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QOJ
ID | 题目 | 提交者 | 结果 | 用时 | 内存 | 语言 | 文件大小 | 提交时间 | 测评时间 |
---|---|---|---|---|---|---|---|---|---|
#449679 | #8473. Matrices and Determinants | 275307894a | AC ✓ | 12ms | 4084kb | C++14 | 3.0kb | 2024-06-21 15:55:33 | 2024-06-21 15:55:34 |
Judging History
answer
#include<bits/stdc++.h>
#define Gc() getchar()
#define Me(x,y) memset(x,y,sizeof(x))
#define Mc(x,y) memcpy(x,y,sizeof(x))
#define d(x,y) ((m)*(x-1)+(y))
#define R(n) (rnd()%(n)+1)
#define Pc(x) putchar(x)
#define LB lower_bound
#define UB upper_bound
#define fi first
#define se second
#define eb emplace_back
#define all(x) x.begin(),x.end()
using namespace std;using ll=long long;using db=double;using lb=long db;using ui=unsigned;using ull=unsigned long long;using pii=pair<int,int>;
const int N=9,M=N*4+5,K=1000+5,mod=1e9+7,Mod=mod-1;const db eps=1e-9;const int INF=2e9+7;mt19937 rnd(time(0));
#define Tp template<typename T>
#define Ts template<typename T,typename... Ar>
namespace Debug{
Tp void _debug(char* f,T t){cerr<<f<<'='<<t<<endl;}
Ts void _debug(char* f,T x,Ar... y){while(*f!=',') cerr<<*f++;cerr<<'='<<x<<",";_debug(f+1,y...);}
#ifdef LOCAL
#define gdb(...) _debug((char*)#__VA_ARGS__,__VA_ARGS__)
#else
#define gdb(...) void()
#endif
}using namespace Debug;
int n,m,k;
using mat=array<array<ll,N>,N>;
mat A,B,C,D,I;
void clr(mat &A){A=I;}
ll Gauss(mat &A){
for(int i=1;i<=n;i++) A[i][i+n]=1;
ll mul=1;
for(int i=1;i<=n;i++){
for(int j=i+1;j<=n;j++) while(A[j][i]){
int x=A[i][i]/A[j][i];
for(int h=i;h<=2*n;h++) A[i][h]-=x*A[j][h];
swap(A[i],A[j]);
mul*=-1;
}
}
for(int i=1;i<=n;i++) mul=mul*A[i][i];
return mul;
}
void inve(mat &A){
for(int i=1;i<=n;i++) A[i][i+n]=1;
for(int i=1;i<=n;i++){
for(int j=i+1;j<=n;j++) if(A[j][i]){swap(A[j],A[i]);break;}
for(int j=i+1;j<=n;j++)while(A[j][i]){
ll x=A[i][i]/A[j][i];
for(int h=i;h<=2*n;h++) A[i][h]-=x*A[j][h];
swap(A[i],A[j]);
}
}
for(int i=n;i;i--){
ll x=A[i][i];
for(int j=i;j<=2*n;j++) A[i][j]/=x;
for(int j=1;j<i;j++){
ll x=A[j][i];
for(int h=i;h<=2*n;h++) A[j][h]-=x*A[i][h];
}
}
for(int i=1;i<=n;i++) for(int j=1;j<=n;j++) A[i][j]=A[i][j+n];
}
mat operator *(const mat &A,const mat &B){
mat C=I;
for(int h=1;h<=n;h++) for(int i=1;i<=n;i++) for(int j=1;j<=n;j++) C[i][j]+=A[i][h]*B[h][j];
return C;
}
void exgcd(ll x,ll y,ll &a,ll &b){
if(!y){a=x;b=0;return;}
exgcd(y,x%y,b,a);b-=x/y*a;
}
void construct(int n,ll k){
ll g=__gcd(k,A[n][n]);
B[n][n]=g;C[n][n]=A[n][n]/g;
if(n>1) construct(n-1,k/g);
for(int i=n-1;i;i--){
ll w=A[i][n];
for(int j=i+1;j<n;j++) w-=B[i][j]*C[j][n];
exgcd(B[i][i],C[n][n],C[i][n],B[i][n]);
