QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#261498 | #7753. Energy Distribution | yinwuxiao | AC ✓ | 2ms | 4052kb | C++14 | 3.5kb | 2023-11-22 22:30:05 | 2024-10-31 10:26:34 |
Judging History
answer
#include <bits/stdc++.h>
using namespace std;
const int N = 105;
const double eps = 1e-6;
int n,m;
double a[N][N];
int c[N],b[N][N],d[N][N];
double w[N];
int gauss() {
int c, r;
for (c = 0, r = 0; c < n; ++c) { // c列r行,遍历列
int t = r;
for (int i = r; i < n; ++i) // 寻找列主元,拿t记录
if (fabs(a[i][c]) > fabs(a[t][c]))
t = i;
if (fabs(a[t][c]) < eps) continue; // 如果列主元为0,不必考虑,当前列全为0
// 交换列主元t行与当前r行的数
for (int i = c; i < n + 1; ++i) swap(a[t][i], a[r][i]);
// 当前列主元已经被交换到了r行,需要从后向前进行处理,避免主对角线元素变成1
for (int i = n; i >= c; --i) a[r][i] /= a[r][c];
// 列主消元
for (int i = r + 1; i < n; ++i)
if (fabs(a[i][c]) > eps)
for (int j = n; j >= c; --j)
a[i][j] -= a[r][j] * a[i][c];
++r;
}
// for (int i=0;i<n;i++){
// for (int j=0;j<n+1;j++)
// cout<<a[i][j]<<" ";
// cout<<endl;
// }
// if (r < n) {
// for (int i = r; i < n; ++i)
// if (fabs(a[i][n]) > eps) return 2; // 0x=1 则无解
// // return 1; // 0x=0 无穷多解
// }
// 上三角阶梯型矩阵
// 直接求解即可,最后一列放置结果
for (int i = n - 1; i >= 0; --i)
{
int jl=-1;
for (int j=0;j<n;j++) if (a[i][j]>0) {jl=j; break;}
for (int j = i + 1; j < n; ++j)
a[i][n] -= a[j][n] * a[i][j];
if (jl!=-1&&jl!=i){
a[jl][n]=a[i][n];
a[i][n]=0;
}
}
return 0;
}
int fa[N];
int find(int x){
return fa[x]==x?x:fa[x]=find(fa[x]);
}
double solve(int x){
int cnt=0;
for (int i=1;i<=m;i++)
if ((x>>(i-1))&1) c[++cnt]=i;
n=cnt;
for (int i=1;i<=n;i++)
for (int j=1;j<=n;j++)
d[i][j]=b[c[i]][c[j]];
memset(a,0,sizeof(a));
for (int i=0;i<n;i++){
for (int j=0;j<n;j++)
a[i][j]=d[i+1][j+1];
a[i][n]=1;
}
for (int i=0;i<n;i++) a[n][i]=1;
a[n][n+1]=1;
n++;
// for (int i=0;i<n;i++){
// for (int j=0;j<n+1;j++)
// cout<<a[i][j]<<" ";
// cout<<endl;
// }
int t = gauss();
n--;
for (int i=0;i<n;i++) w[i+1]=a[i][n+1];
for (int i=1;i<=n;i++) if (w[i]<0) return 0;
// for (int i=1;i<=n;i++){
// cout<<w[i]<<" ";
// }
// cout<<endl;
// for (int i=1;i<=n+1;i++) cout<<w[i]<<endl;
double ans=0;
for (int i=1;i<=n;i++)
for (int j=i;j<=n;j++)
ans+=d[i][j]*w[i]*w[j];
return ans;
}
int main() {
cin >> n;
m=n;
int cnt=0;
for (int i=1;i<=n;i++) fa[i]=i;
for(int i=1;i<=n;i++){
int sum=0;
for (int j=1;j<=n;j++){
cin>>b[i][j];
sum+=b[i][j];
if (b[i][j]>0){
fa[find(i)]=find(j);
}
}
}
double ans=0;
for (int i=1;i<=(1<<m)-1;i++) ans=max(ans,solve(i));
// for (int i=1;i<=m;i++) ans=max(ans,solve(i));
printf("%.8lf", ans);
// if (t == 0) {
// for (int i = 0; i < n; ++i) printf("%.2lf\n", a[i][n]);
// }
// else if (t == 1) puts("Infinite group solutions");
// else puts("No solution");
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: 3856kb
input:
2 0 1 1 0
output:
0.25000000
result:
ok found '0.2500000', expected '0.2500000', error '0.0000000'
Test #2:
score: 0
Accepted
time: 0ms
memory: 3928kb
input:
3 0 2 1 2 0 2 1 2 0
output:
0.57142857
result:
ok found '0.5714286', expected '0.5714290', error '0.0000004'
Test #3:
score: 0
Accepted
time: 0ms
memory: 3980kb
input:
3 0 1 2 1 0 1 2 1 0
output:
0.50000000
result:
ok found '0.5000000', expected '0.5000000', error '0.0000000'
Test #4:
score: 0
Accepted
time: 0ms
memory: 4044kb
input:
4 0 3 1 0 3 0 1 0 1 1 0 2 0 0 2 0
output:
0.75000000
result:
ok found '0.7500000', expected '0.7500000', error '0.0000000'
