# include <iostream.h>
# include <string.h>
# include <stdlib.h>
# include <conio.h>
# include <math.h>
constint max_size=30;
int top=-1;
int accuracy=0;
int iterations=0;
longdouble x0=0;
longdouble x1=0;
longdouble xn=0;
char Non_linear_equation[100]={NULL};
char Stack[max_size][max_size]={NULL};
char Postfix_expression[max_size][max_size]={NULL};
void push(constchar *);
void convert_infix_expression_to_postfix_expression(constchar *);
constchar* pop( );
constlongdouble evaluate_postfix_expression(constlongdouble);
void show_screen( );
void clear_screen( );
void get_input_non_linear_equation( );
void apply_secant_method( );
void show_result( );
/*************************************************************************//*************************************************************************///------------------------------ main( ) ------------------------------///*************************************************************************//*************************************************************************/int main( )
{
clrscr( );
textmode(C4350);
show_screen( );
get_input_non_linear_equation( );
apply_secant_method( );
show_result( );
getch( );
return 0;
}
/*************************************************************************//*************************************************************************///---------------------- Function Definitions -------------------------///*************************************************************************//*************************************************************************//*************************************************************************///-------------------------- 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_infix_expression_to_postfix_expression(const char*) ----///*************************************************************************/void convert_infix_expression_to_postfix_expression(constchar* Expression)
{
char Infix_expression[100]={NULL};
char Symbol_scanned[30]={NULL};
push("(");
strcpy(Infix_expression,Expression);
strcat(Infix_expression,"+0)");
int flag=0;
int count_1=0;
int count_2=0;
int equation_length=strlen(Infix_expression);
if(Infix_expression[0]=='(')
flag=1;
do
{
strset(Symbol_scanned,NULL);
if(flag==0)
{
int count_3=0;
do
{
Symbol_scanned[count_3]=Infix_expression[count_1];
count_1++;
count_3++;
}
while(count_1<=equation_length &&
Infix_expression[count_1]!='(' &&
Infix_expression[count_1]!='+' &&
Infix_expression[count_1]!='-' &&
Infix_expression[count_1]!='*' &&
Infix_expression[count_1]!='/' &&
Infix_expression[count_1]!='^' &&
Infix_expression[count_1]!=')');
flag=1;
}
elseif(flag==1)
{
Symbol_scanned[0]=Infix_expression[count_1];
count_1++;
if(Infix_expression[count_1]!='(' &&
Infix_expression[count_1]!='^' &&
Infix_expression[count_1]!='*' &&
Infix_expression[count_1]!='/' &&
Infix_expression[count_1]!='+' &&
Infix_expression[count_1]!='-' &&
Infix_expression[count_1]!=')')
flag=0;
if(Infix_expression[count_1-1]=='(' &&
(Infix_expression[count_1]=='-' ||
Infix_expression[count_1]=='+'))
flag=0;
}
if(strcmp(Symbol_scanned,"(")==0)
push("(");
elseif(strcmp(Symbol_scanned,")")==0)
{
while(strcmp(Stack[top],"(")!=0)
{
strcpy(Postfix_expression[count_2],pop( ));
count_2++;
}
pop( );
}
elseif(strcmp(Symbol_scanned,"^")==0 ||
strcmp(Symbol_scanned,"+")==0 ||
strcmp(Symbol_scanned,"-")==0 ||
strcmp(Symbol_scanned,"*")==0 ||
strcmp(Symbol_scanned,"/")==0)
{
if(strcmp(Symbol_scanned,"^")==0)
{ }
elseif(strcmp(Symbol_scanned,"*")==0 ||
strcmp(Symbol_scanned,"/")==0)
{
while(strcmp(Stack[top],"^")==0 ||
strcmp(Stack[top],"*")==0 ||
strcmp(Stack[top],"/")==0)
{
strcpy(Postfix_expression[count_2],pop( ));
count_2++;
}
}
elseif(strcmp(Symbol_scanned,"+")==0 ||
strcmp(Symbol_scanned,"-")==0)
{
while(strcmp(Stack[top],"(")!=0)
{
strcpy(Postfix_expression[count_2],pop( ));
count_2++;
}
}
push(Symbol_scanned);
}
else
{
strcat(Postfix_expression[count_2],Symbol_scanned);
count_2++;
}
}
while(strcmp(Stack[top],NULL)!=0);
strcat(Postfix_expression[count_2],"=");
count_2++;
}
/*************************************************************************///---------- evaluate_postfix_expression(const long double) -----------///*************************************************************************/constlongdouble evaluate_postfix_expression(constlongdouble x)
{
longdouble function_value=0;
int count_1=-1;
char Symbol_scanned[30]={NULL};
do
{
count_1++;
strcpy(Symbol_scanned,Postfix_expression[count_1]);
if(strcmp(Symbol_scanned,"^")==0 ||
strcmp(Symbol_scanned,"*")==0 ||