C[i][n]*=w;B[i][n]*=w;
}
}
void Solve(){
int i,j;scanf("%d",&n);
clr(A);
for(i=1;i<=n;i++) for(j=1;j<=n;j++) scanf("%lld",&A[i][j]);
ll mul=Gauss(A);
if(mul<=0){puts("No");return;}
ll k=sqrtl(mul);
if(k*k!=mul){puts("No");return;}
puts("Yes");
clr(D);for(i=1;i<=n;i++) for(j=1;j<=n;j++) D[i][j]=A[i][j+n];
inve(D);
clr(B);clr(C);
construct(n,k);
B=D*B;
for(i=1;i<=n;i++) for(j=1;j<=n;j++) printf("%lld%c",B[i][j]," \n"[j==n]);
for(i=1;i<=n;i++) for(j=1;j<=n;j++) printf("%lld%c",C[i][j]," \n"[j==n]);
B=B*C;
}
int main(){
int t=1;
scanf("%d",&t);
while(t--) Solve();
cerr<<clock()*1.0/CLOCKS_PER_SEC<<'\n';
}
详细
Test #1:
score: 100
Accepted
time: 0ms
memory: 4016kb
input:
3 2 2 0 0 2 2 2 1 1 2 1 1
output:
Yes 1 0 0 2 2 0 0 1 No Yes 1 1
result:
ok OK, Accepted. (3 test cases)
Test #2:
score: 0
Accepted
time: 12ms
memory: 4016kb
input:
10000 3 10 0 1 0 0 4 2 10 0 3 2 -2 5 -6 9 0 2 1 10 4 -7 0 7 7 0 0 -10 0 0 0 -10 -10 8 -7 3 9 3 -3 3 3 5 -7 -9 -8 -6 -2 4 9 -8 4 -3 -3 -4 0 0 0 7 0 0 10 -4 7 0 4 3 -10 1 -3 5 5 -3 9 0 -5 -5 -10 3 0 4 -8 3 10 9 0 0 10 0 -5 -1 4 1 -10 4 0 7 0 0 0 -2 7 0 1 -2 7 5 5 -10 -1 0 4 3 1 4 0 -2 3 2 -4 -1 2 -10 ...
output:
No No Yes -7 7 -154 7 0 0 -1 0 0 0 -1 -10 8 -7 154 9 1 -7 10 0 0 -7 231 0 0 0 10 0 0 0 0 1 No No No Yes -2 9 40 0 10 60 1 -1 0 -5 0 28 0 1 24 0 0 -4 No No No Yes 0 9 18 0 5 9 1 -3 0 -3 0 -20 0 1 -6 0 0 3 No Yes -5 10 40 -7 15 60 -4 8 30 1 -4 -12 0 -2 14 0 0 -5 No No No Yes -1 7 0 -10 10 0 0 1 No Yes...
result:
ok OK, Accepted. (10000 test cases)
Test #3:
score: 0
Accepted
time: 12ms
memory: 4084kb
input:
10000 3 0 -3 5 5 0 0 2 1 0 4 2 0 -2 0 -7 4 6 4 -2 8 -3 -10 3 -8 3 -7 4 -7 -4 5 2 5 0 0 4 0 0 0 7 -8 7 0 1 2 4 6 -8 -6 4 0 7 2 -3 0 0 0 -9 0 0 -9 0 7 8 9 2 4 -7 8 -10 -8 6 8 -1 6 8 -10 -7 3 2 7 7 7 3 0 0 -10 0 4 -2 -10 -2 5 3 -4 2 2 7 1 10 10 9 -1 2 9 -1 0 9 4 -7 2 -10 0 -5 1 -3 9 -10 -6 -3 3 8 -10 -...
output:
Yes 0 -3 -5 5 0 20 2 1 10 1 0 -20 0 1 -10 0 0 5 No No No Yes 0 7 -6 -3 0 0 0 -9 0 0 -1 0 1 8 0 2 7 0 -55 0 0 1 8 0 0 0 9 0 0 0 0 1 No No No Yes 1 -1 0 9 9 0 0 1 No No No No No Yes 7 6 24 3 3 12 4 4 12 1 -6 12 0 6 -6 0 0 -2 No Yes 0 0 0 1 3 0 105 4 -1 -4 0 -3 0 -7 63 1 3 0 -245 0 0 1 63 0 0 0 7 0 0 0...
result:
ok OK, Accepted. (10000 test cases)
Test #4:
score: 0
Accepted
time: 12ms
memory: 4040kb
input:
10000 3 10 3 10 0 10 0 9 7 0 4 -2 0 5 1 8 -8 -1 0 2 -9 -1 2 3 8 -5 -4 3 -7 0 7 6 7 -9 1 0 0 4 9 -10 1 -5 9 9 1 10 0 5 -8 -9 -8 -7 -6 -10 2 -10 -3 0 -10 4 5 2 4 2 4 -5 -7 8 -1 8 -5 -8 -9 6 0 6 3 9 0 0 1 0 3 6 3 2 2 8 -3 8 -5 4 6 0 0 6 0 -6 0 -6 0 0 0 10 8 -9 -10 -4 4 -9 -10 4 -1 0 -3 -4 -7 8 -3 -3 7 ...
