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

 constint max_size=8;

 int n=0;
 int top=-1;

 longdouble h=0;
 longdouble a=0;
 longdouble b=0;

 longdouble ri[max_size][max_size]={0};
 longdouble xn[max_size]={0};
 longdouble fx[max_size]={0};

 char Fx[100]={NULL};
 char Stack[30][30]={NULL};
 char Postfix_expression[30][30]={NULL};

 /*************************************************************************//*************************************************************************///------------------------  Funcion Prototypes  -------------------------///*************************************************************************//*************************************************************************/void push(constchar *);
 void convert_ie_to_pe(constchar *);

 constchar* pop( );
 constlongdouble evaluate_postfix_expression(constlongdouble);

 void show_screen( );
 void clear_screen( );
 void get_input( );
 void apply_trapezoidal_rule( );
 void apply_romberg_method( );
 void show_result( );

 /*************************************************************************//*************************************************************************///------------------------------  main( )  ------------------------------///*************************************************************************//*************************************************************************/int main( )
    {
       clrscr( );
       textmode(C4350);

       show_screen( );
       get_input( );
       apply_trapezoidal_rule( );
       apply_romberg_method( );
       show_result( );

       getch( );
       return 0;
     }

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

       textbackground(1);
       cprintf(" Romberg Integration ");
       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);
    }

 /*************************************************************************///--------------------------  push(const char*)  ------------------------///*************************************************************************/void push(constchar* Operand)
    {
       if(top==(max_size-1))
      {
         cout<<"Error : Stack is full."<<endl;
         cout<<"\n        Press any key to exit.";

         getch( );
         exit(0);
      }

       else
      {
         top++;
         strcpy(Stack[top],Operand);
      }
    }

 /*************************************************************************///------------------------------  pop( )  -------------------------------///*************************************************************************/constchar* pop( )
    {
       char Operand[40]={NULL};

       if(top==-1)
      {
         cout<<"Error : Stack is empty."<<endl;
         cout<<"\n        Press any key to exit.";

         getch( );
         exit(0);
      }

       else
      {
         strcpy(Operand,Stack[top]);
         strset(Stack[top],NULL);
         top--;
      }

       return Operand;
    }

 /*************************************************************************///--------------------  convert_ie_to_pe(const char*)  ------------------///*************************************************************************/void convert_ie_to_pe(constchar* Expression)
    {
       char Infix_expression[100]={NULL};
       char Symbol_scanned[30]={NULL};

       push("(");
       strcpy(Infix_expression,Expression);
       strcat(Infix_expression,"+0)");

       int flag=0;
       int count_1=0;
       int count_2=0;
       int equation_length=strlen(Infix_expression);

       if(Infix_expression[0]=='(')
      flag=1;

       do
      {
         strset(Symbol_scanned,NULL);

         if(flag==0)
        {
           int count_3=0;

           do
              {
             Symbol_scanned[count_3]=Infix_expression[count_1];

             count_1++;
             count_3++;
              }
           while(count_1<=equation_length &&
               Infix_expression[count_1]!='(' &&
                  Infix_expression[count_1]!='+' &&
                 Infix_expression[count_1]!='-' &&
                    Infix_expression[count_1]!='*' &&
                       Infix_expression[count_1]!='/' &&
                      Infix_expression[count_1]!='^' &&
                         Infix_expression[count_1]!=')');


           flag=1;
        }

         elseif(flag==1)
        {
           Symbol_scanned[0]=Infix_expression[count_1];

           count_1++;

           if(Infix_expression[count_1]!='(' &&
             Infix_expression[count_1]!='^' &&
                Infix_expression[count_1]!='*' &&
                   Infix_expression[count_1]!='/' &&
                  Infix_expression[count_1]!='+' &&
                     Infix_expression[count_1]!='-' &&
                    Infix_expression[count_1]!=')')
              flag=0;

           if(Infix_expression[count_1-1]=='(' &&
               (Infix_expression[count_1]=='-' ||
                 Infix_expression[count_1]=='+'))
              flag=0;
        }

         if(strcmp(Symbol_scanned,"(")==0)
        push("(");

         elseif(strcmp(Symbol_scanned,")")==0)
        {
           while(strcmp(Stack[top],"(")!=0)
              {
             strcpy(Postfix_expression[count_2],pop( ));

             count_2++;
              }

           pop( );
        }

         elseif(strcmp(Symbol_scanned,"^")==0 ||
               strcmp(Symbol_scanned,"+")==0 ||
                 strcmp(Symbol_scanned,"-")==0 ||
                       strcmp(Symbol_scanned,"*")==0 ||
                         strcmp(Symbol_scanned,"/")==0)
        {
           if(strcmp(Symbol_scanned,"^")==0)
              {  }

