QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#462004 | #8473. Matrices and Determinants | ucup-team052# | RE | 0ms | 3788kb | C++14 | 3.0kb | 2024-07-03 12:34:22 | 2024-07-03 12:34:22 |
Judging History
answer
#include<bits/stdc++.h>
#ifdef xay5421
#define D(...) fprintf(stderr,__VA_ARGS__)
#define DD(...) D(#__VA_ARGS__ "="),debug_helper::debug(__VA_ARGS__),D("\n")
#include"/home/xay5421/debug.hpp"
#else
#define D(...) ((void)0)
#define DD(...) ((void)0)
#endif
#define pb push_back
#define eb emplace_back
#define SZ(x) ((int)(x).size())
#define each(x,v) for(auto&x:v)
#define rep(i,a,b) for(int i=(a);i<=(b);++i)
#define per(i,a,b) for(int i=(a);i>=(b);--i)
template<class T>void rd(T&x){int f=0,c;while(!isdigit(c=getchar()))f^=!(c^45);x=(c&15);while(isdigit(c=getchar()))x=x*10+(c&15);if(f)x=-x;}
template<class T>void pt(T x,int c=-1){if(x<0)putchar('-'),x=-x;if(x>9)pt(x/10);putchar(x%10+48);if(c!=-1)putchar(c);}
using namespace std;
using LL=long long;
using ULL=unsigned long long;
int T,n;
struct mat{
LL a[4][4];
mat operator*(const mat&b)const{
mat c;
memset(c.a,0,sizeof(a));
rep(i,0,n-1)rep(j,0,n-1)rep(k,0,n-1){
c.a[i][j]+=a[i][k]*b.a[k][j];
}
return c;
}
void add_row(int i,int j,LL k){
rep(t,0,n-1){
a[j][t]+=a[i][t]*k;
}
}
void add_col(int i,int j,LL k){
rep(t,0,n-1){
a[t][j]+=a[t][i]*k;
}
}
void swap_row(int i,int j){swap(a[i],a[j]);}
void swap_col(int i,int j){rep(k,0,n-1)swap(a[k][i],a[k][j]);}
void print(){
rep(i,0,n-1){
rep(j,0,n-1)D("%lld ",a[i][j]);
D("\n");
}
D("\n");
}
};
void exgcd(LL a,LL b,LL&x,LL&y){
if(!b){x=1,y=0;return;}
exgcd(b,a%b,y,x);
y-=a/b*x;
}
LL inv(LL x,LL m){
LL v0,v1;
exgcd(x,m,v0,v1);
v0=(v0%m+m)%m;
assert(1LL*v0*x%m==1);
return v0;
}
void solve(){
cin>>n;
mat A,I;
memset(A.a,0,sizeof(A));
memset(I.a,0,sizeof(I));
rep(i,0,n-1){
rep(j,0,n-1){
cin>>A.a[i][j];
I.a[i][j]=i==j;
}
}
mat B(I),C(I);
// (B*A*C).print();
LL det=1;
rep(i,0,n-1){
if(!A.a[i][i]){
rep(j,i+1,n-1)if(A.a[j][i]){
A.swap_row(i,j);
B.swap_col(i,j);
det=-det;
break;
}
if(!A.a[i][i]){
puts("No");
return;
}
}
rep(j,i+1,n-1){
while(1){
if(abs(A.a[i][i])<abs(A.a[j][i])){
A.swap_row(i,j);
B.swap_col(i,j);
det=-det;
}
if(!A.a[j][i])break;
LL t=A.a[i][i]/A.a[j][i];
A.add_row(j,i,-t);
B.add_col(i,j,t);
}
}
det*=A.a[i][i];
}
if(det<=0){
puts("No");
return;
}
LL val=sqrt(det+0.5);
if(val*val!=det){
puts("No");
return;
}
// (B*A*C).print();
per(i,n-1,0){
LL t=__gcd(val,A.a[i][i]);
rep(j,i+1,n-1){
if(A.a[i][j]%t!=0){
A.add_row(j,i,-inv(A.a[j][j]%t,t)*(A.a[i][j]%t)%t);
B.add_col(i,j,inv(A.a[j][j]%t,t)*(A.a[i][j]%t)%t);
}
}
rep(j,0,n-1){
assert(A.a[i][j]%t==0);
A.a[i][j]/=t;
B.a[j][i]*=t;
}
val/=t;
}
// (B*A*C).print();
puts("Yes");
rep(i,0,n-1)rep(j,0,n-1)printf("%lld%c",B.a[i][j],j==n-1?'\n':' ');
rep(i,0,n-1)rep(j,0,n-1)printf("%lld%c",A.a[i][j],j==n-1?'\n':' ');
}
int main(){
#ifdef xay5421
freopen("a.in","r",stdin);
#endif
cin>>T;
while(T--){
solve();
}
return 0;
}
Details
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Test #1:
score: 100
Accepted
time: 0ms
memory: 3788kb
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: -100
Runtime Error
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 0 0 0 0 -1 0 0 0 -1 -10 8 -7 0 0 1 -7 10 16 0 -7 11 17 0 0 10 0 0 0 0 1 No No No Yes -2 7 40 0 10 60 1 0 0 -5 -1 4 0 1 24 0 0 -4 No No No Yes 0 9 18 0 5 9 1 0 0 -3 -3 -2 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 0 0 -10 10 -7 0 1 No Yes 1 0 ...