#pragma once

#include <QWidget>
#include <QPainter>

const int MAX_POINTS = 16;

class Newton: public QWidget {
    Q_OBJECT

private:
    int numPoints;
    double a[MAX_POINTS]; // Coefficients of Newton polynomial
    double nodeX[MAX_POINTS], nodeY[MAX_POINTS];

    QPointF map(QPointF) const;
    QPointF invMap(QPointF) const;

    double xmin, xmax, ymin, ymax;
    double xCoeff, yCoeff;

public:
    Newton(QWidget *parent = 0);
    void defineMap();
    void drawAxes(QPainter*);
    void drawPoints(QPainter*);
    void drawPolynomial(QPainter*);

protected:
    void paintEvent(QPaintEvent* event);
    void mousePressEvent(QMouseEvent* event);

public slots:
    void clear();
};

// Value of Newton interpolation polynomial in point t
double newtonPolValue(
    int n,              // Number of nodes - 1
    const double* x,    // Nodes of interpolation: x0, x1, ..., xn
    const double* a,    // Coefficients of Newton polynomial
    double t
);

// Compute the coefficients of Newton interpolation polynomial
void computeNewtonPol(
    int n,              // Number of nodes - 1
    const double* x,    // Nodes of interpolation: x0, x1, ..., xn
    const double* y,    // Values in these nodes
    double* a           // Coefficients of Newton polynomial
);