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

 constint max_size=5;

 int n=0;
 int iterations=0;

 char Diagonally_dominant=NULL;

 longdouble input[max_size][max_size]={0};
 longdouble previous_output[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);
 void get_input_linear_equation( );
 void sort_system_of_linear_equations( );
 void apply_guass_seidel_iterative_method( );
 void show_result( );

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

       show_screen( );
       get_size_of_linear_equations( );
       get_input_linear_equation( );

       if(Diagonally_dominant=='Y' || Diagonally_dominant=='y')
      sort_system_of_linear_equations( );

       apply_guass_seidel_iterative_method( );
       show_result( );

       getch( );
       return 0;
    }

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

       textbackground(1);
       cprintf(" Guass-Seidel's Itrative 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( )
    {
       textbackground(8);

       for(int count=0;count<37;count++)
      {
         gotoxy(3,8+count);
         cout<<"                                                                            ";
      }

       gotoxy(1,2);
    }

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

         gotoxy(38,11);
         cout<<"[ Maximum size = 4 ]";

         gotoxy(4,9);
         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(4,15);
       cout<<"Enter the number of iterations that you want to perform = ";

       cin>>iterations;

       gotoxy(4,18);
       cout<<"Do you want to make the System Diagonally Dominant : (Y/N) ? : ";

       cin>>Diagonally_dominant;

       gotoxy(1,2);
    }

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

       for(int count_1=0;count_1<n;count_1++)
      {
         gotoxy(4,(17+(count_1*2)));
         cout<<"                                                                      ";

         gotoxy(4,(17+(count_1*2)));

         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)));

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

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

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

           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(4,9);
       cout<<"Size of the System of Linear Equations = n = "<<n;

       gotoxy(4,13);
       cout<<"System of Linear Equations :";

       gotoxy(4,14);
       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(4,35);
           cout<<"                                                                    ";

           gotoxy(4,35);

           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( )  ----------------///*************************************************************************/void sort_system_of_linear_equations( )
    {
       for(int count_1=0;count_1<(n-1);count_1++)
      {
         for(int count_2=count_1;count_2<(n-1);count_2++)
        {
           for(int count_3=count_1;count_3<(n-1);count_3++)
              {
             longdouble temp[max_size]={0};

             if(fabs(input[count_3][count_1])<
                       fabs(input[(count_3+1)][count_1]))
                {
                   for(int count_4=0;count_4<=n;count_4++)
                  temp[count_4]=input[count_3][count_4];

                   for(int count_5=0;count_5<=n;count_5++)
                  input[count_3][count_5]=
                         input[(count_3+1)][count_5];

                   for(int count_6=0;count_6<=n;count_6++)
                  input[(count_3+1)][count_6]=temp[count_6];
                }
              }
        }
      }
    }

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

       gotoxy(4,10);
       cout<<"Solution :";

       gotoxy(4,11);
       cout<<"ÍÍÍÍÍÍÍÍÍÍ";

       if(n==1)
      {
         gotoxy(4,13);
         cout<<"ÚÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿";

         gotoxy(4,14);
         cout<<"³   n   ³      X1       ³";

         gotoxy(4,15);
         cout<<"ÃÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´";

         gotoxy(4,16);
         cout<<"³       ³               ³";
      }

       elseif(n==2)
      {
         gotoxy(4,13);
         cout<<"ÚÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿";

         gotoxy(4,14);
         cout<<"³   n   ³      X1       ³      X2       ³";

         gotoxy(4,15);
         cout<<"ÃÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´";

         gotoxy(4,16);
         cout<<"³       ³               ³               ³";
      }

       elseif(n==3)
      {
         gotoxy(4,13);
         cout<<"ÚÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿";

         gotoxy(4,14);
         cout<<"³   n   ³      X1       ³      X2       ³      X3       ³";

         gotoxy(4,15);
         cout<<"ÃÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´";

         gotoxy(4,16);
         cout<<"³       ³               ³               ³               ³";
      }

       elseif(n==4)
      {
         gotoxy(4,13);
         cout<<"ÚÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿";

         gotoxy(4,14);
         cout<<"³   n   ³      X1       ³      X2       ³      X3       ³      X4       ³";

         gotoxy(4,15);
         cout<<"ÃÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´";

         gotoxy(4,16);
         cout<<"³       ³               ³               ³               ³               ³";
      }

       for(int count_1=0;count_1<n;count_1++)
      {
         longdouble temp[max_size]={0};

         for(int count_2=0;count_2<=n;count_2++)
        {
           if(count_2!=count_1)
              temp[count_2]=(input[count_1][count_2]/input[count_1][count_1]);
        }

         for(int count_3=0;count_3<=n;count_3++)
        input[count_1][count_3]=temp[count_3];
      }

       for(int count_4=0;count_4<n;count_4++)
      {
         for(int count_5=0;count_5<n;count_5++)
        input[count_4][count_5]*=-1;
      }

