luogu P2455 [SDOI2006]线性方程组 题解

Posted 2020-11-01 Misaka_Azusa

题目链接：https://www.luogu.org/problemnew/show/P2455

嗯...在消元过程中不要直接拿矩阵元素自己消，会把自己消成0.

 1 #include <algorithm>
 2 #include <cstdio>
 3 #include <cmath>
 4 #include <iostream>
 5 using namespace std;
 6 const int maxn = 200;
 7 const double eps = 1e-7;
 8 double A[maxn][maxn], ans[maxn];
 9 int n;
10 int main() 
11 {
12     scanf("%d",&n);
13     for(int i = 1; i <= n; i++)
14     for(int j = 1; j <= n+1; j++)
15     scanf("%lf", &A[i][j]);
16     for(int i = 1; i <= n; i++) 
17     {
18         int p = i;
19         for(int j = i + 1; j <= n; j++)
20           if(fabs(A[j][i]) > fabs(A[p][i])) p = j;
21         for(int j = 1; j <= n + 1; j++) swap(A[p][j],A[i][j]);
22           
23         if(fabs(A[i][i]) < eps) continue;
24         double div = A[i][i];
25         for(int j = 1; j <= n + 1; j++) A[i][j]/=div;
26         for(int j = 1; j <= n; j++)
27         {
28             if(i != j)
29             {
30                 double div = A[j][i];
31                 for(int k = 1; k <= n + 1; k++) A[j][k] -= A[i][k]*div;
32             }
33         }
34     }
35     int NoSolution = 0, ManySolution = 0;
36     for(int i = 1; i <= n; i++)
37     {
38         int Nonum = 0, Manynum = 0;
39         for(int j = 1; j <= n + 1 && fabs(A[i][j]) < eps; j++)
40         Nonum++,Manynum++;
41         if(Manynum > n) ManySolution = 1;
42         if(Nonum == n) NoSolution = 1;
43     }
44         if(NoSolution) {printf("-1");return 0;}
45         if(ManySolution) {printf("0");return 0;}
46     for(int i = n; i >= 1; i--)
47     {
48         ans[i] = A[i][n+1];
49         for(int j = i - 1; j >= 1; j--)
50         {
51             A[j][n+1] -= ans[i] * A[j][i];
52             A[j][i] = 0;
53         }
54     }
55     for(int i = 1; i <= n; i++)
56     printf("x%d=%.2lf\n",i,ans[i] + eps);
57     return 0;
58 }