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

Posted By: Easy Tutor     Category: C++ Programming     Views: 2618

A C++ Program to determine whether the given function is a Cubic Spline or not.

Code for Program to determine whether the given function is a Cubic Spline or not in C++ Programming

 # 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;
 int error_flag=0;

 longdouble xn[max_size]={0};
 longdouble 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(constchar *);
 void convert_ie_to_pe(constchar *,constint);

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

 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(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*,const int)  --------------///*************************************************************************/void convert_ie_to_pe(constchar* Expression,constint 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;
        }

         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[index][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[index][count_2],pop( ));

                   count_2++;
                }
              }

           elseif(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)  ------///*************************************************************************/constlongdouble evaluate_postfix_expression(
                    constlongdouble x,constint index)
    {
       longdouble 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( ));

           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<<"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";

       longdouble 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";

       longdouble six=0;
       longdouble 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";

       longdouble six=0;
       longdouble 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";

       longdouble six=0;
       longdouble 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";

       longdouble d2sx0=0;
       longdouble 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)";

       longdouble dfx0=0;
       longdouble dfxn=0;
       longdouble dsx0=0;
       longdouble 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;
      }

       elseif(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.";

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

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

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

         elseif(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( );
        }

         elseif(Choice=='C' || Choice=='c')
        {
           check_clamped_boundry_conditions( );
           show_result( );
        }

         else
        {
           cout<<"Esc";

           exit(0);
        }
      }

       gotoxy(1,2);
    }
  
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Easy Tutor
Easy Tutor author of Program to determine whether the given function is a Cubic Spline or not is from United States. Easy Tutor says

Hello Friends,

I am Free Lance Tutor, who helped student in completing their homework.

I have 4 Years of hands on experience on helping student in completing their homework. I also guide them in doing their final year projects.

I have share many programs on this website for everyone to use freely, if you need further assistance, than please contact me on easytutor.2ya [at the rate] gmail [dot] com

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