# 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; long double h=0; long double x=0; long double x0=0; long double y0=0; long double xn[max_size]={0}; long double yn[max_size]={0}; char Fx[100]={NULL}; char Stack[30][30]={NULL}; char Postfix_expression[30][30]={NULL}; //------------------------ Funcion Prototypes -------------------------// void push(const char *); void convert_ie_to_pe(const char *); const char* pop( ); const long double evaluate_pe(const long double,const long double); void show_screen( ); void clear_screen( ); void get_input( ); void apply_mid_point_method( ); void show_result( ); //------------------------------ main( ) ------------------------------// int main( ) { clrscr( ); textmode(C4350); show_screen( ); get_input( ); apply_mid_point_method( ); show_result( ); getch( ); return 0; } //------------------------ Funcion Definitions ------------------------// //-------------------------- show_screen( ) ---------------------------// void show_screen( ) { cprintf(\"\\n********************************************************************************\"); cprintf(\"*****************************- -*****************************\"); cprintf(\"*----------------------------- \"); textbackground(1); cprintf(\" Mid-Point 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(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*) ------------------// void convert_ie_to_pe(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_pe(const long double,const long double) -----------// const long double evaluate_pe(const long double x,const long double y) { 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],\"y\")==0) operand[count_2]=y; 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 if(strcmp(Operand[count_2],\"siny\")==0) operand[count_2]=sinl(y); else if(strcmp(Operand[count_2],\"cosy\")==0) operand[count_2]=cosl(y); else if(strcmp(Operand[count_2],\"tany\")==0) operand[count_2]=tanl(y); else if(strcmp(Operand[count_2],\"lny\")==0) operand[count_2]=logl(y); else if(strcmp(Operand[count_2],\"logy\")==0) operand[count_2]=log10l(y); 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( ) { gotoxy(6,10); cout<<\"Input :\"; gotoxy(6,11); cout<<\"ÍÍÍÍÍÍÍ\"; 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<<\" any number and all above functions with y.\"; gotoxy(6,14); cout<<\"Enter the Function : f(x,y) = \"; cin>>Fx; convert_ie_to_pe(Fx); gotoxy(6,17); cout<<\"Enter the value of xn = \"; cin>>x; gotoxy(6,19); cout<<\"Enter the value of x0 = \"; cin>>x0; gotoxy(6,21); cout<<\"Enter the value of y0 = \"; cin>>y0; gotoxy(6,23); cout<<\"Enter the value of h = \"; cin>>h; } //----------------------- apply_mid_point_method( ) -------------------// void apply_mid_point_method( ) { clear_screen( ); gotoxy(6,9); cout<<\"Solution :\"; gotoxy(6,10); cout<<\"ÍÍÍÍÍÍÍÍÍÍ\"; gotoxy(25,12); cout<<\"ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿\"; gotoxy(25,13); cout<<\"³ x ³ y ³\"; gotoxy(25,14); cout<<\"ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ\"; gotoxy(25,15); cout<<\"³ ³ ³\"; xn[0]=x0; yn[0]=y0; do { xn[(n+1)]=(xn[n]+h); n++; } while(xn[n]<x); 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(25,16); for(int count_2=0;count_2<=n;count_2++) { gotoxy(27,wherey( )); cout<<xn[count_2]; gotoxy(43,wherey( )); cout<<yn[count_2]; if(count_2==0) yn[(count_2+1)]=(yn[count_2]+(h*evaluate_pe(xn[count_2],yn[count_2]))); else yn[(count_2+1)]=(yn[(count_2-1)]+(2*h*evaluate_pe(xn[count_2],yn[count_2]))); gotoxy(25,(wherey( )+2)); } gotoxy(25,43); cout<<\"Press any key to continue...\"; getch( ); } //--------------------------- show_result( ) --------------------------// void show_result( ) { clear_screen( ); gotoxy(6,9); cout<<\"Mid-Point Method :\"; gotoxy(6,10); cout<<\"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ\"; gotoxy(10,12); cout<<\"y(n+1) = y(n-1) + [ 2h * f(xn,yn) ] , for n=1,2,3,... \"; gotoxy(6,17); cout<<\"Estimated Value :\"; gotoxy(6,18); cout<<\"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ\"; gotoxy(8,20); cout<<\"Estimated differential value = \"<<yn[n]; gotoxy(1,2); }