output:
No No No No Yes -1 -3 0 -10 10 0 0 1 No No No No No Yes 1 -7 0 3 3 0 0 1 No Yes 1 8 0 10 10 0 0 1 No Yes 3 7 0 1 3 0 0 1 No No No Yes 8 8 7 8 1 -8 0 8 No Yes 1 0 -2 0 0 5 -5 2 -2 -2 2 0 0 5 0 0 0 1 No No No No No Yes 2 6 3 6 3 6 0 -2 No No No Yes 0 0 -6 12 0 5 -9 114 1 -2 -9 0 0 10 5 180 -10 0 0 -11...
result:
ok OK, Accepted. (10000 test cases)
Test #5:
score: 0
Accepted
time: 12ms
memory: 4024kb
input:
10000 3 1 -1 0 0 4 0 1 3 9 3 5 6 6 10 -2 -5 10 -4 -7 3 -6 0 1 7 9 -8 0 0 -6 4 -10 4 9 -4 4 -2 3 -7 0 -8 0 -2 -1 -2 3 -4 4 0 0 0 -4 9 -10 0 7 1 0 0 3 -8 7 10 -5 4 -10 8 7 -1 5 4 7 10 -1 -7 0 1 -1 8 7 -4 3 7 0 0 10 7 -1 1 0 1 3 -5 0 -6 6 0 -1 1 7 1 3 -10 1 0 0 -8 -4 0 0 5 4 -9 4 -6 -5 -2 -10 2 4 4 7 -...
output:
Yes 1 -2 -9 0 2 6 1 0 0 1 3 9 0 2 -9 0 0 3 No Yes -6 -3 1 7 3 -8 0 0 -6 1 9 0 0 -18 0 0 0 1 No Yes 0 0 0 -4 9 -10 -15 7 1 0 0 3 -8 7 10 -5 1 0 0 0 0 1 30 0 0 0 -20 0 0 0 0 1 No Yes 7 0 0 10 -1 -1 1 0 1 1 0 0 0 -7 0 0 0 1 No Yes 1 0 0 0 4 -4 0 0 5 -10 1 0 0 -2 0 0 0 1 No Yes 4 -7 0 -3 7 10 5 -9 0 2 9...
result:
ok OK, Accepted. (10000 test cases)
Test #6:
score: 0
Accepted
time: 12ms
memory: 4032kb
input:
10000 3 6 0 0 -10 4 -7 8 0 6 2 8 -2 5 7 4 1 0 0 10 10 0 -10 -10 -6 -10 1 6 10 0 0 0 4 4 3 3 -3 -6 -8 -9 1 -9 -4 6 -6 9 0 -1 0 4 0 7 0 0 -2 7 -10 -1 -10 7 0 -1 0 2 0 7 4 2 -10 6 -2 5 -1 -7 3 3 8 -9 0 9 -6 5 -8 1 9 4 -5 7 -2 -2 -6 -2 -10 4 -1 -10 5 10 -1 -7 2 10 4 1 0 -3 -7 10 -10 4 -3 0 0 1 0 0 0 -3 ...
output:
Yes 3 6 33 -5 -12 -66 4 8 46 2 4 -7 0 -2 -13 0 0 3 No Yes 1 0 0 10 10 0 -1 -10 -6 1 0 6 10 0 0 0 1 0 0 0 0 -10 1 0 0 0 10 0 0 0 0 1 No Yes 0 7 0 21 1 7 0 0 5 7 10 -72 0 2 0 7 -2 0 -10 146 0 1 0 -21 0 0 5 -8 0 0 0 7 No Yes 3 3 No Yes 1 0 -3 -7 10 -1 4 -3 0 0 1 0 0 0 -3 -10 1 0 0 0 0 10 0 0 0 0 1 0 0 ...
result:
ok OK, Accepted. (10000 test cases)
Test #7:
score: 0
Accepted
time: 12ms
memory: 4016kb
input:
10000 3 7 0 0 10 4 5 8 0 7 1 6 3 0 1 0 7 -3 0 5 -8 7 3 -2 -10 2 9 -3 2 -10 5 5 3 1 0 0 0 -2 0 4 9 -8 4 -2 -2 -4 -7 -1 -8 -4 7 4 10 -2 8 -1 4 -6 2 3 3 4 5 0 -2 0 -10 -6 0 4 10 0 10 -6 1 -2 9 10 -6 -7 -3 9 -5 9 -6 6 4 3 7 3 1 0 0 3 0 0 -10 3 0 0 1 3 -10 4 -1 -7 -10 1 5 2 1 -3 1 -4 5 4 6 -2 6 6 4 0 0 0...
output:
Yes 7 28 -182 10 42 -273 8 32 -207 1 -8 -10 0 2 48 0 0 7 No No No Yes 1 0 0 0 -2 4 4 9 -16 1 0 0 0 1 -8 0 0 -4 No No No No No Yes 0 0 0 10 -1 2 0 -1 0 0 1 0 0 -7 8 -7 7 0 33 0 0 1 12 0 0 0 10 0 0 0 0 1 No Yes 3 3 No Yes 1 5 0 4 4 0 0 1 No No No Yes -3 10 -39 8 2 1 -4 -9 9 0 0 -7 1 0 0 0 1 0 0 0 0 1 ...
