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

 # 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 error_flag=0;

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

 char Sx[max_size][100]={NULL};
 char Dsx[max_size][100]={NULL};
 char D2sx[max_size][100]={NULL};

 char Stack[30][30]={NULL};
 char Postfix_expression[max_size][30][30]={NULL};



 //------------------------  Funcion Prototypes  -------------------------//



 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 get_polynomials( );
 void get_first_derivatives( );
 void get_second_derivatives( );
 void check_condition_1( );
 void check_condition_2( );
 void check_condition_3( );
 void check_condition_4( );
 void check_condition_5( );
 void check_natural_boundry_conditions( );
 void check_clamped_boundry_conditions( );
 void show_result( );



 //------------------------------  main( )  ------------------------------//



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

       show_screen( );
       get_input( );
       get_polynomials( );
       get_first_derivatives( );
       get_second_derivatives( );

       check_condition_1( );

       if(!error_flag)
      check_condition_2( );

       if(!error_flag)
      check_condition_3( );

       if(!error_flag)
      check_condition_4( );

       if(!error_flag)
      check_condition_5( );

       show_result( );

       getch( );

       return 0;
     }



 //------------------------  Funcion Definitions  ------------------------//




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


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

       textbackground(1);
       cprintf(\" Cubic Spline Functions \");
       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 = 3  |  max. n = 12 ]\";

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

         cin>>n;

         if(n<3 || 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<3 || n>12);

       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\";

       gotoxy(25,15);

       for(int count_2=0;count_2<n;count_2++)
      {
         gotoxy(25,(wherey( )+1));

         gotoxy(27,wherey( ));
         cin>>xn[count_2];

         gotoxy(43,(wherey( )-1));
         cin>>fx[count_2];
      }

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

       getch( );
    }


 //------------------------  get_polynomials( )  -------------------------//


 void get_polynomials( )
    {
       clear_screen( );

       gotoxy(6,9);
       cout<<\"Cubic Polynomials :\";

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

       gotoxy(6,12);
       cout<<\"Note : Write the Polynomials with proper Braces e.g; 2x+3 as (2*x)+3.\";

       gotoxy(10,15);

       for(int count=0;count<(n-1);count++)
      {
         gotoxy(10,(wherey( )+1));
         cout<<\"S\"<<count<<\"(x) =  \";

         gotoxy(wherex( ),wherey( ));
         cin>>Sx[count];

         convert_ie_to_pe(Sx[count],count);
      }

       gotoxy(25,44);
       cout<<\"Press any key to continue...\";

       getch( );
    }


 //----------------------  get_first_derivatives( )  ---------------------//


 void get_first_derivatives( )
    {
       clear_screen( );

       gotoxy(6,9);
       cout<<\"First Derivatives :\";

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

       gotoxy(6,12);
       cout<<\"Note : Write the function with proper Braces e.g; 2x+3 as (2*x)+3.\";

       gotoxy(10,15);

       for(int count=0;count<(n-1);count++)
      {
         gotoxy(10,(wherey( )+1));
         cout<<\"S\'\"<<count<<\"(x) =  \";

         gotoxy(wherex( ),wherey( ));
         cin>>Dsx[count];
      }

       gotoxy(25,44);
       cout<<\"Press any key to continue...\";

       getch( );
    }


 //---------------------  get_second_derivatives( )  ---------------------//


 void get_second_derivatives( )
    {
       clear_screen( );

       gotoxy(6,9);
       cout<<\"Second Derivatives :\";

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

       gotoxy(6,12);
       cout<<\"Note : Write the function with proper Braces e.g; 2x+3 as (2*x)+3.\";

       gotoxy(10,15);

       for(int count=0;count<(n-1);count++)
      {
         gotoxy(10,(wherey( )+1));
         cout<<\"S\\\"\"<<count<<\"(x) =  \";

         gotoxy(wherex( ),wherey( ));
         cin>>D2sx[count];
      }

       gotoxy(25,44);
       cout<<\"Press any key to continue...\";

       getch( );
    }


 //------------------------  check_condition_1( )  -----------------------//


 void check_condition_1( )
    {
       clear_screen( );

       gotoxy(6,9);
       cout<<\"Condition-I :\";

