C++ Programming Tutorial

 
 
 
 

Image

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

 const int max_size=13;

 int n=0;
 int top=-1;
 int choice=0;

 long double h=0;
 long double x0=0;

 long double xn[max_size]={0};
 long double fx[max_size]={0};

 char Fx[100]={NULL};
 char Dfx[100]={NULL};
 char Stack[30][30]={NULL};
 char Postfix_expression[2][30][30]={NULL};

 void push(const char *);
 void convert_ie_to_pe(const char *,const int);

 const char* pop( );
 const long double evaluate_postfix_expression(const long double,const int);

 void show_screen( );
 void clear_screen( );
 void get_input( );
 void estimate_dfx( );

 const int get_index(const long double);

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

       show_screen( );
       get_input( );
       estimate_dfx( );

       return 0;
     }



 //--------------------------  show_screen( )  ---------------------------//


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

       textbackground(1);
       cprintf(\" Numerical Differentiation \");
       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(const char* 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( )  -------------------------------//


 const char* 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*,const int)  ------------//


 void convert_ie_to_pe(const char* Expression,const int index)
    {
       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;
        }

         else if(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(\"(\");

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

             count_2++;
              }

           pop( );
        }

         else if(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)
              {  }

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

                   count_2++;
                }
              }

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

                   count_2++;
                }
              }

           push(Symbol_scanned);
        }

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

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

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


 //-----  evaluate_postfix_expression(const long double,const int)  ------//


 const long double evaluate_postfix_expression(
                    const long double x,const int index)
    {
       long double function_value=0;

       int count_1=-1;

       char Symbol_scanned[30]={NULL};

       do
      {
         count_1++;

         strcpy(Symbol_scanned,Postfix_expression[index][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( ));

           long double operand[2]={0};
           long double 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;

             else if(strcmp(Operand[count_2],\"e\")==0)
                operand[count_2]=2.718282;

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

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

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

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

             else if(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);
        }

         else if(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<<\"Number of Distinct Data Points :\";

         gotoxy(6,10);
         cout<<\"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ\";

         gotoxy(27,13);
         cout<<\"[ min. n = 2  |  max. n = 12 ]\";

         gotoxy(6,12);
         cout<<\"Enter the max. number of distinct data points = n = \";

         cin>>n;

         if(n<2 || n>12)
        {
           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>12);

       gotoxy(6,16);
       cout<<\"Enter the value of x0 = \";

       cin>>x0;

       gotoxy(6,18);
       cout<<\"Enter the value of h = \";

       cin>>h;

       gotoxy(6,24);
       cout<<\"Input Mode :\";

       gotoxy(6,25);
       cout<<\"ÍÍÍÍÍÍÍÍÍÍÍÍ\";

       gotoxy(8,28);
       cout<<\"Press : \";

       gotoxy(10,30);
       cout<<\"- \'Y\' or <Enter> to enter function\";

       gotoxy(10,32);
       cout<<\"- \'N\' or <Any other key> to enter values of the function\";

       gotoxy(8,35);
       cout<<\"Enter your choice : \";

       char Choice=NULL;

       Choice=getch( );

       if(Choice==\'y\' || Choice==\'Y\' || int(Choice)==13)
      {
         choice=1;

         gotoxy(28,35);
         cout<<\"Y\";
      }

       else
      {
         gotoxy(28,35);
         cout<<\"N\";
      }

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

       getch( );

       if(choice)
      {
         clear_screen( );

         gotoxy(6,11);
         cout<<\"Non-Linear Function :\";

         gotoxy(6,12);
         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;

         gotoxy(6,17);
         cout<<\"Enter the Differential Function : f\'(x) = \";

         cin>>Dfx;

         convert_ie_to_pe(Fx,0);
         convert_ie_to_pe(Dfx,1);
      }

       clear_screen( );

       gotoxy(6,9);
       cout<<\"Data Points & Values of Function :\";

       gotoxy(6,10);
       cout<<\"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ\";

       gotoxy(25,12);
       cout<<\"ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿\";

       gotoxy(25,13);
       cout<<\"³       x       ³     f(x)      ³\";

       gotoxy(25,14);
       cout<<\"ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ\";

       gotoxy(25,15);
       cout<<\"³               ³               ³\";

       for(int count_1=0;count_1<n;count_1++)
      {
         gotoxy(25,(wherey( )+1));
         cout<<\"³               ³               ³\";

         gotoxy(25,(wherey( )+1));
         cout<<\"³               ³               ³\";
      }

       gotoxy(25,(wherey( )+1));
       cout<<\"ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ\";

       xn[0]=x0;

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

       gotoxy(25,16);

       for(int count_3=0;count_3<n;count_3++)
      {
         gotoxy(27,wherey( ));
         cout<<xn[count_3];

         if(choice)
        {
           fx[count_3]=evaluate_postfix_expression(xn[count_3],0);

           gotoxy(43,wherey( ));
           cout<<fx[count_3];
        }

         else
        {
           gotoxy(43,wherey( ));
           cin>>fx[count_3];
        }

         if(choice)
        gotoxy(25,(wherey( )+2));

         else
        gotoxy(25,(wherey( )+1));
      }

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

       getch( );
    }


 //-------------------  get_index(const long double)  --------------------//


 const int get_index(const long double x)
    {
       for(int count=0;count<n;count++)
      {
         if(xn[count]==x)
        break;
      }

       return count;
    }


 //----------------------------  estimate_dfx( )  ------------------------//


 void estimate_dfx( )
    {
       clear_screen( );

       gotoxy(6,9);
       cout<<\"Difference Formulas of Order 1 :\";