result:
ok OK, Accepted. (10000 test cases)
Test #8:
score: 0
Accepted
time: 12ms
memory: 3828kb
input:
10000 3 0 2 0 8 -7 -6 -3 -8 0 2 -2 9 1 6 4 -9 0 2 7 -2 0 0 0 -1 0 -8 0 -7 7 9 1 4 -8 -7 -9 2 9 7 -8 -8 2 2 0 10 9 9 -10 7 2 -9 0 -6 -9 3 6 7 9 2 7 -9 0 8 10 1 9 4 9 1 -10 -10 2 1 10 -1 -1 7 -1 -3 5 -7 10 8 3 0 0 10 -9 -4 9 -10 0 -4 4 -1 -3 2 -10 8 -7 4 4 1 -9 7 -1 -2 -1 7 -6 2 -6 9 9 0 3 -2 1 -2 -5 ...
output:
Yes 0 2 6 8 -7 -756 -3 -8 252 1 0 -552 0 1 18 0 0 -6 No Yes -9 0 37 -392 -2 0 8 -84 -1 0 0 0 -7 1 0 0 1 0 8 0 0 7 65 1 0 0 2 -21 0 0 0 -2 No Yes 3 9 2 9 -3 9 0 -3 No Yes 3 3 No No No No No No No No Yes 9 44 560 -7 -33 -420 0 2 28 1 20 -43 0 -4 98 0 0 -7 No No No No No No No No Yes 3 10 0 1 3 0 0 1 N...
result:
ok OK, Accepted. (10000 test cases)
Test #9:
score: 0
Accepted
time: 12ms
memory: 4024kb
input:
10000 3 9 -3 0 0 10 0 0 -7 10 4 -2 -5 -8 5 -1 -1 -9 -3 -3 1 -2 0 -10 1 -8 4 3 8 7 5 0 -10 0 0 2 -5 4 9 -5 -4 -8 0 -4 -9 -9 -9 -4 -10 2 4 9 9 -9 4 2 0 -10 -9 0 0 9 0 -9 0 9 0 10 1 0 5 4 5 -9 3 -1 9 -10 9 -6 1 5 -5 4 -9 -2 -9 10 1 4 4 1 10 -10 0 9 -6 -8 -6 -9 2 2 -4 9 -7 -7 3 4 0 -2 5 0 0 -4 -3 -8 10 ...
output:
Yes -3 -3 -90 0 10 30 0 -7 -20 -3 0 -270 0 1 -30 0 0 10 No Yes -2 7 -65 0 -10 20 0 2 -5 -4 0 -130 0 1 10 0 0 5 No No No Yes 2 2 No No No No No No No No No No No No No Yes 0 3 8 -180 -1 2 -2 0 0 5 3 -360 0 0 5 30 10 0 0 -498 0 1 0 -228 0 0 1 18 0 0 0 -3 No No No Yes -1 10 0 -8 8 0 0 1 No No No Yes 8 ...
result:
ok OK, Accepted. (10000 test cases)
Test #10:
score: 0
Accepted
time: 12ms
memory: 4012kb
input:
10000 3 8 -4 -6 -6 10 0 0 1 0 3 -6 3 -9 10 8 -1 -3 -8 0 4 0 0 -1 3 -4 8 -6 5 0 0 9 0 6 0 10 2 1 10 3 9 5 2 0 0 -10 -8 0 9 3 8 1 -9 -10 3 4 -9 3 -9 4 -8 -6 1 -4 -10 0 0 10 4 0 0 0 8 10 0 0 4 0 -5 -10 8 10 -6 -2 -1 -10 -7 -2 -10 -7 -6 -10 -10 4 0 0 -9 -2 -1 -3 4 -6 0 0 0 -3 -9 0 0 9 4 10 7 -8 -5 -10 2...
output:
Yes 4 -4 -6 -3 10 6 0 1 0 2 0 -6 0 1 0 0 0 -3 No No No Yes 9 2 2 0 0 -10 -8 -2 9 1 5 0 0 -20 0 0 0 1 No Yes 4 15 -5 -4 5 15 -5 10 -2 -6 2 0 -4 -17 6 0 -2 6 -1 0 0 -2 2 0 0 0 5 0 0 0 0 1 No Yes 0 0 -9 -2 -1 0 4 -6 0 0 0 -3 -9 1 0 9 1 3 0 0 0 27 0 0 0 0 1 0 0 0 0 1 No Yes -1 10 0 -10 10 0 0 1 No No No...
result:
ok OK, Accepted. (10000 test cases)