Newton.pas

Uses crt, sysutils;

Function calculateX(xFrom, i, step : real) : real;
Begin
    calculateX := xFrom + i * step;
End;

Function yFormula(x : real) : real;
Begin
    yFormula := exp(-(x - 2) * (x - 2));
End;

Function getQ(x0, h : real) : string;
Begin
    getQ := '(x - ' + FloatToStrF(x0,ffgeneral,7,6) + ')/' + FloatToStrF(h,ffgeneral,7,6);
End;

Function calculateYDelta(xFrom, step : real; power, i : integer) : real;
Begin
    If (power <= 1) Then
        calculateYDelta := yFormula(calculateX(xFrom, i, step))
    Else
        calculateYDelta := calculateYDelta(xFrom, step, power - 1, i) - calculateYDelta(xFrom, step, power - 1, i + 1);
End;

Procedure printNewton1(xFrom, step : real; n : integer; q : string);
Var
    fact, yDelta : real;
    i, j : integer;
Begin
    write('P(x) = ', calculateYDelta(xFrom, step, 0, 0):0:6);
    fact := 1;
    For i := 1 To n Do Begin
        fact *= i;
        yDelta := calculateYDelta(xFrom, step, i, 0);
        If (yDelta < 0) Then Begin
            yDelta *= -1;
            write(' - ');
        End
        Else
            write(' + ');
        write((yDelta / fact):0:6, '(' + q + ')');
        For j := 2 To i Do
            write('(' + q + ' - ', j - 1, ')');
    End;
End;

Procedure printNewton2(xFrom, step : real; n : integer; q : string);
Var
    fact, yDelta : real;
    i, j : integer;
Begin
    write('P(x) = ', calculateYDelta(xFrom, step, 0, n):0:6);
    fact := 1;
    For i := 1 To n Do Begin
        fact *= i;
        yDelta := calculateYDelta(xFrom, step, i, n - i);
        If (yDelta < 0) Then Begin
            yDelta *= -1;
            write(' - ');
        End
        Else
            write(' + ');
        write((yDelta / fact):0:6, '(' + q + ')');
        For j := 2 To i Do
            write('(' + q + ' + ', j - 1, ')');
    End;
End;

Var
    xFrom, xTo, step : real;
    n : integer;
    q : string;
Begin
    xFrom := 2;
    xTo := 4;
    step := 0.2;

    n := Trunc((xTo - xFrom) / step);

    q := getQ(xFrom, step);
    printNewton1(xFrom, step, n, q);

    writeln;

    q := getQ(xTo, step);
    printNewton2(xFrom, step, n, q);
End.