C++ Programming Blog

 
 
 

Image

 # include <iostream.h>
 # include   <stdlib.h>
 # include   <string.h>
 # include    <stdio.h>
 # include    <conio.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 difference_table[max_size][max_size]={0};

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

 void push(const char *);
 void convert_infix_expression_to_postfix_expression(const char *);

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

 void show_screen( );
 void clear_screen( );
 void get_input( );
 void construct_difference_table( );
 void show_difference_table( );
 void estimate_pnx( );

 const long double compute_newtons_fdif(const long double,const int);

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

       show_screen( );
       get_input( );
       construct_difference_table( );
       show_difference_table( );
       estimate_pnx( );

       return 0;
     }


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


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

       textbackground(1);
       cprintf(\" Newton\'s Forward Difference Interpolation Formula \");
       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(3,8+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_infix_expression_to_postfix_expression(const char*)  ----//


 void convert_infix_expression_to_postfix_expression(const char* 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;
        }

         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[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[count_2],pop( ));

                   count_2++;
                }
              }

           else if(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)  -----------//


 const long double evaluate_postfix_expression(const long double x)
    {
       long double 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( ));

           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>>Non_linear_equation;

         convert_infix_expression_to_postfix_expression(Non_linear_equation);
      }

       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)
        {
           difference_table[0][count_3]=evaluate_postfix_expression(xn[count_3]);

           gotoxy(43,wherey( ));
           cout<<difference_table[0][count_3];
        }

         else
        {
           gotoxy(43,wherey( ));
           cin>>difference_table[0][count_3];
        }

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

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

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

       getch( );
    }


 //-----------------------  construct_difference_table( )  -----------------------//


 void construct_difference_table( )
    {
       for(int count_1=1;count_1<n;count_1++)
      {
         for(int count_2=count_1;count_2<n;count_2++)
        {
           long double fx1=difference_table[(count_1-1)][(count_2-1)];
           long double fx2=difference_table[(count_1-1)][count_2];

           difference_table[count_1][count_2]=fx2-fx1;
        }
      }
    }


 //--------------------------  show_difference_table( )  -------------------------//


 void show_difference_table( )
    {
       clear_screen( );

       gotoxy(4,10);
       cout<<\"Difference Table :\";

       gotoxy(4,11);
       cout<<\"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ\";

       gotoxy(4,13);
       cout<<\"ÚÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ\";

       gotoxy(4,14);
       cout<<\"³   x    ³     f(x)      \";

       gotoxy(4,15);
       cout<<\"ÃÄÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄÄ\";

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

       int x_cord=4;
       int y_cord=17;

       for(int count_1=0;count_1<n;count_1++)
      {
         gotoxy(x_cord,y_cord);
         cout<<\"³        ³              \";

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

         gotoxy((x_cord+2),y_cord);
         cout<<xn[count_1];

         gotoxy((x_cord+11),y_cord);
         cout<<difference_table[0][count_1];

         y_cord+=2;
      }

       gotoxy(x_cord,y_cord);
       cout<<\"ÀÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄ\";

       x_cord=28;

       int count_2=0;

       for(int count_3=1;count_3<n;count_3++)
      {
         gotoxy(x_cord,13);
         cout<<\"ÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ\";

         gotoxy(x_cord,14);
         cout<<\"³\";

         gotoxy(x_cord,15);
         cout<<\"ÅÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ\";

         gotoxy(x_cord,16);
         cout<<\"³\";

         gotoxy(x_cord,y_cord);
         cout<<\"ÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ\";

         gotoxy((x_cord+6),14);
         cout<<count_3;

         if(count_3==1)
        cout<<\"st\";

         else if(count_3==2)
        cout<<\"nd\";

         else if(count_3==3)
        cout<<\"rd\";

         else
        cout<<\"th\";

         y_cord=17;

         for(int count_4=0;count_4<n;count_4++)
        {
           gotoxy(x_cord,y_cord);
           cout<<\"³\";

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

           if(count_4>=count_3)
              {
             gotoxy((x_cord+2),(y_cord-count_3));
             cout<<difference_table[count_3][count_4];
              }

           y_cord+=2;
        }

         x_cord+=16;
         count_2++;

         if((count_2%3)==0 && count_3<(n-1))
        {
           gotoxy(x_cord,13);
           cout<<\"ÂÄÄ\";

           gotoxy(x_cord,14);
           cout<<\"³\";

           gotoxy(x_cord,15);
           cout<<\"ÅÄÄ\";

           gotoxy(x_cord,16);
           cout<<\"³\";

           gotoxy(x_cord,y_cord);
           cout<<\"ÁÄÄ\";

           y_cord=17;

           for(int count_5=0;count_5<n;count_5++)
              {
             gotoxy(x_cord,y_cord);
             cout<<\"³\";