strcmp(Symbol_scanned,"/")==0 ||
strcmp(Symbol_scanned,"+")==0 ||
strcmp(Symbol_scanned,"-")==0)
{
char Result[30]={NULL};
char Operand[2][30]={NULL};
strcpy(Operand[0],pop( ));
strcpy(Operand[1],pop( ));
longdouble operand[2]={0};
longdouble result=0;
char *endptr;
for(int count_2=0;count_2<2;count_2++)
{
int flag=0;
if(Operand[count_2][0]=='-')
{
int length=strlen(Operand[count_2]);
for(int count_3=0;count_3<(length-1);count_3++)
Operand[count_2][count_3]=Operand[count_2][(count_3+1)];
Operand[count_2][count_3]=NULL;
flag=1;
}
if(strcmp(Operand[count_2],"x")==0)
operand[count_2]=x;
elseif(strcmp(Operand[count_2],"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;
}
/*************************************************************************///-------------------------- show_screen( ) ---------------------------///*************************************************************************/void show_screen( )
{
cprintf("\n********************************************************************************");
cprintf("******************************- -*******************************");
cprintf("*------------------------------ ");
textbackground(1);
cprintf(" Secant Method ");
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);
}
/*************************************************************************///------------------- get_input_non_linear_equation( ) -----------------///*************************************************************************/void get_input_non_linear_equation( )
{
gotoxy(4,11);
cout<<"Non-Linear Equation with One Variable:";
gotoxy(4,12);
cout<<"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ";
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(4,15);
cout<<"Enter the Function with variabel x = f(x) = ";
cin>>Non_linear_equation;
gotoxy(4,20);
cout<<"Enter the first initial value = x0 = ";
cin>>x0;
gotoxy(4,22);
cout<<"Enter the second initial value = x1 = ";
cin>>x1;
gotoxy(4,26);
cout<<"Enter the number of accuracy required = k = ";
cin>>accuracy;
gotoxy(1,2);
}
/*************************************************************************///--------------------- apply_secant_method( ) ------------------------///*************************************************************************/void apply_secant_method( )
{
clear_screen( );
gotoxy(4,10);
cout<<"Solution :";
gotoxy(4,11);
cout<<"ÍÍÍÍÍÍÍÍÍÍ";
convert_infix_expression_to_postfix_expression(Non_linear_equation);
longdouble k=0.5;
for(int count_1=1;count_1<=accuracy;count_1++)
k*=0.1;
gotoxy(4,13);
cout<<"ÚÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿";
gotoxy(4,14);
cout<<"³ n ³ X(n-1) ³ Xn ³ X(n+1) ³ Accuracy ³";
gotoxy(4,15);
cout<<"ÃÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´";
gotoxy(4,16);
cout<<"³ ³ ³ ³ ³ ³";
longdouble x1=::x0;
longdouble x2=::x1;
longdouble fx1=0;
longdouble fx2=0;
int count_2=1;
int x_cord=4;
int y_cord=17;
do
{
gotoxy(x_cord,y_cord);
cout<<"³ ³ ³ ³ ³ ³";
gotoxy(x_cord,(y_cord+1));
cout<<"³ ³ ³ ³ ³ ³";
fx1=evaluate_postfix_expression(x1);
fx2=evaluate_postfix_expression(x2);
gotoxy((x_cord+3),y_cord);
cout<<count_2;
gotoxy((x_cord+8),y_cord);
cout<<x1;
gotoxy((x_cord+25),y_cord);
cout<<x2;
xn=(((x1*fx2)-(x2*fx1))/(fx2-fx1));
x1=x2;
x2=xn;
gotoxy((x_cord+42),y_cord);
cout<<xn;
gotoxy((x_cord+59),y_cord);
cout<<fabs(xn-x1);
y_cord+=2;
if((count_2%12)==0 && fabs(xn-x1)>k)
{
y_cord=17;
gotoxy(30,44);
cout<<"Press any key to continue...";
getch( );
for(int count_3=1;count_3<25;count_3++)
{
gotoxy(3,(16+count_3));
cout<<" ";
}
}
count_2++;
iterations++;
}
while(fabs(xn-x1)>k);
gotoxy(x_cord,y_cord);
cout<<"ÀÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ";
gotoxy(30,44);
cout<<"Press any key to continue...";
getch( );
}
/*************************************************************************///--------------------------- show_result( ) --------------------------///*************************************************************************/void show_result( )
{
clear_screen( );
gotoxy(6,10);
cout<<"Function of Non-Linear Equation :";
gotoxy(6,11);
cout<<"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ";
gotoxy(10,13);
cout<<"f(x) = "<<Non_linear_equation;
gotoxy(6,17);
cout<<"First initial Value = x0 = "<<x0;
gotoxy(6,19);
cout<<"Second initial Value = x1 = "<<x1;
gotoxy(6,22);
cout<<"Accuracy Required = kD = "<<accuracy<<"D";
gotoxy(6,28);
cout<<"Required Root :";
gotoxy(6,29);
cout<<"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍ";
gotoxy(10,31);
cout<<"x = "<<xn;
gotoxy(10,33);
cout<<"Number of Iterations = "<<iterations;
gotoxy(1,2);
}