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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