QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#638943 | #7753. Energy Distribution | Yeyin_0 | TL | 9ms | 3972kb | C++23 | 2.2kb | 2024-10-13 17:23:04 | 2024-10-13 17:23:04 |
Judging History
answer
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define OPFI(x) freopen(#x".in", "r", stdin);\
freopen(#x".out", "w", stdout)
#define REP(i, a, b) for(int i=(a); i<=(b); ++i)
#define REPd(i, a, b) for(int i=(a); i>=(b); --i)
inline ll rd(){
ll r=0, k=1; char c=0; while(!isdigit(c=getchar())) if(c=='-') k=-k;
while(isdigit(c)) r=r*10+c-'0', c=getchar(); return r*k;
}
const int N=110;
ll n, w[N][N];
double a[N][N], b[N];
bool check(double lmd, int state){
REP(i, 1, n){
if((state>>(i-1))&1)
{
REP(j, 1, n) a[i][j]=w[i][j];
b[i]=lmd;
}
else
{
REP(j, 1, n)
if(i==j) a[i][j]=1;
else a[i][j]=0;
b[i]=0;
}
}
REP(i, 1, n){
int t=i;
REP(j, i+1, n) if(abs(a[j][i])>1e-7&&(abs(a[t][i])>abs(a[j][i])||abs(a[t][i])<1e-7)) t=j;
REP(j, i, n) swap(a[t][j], a[i][j]);
if(abs(a[i][i])<1e-8){
return 0;
}
swap(b[t], b[i]);
double e=a[i][i];
REP(j, i, n) a[i][j]/=e;
b[i]/=e;
REP(j, i+1, n){
double d=a[j][i];
REP(k, i, n) a[j][k]-=d*a[i][k];
b[j]-=d*b[i];
}
}
REPd(i, n, 1) REP(j, 1, i-1) b[j]-=a[j][i]*b[i], a[j][i]=0;
double sum=0;
REP(i, 1, n) sum+=b[i];
return sum<1;
}
int main(){
//OPFI(test);
n=rd();
REP(i, 1, n)
REP(j, 1, n)
w[i][j]=rd();
double Ans=0;
REP(i,1,(1<<n)-1)
{
double l=0, r=1e6;
while(r-l>1e-12){
double mid=(l+r)/2;
if(check(mid,i)){
l=mid;
}else{
r=mid;
}
}
double ans=0;
REP(i, 1, n)
{
if(b[i]<0||b[i]>1) goto out;
}
REP(i, 1, n) REP(j, i+1, n) ans+=b[i]*b[j]*w[i][j];
//REP(i, 1, n) cerr<<b[i]<<endl;
Ans=max(Ans,ans);
/*if(ans==Ans)
{
REP(i,1,n) cout<<b[i]<<" ";
cout<<endl;
}*/
out:;
}
printf("%.10f\n", Ans);
return 0;
}
Details
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Test #1:
score: 100
Accepted
time: 0ms
memory: 3848kb
input:
2 0 1 1 0
output:
0.2500000000
result:
ok found '0.2500000', expected '0.2500000', error '0.0000000'
Test #2:
score: 0
Accepted
time: 0ms
memory: 3972kb
input:
3 0 2 1 2 0 2 1 2 0
output:
0.5714285714
result:
ok found '0.5714286', expected '0.5714290', error '0.0000004'
Test #3:
score: 0
Accepted
time: 0ms
memory: 3952kb
input:
3 0 1 2 1 0 1 2 1 0
output:
0.5000000000
result:
ok found '0.5000000', expected '0.5000000', error '0.0000000'
Test #4:
score: 0
Accepted
time: 0ms
memory: 3856kb
input:
4 0 3 1 0 3 0 1 0 1 1 0 2 0 0 2 0
output:
0.7500000000
result:
ok found '0.7500000', expected '0.7500000', error '0.0000000'
Test #5:
score: 0
Accepted
time: 1ms
memory: 3848kb
input:
5 0 0 0 4 4 0 0 2 0 4 0 2 0 2 0 4 0 2 0 0 4 4 0 0 0
output:
1.0000000000
result:
ok found '1.0000000', expected '1.0000000', error '0.0000000'
Test #6:
score: 0
Accepted
time: 1ms
memory: 3864kb
input:
6 0 9 5 5 10 6 9 0 0 0 0 1 5 0 0 0 3 0 5 0 0 0 10 5 10 0 3 10 0 0 6 1 0 5 0 0
output:
2.8571428571
result:
ok found '2.8571429', expected '2.8571430', error '0.0000001'
Test #7:
score: 0
Accepted
time: 2ms
memory: 3788kb
input:
7 0 0 0 0 50 10 45 0 0 0 0 0 3 1 0 0 0 0 0 4 16 0 0 0 0 44 0 0 50 0 0 44 0 37 6 10 3 4 0 37 0 2 45 1 16 0 6 2 0
output:
12.5115848007
result:
ok found '12.5115848', expected '12.5115850', error '0.0000000'
Test #8:
score: 0
Accepted
time: 4ms
memory: 3864kb
input:
8 0 0 56 0 0 58 16 0 0 0 37 20 0 82 0 0 56 37 0 0 98 0 83 0 0 20 0 0 0 0 100 0 0 0 98 0 0 62 29 0 58 82 0 0 62 0 43 0 16 0 83 100 29 43 0 4 0 0 0 0 0 0 4 0
output:
25.0091178965
result:
ok found '25.0091179', expected '25.0091180', error '0.0000000'
Test #9:
score: 0
Accepted
time: 9ms
memory: 3920kb
input:
9 0 0 0 135 0 0 0 448 476 0 0 0 0 0 0 208 17 0 0 0 0 467 1 0 0 0 134 135 0 467 0 0 0 92 369 207 0 0 1 0 0 176 0 235 0 0 0 0 0 176 0 65 363 413 0 208 0 92 0 65 0 0 0 448 17 0 369 235 363 0 0 0 476 0 134 207 0 413 0 0 0
output:
119.0000000000
result:
ok found '119.0000000', expected '119.0000000', error '0.0000000'
Test #10:
score: -100
Time Limit Exceeded
input:
10 0 0 0 289 0 397 0 0 140 155 0 0 28 101 35 614 0 0 545 300 0 28 0 0 329 702 0 242 0 298 289 101 0 0 0 0 0 0 720 0 0 35 329 0 0 0 0 38 0 0 397 614 702 0 0 0 229 0 0 0 0 0 0 0 0 229 0 317 0 0 0 0 242 0 38 0 317 0 961 309 140 545 0 720 0 0 0 961 0 92 155 300 298 0 0 0 0 309 92 0