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

             y_cord+=2;
              }

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

           getch( );

           y_cord=13;
           x_cord=28;

           for(int count_6=0;count_6<=(n+2);count_6++)
              {
             gotoxy(x_cord,y_cord);
             cout<<\"                                                   \";

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

             y_cord+=2;
              }

           y_cord-=2;
           count_2=0;
           count_3--;
        }
      }

       gotoxy(x_cord,13);
       cout<<\"¿\";

       gotoxy(x_cord,14);
       cout<<\"³\";

       gotoxy(x_cord,16);
       cout<<\"³\";

       y_cord=17;

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

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

         y_cord+=2;
      }

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

       gotoxy(x_cord,y_cord);
       cout<<\"Ù\";

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

       getch( );
    }


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


 const long double compute_newtons_fdif(const long double x,const int n)
    {
       long double s=0;
       long double pnx=0;
       long double temp=0;
       long double n_factorial=1;

       s=((x-x0)/h);

       pnx=difference_table[0][0];

       for(int count_1=0;count_1<n;count_1++)
      {
         temp=s;
         temp*=difference_table[(count_1+1)][(count_1+1)];
         temp/=n_factorial;

         for(int count_2=0;count_2<count_1;count_2++)
        temp*=(s-(count_2+1));

         pnx+=temp;
         n_factorial*=(count_1+2);
      }

       return pnx;
    }


 //----------------------------  estimate_pnx( )  ------------------------//


 void estimate_pnx( )
    {
       clear_screen( );

       gotoxy(6,10);
       cout<<\"Estimation of Pn(x) :\";

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

       char Choice=NULL;

       int n=0;

       long double x=0;
       long double fx=0;
       long double pnx=0;

       do
      {
         Choice=NULL;

         n=0;
         x=0;
         fx=0;
         pnx=0;

         gotoxy(10,13);
         cout<<\"Enter the value of n = \";

         cin>>n;

         gotoxy(10,15);
         cout<<\"Enter the value of x = \";

         cin>>x;

         pnx=compute_newtons_fdif(x,n);

         gotoxy(10,20);
         cout<<\"The estimated value of P\"<<n<<\"(\"<<x<<\")  =  \"<<pnx;

         if(choice)
        {
           fx=evaluate_postfix_expression(x);

           gotoxy(10,23);
           cout<<\"The Actual value of f\"<<\"(\"<<x<<\")  =  \"<<fx;

           gotoxy(10,25);
           cout<<\"Absolute Error = E(abs) =  \"<<fabs((fx-pnx));
        }

         gotoxy(12,40);
         cout<<\"Press <Esc> to exit, \'V\' to view Difference Table again\";

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

         Choice=getch( );

         if(int(Choice)!=27 && Choice!=\'v\' && Choice!=\'V\')
        {
           gotoxy(10,13);
           cout<<\"                                                    \";

           gotoxy(10,15);
           cout<<\"                                                    \";

           gotoxy(10,20);
           cout<<\"                                                    \";

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

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

           gotoxy(12,40);
           cout<<\"                                                         \";

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

         else if(Choice==\'v\' || Choice==\'V\')
        {
           show_difference_table( );
           estimate_pnx( );
        }

         else if(int(Choice)==27)
        exit(0);
      }
       while(1);
    }

    Related Post:
  1. Program that takes short date from a user and displays long date

  2. Program to read a Non-Linear equation in one variable, then evaluate it using Modified False-Position Method and display its kD accurate root

  3. Program to illustrate supplying of values to pointer variables

  4. Program to fill different types of geometric shapes using Flood Fill Algorithm

  5. Program of declaration of default arguments during creation of function

  6. Program to illustrate classes with inline functions

  7. Program that performs addition of 2 matrix using friend function

  8. Program that differentiate b/w the variables of the storage class Auto and Static along with global variables

  9. Program to illustrate the passing of values to constructor in classes

  10. Program to print an array before and after adding 5 to its contents using pointers

  11. Program to find largest integer among the three and display it using function with return type

  12. Program to draw a Cubic Bezier Curve

  13. Program of displaying product inventory by converting one class to another class

  14. Program to show the 3D Shearing Transformation along z-axis

  15. Program of address calculation sort

  16. PROGRAM TO IMPLEMENT RECURSIVE DESCENT PARSER

  17. Program to show the 3D Shearing Transformation along x-axis

  18. Program to estimate the value of First Derivative of the function at the given points from the given data using Central Difference Formula of order 4

  19. Program to illustrate the implementation of Scaling Transformation along Arbitrary Direction

  20. Program of inheritance using shape class and area calculation