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

 constint max_size=13;

 int n=0;
 int top=-1;

 longdouble h=0;
 longdouble x=0;
 longdouble x0=0;
 longdouble y0=0;
 longdouble two_stage_result=0;
 longdouble three_stage_result=0;

 longdouble xx[max_size]={0};
 longdouble yy2[max_size]={0};
 longdouble yy3[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_pe(constlongdouble,constlongdouble);

 void show_screen( );
 void clear_screen( );
 void get_input( );
 void apply_runge_kutta_method( );
 void show_result( );

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

       show_screen( );
       get_input( );
       apply_runge_kutta_method( );
       show_result( );

       getch( );
       return 0;
     }

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

       textbackground(1);
       cprintf(" Numerical 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_pe(const long double,const long double)  ---------///*************************************************************************/constlongdouble evaluate_pe(constlongdouble x,constlongdouble y)
    {
       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],"y")==0)
                operand[count_2]=y;

             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);

             elseif(strcmp(Operand[count_2],"siny")==0)
                operand[count_2]=sinl(y);

             elseif(strcmp(Operand[count_2],"cosy")==0)
                operand[count_2]=cosl(y);

             elseif(strcmp(Operand[count_2],"tany")==0)
                operand[count_2]=tanl(y);

             elseif(strcmp(Operand[count_2],"lny")==0)
                operand[count_2]=logl(y);

             elseif(strcmp(Operand[count_2],"logy")==0)
                operand[count_2]=log10l(y);

             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( )
    {
       clear_screen( );

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

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

       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<<"                        any number and all above functions with y.";

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

       cin>>Fx;

       convert_ie_to_pe(Fx);

       gotoxy(6,17);
       cout<<"Enter the value of xn = ";

       cin>>x;

       gotoxy(6,19);
       cout<<"Enter the value of x0 = ";

       cin>>x0;

       gotoxy(6,21);
       cout<<"Enter the value of y0 = ";

       cin>>y0;

       gotoxy(6,23);
       cout<<"Enter the value of h = ";

       cin>>h;
    }

 /*************************************************************************///--------------------  apply_ruunge_kutta_method( )  -------------------///*************************************************************************/void apply_runge_kutta_method( )
    {
       xx[0]=x0;
       yy2[0]=y0;
       yy3[0]=y0;

       do
      {
         xx[(n+1)]=(xx[n]+h);
         n++;
      }
       while(xx[n]<x);

       longdouble k1=0;
       longdouble k2=0;
       longdouble ynp1=0;
       longdouble xn=x0;
       longdouble yn=y0;

       for(int count_1=0;count_1<n;count_1++)
      {
         k1=0;
         k2=0;
         ynp1=0;

         k1=evaluate_pe(xn,yn);
         k2=evaluate_pe((xn+h),(yn+(h*k1)));

         ynp1=(yn+((h*(k1+k2))/2));

         yn=ynp1;
         xn+=h;
         yy2[(count_1+1)]=ynp1;
      }

       two_stage_result=ynp1;

       longdouble k3=0;
       longdouble k4=0;

       xn=x0;
       yn=y0;

       for(int count_2=0;count_2<n;count_2++)
      {
         k1=0;
         k2=0;
         k3=0;
         k4=0;
         ynp1=0;

         k1=evaluate_pe(xn,yn);
         k2=evaluate_pe((xn+(h/2)),(yn+((h*k1)/2)));
         k3=evaluate_pe((xn+(h/2)),(yn+((h*k2)/2)));
         k4=evaluate_pe((xn+h),(yn+(h*k3)));

         ynp1=(yn+((h*(k1+(2*k2)+(2*k3)+k4))/6));

         yn=ynp1;
         xn+=h;
         yy3[(count_2+1)]=ynp1;
      }

       three_stage_result=ynp1;

       clear_screen( );

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

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

       gotoxy(18,12);
       cout<<"ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿";

       gotoxy(18,13);
       cout<<"³       x       ³  2-stage  y   ³  3-stage  y   ³";

       gotoxy(18,14);
       cout<<"ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´";

       gotoxy(18,15);
       cout<<"³               ³               ³               ³";

       for(int count_3=0;count_3<=n;count_3++)
      {
         gotoxy(18,(wherey( )+1));
         cout<<"³               ³               ³               ³";

         gotoxy(18,(wherey( )+1));
         cout<<"³               ³               ³               ³";
      }

       gotoxy(18,(wherey( )+1));
       cout<<"ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ";

       gotoxy(25,16);

       for(int count_4=0;count_4<=n;count_4++)
      {
         gotoxy(20,wherey( ));
         cout<<xx[count_4];

         gotoxy(36,wherey( ));
         cout<<yy2[count_4];

         gotoxy(52,wherey( ));
         cout<<yy3[count_4];

         gotoxy(25,(wherey( )+2));
      }

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

       getch( );

    }

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

       gotoxy(6,9);
       cout<<"Runge-Kutta Methods :";

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

       gotoxy(6,12);
       cout<<"2-Stage Method :  y(n+1) = yn + (h/2)(k1+k2)";

       gotoxy(40,14);
       cout<<"where :   k1 = f(xn,yn)";

       gotoxy(40,15);
       cout<<"          k2 = f(xn+h,yn+hk1)";

       gotoxy(6,18);
       cout<<"3-Stage Method:   y(n+1) = yn + (h/6)(k1+2k2+2k3+k4)";

       gotoxy(40,20);
       cout<<"where :  k1 = f(xn,yn)";

       gotoxy(40,21);
       cout<<"         k2 = f(xn+(h/2),yn+(h/2)k1)";

       gotoxy(40,22);
       cout<<"         k3 = f(xn+(h/2),yn(h/2)k2)";

       gotoxy(40,23);
       cout<<"         k4 = f(xn+h,yn+hk3)";

       gotoxy(6,25);
       cout<<"Estimated Value :";

       gotoxy(6,26);
       cout<<"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ";

       gotoxy(8,28);
       cout<<"Estimated Differential Value (using 2-Stage Method) = "<<two_stage_result;

       gotoxy(8,30);
       cout<<"Estimated Differential Value (using 3-Stage Method) = "<<three_stage_result;

       gotoxy(1,2);
    }