ra[i][j] = a[i][j];
for (int i = 1; i <= n; ++i)
for (int j = 1; j <= n; ++j)
cin >> b[i][j], rb[i][j] = b[i][j], res[i][j] = b[i][j];
for (int i = 1; i <= n; ++i)
f[i][i] = 1;
int lst = rd() % n + 1;
for (int w = 1; w <= n/2; ++w) {
int x = rd() % n + 1;
seq.emplace_back(pii(lst, x));
lst = x;
}
for (auto [x, y] : seq)
for (int k = 1; k <= n; ++k)
Add(ra[y][k], ra[x][k]), Add(f[y][k], f[x][k]);
for (int c = 1; c <= n; ++c) {
bool err = 0;
for (int w = 1; w <= 13; ++w) {
int i = rd() % n + 1;
int sum = 0;
for (int k = 1; k <= n; ++k)
sum = (sum + ll(ra[i][k]) * b[k][c]) % mod;
// printf("c=%d,i=%d,sum=%d\n", i, c, sum);
if (sum != f[i][c]) {
err = 1;
break;
}
}
if (err) col[++cc] = c; //, printf("Err,c=%d\n", c);
}
assert(cc <= 12);
memset(f, 0, sizeof f);
for (int i = 1; i <= n; ++i)
f[i][i] = 1;
for (int i = 1; i <= n; ++i)
for (int j = 1; j <= n; ++j)
ra[i][j] = a[i][j];
for (auto [x, y] : seq)
for (int k = 1; k <= n; ++k)
Add(ra[k][y], ra[k][x]), Add(f[k][y], f[k][x]);
for (int r = 1; r <= n; ++r) {
bool err = 0;
for (int w = 1; w <= 13; ++w) {
int j = rd() % n + 1;
int sum = 0;
for (int k = 1; k <= n; ++k)
sum = (sum + ll(b[r][k]) * ra[k][j]) % mod;
if (sum != f[r][j]) {
err = 1;
break;
}
}
if (err) row[++cr] = r, type[r] = 1; //, printf("Err,r=%d\n", r);
}
fprintf(stderr, "cr=%d\n", cr);
assert(cr <= 12);
for (int w = 1; w <= cc; ++w) {
memset(eq, 0, sizeof eq);
int c = col[w];
for (int i = 1; i <= n; ++i) {
if (i == c) ++eq[i][cr + 1];
int cur = 0;
for (int r = 1; r <= n; ++r)
if (type[r])
eq[i][++cur] = a[i][r];
else
eq[i][cr + 1] = ((eq[i][cr + 1] - ll(a[i][r]) * b[r][c]) % mod + mod) % mod;
}
gauss(eq, n,cr);
int cur = 0;
for (int r = 1; r <= n; ++r)
if (type[r]) {
++cur;
if (res[r][c] != eq[cur][cr + 1]) ans.emplace_back(one{r, c, eq[cur][cr + 1]});
}
}
std::sort(ans.begin(),ans.end());
cout << ans.size() << '\n';
for (auto P : ans)
cout << P.x << " " << P.y << " " << P.v << '\n';
return 0;
}
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 0ms
memory: 19652kb
input:
1 953176428 107682094
output:
0
result:
ok single line: '0'
Test #2:
score: 0
Accepted
time: 1326ms
memory: 98228kb
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: 1336ms
memory: 98228kb
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: 1366ms
memory: 98284kb
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: 0
Accepted
time: 1346ms
memory: 98432kb
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...
output:
5 30 992 620409139 585 130 391404065 910 139 921101622 1292 496 462362602 1579 1776 163902318
result:
ok 6 lines
Test #6:
score: 0
Accepted
time: 1436ms
memory: 98400kb
input:
2000 620840546 358023079 309405838 45500223 855686733 508959744 51181469 968972877 537705762 129000719 720633908 884983092 862573877 806580605 252024754 680227415 839963816 519838198 171117282 55679929 677376107 529124099 733179585 20941462 208815360 171000233 981430676 830346879 857681989 863823572...
output:
6 708 1628 497911789 714 1597 924600947 1105 1248 334964897 1209 1517 696980563 1386 1495 446362422 1427 979 599811696
result:
ok 7 lines
Test #7:
score: 0
Accepted
time: 1446ms
memory: 98248kb
input:
1999 199111744 347283243 902808247 73043926 77805820 474451787 854137221 262193129 508272500 493604512 479354501 851331944 65939325 676555110 301252826 583818606 235970147 545653095 120576387 825367169 249335412 365652469 200134563 609796865 481733518 594700892 34132902 906919419 939234722 888820985...
output:
7 43 586 272473841 116 1477 158203105 122 1169 761579075 477 1913 749351268 592 583 329485518 662 1400 622650552 1563 148 498180819
result:
ok 8 lines
Test #8:
score: -100
Time Limit Exceeded
input:
1999 95525499 999471184 616044299 270968642 734163712 806403756 187471687 954208629 738712543 303515182 65192240 341396506 976491262 49950446 564351227 957716298 984366409 189359888 6212233 992086125 956271984 926015141 961718572 628613990 96751949 438018145 639769590 234289696 391888974 135327482 5...
output:
8 279 1620 990329039 882 1321 138573187 1060 836 505053059 1155 214 213425345 1525 906 706361973 1553 569 257967325 1601 1141 127915131 1898 738 215879720