       gotoxy(6,10);
       cout<<\"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ\";

       gotoxy(8,12);
       cout<<\"Backward Difference Formula :  f\'(x) ÷ [f(x)-f(x-h)]/h\";

       gotoxy(8,14);
       cout<<\"Forward Difference Formula  :  f\'(x) ÷ [f(x+h)-f(x)]/h\";

       gotoxy(6,18);
       cout<<\"Estimation of First Derivative - f\'(x) :\";

       gotoxy(6,19);
       cout<<\"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ\";

       char Choice=NULL;

       long double x=0;
       long double dfx=0;
       long double actual_dfx=0;

       do
      {
         Choice=NULL;

         gotoxy(8,21);
         cout<<\"Press :\";

         gotoxy(10,23);
         cout<<\"<B> to estimate f\'(x) using Backward Difference Formula\";

         gotoxy(10,25);
         cout<<\"<F> to estimate f\'(x) using Forward Difference Formula\";

         gotoxy(10,27);
         cout<<\"<E> to exit\";

         do
        {
           gotoxy(8,30);
           cout<<\"Enter your choice : \";

           Choice=getche( );
           Choice=toupper(Choice);

           if(Choice==\'B\' || Choice==\'F\' || Choice==\'E\')
              break;

           else
              {
             gotoxy(18,35);
             cout<<\"Wrong Choice. Please select a valid Choice.\";

             gotoxy(25,37);
             cout<<\"Press any Key to continue...\";

             getch( );

             gotoxy(18,35);
             cout<<\"                                           \";

             gotoxy(25,37);
             cout<<\"                                           \";

             gotoxy(8,30);
             cout<<\"                                          \";
              }
        }
         while(1);

         if(Choice==\'E\')
        exit(0);

         gotoxy(8,21);
         cout<<\"                                                       \";

         gotoxy(10,23);
         cout<<\"                                                       \";

         gotoxy(10,25);
         cout<<\"                                                       \";

         gotoxy(10,27);
         cout<<\"                                                       \";

         gotoxy(8,30);
         cout<<\"                                                       \";

         Input_x_again:

         x=0;
         dfx=0;
         actual_dfx=0;

         gotoxy(10,21);
         cout<<\"Enter the value of x = \";

         cin>>x;

         if(x>=xn[0] && x<=xn[(n-2)] && Choice==\'B\')
        {
           int index=0;

           index=get_index(x);

           long double fxph=::fx[(index+1)];
           long double fx=::fx[index];

           dfx=((fxph-fx)/h);
        }

         else if(x>=xn[1] && x<=xn[(n-1)] && Choice==\'F\')
        {
           int index=0;

           index=get_index(x);

           long double fx=::fx[index];
           long double fxmh=::fx[(index-1)];

           dfx=((fx-fxmh)/h);
        }

         else
        {
           gotoxy(8,25);
           cout<<\"Error: Please enter the valid value of x for the selected formula.\";

           gotoxy(15,27);
           cout<<\"Press any Key to enter the value of x again...\";

           getch( );

           gotoxy(8,25);
           cout<<\"                                                                  \";

           gotoxy(15,27);
           cout<<\"                                                 \";

           gotoxy(10,21);
           cout<<\"                                                 \";

           goto Input_x_again;
        }

         gotoxy(10,25);
         cout<<\"The estimated value of f\'(\"<<x<<\")  ÷  \"<<dfx;

         if(choice)
        {
           actual_dfx=evaluate_postfix_expression(x,1);

           gotoxy(10,27);
           cout<<\"The Actual value of f\'(\"<<x<<\")  =  \"<<actual_dfx;

           gotoxy(10,31);
           cout<<\"Absolute Error = E(abs) =  \"<<fabs((actual_dfx-dfx));
        }

         gotoxy(25,42);
         cout<<\"Press any other key to continue...\";

         getch( );

         gotoxy(10,21);
         cout<<\"                                                    \";

         gotoxy(10,25);
         cout<<\"                                                    \";

         gotoxy(10,27);
         cout<<\"                                                    \";

         gotoxy(10,31);
         cout<<\"                                                    \";

         gotoxy(25,42);
         cout<<\"                                                    \";
      }
       while(1);
    }

    Related Post:
  1. Program to perform radix sort

  2. Program of scanfill algorithm

  3. Program to read marks of 10 students for 4 subjects and compute and display total marks and status of each student

  4. Program to swap two integers

  5. Represent a polynomial in terms of a singly linked list and then add two three variables polynomials

  6. Program to implement Add and Subtract function on Big Number Class

  7. Program of scaling about reference point

  8. Program to show the Simple implementation of Hashing

  9. Program that prints all the even numbers b/w 0 to 50 ( using while, do-while and for loop )

  10. Program to estimate the value of Third Derivative of the function at the given points from the given data using Central Difference Formula of order 2

  11. Program to illustrate the 2D array of int using pointers

  12. Program to read a Non-Linear equation in one variable, then evaluate it using Newton-Raphson Method and display its kD accurate root

  13. Program to determine whether the given function is a Cubic Spline or not

  14. Program to sort that set of strings in ascending and descending order of their weights. The sorted output is to be displayed on the screen

  15. Program that reads a number ,coumputes and displays its factorial using do-while loop

  16. Program to illustrate the use of call-by-value method in functions

  17. Program to illustrate the use of inline functions

  18. Program to construct Newtons Backward Difference Interpolation Formula from the given distinct equally spaced data points

  19. Program for election contest among five candidates

  20. Program that reads a number and displays it with its digits in reverse order using do-while loop