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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#638935#7753. Energy DistributionYeyin_0TL 11ms3920kbC++232.2kb2024-10-13 17:22:142024-10-13 17:22:14

Judging History

你现在查看的是最新测评结果

  • [2024-10-31 10:22:30]
  • hack成功,自动添加数据
  • (/hack/1089)
  • [2024-10-13 17:22:14]
  • 评测
  • 测评结果:TL
  • 用时:11ms
  • 内存:3920kb
  • [2024-10-13 17:22:14]
  • 提交

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=1e12;
        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: 3912kb

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: 3840kb

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: 3784kb

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: 3852kb

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: 3908kb

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: 3920kb

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: 3856kb

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: 5ms
memory: 3848kb

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: 11ms
memory: 3912kb

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

output:


result: