Objects and Strings - A Concise and Practical Introduction to Programming Algorithms in Java - page 124

- the number of gold medals of a is less than the number of gold medals
of b ,or

- the number of gold medals are identical but the number of silver
medals of a is less than the number of silver medals of b ,or

- the number of gold and silver medals are identical but the number of
bronze medals of a is less than the number of silver medals of b .
Exercise 5.4 (A class for polynomials)

Consider defining a class for storing polynomials of arbitrary degree as
follows:

Program 5.13 A class for polynomials
class Polynomial
int degree ;
long []

coefficient ;

...
}

Observe that a polynomial of degree d has d + 1 coecients. Provide
a constructor Polynomial(int deg) for that class that initializes all
deg+1 coecients to zero. Then design and implement the following
static functions:

- A clone function static Polynomial copy(Polynomial source);

- A display procedure static void display(Polynomial source);
- An equality predicate:
static boolean equalTo(Polynomial P, Polynomial Q);

- A function static Polynomial derivative(Polynomial source);
that computes the derivative of a polynomial.

- A function static Polynomial add(Polynomial P, Polynomial Q);
that adds two polynomials. Similarly, a function that subtracts two
polynomials:
static Polynomial subtract(Polynomial P, Polynomial Q);

- A function static long evaluate(Polynomial source, long x);
that evaluates the polynomial at value x . What is the time complexity
of this function? Horner proposed a scheme for evaluating polynomials
using only d multiplications and d additions using the following
schema:

P ( x )=( ... (( p d x + p d− 1 ) x + p d− 2 ) x + ... ) x + p 0