           elseif(strcmp(Symbol_scanned,"*")==0 ||
                          strcmp(Symbol_scanned,"/")==0)
              {
             while(strcmp(Stack[top],"^")==0 ||
                     strcmp(Stack[top],"*")==0 ||
                       strcmp(Stack[top],"/")==0)
                {
                   strcpy(Postfix_expression[count_2],pop( ));

                   count_2++;
                }
              }

           elseif(strcmp(Symbol_scanned,"+")==0 ||
                    strcmp(Symbol_scanned,"-")==0)
              {
             while(strcmp(Stack[top],"(")!=0)
                {
                   strcpy(Postfix_expression[count_2],pop( ));

                   count_2++;
                }
              }

           push(Symbol_scanned);
        }

         else
        {
           strcat(Postfix_expression[count_2],Symbol_scanned);

           count_2++;
        }
      }
       while(strcmp(Stack[top],NULL)!=0);

       strcat(Postfix_expression[count_2],"=");
       count_2++;
    }

 /*************************************************************************///----------  evaluate_postfix_expression(const long double)  -----------///*************************************************************************/constlongdouble evaluate_postfix_expression(constlongdouble x)
    {
       longdouble function_value=0;

       int count_1=-1;

       char Symbol_scanned[30]={NULL};

       do
      {
         count_1++;

         strcpy(Symbol_scanned,Postfix_expression[count_1]);

         if(strcmp(Symbol_scanned,"^")==0 ||
              strcmp(Symbol_scanned,"*")==0 ||
                strcmp(Symbol_scanned,"/")==0 ||
                  strcmp(Symbol_scanned,"+")==0 ||
                    strcmp(Symbol_scanned,"-")==0)

        {
           char Result[30]={NULL};
           char Operand[2][30]={NULL};

           strcpy(Operand[0],pop( ));
           strcpy(Operand[1],pop( ));

           longdouble operand[2]={0};
           longdouble result=0;

           char *endptr;

           for(int count_2=0;count_2<2;count_2++)
              {
             int flag=0;

             if(Operand[count_2][0]=='-')
                {
                   int length=strlen(Operand[count_2]);

                   for(int count_3=0;count_3<(length-1);count_3++)
                  Operand[count_2][count_3]=Operand[count_2][(count_3+1)];

                   Operand[count_2][count_3]=NULL;

                   flag=1;
                }

             if(strcmp(Operand[count_2],"x")==0)
                operand[count_2]=x;

             elseif(strcmp(Operand[count_2],"e")==0)
                operand[count_2]=2.718282;

             elseif(strcmp(Operand[count_2],"sinx")==0)
                operand[count_2]=sinl(x);

             elseif(strcmp(Operand[count_2],"cosx")==0)
                operand[count_2]=cosl(x);

             elseif(strcmp(Operand[count_2],"tanx")==0)
                operand[count_2]=tanl(x);

             elseif(strcmp(Operand[count_2],"lnx")==0)
                operand[count_2]=logl(x);

             elseif(strcmp(Operand[count_2],"logx")==0)
                operand[count_2]=log10l(x);

             else
                operand[count_2]=strtod(Operand[count_2],&endptr);

             if(flag)
                operand[count_2]*=-1;
              }

           switch(Symbol_scanned[0])
              {
             case'^' : result=powl(operand[1],operand[0]);
                    break;

             case'*' : result=operand[1]*operand[0];
                    break;

             case'/' : result=operand[1]/operand[0];
                    break;

             case'+' : result=operand[1]+operand[0];
                    break;

             case'-' : result=operand[1]-operand[0];
                    break;
              }

           gcvt(result,25,Result);

           push(Result);
        }

         elseif(strcmp(Symbol_scanned,"=")!=0)
        push(Symbol_scanned);
      }
       while(strcmp(Symbol_scanned,"=")!=0);

       char Function_value[30]={NULL};
       char *endptr;

       strcpy(Function_value,pop( ));
       function_value=strtod(Function_value,&endptr);

       return function_value;
    }

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

         gotoxy(6,9);
         cout<<"Input :";

         gotoxy(6,10);
         cout<<"ÍÍÍÍÍÍÍ";

         gotoxy(37,13);
         cout<<"[ n = 2,4,8 ]";

         gotoxy(6,12);
         cout<<"Enter the max. number of sub-intervals = n = ";

         cin>>n;

         if(n!=2 && n!=4 && n!=8)
        {
           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!=2 && n!=4 && n!=8);

       gotoxy(6,16);
       cout<<"Enter the value of Lower limit = a = ";

       cin>>a;

       gotoxy(6,18);
       cout<<"Enter the value of Upper Limit = b = ";

       cin>>b;

       gotoxy(25,43);
       cout<<"Press any key to continue...";

       getch( );

       clear_screen( );

       gotoxy(6,10);
       cout<<"Non-Linear Function :";

