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QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#297679#7753. Energy Distributionucup-team139AC ✓5ms3828kbC++233.2kb2024-01-04 22:35:422024-01-04 22:35:44

Judging History

你现在查看的是测评时间为 2024-01-04 22:35:44 的历史记录

  • [2024-10-31 10:27:37]
  • 自动重测本题所有获得100分的提交记录
  • 测评结果:AC
  • 用时:5ms
  • 内存:4048kb
  • [2024-10-31 10:22:30]
  • hack成功,自动添加数据
  • (/hack/1089)
  • [2024-01-04 22:35:44]
  • 评测
  • 测评结果:100
  • 用时:5ms
  • 内存:3828kb
  • [2024-01-04 22:35:42]
  • 提交

answer

#include<bits/stdc++.h>
using namespace std;

#define rep(i, a, b) for(int i = a; i < (b); ++i)
#define all(x) begin(x), end(x)
#define sz(x) (int)(x).size()
typedef long long ll;
typedef pair<int, int> pii;
typedef vector<int> vi;

typedef double T; //oppure modular<mod>
typedef vector<T> vd;
const double eps = 1e-8;
vi col; //globale per ricavare il sottospazio
int solveLinear(vector<vd>& A, vd& b, vd& x) {
    int n = sz(A), m = sz(x), rank = 0, br, bc;
    if (n) assert(sz(A[0]) == m);
    col.resize(m); iota(all(col), 0);
    rep(i,0,n) {
        T v, bv = 0;
        rep(r,i,n) rep(c,i,m)
        if ((v = fabs(A[r][c])) > bv)
            br = r, bc = c, bv = v;
        if (bv <= eps) {
            rep(j,i,n) if (fabs(b[j]) > eps) return -1;
            break;
        }
        swap(A[i], A[br]); swap(b[i], b[br]);
        swap(col[i], col[bc]);
        rep(j,0,n) swap(A[j][i], A[j][bc]);
        bv = T(1)/A[i][i];
        rep(j,i+1,n) {
            T fac = A[j][i] * bv;
            b[j] -= fac * b[i];
            rep(k,i+1,m) A[j][k] -= fac*A[i][k];
        }
        rank++;
    }
    x.assign(m, T(0));
    for (int i = rank; i--;) {
        b[i] = b[i]/A[i][i];
        x[col[i]] = b[i];
        rep(j,0,i) {
            b[j] -= A[j][i] * b[i];
        }
    }
    return rank; // (multiple solutions if rank < m)
}

void solve(int t){
    int n;
    cin>>n;
    
    vector w(n,vector(n,0));
    for(auto &i : w)for(auto &j : i)cin>>j;
    
    double ans = 0.0;
    for(int mask=1;mask<(1<<n);mask++){
        bool ok=true;
        vector<int> nodi;
        
        for(int j=0;j<n;j++){
            if(mask&(1<<j))nodi.push_back(j);
        }
        
        for(auto j : nodi){
            for(auto k : nodi){
                if(j==k)continue;
                assert(w[j][k]==w[k][j]);
                if(w[j][k]==0)ok=false;
            }
        }
        
        if(!ok)continue;
        
        vector<vd> A;
        vd B,x;
        
        x.resize(nodi.size());
        for(auto a : nodi){
            for(auto b : nodi){
                if(a==b)continue;
                
                vd tmp;
                for(auto i : nodi){
                    if(i==a)tmp.push_back(-w[a][b]);
                    else if(i==b)tmp.push_back(w[a][b]);
                    else tmp.push_back(w[a][i]-w[b][i]);
                }
                
                A.push_back(tmp);
                B.push_back(0);
            }
        }
        
        A.push_back(vd(nodi.size(),1));
        B.push_back(1);
        
        int rank = solveLinear(A,B,x);
        //assert(rank!=-1);
        if(rank==-1)continue;
        assert(rank==(int)x.size());
        
        double curr=0;
        for(int i=0;i<(int)x.size();i++){
            if(x[i]<-1e-8){
                curr=0.0;
                break;
            }
            for(int j=0;j<i;j++){
                curr+=x[i]*x[j]*w[nodi[i]][nodi[j]];
            }
        }
        ans=max(ans,curr);
    }
    
    cout<<setprecision(20)<<ans<<"\n";
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    
    int t=1;
    //cin>>t;
    for(int i=1;i<=t;i++)solve(i);
    
    return 0;
}

这程序好像有点Bug,我给组数据试试?