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

       gotoxy(12,12);
       cout<<\"S is a Cubic Polynomial, denoted by Si, on the interval [xi,xi+1]\";

       gotoxy(6,14);
       cout<<\"for each i=0,1,2,...,n-1.\";

       gotoxy(10,15);

       for(int count=0;count<(n-1);count++)
      {
         gotoxy(10,(wherey( )+2));
         cout<<\"S\"<<count<<\"(x) =  \"<<Sx[count]<<\"     , \"<<xn[count]<<\"óxó\"<<xn[(count+1)];
      }

       gotoxy(10,(wherey( )+3));
       cout<<\"*** Condition-I proved.\";

       gotoxy(25,44);
       cout<<\"Press any key to continue...\";

       getch( );
    }


 //------------------------  check_condition_2( )  -----------------------//


 void check_condition_2( )
    {
       clear_screen( );

       gotoxy(6,9);
       cout<<\"Condition-II :\";

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

       gotoxy(10,12);
       cout<<\"S(xi) = f(xi)       , for each i=0,1,2,...,n\";

       long double sx=0;

       gotoxy(10,14);

       for(int count=0;count<n;count++)
      {
         sx=0;

         if(count==(n-1))
        sx=evaluate_postfix_expression(xn[count],(count-1));

         else
        sx=evaluate_postfix_expression(xn[count],count);

         gotoxy(10,(wherey( )+2));
         cout<<\"S(\"<<xn[count]<<\") =  \"<<sx;

         gotoxy(35,wherey( ));
         cout<<\"f(\"<<xn[count]<<\") =  \"<<fx[count];

         gotoxy(60,wherey( ));

         if(sx==fx[count])
        cout<<\",  Ok\";

         else
        {
           cout<<\",  Failed\";

           error_flag=1;

           break;
        }
      }

       gotoxy(10,(wherey( )+3));

       if(!error_flag)
      cout<<\"*** Condition-II proved.\";

       else
      cout<<\"*** Condition-II failed.\";

       gotoxy(25,44);
       cout<<\"Press any key to continue...\";

       getch( );
    }


 //------------------------  check_condition_3( )  -----------------------//


 void check_condition_3( )
    {
       clear_screen( );

       gotoxy(6,9);
       cout<<\"Condition-III :\";

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

       gotoxy(10,12);
       cout<<\"Si(xi+1) = Si+1(xi+1)       , each for i=0,1,2,...,n-2\";

       long double six=0;
       long double sip1x=0;

       gotoxy(10,14);

       for(int count=0;count<(n-2);count++)
      {
         six=0;
         sip1x=0;

         six=evaluate_postfix_expression(xn[(count+1)],count);
         sip1x=evaluate_postfix_expression(xn[(count+1)],(count+1));

         gotoxy(10,(wherey( )+2));
         cout<<\"S\"<<count<<\"(\"<<xn[(count+1)]<<\") =  \"<<six;

         gotoxy(35,wherey( ));
         cout<<\"S\"<<(count+1)<<\"(\"<<xn[(count+1)]<<\") =  \"<<sip1x;

         gotoxy(60,wherey( ));

         if(six==sip1x)
        cout<<\",  Ok\";

         else
        {
           cout<<\",  Failed\";

           error_flag=1;

           break;
        }
      }

       gotoxy(10,(wherey( )+3));

       if(!error_flag)
      cout<<\"*** Condition-III proved.\";

       else
      cout<<\"*** Condition-III failed.\";

       gotoxy(25,44);
       cout<<\"Press any key to continue...\";

       getch( );
    }


 //------------------------  check_condition_4( )  -----------------------//


 void check_condition_4( )
    {
       for(int count_1=0;count_1<n;count_1++)
      {
         for(int count_2=0;count_2<30;count_2++)
        strset(Postfix_expression[count_1][count_2],NULL);

         convert_ie_to_pe(Dsx[count_1],count_1);
      }

       clear_screen( );

       gotoxy(6,9);
       cout<<\"Condition-IV :\";

