Contoh Interpolasi Polinomial dengan java

public class Polynomial {

    private int[] coef;  // coefficients

    private int deg;     // degree of polynomial (0 for the zero polynomial)

    // a * x^b

    public Polynomial(int a, int b)

    {

        coef = new int[b+1];

        coef[b] = a;

        deg = degree();

    }

    // return the degree of this polynomial (0 for the zero polynomial)

    public int degree() {

        int d = 0;

        for (int i = 0; i < coef.length; i++)

            if (coef[i] != 0) d = i;

        return d;

    }

    // return c = a + b

    public Polynomial plus(Polynomial b) {

        Polynomial a = this;

        Polynomial c = new Polynomial(0, Math.max(a.deg, b.deg));

        for (int i = 0; i <= a.deg; i++) c.coef[i] += a.coef[i];

        for (int i = 0; i <= b.deg; i++) c.coef[i] += b.coef[i];

        c.deg = c.degree();

        return c;

    }

    // return (a - b)

    public Polynomial minus(Polynomial b) {

        Polynomial a = this;

        Polynomial c = new Polynomial(0, Math.max(a.deg, b.deg));

        for (int i = 0; i <= a.deg; i++) c.coef[i] += a.coef[i];

        for (int i = 0; i <= b.deg; i++) c.coef[i] -= b.coef[i];

        c.deg = c.degree();

        return c;

    }

    // return (a * b)

    public Polynomial times(Polynomial b) {

        Polynomial a = this;

        Polynomial c = new Polynomial(0, a.deg + b.deg);

        for (int i = 0; i <= a.deg; i++)

            for (int j = 0; j <= b.deg; j++)

                c.coef[i+j] += (a.coef[i] * b.coef[j]);

        c.deg = c.degree();

        return c;

    }

    // return a(b(x))  - compute using Horner's method

    public Polynomial compose(Polynomial b) {

        Polynomial a = this;

        Polynomial c = new Polynomial(0, 0);

        for (int i = a.deg; i >= 0; i--) {

            Polynomial term = new Polynomial(a.coef[i], 0);

            c = term.plus(b.times(c));

        }

        return c;

    }

    // do a and b represent the same polynomial?

    public boolean eq(Polynomial b) {

        Polynomial a = this;

        if (a.deg != b.deg) return false;

        for (int i = a.deg; i >= 0; i--)

            if (a.coef[i] != b.coef[i]) return false;

        return true;

    }

    // use Horner's method to compute and return the polynomial evaluated at x

    public int evaluate(int x) {

        int p = 0;

        for (int i = deg; i >= 0; i--)

            p = coef[i] + (x * p);

        return p;

    }

    // differentiate this polynomial and return it

    public Polynomial differentiate() {

        if (deg == 0) return new Polynomial(0, 0);

        Polynomial deriv = new Polynomial(0, deg - 1);

        deriv.deg = deg - 1;

        for (int i = 0; i < deg; i++)

            deriv.coef[i] = (i + 1) * coef[i + 1];

        return deriv;

    }

    // convert to string representation

    public String toString() {

        if (deg ==  0) return "" + coef[0];

        if (deg ==  1) return coef[1] + "x + " + coef[0];

        String s = coef[deg] + "x^" + deg;

        for (int i = deg-1; i >= 0; i--) {

            if      (coef[i] == 0) continue;

            else if (coef[i]  > 0) s = s + " + " + ( coef[i]);

            else if (coef[i]  < 0) s = s + " - " + (-coef[i]);

            if      (i == 1) s = s + "x";

            else if (i >  1) s = s + "x^" + i;

        }

        return s;

    }

    // test client

    public static void main(String[] args) {

        Polynomial zero = new Polynomial(0, 0);

        Polynomial p1   = new Polynomial(4, 3);

        Polynomial p2   = new Polynomial(3, 2);

        Polynomial p3   = new Polynomial(1, 0);

        Polynomial p4   = new Polynomial(2, 1);

        Polynomial p    = p1.plus(p2).plus(p3).plus(p4);   // 4x^3 + 3x^2 + 1

        Polynomial q1   = new Polynomial(3, 2);

        Polynomial q2   = new Polynomial(5, 0);

        Polynomial q    = q1.plus(q2);                     // 3x^2 + 5

        Polynomial r    = p.plus(q);

        Polynomial s    = p.times(q);

        Polynomial t    = p.compose(q);

        System.out.println("zero(x) =     " + zero);

        System.out.println("p(x) =        " + p);

        System.out.println("q(x) =        " + q);

        System.out.println("p(x) + q(x) = " + r);

        System.out.println("p(x) * q(x) = " + s);

        System.out.println("p(q(x))     = " + t);

        System.out.println("0 - p(x)    = " + zero.minus(p));

        System.out.println("p(3)        = " + p.evaluate(3));

        System.out.println("p'(x)       = " + p.differentiate());

        System.out.println("p''(x)      = " + p.differentiate().differentiate());

   }

}

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