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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#369275 | #7612. Matrix Inverse | Delay_for_five_minutes# | RE | 591ms | 35232kb | C++20 | 4.4kb | 2024-03-27 22:54:25 | 2024-03-27 22:55:57 |
Judging History
answer
#include <bits/stdc++.h>
using namespace std;
int a[2005][2005];
int a2[2005][2005];
int n;
const int T = 2;
bool ok[2005];
int I[2005];
const int mod = 1e9 + 7;
typedef pair<int,int> pii;
mt19937 rnd(0);
int AI[2005];
int AI2[2005];
void test() {
for(int i = 1;i <= n;i++) I[i] = rnd()%(mod - 1) + 1;
for(int i = 1;i <= n;i++) { //[i,1]
AI[i] = 0;
for(int j = 1;j <= n;j++) { //A[i][j]
AI[i] = (AI[i] + 1LL * a[i][j] * I[j]) % mod;
}
}
for(int i = 1;i <= n;i++) {
AI2[i] = 0;
for(int j = 1;j <= n;j++) {
AI2[i] = (AI2[i] + 1LL * a2[i][j] * AI[j]) % mod;
}
AI2[i] = (I[i] - AI2[i] + mod) % mod;
}
for(int i = 1;i <= n;i++) {
if(AI2[i] != 0) ok[i] = 1; ///第i行
}
}
vector<int> get_row() {
memset(ok,0,sizeof(ok)) ;
for(int i = 1;i <= T;i++) {
test() ;
}
vector<int> ans;
for(int i = 1;i <= n;i++) {
if(ok[i]) ans.push_back(i) ;
}
return ans;
}
vector<int> row , col;
int id(int i,int j) {
return (i - 1) * col.size() + j ;
}
pair<int,int> to(int k) {
int c = (k - 1) % col.size() + 1;
int r = (k - c) / col.size() + 1;
// printf("RC %d %d\n",r,c);
return (pair<int,int>){row[r - 1] , col[c - 1]} ;
}
int mat[150][150] , b[150];
int sol[150];
int fpow(int a,int b) {
int ans = 1;
while(b) {
if(b & 1) ans = 1LL * ans * a %mod;
a = 1LL * a * a %mod; b>>= 1;
}
return ans;
}
void solve(int n) {
vector<int> id(n + 1);
for(int i = 1;i < n;i++) {
int cur = -1;
for(int j = i;j <= n;j++) {
if(mat[j][i]) {cur = j ;break ;}
}
assert(cur != -1) ;
for(int j = 1;j <= n;j++) swap(mat[i][j] , mat[cur][j]) ;
swap(b[i] , b[cur]) ;
int rr = fpow(mat[i][i] , mod - 2) ;
for(int j = i + 1;j <= n;j++) {
int f = (mod - 1LL * mat[j][i] * rr%mod) % mod;
for(int k = i;k <= n;k++) mat[j][k] = (mat[j][k] + 1LL * mat[i][k] * f) % mod;
b[j] = (b[j] + 1LL * b[i] * f) % mod;
}
}
// for(int i = 1;i <= n;i++) {
// for(int j = 1;j <= n;j++) printf("%d ",mat[i][j]) ;
// printf(": %d\n",b[i]) ;
// }
for(int i = n;i >= 1;i--) {
int sum = b[i];
for(int j = i + 1;j <= n;j++) {
sum = (sum - 1LL * sol[j] * mat[i][j]%mod + mod) % mod;
}
sol[i] = 1LL * sum * fpow(mat[i][i] , mod - 2) % mod;
// printf("%d %d %d\n",i,sol[id[i]] , id[i]);
}
return ;
}
int main() {
ios::sync_with_stdio(false) ; cin.tie(0) ; cout.tie(0) ;
cin >> n;
for(int i = 1;i <= n;i++) {
for(int j = 1;j <= n;j++) cin >> a[i][j];
}
for(int i = 1;i <= n;i++) {
for(int j = 1;j <= n;j++) cin >> a2[i][j];
}
row = get_row() ;
for(int i = 1;i <= n;i++) {
for(int j = 1;j < i;j++) swap(a[i][j] , a[j][i]) , swap(a2[i][j] , a2[j][i]) ;
}
col = get_row() ;
for(int i = 1;i <= n;i++) {
for(int j = 1;j < i;j++) swap(a[i][j] , a[j][i]) , swap(a2[i][j] , a2[j][i]) ;
}
int cnt = 0;
// printf("R %d %d\n",row.size() , col.size()) ;
for(int i = 0;i < col.size();i++) {
for(int j = 1;j <= row.size();j++) { ///A的第j行,和A'的col[i]列
int cc = 0; ++cnt ;
if(j == col[i]) b[cnt] = 1;
else b[cnt] = 0;
for(int k = 1;k <= n;k++) {
if(cc < col.size() && k == row[cc]) { //第k列
mat[cnt][id(cc + 1 , i + 1)] = a[j][k] ;
++cc ;
}
b[cnt] = (b[cnt] - 1LL * a[j][k] * a2[k][col[i]]%mod + mod) % mod;
}
}
}
// for(int i = 1;i <= cnt;i++) {
// for(int j = 1;j <= cnt;j++) printf("%d ",mat[i][j]) ;
// printf(": %d\n",b[i]) ;
// }
solve(cnt ) ;
vector<pair<pii,int> > ans;
for(int i = 1;i <= cnt;i++) {
if(sol[i]) {
// printf("I %d %d\n",i,sol[i]) ;
pii t = to(i) ;
ans.push_back({t , (a2[t.first][t.second] + sol[i]) % mod}) ;
}
}
cout << ans.size() << '\n' ;
sort(ans.begin() , ans.end()) ;
for(auto [x,y] : ans) {
cout << x.first <<' ' << x.second <<' ' << y << '\n' ;
}
return 0;
}
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 1ms
memory: 5672kb
input:
1 953176428 107682094
output:
0
result:
ok single line: '0'
Test #2:
score: 0
Accepted
time: 570ms
memory: 35028kb
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: 564ms