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 1ms
memory: 3644kb

input:

2
0 1
1 0

output:

0.25

result:

ok found '0.2500000', expected '0.2500000', error '0.0000000'

Test #2:

score: 0
Accepted
time: 0ms
memory: 3764kb

input:

3
0 2 1
2 0 2
1 2 0

output:

0.57142857142857139685

result:

ok found '0.5714286', expected '0.5714290', error '0.0000004'

Test #3:

score: 0
Accepted
time: 0ms
memory: 3644kb

input:

3
0 1 2
1 0 1
2 1 0

output:

0.5

result:

ok found '0.5000000', expected '0.5000000', error '0.0000000'

Test #4:

score: 0
Accepted
time: 0ms
memory: 3656kb

input:

4
0 3 1 0
3 0 1 0
1 1 0 2
0 0 2 0

output:

0.75

result:

ok found '0.7500000', expected '0.7500000', error '0.0000000'

Test #5:

score: 0
Accepted
time: 1ms
memory: 3824kb

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

result:

ok found '1.0000000', expected '1.0000000', error '0.0000000'

Test #6:

score: 0
Accepted
time: 0ms
memory: 3656kb

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:

2.8571428571428567622

result:

ok found '2.8571429', expected '2.8571430', error '0.0000000'

Test #7:

score: 0
Accepted
time: 1ms
memory: 3828kb

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:

12.511584800741426093

result:

ok found '12.5115848', expected '12.5115850', error '0.0000000'

Test #8:

score: 0
Accepted
time: 1ms
memory: 3684kb

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:

25.009117896522486291

result:

ok found '25.0091179', expected '25.0091180', error '0.0000000'

Test #9:

score: 0
Accepted
time: 1ms
memory: 3764kb

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

result:

ok found '119.0000000', expected '119.0000000', error '0.0000000'

Test #10:

score: 0
Accepted
time: 1ms
memory: 3656kb

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:

240.25

result:

ok found '240.2500000', expected '240.2500000', error '0.0000000'

Test #11:

score: 0
Accepted
time: 5ms
memory: 3784kb

input:

10
0 295 2 809 333 880 284 305 41 295
295 0 512 1000 281 153 42 550 962 930
2 512 0 727 709 969 665 973 301 410
809 1000 727 0 282 551 960 804 274 956
333 281 709 282 0 613 505 406 896 441
880 153 969 551 613 0 769 770 40 288
284 42 665 960 505 769 0 919 989 490
305 550 973 804 406 770 919 0 400 209...

output:

327.37365896668552523

result:

ok found '327.3736590', expected '327.3736590', error '0.0000000'

Test #12:

score: 0
Accepted
time: 1ms
memory: 3760kb

input:

10
0 403 2 164 0 399 279 156 109 472
403 0 292 279 100 326 153 124 103 426
2 292 0 0 58 87 0 177 324 334
164 279 0 0 256 188 0 257 467 23
0 100 58 256 0 453 75 21 0 309
399 326 87 188 453 0 0 319 395 434
279 153 0 0 75 0 0 342 431 72
156 124 177 257 21 319 342 0 265 0
109 103 324 467 0 395 431 265 0...

output:

155.3703581450353397

result:

ok found '155.3703581', expected '155.3703580', error '0.0000000'

Test #13:

score: 0
Accepted
time: 0ms
memory: 3772kb

input:

10
0 3 10 8 0 3 3 8 9 6
3 0 6 10 0 10 9 9 4 9
10 6 0 7 1 5 6 8 0 0
8 10 7 0 10 6 0 6 9 4
0 0 1 10 0 1 0 2 0 1
3 10 5 6 1 0 6 4 0 4
3 9 6 0 0 6 0 10 0 8
8 9 8 6 2 4 10 0 0 2
9 4 0 9 0 0 0 0 0 10
6 9 0 4 1 4 8 2 10 0

output:

3.133273703041145275

result:

ok found '3.1332737', expected '3.1332740', error '0.0000001'

Test #14:

score: 0
Accepted
time: 1ms
memory: 3592kb

input:

