【SDOI2006】线性方程组

题面

https://www.luogu.org/problem/P2455

题解

#include<iostream>
#include<iomanip>
#include<cmath>
#include<cstdio>
#define eps 1e-5
using namespace std;

int n,i,j,k,x,p;
double a[105][105],ta[105][105],ans[105],t,Max,sum;
bool book[105];

bool check(){
  int i,j,k;
  for (i=1;i<=n;i++) {
    bool s=0;
    for (j=1;j<=n+1;j++) if (ta[i][j]!=0) s=1;
    if (!s) return 1;
  }
  for (i=1;i<=n;i++)
    for (j=i+1;j<=n;j++) {
      bool s=0;
      double x=ta[i][1]/ta[j][1];
      for (k=1;k<=n+1;k++) if (ta[i][k]/ta[j][k]!=x) s=1;
      if (!s) return 1;
    }
  return 0;
}

int main(){
    cin>>n;
    bool yichang=0;
    for (i=1;i<=n;i++)
      for (j=1;j<=n+1;j++) {cin>>a[i][j]; ta[i][j]=a[i][j]=a[i][j]*1.0;}
    for (x=1;x<=n;x++){
        Max=0;
        for (j=x;j<=n;j++) if (fabs(a[j][x])>Max){Max=a[j][x];p=j;}
        for (j=x;j<=n+1;j++){t=a[x][j];a[x][j]=a[p][j];a[p][j]=t;} 
        for (j=x+1;j<=n+1;j++) {
          if(fabs(a[x][x])<eps) {ans[x]=2.3333; book[x]=1; yichang=1; goto L1;} 
          else a[x][j]=(a[x][j]*1.0)/(a[x][x]*1.0);
        }
        a[x][x]=1;
        for (j=x+1;j<=n;j++){
          t=a[j][x];
          for (k=x;k<=n+1;k++) a[j][k]=a[j][k]-t*a[x][k];
          a[j][x]=0;
        }
        L1:;
    }
    if (a[n][n]==0) {
      yichang=1;
      ans[n]=2.333;
    }
    else {
      ans[n]=a[n][n+1];
    }
    
    for (i=n-1;i>=1;i--) if (!book[i]) {
      sum=0;
      for (j=i+1;j<=n;j++) sum=sum+a[i][j]*ans[j];
      ans[i]=(a[i][n+1]-sum)/a[i][i];
    }
    bool can=1;
    for (i=1;i<=n;i++) {
      double ansx=0;
      for (j=1;j<=n;j++) ansx+=(ans[j]*ta[i][j]);
      if (fabs(ansx-ta[i][n+1])>eps) can=0;
    }
    if (yichang) {
      if (can) printf("0"); else printf("-1");
      return 0;
    }
    if (check()) {
      puts("0");
      return 0;
    }
    for (i=1;i<=n;i++) {
      printf("x%d=",i);
      if (fabs(ans[i])<eps) ans[i]=0.0;
      printf("%.2lf\n",ans[i]);
    }
}