【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 ;

 }