10
0 52 25 22 39 47 85 63 8 2
52 0 0 87 2 20 50 87 88 6
25 0 0 77 27 58 81 0 98 0
22 87 77 0 28 0 49 53 59 0
39 2 27 28 0 0 65 76 0 0
47 20 58 0 0 0 88 0 0 3
85 50 81 49 65 88 0 60 85 1
63 87 0 53 76 0 60 0 76 88
8 88 98 59 0 0 85 76 0 0
2 6 0 0 0 3 1 88 0 0

output:

29.54294684842743024

result:

ok found '29.5429468', expected '29.5429470', error '0.0000000'

Test #15:

score: 0
Accepted
time: 1ms
memory: 3592kb

input:

10
0 79 0 192 19 79 0 0 0 0
79 0 0 0 164 100 74 0 26 176
0 0 0 0 184 153 152 0 0 39
192 0 0 0 0 90 54 0 18 0
19 164 184 0 0 195 107 0 8 53
79 100 153 90 195 0 0 124 96 149
0 74 152 54 107 0 0 181 28 0
0 0 0 0 0 124 181 0 0 3
0 26 0 18 8 96 28 0 0 0
0 176 39 0 53 149 0 3 0 0

output:

59.383410497165868946

result:

ok found '59.3834105', expected '59.3834100', error '0.0000000'

Test #16:

score: 0
Accepted
time: 1ms
memory: 3820kb

input:

10
0 416 0 476 0 0 2 0 204 750
416 0 0 850 0 0 471 0 835 67
0 0 0 0 184 274 0 135 557 709
476 850 0 0 904 0 0 556 0 0
0 0 184 904 0 141 0 0 0 0
0 0 274 0 141 0 0 167 486 0
2 471 0 0 0 0 0 0 617 0
0 0 135 556 0 167 0 0 241 226
204 835 557 0 0 486 617 241 0 0
750 67 709 0 0 0 0 226 0 0

output:

226

result:

ok found '226.0000000', expected '226.0000000', error '0.0000000'

Test #17:

score: 0
Accepted
time: 1ms
memory: 3700kb

input:

10
0 777 0 543 382 5 266 0 255 250
777 0 0 0 0 0 566 637 0 469
0 0 0 0 183 671 0 711 335 294
543 0 0 0 929 475 0 925 0 46
382 0 183 929 0 777 674 399 0 732
5 0 671 475 777 0 0 814 453 0
266 566 0 0 674 0 0 0 0 703
0 637 711 925 399 814 0 0 654 928
255 0 335 0 0 453 0 654 0 0
250 469 294 46 732 0 703...

output:

272.27105674229198939

result:

ok found '272.2710567', expected '272.2710570', error '0.0000000'

Test #18:

score: 0
Accepted
time: 1ms
memory: 3744kb

input:

10
0 1 0 0 0 0 4 0 0 0
1 0 0 2 3 0 5 0 0 0
0 0 0 1 0 0 0 0 0 0
0 2 1 0 0 2 3 0 0 3
0 3 0 0 0 0 0 0 0 1
0 0 0 2 0 0 4 0 0 0
4 5 0 3 0 4 0 0 3 0
0 0 0 0 0 0 0 0 0 5
0 0 0 0 0 0 3 0 0 1
0 0 0 3 1 0 0 5 1 0

output:

1.25

result:

ok found '1.2500000', expected '1.2500000', error '0.0000000'

Test #19:

score: 0
Accepted
time: 1ms
memory: 3824kb

input:

10
0 0 1 0 0 1 0 0 0 0
0 0 0 0 0 0 0 1 0 0
1 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 1 0 1
0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 0 0 1
0 1 1 1 0 1 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 1 0 0 0

output:

0.25

result:

ok found '0.2500000', expected '0.2500000', error '0.0000000'

Test #20:

score: 0
Accepted
time: 1ms
memory: 3588kb

input:

10
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 622 0 0 0 0 0 0
0 0 622 0 0 0 0 0 0 585
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 982
0 0 0 0 0 0 0 0 0 0
0 0 0 585 0 0 0 982 0 0

output:

245.5

result:

ok found '245.5000000', expected '245.5000000', error '0.0000000'

Test #21:

score: 0
Accepted
time: 1ms
memory: 3696kb

input:

10
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0

output:

0

result:

ok found '0.0000000', expected '0.0000000', error '-0.0000000'

Extra Test:

score: 0
Extra Test Passed