#include<stdio.h>
#include<math.h>
main() {
  int n,i,j,k,imax;
  printf("Nhap co ma tran cua Ax=b\nn= "); scanf("%d",&n);
  float a[n][n+1],p;
  printf("Nhap gia tri cho ma tran:\n");
  for(i=0;i<n;i++) {
    printf("Hang thu %d: ",i+1);
    for(j=0;j<n+1;j++) scanf("%f",&a[i][j]);
  }
  /*Gauss Elimination + Interchange*/
  for(k=0;k<n-1;k++) {
    imax=k;
    for(i=k+1;i<n;i++) if(fabs(a[i][k])>fabs(a[imax][k])) imax=i;
    for(j=0;j<n+1;j++) {
      p=a[k][j];
      a[k][j]=a[imax][j];
      a[imax][j]=p;
    }
    for(i=k+1;i<n;i++) {
      p=a[i][k]/a[k][k];
      for(j=k;j<n+1;j++) a[i][j]-=p*a[k][j];
    }
  }
  /*Jordan Elimination*/
  for(k=n-1;k>0;k--) for(i=k-1;i>=0;i--) {
    p=a[i][k]/a[k][k];
    for(j=k;j<n+1;j++) a[i][j]-=p*a[k][j];
  }
  /*Show solution*/
  printf("Nghiem he phuong trinh la:\n");
  for(i=0;i<n;i++) printf("x%d= %.2f\n",i+1,a[i][n]/a[i][i]);
}
// Interchange: tim so co abs lon nhat de trao hang tu do, nham de phep chia cho a[k][k] it sai so do so qua gan 0
// imax de luu lai vi tri hang cua phan tu lon nhat do
// p vua la bien trung gian de trao doi hang, vua la bien trung gian trong phep khu Gauss va Jordan (tan dung bien p de lam nhieu viec)