【luogu P2455 [SDOI2006]线性方程组】 题解

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

无解：最后一列对应元素不为0，前面全是0.

无穷解：一行全是0.

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.

 #include <algorithm>
 #include <cstdio>
 #include <cmath>
 #include <iostream>
 using namespace std;
 const int maxn = ;
 const double eps = 1e-;
 double A[maxn][maxn], ans[maxn];
 int n;
 int main()
 {
     scanf("%d",&n);
     for(int i = ; i <= n; i++)
     for(int j = ; j <= n+; j++)
     scanf("%lf", &A[i][j]);
     for(int i = ; i <= n; i++)
     {
         int p = i;
         for(int j = i + ; j <= n; j++)
           if(fabs(A[j][i]) > fabs(A[p][i])) p = j;
         for(int j = ; j <= n + ; j++) swap(A[p][j],A[i][j]);

         if(fabs(A[i][i]) < eps) continue;
         double div = A[i][i];
         for(int j = ; j <= n + ; j++) A[i][j]/=div;
         for(int j = ; j <= n; j++)
         {
             if(i != j)
             {
                 double div = A[j][i];
                 for(int k = ; k <= n + ; k++) A[j][k] -= A[i][k]*div;
             }
         }
     }
     int NoSolution = , ManySolution = ;
     for(int i = ; i <= n; i++)
     {
         int Nonum = , Manynum = ;
         for(int j = ; j <= n +  && fabs(A[i][j]) < eps; j++)
         Nonum++,Manynum++;
         if(Manynum > n) ManySolution = ;
         if(Nonum == n) NoSolution = ;
     }
         if(NoSolution) {printf("-1");return ;}
         if(ManySolution) {printf("");return ;}
     for(int i = n; i >= ; i--)
     {
         ans[i] = A[i][n+];
         for(int j = i - ; j >= ; j--)
         {
             A[j][n+] -= ans[i] * A[j][i];
             A[j][i] = ;
         }
     }
     for(int i = ; i <= n; i++)
     printf("x%d=%.2lf\n",i,ans[i] + eps);
     return ;
 }