# include <iostream.h>
 # include   <stdlib.h>
 # include    <stdio.h>
 # include    <conio.h>
 # include     <math.h>

 constint max_size=5;

 int n=0;

 char Partial_pivoting=NULL;

 longdouble input[max_size][max_size]={0};
 longdouble output[max_size]={0};

 void show_screen( );
 void clear_screen( );
 void get_size_of_linear_equations( );
 void show_input(constint,constint,constint=0);
 void get_input_linear_equation( );
 void sort_system_of_linear_equations(constint);
 void apply_gaussian_method( );
 void generate_result( );
 void show_result( );

 int main( )
    {
       clrscr( );
       textmode(C4350);

       show_screen( );
       get_size_of_linear_equations( );
       get_input_linear_equation( );
       apply_gaussian_method( );
       generate_result( );
       show_result( );

       getch( );
       return 0;
    }

 /*************************************************************************///--------------------------  show_screen( )  ---------------------------///*************************************************************************/void show_screen( )
    {
       cprintf("\n********************************************************************************");
       cprintf("***********************-                               -************************");
       cprintf("*----------------------- ");

       textbackground(1);
       cprintf(" Gaussian Elimination Method ");
       textbackground(8);

       cprintf(" ------------------------*");
       cprintf("*-*********************-                               -**********************-*");
       cprintf("*-****************************************************************************-*");

       for(int count=0;count<42;count++)
      cprintf("*-*                                                                          *-*");

       gotoxy(1,46);
       cprintf("*-****************************************************************************-*");
       cprintf("*------------------------------------------------------------------------------*");
       cprintf("********************************************************************************");

       gotoxy(1,2);
    }

 /*************************************************************************///-------------------------  clear_screen( )  ---------------------------///*************************************************************************/void clear_screen( )
    {
       for(int count=0;count<37;count++)
      {
         gotoxy(5,8+count);
         cout<<"                                                                        ";
      }

       gotoxy(1,2);
    }

 /*************************************************************************///------------------  get_size_of_linear_equations( )  ------------------///*************************************************************************/void get_size_of_linear_equations( )
    {
       do
      {
         clear_screen( );

         gotoxy(40,11);
         cout<<"[ Maximum size = 4 ]";

         gotoxy(6,9);
         cout<<"Enter the size of the System of Linear Equations = n = ";

         cin>>n;

         if(n<=0 || n>max_size)
        {
           gotoxy(12,25);
           cout<<"Error : Wrong Input. Press <Esc> to exit or any other key";

           gotoxy(12,26);
           cout<<"        to try again.";

           n=int(getche( ));

           if(n==27)
              exit(0);
        }
      }
       while(n<=0 || n>max_size);

       gotoxy(6,15);
       cout<<"Do you want to use Partial Pivoting : (Y/N) ? : ";

       cin>>Partial_pivoting;

       gotoxy(1,2);
    }

 /*************************************************************************///-------------  show_input(const int,const int,const int)  -------------///*************************************************************************/void show_input(constint x,constint y,constint y_cord)
    {
       int counter=0;
       int number_of_inputs=((x*n)+y+x);

       for(int count_1=0;count_1<n;count_1++)
      {
         gotoxy(6,(17+(count_1*2)+y_cord));
         cout<<"                                                                      ";

         gotoxy(6,(17+(count_1*2)+y_cord));

         for(int count_2=0;count_2<=n;count_2++)
        {
           if(counter==(number_of_inputs+1))
              textbackground(12);

           else
              textbackground(8);

           if(count_2==n)
              gotoxy((wherex( )+5),(17+(count_1*2)+y_cord));

           gotoxy(wherex( ),(17+(count_1*2)+y_cord));
           cprintf("      ");

           if(count_2==n)
              gotoxy((wherex( )-5),(17+(count_1*2)+y_cord));

           gotoxy((wherex( )-6),(17+(count_1*2)+y_cord));

           if(counter<=number_of_inputs && counter!=-1)
              {
             if(count_2==n)
                {
                   cout<<"  =  ";
                   cout<<input[count_1][count_2];
                }

             elseif(count_2==0)
                cout<<input[count_1][count_2]<<" x"<<(count_2+1);

             else
                cout<<fabs(input[count_1][count_2])<<" x"<<(count_2+1);
              }

           elseif(count_2==n)
              cout<<"  =  b"<<(count_1+1);