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

       gotoxy(6,37);
       cout<<"Note : Write the function with proper Braces ( ) e.g; 2x+3 as (2*x)+3";

       gotoxy(6,40);
       cout<<"Available Operators  :  ^ (raised to power) , * , / , + , -";

       gotoxy(6,42);
       cout<<"Available Operands   :  x , e , sinx , cosx , tanx , lnx , logx ,";

       gotoxy(6,44);
       cout<<"                        n = any number";

       gotoxy(6,14);
       cout<<"Enter the Function : f(x) = ";

       cin>>Fx;

       convert_ie_to_pe(Fx);
    }

 /*************************************************************************///----------------------  apply_trapezoidal_rule( )  --------------------///*************************************************************************/void apply_trapezoidal_rule( )
    {
       int count_1=0;

       for(int count_2=1;count_2<=n;count_2+=count_2)
      {
         for(int count_3=0;count_3<max_size;count_3++)
        {
           xn[count_3]=0;
           fx[count_3]=0;
        }

         h=((b-a)/count_2);
         xn[0]=a;

         for(int count_4=0;count_4<count_2;count_4++)
        xn[(count_4+1)]=(xn[count_4]+h);

         for(int count_5=0;count_5<=count_2;count_5++)
        fx[count_5]=evaluate_postfix_expression(xn[count_5]);

         for(int count_6=1;count_6<count_2;count_6++)
        ri[count_1][0]+=fx[count_6];

         ri[count_1][0]*=2;
         ri[count_1][0]+=fx[0];
         ri[count_1][0]+=fx[count_2];
         ri[count_1][0]*=(h/2);

         count_1++;
      }
    }

 /*************************************************************************///----------------------  apply_romberg_method( )  ----------------------///*************************************************************************/void apply_romberg_method( )
    {
       int counter=0;

       switch(n)
      {
         case 2 : counter=1;
              break;

         case 4 : counter=2;
              break;

         case 8 : counter=3;
              break;
      }

       for(int count_1=1;count_1<=counter;count_1++)
      {
         for(int count_2=count_1;count_2<=counter;count_2++)
        {
           longdouble rjk_1=0;
           longdouble rj_1k_1=0;

           rjk_1=ri[count_2][(count_1-1)];
           rj_1k_1=ri[(count_2-1)][(count_1-1)];

           ri[count_2][count_1]=(((powl(4,count_1)*rjk_1)-rj_1k_1)/(powl(4,count_1)-1));
        }
      }
    }

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

       int counter=0;

       switch(n)
      {
         case 2 : counter=1;
              break;

         case 4 : counter=2;
              break;

         case 8 : counter=3;
              break;
      }

       gotoxy(6,10);
       cout<<"Solution :";

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

       if(n==1)
      {
         gotoxy(6,13);
         cout<<"ÚÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ¿";
      }

       elseif(n==2)
      {
         gotoxy(6,13);
         cout<<"ÚÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿";
      }

       elseif(n==4)
      {
         gotoxy(6,13);
         cout<<"ÚÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿";
      }

       elseif(n==8)
      {
         gotoxy(6,13);
         cout<<"ÚÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿";
      }

       if(n==1)
      {
         gotoxy(6,14);
         cout<<"³ Number of ³ Trapezoidal ³";
      }

       elseif(n==2)
      {
         gotoxy(6,14);
         cout<<"³ Number of ³ Trapezoidal ³ Romberg Values ³";
      }

       elseif(n==4)
      {
         gotoxy(6,14);
         cout<<"³ Number of ³ Trapezoidal ³      Romberg  Values      ³";
      }

       elseif(n==8)
      {
         gotoxy(6,14);
         cout<<"³ Number of ³ Trapezoidal ³             Romberg  Values             ³";
      }

       if(n==1)
      {
         gotoxy(6,15);
         cout<<"³           ³             ³";
      }

       elseif(n==2)
      {
         gotoxy(6,15);
         cout<<"³        ³          ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´";
      }

       elseif(n==4)
      {
         gotoxy(6,15);
         cout<<"³           ³             ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ´";
      }