       int x_cord=4;
       int y_cord=17;

       for(int count_6=0;count_6<=iterations;count_6++)
      {
         if(n==1)
        {
           gotoxy(x_cord,y_cord);
           cout<<"³       ³               ³";

           gotoxy(x_cord,(y_cord+1));
           cout<<"³       ³               ³";
        }

         elseif(n==2)
        {
           gotoxy(x_cord,y_cord);
           cout<<"³       ³               ³               ³";

           gotoxy(x_cord,(y_cord+1));
           cout<<"³       ³               ³               ³";
        }

         elseif(n==3)
        {
           gotoxy(x_cord,y_cord);
           cout<<"³       ³               ³               ³               ³";

           gotoxy(x_cord,(y_cord+1));
           cout<<"³       ³               ³               ³               ³";
        }

         elseif(n==4)
        {
           gotoxy(x_cord,y_cord);
           cout<<"³       ³               ³               ³               ³               ³";

           gotoxy(x_cord,(y_cord+1));
           cout<<"³       ³               ³               ³               ³               ³";
        }

         gotoxy((x_cord+3),y_cord);
         cout<<count_6;

         gotoxy((x_cord+10),y_cord);
         cout<<output[0];

         if(n>=2)
        {
           gotoxy((x_cord+26),y_cord);
           cout<<output[1];
        }

         if(n>=3)
        {
           gotoxy((x_cord+42),y_cord);
           cout<<output[2];
        }

         if(n>=4)
        {
           gotoxy((x_cord+58),y_cord);
           cout<<output[3];
        }

         for(int count_7=0;count_7<n;count_7++)
        {
           output[count_7]=0;

           for(int count_8=0;count_8<n;count_8++)
              {
             if(count_8!=count_7)
                output[count_7]+=(input[count_7][count_8]*previous_output[count_8]);
              }

           output[count_7]+=input[count_7][count_8];
           previous_output[count_7]=output[count_7];
        }

         y_cord+=2;

         if((count_6%12)==0 && count_6<iterations && count_6>0)
        {
           y_cord=17;

           gotoxy(30,44);
           cout<<"Press any key to continue...";
           getch( );

           for(int count_9=1;count_9<25;count_9++)
              {
             gotoxy(3,(16+count_9));
             cout<<"                                                                            ";
              }
        }
      }

       if(n==1)
      {
         gotoxy(x_cord,y_cord);
         cout<<"ÀÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ";
      }

       elseif(n==2)
      {
         gotoxy(x_cord,y_cord);
         cout<<"ÀÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ";
      }

       elseif(n==3)
      {
         gotoxy(x_cord,y_cord);
         cout<<"ÀÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ";
      }

       elseif(n==4)
      {
         gotoxy(x_cord,y_cord);
         cout<<"ÀÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ";
      }

       gotoxy(30,44);
       cout<<"Press any key to continue...";
       getch( );
    }

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

       gotoxy(4,9);
       cout<<"Gauss-Seidel System of Linear Equations :";

       gotoxy(4,10);
       cout<<"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ";

       for(int count_1=0;count_1<n;count_1++)
      {
         gotoxy(4,(13+(count_1*3)));
         cout<<"x"<<(count_1+1);

         gotoxy((wherex( )-1),(wherey( )-1));
         cout<<"(k+1)";

         gotoxy((wherex( )-3),(wherey( )+1));
         cout<<"    =  ";

         for(int count_2=0;count_2<=n;count_2++)
        {
           gotoxy(wherex( ),(13+(count_1*3)));

           if(count_2!=count_1 && count_2<n)
              {
             if(count_2!=0)
                cout<<fabs(input[count_1][count_2])<<" x"<<(count_2+1);

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

             gotoxy((wherex( )-1),(wherey( )-1));

             if(count_2<count_1)
                cout<<"(k+1)";

             else
                cout<<"(k)";

             gotoxy((wherex( )-1),(wherey( )+1));

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

             else
                cout<<" - ";
              }

           elseif(count_2!=count_1)
              cout<<fabs(input[count_1][count_2]);
        }
      }

       if(Diagonally_dominant=='Y' || Diagonally_dominant=='y')
      {
         gotoxy(4,26);
         cout<<"Note: The given System of Linear Equations is solved by making it";

         gotoxy(10,28);
         cout<<"Diagonally Dominant.";
      }

       gotoxy(4,31);
       cout<<"Result of Given System of Linear Equations :";

       gotoxy(4,32);
       cout<<"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ";

       for(int count_3=0;count_3<n;count_3++)
      {
         gotoxy(8,(34+count_3+count_3));
         cout<<"x"<<(count_3+1)<<" = "<<output[count_3];
      }

       gotoxy(4,(36+count_3+count_3));
       cout<<"* Number of Iterations for the above result = "<<iterations<<".";

       gotoxy(1,2);
    }