memory: 35232kb
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: 579ms
memory: 35196kb
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: 555ms
memory: 34984kb
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: 552ms
memory: 35020kb
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: 563ms
memory: 34972kb
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: 0
Accepted
time: 554ms
memory: 34948kb
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
result:
ok 9 lines
Test #9:
score: 0
Accepted
time: 580ms
memory: 35020kb
input:
1996 283446729 904496697 172085277 783069511 818458698 756950687 658910284 99042559 674918562 839616643 448339652 245867480 780073469 684157018 540143866 106204044 613514272 978909042 463995202 654242309 233752461 442383227 477386126 286799884 347610798 141921338 587706626 348419066 962374154 132965...
output:
9 309 1146 916944155 993 1418 998808956 1136 629 476558426 1232 181 439191299 1268 169 491439673 1314 1282 443126632 1415 447 825877434 1541 1779 159693126 1971 1624 228388510
result:
ok 10 lines
Test #10:
score: 0
Accepted
time: 575ms
memory: 35052kb
input:
2000 805314295 257118023 408649013 403270425 561279436 651061472 951531903 607216144 450523182 22974988 674008912 524751540 430060765 578271056 821812595 450493650 896882866 256881145 794394659 634756412 525452196 456872277 895856586 30892092 953830689 157566519 434684214 457301058 431434093 3366527...
output:
10 86 1649 33550286 277 1565 703044124 280 410 767223588 1104 2000 542808584 1165 1837 79761216 1198 360 199585712 1555 178 236137043 1785 1339 983174708 1869 827 135692552 1905 106 851820078
result:
ok 11 lines
Test #11:
score: 0
Accepted
time: 578ms
memory: 35080kb
input:
2000 817831410 837938066 689510456 728988871 925783369 338613646 248460715 797908768 377220868 479079342 718258246 570192472 123025052 702404754 46773852 774152140 719909131 276906493 812767887 453766159 835272763 672918600 773064126 85235335 702812671 696620460 835547337 762745753 759411320 8083624...
output:
11 1 1476 149884243 374 1642 562186259 561 1959 143239748 631 973 100680542 888 1538 726522334 977 526 154377214 1252 262 533011147 1327 1409 392931391 1516 1778 182730233 1782 369 67351156 1855 441 263735571
result:
ok 12 lines
Test #12:
score: 0
Accepted
time: 1ms
memory: 5584kb
input:
1 320856661 676593229
output:
1 1 1 914973852
result:
ok 2 lines
Test #13:
score: 0
Accepted
time: 572ms
memory: 35140kb
input:
2000 518876875 70744495 932244095 614062954 626814336 829150893 998680280 234000933 386686857 577640648 274534113 991968823 338694676 262803592 479224937 248407688 347367787 652722556 999864985 89935946 408575273 342878274 571453557 392556701 38963300 523278627 865830573 710529656 364067377 62819930...
output:
12 268 1341 872543861 301 670 83707290 404 923 771911145 515 915 315878115 531 1675 222526996 546 1464 698683617 667 1134 328997403 785 1886 372491749 1122 279 94873268 1178 1415 973999117 1868 1621 302520255 1969 339 658284571
result:
ok 13 lines
Test #14:
score: 0
Accepted
time: 591ms
memory: 34964kb
input:
1999 126132375 800032351 262637151 998840174 328383619 204918469 536208333 513995901 829164057 538609601 377089892 540716849 41937614 354466066 523585800 195798378 326644387 4751170 678657258 271678980 62983734 10852818 684364703 373677368 25240334 568320119 962133095 18314188 863238520 867505712 18...
output:
12 317 534 317967235 317 1221 672781882 317 1395 757051682 317 1533 223265150 663 534 107325986 663 1221 501079553 663 1395 352817739 663 1533 961065190 924 534 339954283 924 1221 188373539 924 1395 39691647 924 1533 854538181
result:
ok 13 lines
Test #15:
score: -100
Runtime Error
input:
1999 370828093 828933278 920173220 740771905 268813966 910479507 392970052 847922924 19573719 825413514 991590471 856671077 993900741 952892873 394675610 837428479 238861594 63756696 803502792 305104791 697054451 370933149 158939288 892700051 963947171 577946344 905348316 23696678 792096181 44575458...