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

       gotoxy(10,12);
       cout<<\"S\'i(xi+1) = S\'i+1(xi+1)       , for each i=0,1,2,...,n-2\";

       long double six=0;
       long double sip1x=0;

       gotoxy(10,14);

       for(int count_3=0;count_3<(n-2);count_3++)
      {
         six=0;
         sip1x=0;

         six=evaluate_postfix_expression(xn[(count_3+1)],count_3);
         sip1x=evaluate_postfix_expression(xn[(count_3+1)],(count_3+1));

         gotoxy(10,(wherey( )+2));
         cout<<\"S\'\"<<count_3<<\"(\"<<xn[(count_3+1)]<<\") =  \"<<six;

         gotoxy(35,wherey( ));
         cout<<\"S\'\"<<(count_3+1)<<\"(\"<<xn[(count_3+1)]<<\") =  \"<<sip1x;

         gotoxy(60,wherey( ));

         if(six==sip1x)
        cout<<\",  Ok\";

         else
        {
           cout<<\",  Failed\";

           error_flag=1;

           break;
        }
      }

       gotoxy(10,(wherey( )+3));

       if(!error_flag)
      cout<<\"*** Condition-IV proved.\";

       else
      cout<<\"*** Condition-IV failed.\";

       gotoxy(25,44);
       cout<<\"Press any key to continue...\";

       getch( );
    }


 //------------------------  check_condition_5( )  -----------------------//


 void check_condition_5( )
    {
       for(int count_1=0;count_1<n;count_1++)
      {
         for(int count_2=0;count_2<30;count_2++)
        strset(Postfix_expression[count_1][count_2],NULL);

         convert_ie_to_pe(D2sx[count_1],count_1);
      }

       clear_screen( );

       gotoxy(6,9);
       cout<<\"Condition-V :\";

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

       gotoxy(10,12);
       cout<<\"S\\\"i(xi+1) = S\\\"i+1(xi+1)       , for each i=0,1,2,...,n-2\";

       long double six=0;
       long double sip1x=0;

       gotoxy(10,14);

       for(int count_3=0;count_3<(n-2);count_3++)
      {
         six=0;
         sip1x=0;

         six=evaluate_postfix_expression(xn[(count_3+1)],count_3);
         sip1x=evaluate_postfix_expression(xn[(count_3+1)],(count_3+1));

         gotoxy(10,(wherey( )+2));
         cout<<\"S\\\"\"<<count_3<<\"(\"<<xn[(count_3+1)]<<\") =  \"<<six;

         gotoxy(35,wherey( ));
         cout<<\"S\\\"\"<<(count_3+1)<<\"(\"<<xn[(count_3+1)]<<\") =  \"<<sip1x;

         gotoxy(60,wherey( ));

         if(six==sip1x)
        cout<<\",  Ok\";

         else
        {
           cout<<\",  Failed\";

           error_flag=1;

           break;
        }
      }

       gotoxy(10,(wherey( )+3));

       if(!error_flag)
      cout<<\"*** Condition-V proved.\";

       else
      cout<<\"*** Condition-V failed.\";

       gotoxy(25,44);
       cout<<\"Press any key to continue...\";

       getch( );
    }


 //---------------  check_natural_boundry_conditions( )  -----------------//


 void check_natural_boundry_conditions( )
    {
       for(int count_1=0;count_1<n;count_1++)
      {
         for(int count_2=0;count_2<30;count_2++)
        strset(Postfix_expression[count_1][count_2],NULL);

         convert_ie_to_pe(D2sx[count_1],count_1);
      }

       clear_screen( );

       gotoxy(6,9);
       cout<<\"Natural Boundry Conditions :\";

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

       gotoxy(10,12);
       cout<<\"S\\\"(x0) = S\\\"(xn) = 0\";

       long double d2sx0=0;
       long double d2sxn=0;

       d2sx0=evaluate_postfix_expression(xn[0],0);
       d2sxn=evaluate_postfix_expression(xn[(n-1)],(n-2));

       gotoxy(10,16);
       cout<<\"S\\\"(\"<<xn[0]<<\") =  \"<<d2sx0;

       gotoxy(10,18);
       cout<<\"S\\\"(\"<<xn[(n-1)]<<\") =  \"<<d2sxn;

       gotoxy(10,22);

       if(d2sx0==0 && d2sxn==0)
      {
         cout<<\"S\\\"(\"<<xn[0]<<\") = S\\\"(\"<<xn[(n-1)]<<\") = 0          ,  Ok\";

         error_flag=4;
      }

       else
      {
         cout<<\"S\\\"(\"<<xn[0]<<\") != S\\\"(\"<<xn[(n-1)]<<\") != 0          ,  Failed\";

         error_flag=2;
      }

       gotoxy(10,25);

       if(error_flag==4)
      cout<<\"*** Natural or Free Boundry Conditions proved.\";