       elseif(n==8)
      {
         gotoxy(6,15);
         cout<<"³           ³             ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ´";
      }

       if(n==1)
      {
         gotoxy(6,16);
         cout<<"³ Intervals ³    Sums     ³";
      }

       elseif(n==2)
      {
         gotoxy(6,16);
         cout<<"³ Intervals ³    Sums     ³  1ts Order     ³";
      }

       elseif(n==4)
      {
         gotoxy(6,16);
         cout<<"³ Intervals ³    Sums     ³  1ts Order  ³  2nd Order  ³";
      }

       elseif(n==8)
      {
         gotoxy(6,16);
         cout<<"³ Intervals ³    Sums     ³  1ts Order  ³  2nd Order  ³  3rd Order  ³";
      }

       if(n==1)
      {
         gotoxy(6,17);
         cout<<"ÃÄÄÄÄÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄ´";
      }

       elseif(n==2)
      {
         gotoxy(6,17);
         cout<<"ÃÄÄÄÄÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´";
      }

       elseif(n==4)
      {
         gotoxy(6,17);
         cout<<"ÃÄÄÄÄÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄ´";
      }

       elseif(n==8)
      {
         gotoxy(6,17);
         cout<<"ÃÄÄÄÄÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄ´";
      }

       if(n==1)
      {
         gotoxy(6,18);
         cout<<"³           ³             ³";
      }

       elseif(n==2)
      {
         gotoxy(6,18);
         cout<<"³           ³             ³                ³";
      }

       elseif(n==4)
      {
         gotoxy(6,18);
         cout<<"³           ³             ³             ³             ³";
      }

       elseif(n==8)
      {
         gotoxy(6,18);
         cout<<"³           ³             ³             ³             ³             ³";
      }

       int y_cord=19;
       int intervals=1;

       for(int count_1=0;count_1<=counter;count_1++)
      {
         if(n==1)
        {
           gotoxy(6,y_cord);
           cout<<"³           ³             ³";

           gotoxy(6,(y_cord+1));
           cout<<"³           ³             ³";
        }

         elseif(n==2)
        {
           gotoxy(6,y_cord);
           cout<<"³           ³             ³                ³";

           gotoxy(6,(y_cord+1));
           cout<<"³           ³             ³                ³";
        }

         elseif(n==4)
        {
           gotoxy(6,y_cord);
           cout<<"³           ³             ³             ³             ³";

           gotoxy(6,(y_cord+1));
           cout<<"³           ³             ³             ³             ³";
        }

         elseif(n==8)
        {
           gotoxy(6,y_cord);
           cout<<"³           ³             ³             ³             ³             ³";

           gotoxy(6,(y_cord+1));
           cout<<"³           ³             ³             ³             ³             ³";
        }

         gotoxy(11,(19+(count_1*2)));
         cout<<intervals;

         intervals+=intervals;
         y_cord+=2;
      }

       for(int count_2=0;count_2<=counter;count_2++)
      {
         for(int count_3=0;count_3<=counter;count_3++)
        {
           if(count_2==0)
              {
             gotoxy(20,(19+(count_3*2)));
             cout<<ri[count_3][0];
              }

           elseif(count_2==1 && count_3>=count_2)
              {
             gotoxy(34,(19+(count_3*2)));
             cout<<ri[count_3][1];
              }

           elseif(count_2==2 && count_3>=count_2)
              {
             gotoxy(48,(19+(count_3*2)));
             cout<<ri[count_3][2];
              }

           elseif(count_2==3 && count_3>=count_2)
              {
             gotoxy(62,(19+(count_3*2)));
             cout<<ri[count_3][3];
              }
        }
      }

       if(n==1)
      {
         gotoxy(6,y_cord);
         cout<<"ÀÄÄÄÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÙ";
      }

       elseif(n==2)
      {
         gotoxy(6,y_cord);
         cout<<"ÀÄÄÄÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ";
      }

       elseif(n==4)
      {
         gotoxy(6,y_cord);
         cout<<"ÀÄÄÄÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÙ";
      }

       elseif(n==8)
      {
         gotoxy(6,y_cord);
         cout<<"ÀÄÄÄÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÙ";
      }

       gotoxy(6,32);
       cout<<"              bô";

       gotoxy(6,34);
       cout<<"              aõ";

       gotoxy(6,33);
       cout<<"Estimation of  ³f(x)dx :";

       gotoxy(6,35);
       cout<<"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ";

       gotoxy(8,37);
       cout<<"Estimated Integral Value = ";

       cout<<ri[counter][counter];

       gotoxy(1,2);
    }