           else
              cout<<"a"<<(count_1+1)<<(count_2+1)<<" x"<<(count_2+1);

           if(count_2<(n-1) && input[count_1][(count_2+1)]>=0)
              cout<<"  +  ";

           elseif(count_2<(n-1))
              cout<<"  -  ";

           counter++;
        }
      }
    }

 /*************************************************************************///--------------------  get_input_linear_equation( )  -------------------///*************************************************************************/void get_input_linear_equation( )
    {
       clear_screen( );

       gotoxy(6,9);
       cout<<"Size of the System of Linear Equations = n = "<<n;

       gotoxy(6,13);
       cout<<"System of Linear Equations :";

       gotoxy(6,14);
       cout<<"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ";

       show_input(0,-1);

       for(int count_1=0;count_1<n;count_1++)
      {
         for(int count_2=0;count_2<=n;count_2++)
        {
           gotoxy(5,35);
           cout<<"                                                                    ";

           gotoxy(6,35);

           if(count_2<n)
             cout<<"Enter the value of a"<<(count_1+1)<<(count_2+1)<<" =  ";

           else
             cout<<"Enter the value of b"<<(count_1+1)<<" =  ";

           cin>>input[count_1][count_2];

           show_input(count_1,count_2);
        }
      }
    }

 /*************************************************************************///-------------  sort_system_of_linear_equations(const int)  ------------///*************************************************************************/void sort_system_of_linear_equations(constint start_position)
    {
       for(int count_1=start_position;count_1<(n-1);count_1++)
      {
         for(int count_2=start_position;count_2<(n-1);count_2++)
        {
           longdouble temp[max_size]={0};

           if(fabs(input[count_2][start_position])<fabs(input[(count_2+1)][start_position]))
              {
             for(int count_3=0;count_3<=n;count_3++)
                temp[count_3]=input[count_2][count_3];

             for(int count_4=0;count_4<=n;count_4++)
                input[count_2][count_4]=input[(count_2+1)][count_4];

             for(int count_5=0;count_5<=n;count_5++)
                input[(count_2+1)][count_5]=temp[count_5];
              }
        }
      }
    }

 /*************************************************************************///-----------------------  apply_gaussian_method( )  --------------------///*************************************************************************/void apply_gaussian_method( )
    {
       for(int count_1=0;count_1<(n-1);count_1++)
      {
         if(Partial_pivoting=='Y' || Partial_pivoting=='y')
        sort_system_of_linear_equations(count_1);

         for(int count_2=(count_1+1);count_2<n;count_2++)
        {
           longdouble multiplier=
              (input[count_2][count_1]/input[count_1][count_1]);

           for(int count_3=0;count_3<=n;count_3++)
              {
             longdouble temp=(input[count_1][count_3]*multiplier);
             input[count_2][count_3]=(input[count_2][count_3]-temp);
              }
        }
      }
    }

 /*************************************************************************///------------------------  generate_result( )  -------------------------///*************************************************************************/void generate_result( )
    {
       for(int count_1=(n-1);count_1>=0;count_1--)
      {
         output[count_1]=input[count_1][n];

         for(int count_2=(n-1);count_2>count_1;count_2--)
        input[count_1][count_2]=(input[count_1][count_2]*output[count_2]);

         for(int count_3=(n-1);count_3>count_1;count_3--)
        output[count_1]-=input[count_1][count_3];

         output[count_1]/=input[count_1][count_1];
      }
    }

 /*************************************************************************///-----------------------------  show_result( )  ------------------------///*************************************************************************/void show_result( )
    {
       clear_screen( );

       gotoxy(6,10);
       cout<<"Solved System of Linear Equations :";

       gotoxy(6,11);
       cout<<"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ";

       show_input((n-1),n,-4);

       gotoxy(6,26);
       cout<<"Result of Given System of Linear Equations :";

       gotoxy(6,27);
       cout<<"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ";

       for(int count=0;count<n;count++)
      {
         gotoxy(10,(29+count+count));
         cout<<"x"<<(count+1)<<" = "<<output[count];
      }

       if(Partial_pivoting=='Y' || Partial_pivoting=='y')
      {
         gotoxy(6,41);
         cout<<"Note : The given System of Linear Equations is solved by using";

         gotoxy(6,43);
         cout<<"       Partial Pivoting.";
      }

       gotoxy(1,2);
    }