       else
      cout<<\"*** Natural or Free Boundry Conditions Failed.\";

       gotoxy(25,44);
       cout<<\"Press any key to continue...\";

       getch( );
    }


 //---------------  check_clamped_boundry_conditions( )  -----------------//


 void check_clamped_boundry_conditions( )
    {
       for(int count_1=0;count_1<n;count_1++)
      {
         for(int count_2=0;count_2<30;count_2++)
        strset(Postfix_expression[count_1][count_2],NULL);

         convert_ie_to_pe(Dsx[count_1],count_1);
      }

       clear_screen( );

       gotoxy(6,9);
       cout<<\"Clamped Boundry Conditions :\";

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

       gotoxy(10,12);
       cout<<\"S\'(x0) = f\'(x0)          &&         S\'(xn) = f\'(xn)\";

       long double dfx0=0;
       long double dfxn=0;
       long double dsx0=0;
       long double dsxn=0;

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

       cin>>dfx0;

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

       cin>>dfxn;

       dsx0=evaluate_postfix_expression(xn[0],0);
       dsxn=evaluate_postfix_expression(xn[(n-1)],(n-2));

       gotoxy(10,22);
       cout<<\"S\'(\"<<xn[0]<<\") =  \"<<dsx0;

       gotoxy(10,24);
       cout<<\"S\'(\"<<xn[(n-1)]<<\") =  \"<<dsxn;

       gotoxy(10,28);

       if(dsx0==dfx0)
      {
         cout<<\"S\'(\"<<xn[0]<<\") = f\'(\"<<xn[0]<<\")         , Ok\";

         error_flag=5;
      }

       else
      {
         cout<<\"S\'(\"<<xn[0]<<\") != f\'(\"<<xn[0]<<\")         , Failed\";

         error_flag=3;
      }

       gotoxy(10,30);

       if(dsxn==dfxn)
      {
         cout<<\"S\'(\"<<xn[(n-1)]<<\") = f\'(\"<<xn[(n-1)]<<\")         , Ok\";

         error_flag=5;
      }

       else if(dsxn!=dfxn)
      {
         cout<<\"S\'(\"<<xn[(n-1)]<<\") != f\'(\"<<xn[(n-1)]<<\")         , Failed \";

         error_flag=3;
      }

       gotoxy(10,33);

       if(error_flag==5)
      cout<<\"*** Clamped Boundry Conditions proved.\";

       else
      cout<<\"*** Clamped Boundry Conditions Failed.\";

       gotoxy(25,44);
       cout<<\"Press any key to continue...\";

       getch( );
    }


 //---------------------------  show_result( )  --------------------------//


 void show_result( )
    {
       clear_screen( );

       gotoxy(6,9);
       cout<<\"Result :\";

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

       gotoxy(10,12);

       if(error_flag==1)
      cout<<\"The given function is not a Cubic Spline.\";

       else
      {
         if(error_flag==0)
        cout<<\"The given function is a Cubic Spline.\";

         else if(error_flag==2)
        cout<<\"The given function is a Cubic Spline but not Natural Spline.\";

         else if(error_flag==3)
        cout<<\"The given function is a Cubic Spline but not Clamped Spline.\";

         else if(error_flag==4)
        cout<<\"The given function is a Natural Cubic Spline.\";

         else if(error_flag==5)
        cout<<\"The given function is a Clamped Cubic Spline.\";

         gotoxy(6,19);
         cout<<\"Nature of Spline Function :\";

         gotoxy(6,20);
         cout<<\"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ\";

         gotoxy(8,23);
         cout<<\"Press :\";

         gotoxy(10,25);
         cout<<\"- <N> to Test for Natural Cubic Spline\";

         gotoxy(10,27);
         cout<<\"- <C> to Test for Clamped Cubic Spline\";

         gotoxy(10,29);
         cout<<\"- <Esc> to Exit\";

         gotoxy(6,32);
         cout<<\"Enter your choice :  \";

         char Choice=getch( );


         if(Choice==\'N\' || Choice==\'n\')
        {
           check_natural_boundry_conditions( );
           show_result( );
        }

         else if(Choice==\'C\' || Choice==\'c\')
        {
           check_clamped_boundry_conditions( );
           show_result( );
        }

         else
        {
           cout<<\"Esc\";

           exit(0);
        }
      }

       gotoxy(1,2);
    }