program newton;

uses crt;



const n=5;

type pole=array[0..n] of  real;



var a,x,clen:pole;

      pocet,m,r, i,j,k,p,radu: integer;   y,bod:real;



begin

clrscr;

write('Zadej pocet bodu, maximálne 6:'); read(pocet);

writeln;

 {vypln prvky pole nulami}

if pocet<n+1 then

               for  i:=0 to N do begin a[i]:=0; x[i]:=0; end;

m:=pocet-1; r:=pocet-1;

for i:=0 to m do  begin

                  write(' Zadej bod:x[',i,']:');  read(x[i]);

                  write('       f(x[',i,']):');   read(a[i])

                  end;



k:=1; { dif[0]:=a[0];  }

for j:=r downto 1 do begin

                  for i:=n   downto 1  do begin

                                 p:=i+k-1;

                                 if (k<=p) and (p<=M) then

                                    a[p]:=(a[p]-a[p-1])/(x[p]-x[p-k]);

                                          end;

                {  dif[k]:=a[k]; }

                { z[j]:=x[m]-x[m-k];}

                    k:=k+1;

                     end;

clen[0]:=a[0]-a[1]*x[0]+a[2]*x[1]*x[0]-a[3]*x[2]*x[1]*x[0]

- a[4]*x[3]* x[2]* x[1]* x[0]-a[5]* x[4]* x[3]* x[2]* x[1]* x[0];

clen[1]:=a[1]-a[2]*( x[1]+x[0]) +a[3]*( x[2]*x[1]+ x[2]*x[0]

+ x[1]*x[0]) -a[4]*(x[3]*x[2]*x[1]+x[3]*x[2]*x[0]+ x[3]*x[1]*x[0]

+ x[2]*x[1]*x[0]) +a[5]*(x[4]*x[3]*x[2]*x[1]+x[4]*x[3]*x[2]*x[0]

+ x[4]*x[2]*x[1]*x[0]+ x[3]*x[2]*x[1]*x[0]);

clen[2]:=a[2]- a[3]*(x[2]+ x[1]+x[0])+a[4]*(x[3]*x[2]+x[3]*x[1]

+ x[2]*x[1]+x[2]*x[1]+ x[1]*x[0]) -a[5]*(x[4]*x[3]*x[2]+ x[4]*x[3]*x[1]

+ x[4]*x[2]*x[1]+ x[4]*x[2]*x[0]+x[4]*x[1]*x[0]+ x[3]*x[2]*x[1]

+ x[3]*x[2]*x[0]+ x[3]*x[1]*x[0]+ x[2]*x[1]*x[0]);

clen[3]:=  a[3] -a[4]*(x[3]+x[2]+ x[1]+x[0]) +a[5]*(x[4]*x[3]

+ x[4]*x[2]+ x[4]*x[1]+ x[4]*x[0]+ x[3]*x[2]+ x[3]*x[1]+ x[3]*x[0]

+ x[2]*x[1]+ x[2]*x[0]+ x[1]*x[0]);

clen[4]:=a[4] -a[5]*(x[4]+x[3]+x[2]+x[1]+x[0]);

clen[5]:=a[5];

writeln;

writeln;

writeln;

writeln('Newtonùv interpolacni polynom:');

writeln;

writeln('pomerne diference:');

writeln;

for i:=0 to pocet-1 do write('a',i,' = ',a[i]:5:5,'   ');

writeln;

writeln;

writeln; radu:=pocet-1;

writeln('Polynom  ',radu:2,'. radu:');

writeln;

write('N',pocet-1,'(x) = ',clen[5]:7:5,'*x^5 + ', clen[4]:7:5,'*x^4 + ');

write(clen[3]:7:5,'*x^3 + ',clen[2]:7:5,'*x^2 + ',clen[1]:7:5,'*x + ',clen[0]:7:5);

writeln;

writeln('Vypocet hodnoty f(x) v bode x');

writeln;

write('Zadani bodu x: ');

read(bod);

y:=a[0]+a[1]*(bod-x[0])+a[2]*(bod-x[0])*(bod-x[1])

+a[3]* (bod-x[0])* (bod-x[1])* (bod-x[2])

+a[4]* (bod-x[0])* (bod-x[1])* (bod-x[2])

+a[4]* (bod-x[0])* (bod-x[1])* (bod-x[2])* (bod-x[3])

+a[5]* (bod-x[0])* (bod-x[1])* (bod-x[2])* (bod-x[3])* (bod-x[4]);

write(' Hodnota f(',bod:3:3,') = ',y:3:3);

repeat until keypressed;

end.