# 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); }