Class SparsePoly

java.lang.Object
it.unimi.di.prog2.h09.SparsePoly
public class SparsePoly extends Object
SparsePolys are immutable polynomials with integer coefficients such that the number of nonzero coefficient is small with respect to the degree.

A typical Poly is \( p = c_0 + c_1 x + c_2 x^2 + \cdots + c_n x^n \).

  • Field Details

  • Constructor Details

    • SparsePoly

      public SparsePoly()
      Initializes this to be the zero polynomial, that is \( p = 0 \).

    • SparsePoly

      public SparsePoly(int c, int n) throws IllegalArgumentException
      Initializes this to be the polynomial \(p = cx^n\).
      Parameters:
      c - the coefficient.
      n - the degree.
      Throws:
      IllegalArgumentException - if n < 0.

    • SparsePoly

      private SparsePoly(List<SparsePoly.Term> lst)
      Initializes this to be the polynomial from a list of terms in increasing degree order.
      Parameters:
      lst - the not null list, not containing nulls and in increasing degree order.

  • Method Details

    • findByDegree

      private static int findByDegree(List<SparsePoly.Term> lst, int d)
      Finds the index of a term of given degree in a list of terms in increasing degree order.
      Parameters:
      lst - the not null list of not null terms and in increasing degree order.
      d - the degree.
      Returns:
      the index of a term of given degree, or -1 if none is present.

    • coeff

      public int coeff(int d)
      Returns the coefficient of the term of given exponent.
      Parameters:
      d - the exponent of the term to consider.
      Returns:
      the coefficient of the considered term.

    • degree

      public int degree()
      Returns the degree of this polynomial.
      Returns:
      the largest exponent with a non-zero coefficient; returns 0 if this is the zero Poly.

    • addTerm

      private static void addTerm(List<SparsePoly.Term> lst, SparsePoly.Term term)
      Adds a term to a list of terms in increasing degree order.

      The list will remain in increasing degree order, in case a term with the same degree was present, the two will be added (and removed if the coefficient will become 0).

      Parameters:
      lst - the not null list of not null terms in increasing degree order.
      term - the not null term.

    • add

      public SparsePoly add(SparsePoly q) throws NullPointerException
      Performs polynomial addition.

      If \( p \) is this polynomial, returns \( p + q \).

      Parameters:
      q - the polynomial to add to this one.
      Returns:
      the sum among this and the given polynomial.
      Throws:
      NullPointerException - if q is null.

    • mul

      public SparsePoly mul(SparsePoly q) throws NullPointerException
      Performs polynomial multiplication.

      If \( p \) is this polynomial, returns \( p q \).

      Parameters:
      q - the polynomial to multiply by this one.
      Returns:
      the product among this and the given polynomial.
      Throws:
      NullPointerException - if q is null.

    • sub

      public SparsePoly sub(SparsePoly q) throws NullPointerException
      Performs polynomial subtraction.

      If \( p \) is this polynomial, returns \( p - q \).

      Parameters:
      q - the polynomial to subtract from this one.
      Returns:
      the subtraction among this and the given polynomial.
      Throws:
      NullPointerException - if q is null.

    • minus

      public SparsePoly minus()
      Returns the negate polynomial.

      If \( p \) is this polynomial, returns \( -p \).

      Returns:
      this polynomial multiplied by \( -1 \).