Test #5:
score: 0
Accepted
time: 0ms
memory: 3976kb
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:
1.00000000
result:
ok found '1.0000000', expected '1.0000000', error '0.0000000'
Test #6:
score: 0
Accepted
time: 1ms
memory: 3992kb
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:
2.85714286
result:
ok found '2.8571429', expected '2.8571430', error '0.0000000'
Test #7:
score: 0
Accepted
time: 1ms
memory: 3932kb
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:
12.51158480
result:
ok found '12.5115848', expected '12.5115850', error '0.0000000'
Test #8:
score: 0
Accepted
time: 1ms
memory: 3932kb
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:
25.00911790
result:
ok found '25.0091179', expected '25.0091180', error '0.0000000'
Test #9:
score: 0
Accepted
time: 1ms
memory: 3932kb
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:
119.00000000
result:
ok found '119.0000000', expected '119.0000000', error '0.0000000'
Test #10:
score: 0
Accepted
time: 2ms
memory: 3888kb
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:
240.25000000
result:
ok found '240.2500000', expected '240.2500000', error '0.0000000'
Test #11:
score: 0
Accepted
time: 2ms
memory: 3936kb
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:
327.37365897
result:
ok found '327.3736590', expected '327.3736590', error '0.0000000'
Test #12:
score: 0
Accepted
time: 2ms
memory: 3904kb
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:
155.37035815
result:
ok found '155.3703581', expected '155.3703580', error '0.0000000'
Test #13:
score: 0
Accepted
time: 2ms
memory: 4036kb
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:
3.13327370
result:
ok found '3.1332737', expected '3.1332740', error '0.0000001'
Test #14:
score: 0
Accepted
time: 2ms
memory: 4036kb
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:
29.54294685
result:
ok found '29.5429468', expected '29.5429470', error '0.0000000'
Test #15:
score: 0
Accepted
time: 2ms
memory: 3992kb
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:
59.38341050
result:
ok found '59.3834105', expected '59.3834100', error '0.0000000'
Test #16:
score: 0
Accepted
time: 2ms
memory: 3916kb
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:
226.00000000
result:
ok found '226.0000000', expected '226.0000000', error '0.0000000'
Test #17:
score: 0
Accepted
time: 2ms
memory: 4052kb
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:
272.27105674
result:
ok found '272.2710567', expected '272.2710570', error '0.0000000'
Test #18:
score: 0
Accepted
time: 2ms
memory: 3876kb
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:
1.25000000
result:
ok found '1.2500000', expected '1.2500000', error '0.0000000'
Test #19:
score: 0
Accepted
time: 0ms
memory: 4036kb
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:
0.25000000
result:
ok found '0.2500000', expected '0.2500000', error '0.0000000'
Test #20:
score: 0
Accepted
time: 2ms
memory: 3884kb
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:
245.50000000
result:
ok found '245.5000000', expected '245.5000000', error '0.0000000'
Test #21:
score: 0
Accepted
time: 2ms
memory: 3924kb
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:
0.00000000
result:
ok found '0.0000000', expected '0.0000000', error '-0.0000000'
Extra Test:
score: 0
Extra Test Passed