Lecture 9

src/main/java/it/unimi/di/prog2/e09/Poly.java

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+/*
+
+Copyright 2024 Massimo Santini
+
+This file is part of "Programmazione 2 @ UniMI" teaching material.
+
+This is free software: you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation, either version 3 of the License, or
+(at your option) any later version.
+
+This material is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this file.  If not, see <https://www.gnu.org/licenses/>.
+
+*/
+
+package it.unimi.di.prog2.e09;
+
+import it.unimi.di.prog2.h08.impl.NegativeExponentException;
+
+/**
+ * {@code Poly}s are immutable polynomials with integer coefficients.
+ *
+ * <p>A typical {@code Poly} is \( p = c_0 + c_1 x + c_2 x^2 + \cdots + c_n x^n \).
+ */
+public class Poly { // we don't extend Cloneable, see EJ 3.13
+
+  // Fields
+
+  /** The array of coefficients, the {@code terms[i]} is the coefficient of \( x^i \). */
+  private final int[] terms;
+
+  /** The degree of the polynomial. */
+  private final int deg;
+
+  // Constructors
+
+  /** Initializes this to be the zero polynomial, that is \( p = 0 \). */
+  public Poly() {
+    terms = new int[1];
+    deg = 0;
+  }
+
+  /**
+   * Initializes this to be the polynomial \(p = cx^n\).
+   *
+   * @param c the coefficient.
+   * @param n the degree.
+   * @throws NegativeExponentException if {@code n} &lt; 0.
+   */
+  public Poly(int c, int n) throws NegativeExponentException {
+    if (n < 0)
+      throw new NegativeExponentException("Can't create a monomial with negative exponent");
+    if (c == 0) deg = 0;
+    else deg = n;
+    terms = new int[deg + 1];
+    terms[deg] = c;
+  }
+
+  /**
+   * Initializes a polynomial of given degree (with all coefficients equal to 0).
+   *
+   * @param n the degree, must be non negative.
+   */
+  private Poly(int n) {
+    deg = n;
+    terms = new int[deg + 1];
+  }
+
+  // Methods
+
+  /**
+   * A factory method returning a monomial. (see EJ 2.1)
+   *
+   * @param c the coefficient.
+   * @param n the degree.
+   * @throws NegativeExponentException if {@code n} &lt; 0.
+   * @return the monomial, if {@code n} &gt;= 0.
+   */
+  public static Poly monomialWithCoeffAndDegree(int c, int n) {
+    return new Poly(c, n);
+  }
+
+  /**
+   * Returns the degree of this polynomial.
+   *
+   * @return the largest exponent with a non-zero coefficient; returns 0 if this is the zero {@code
+   *     Poly}.
+   */
+  public int degree() {
+    return deg;
+  }
+
+  /**
+   * Returns the coefficient of the term of given exponent.
+   *
+   * @param d the exponent of the term to consider.
+   * @return the coefficient of the considered term.
+   */
+  public int coeff(int d) {
+    if (d < 0 || d > deg) return 0;
+    else return terms[d];
+  }
+
+  /**
+   * Performs polynomial addition.
+   *
+   * <p>If \( p \) is this polynomial, returns \( p + q \).
+   *
+   * @param q the polynomial to add to this one.
+   * @return the sum among this and the given polynomial.
+   * @throws NullPointerException if {@code q} is {@code null}.
+   */
+  public Poly add(Poly q) throws NullPointerException {
+    return null; // add missing implementation
+  }
+
+  /**
+   * Performs polynomial multiplication.
+   *
+   * <p>If \( p \) is this polynomial, returns \( p q \).
+   *
+   * @param q the polynomial to multiply by this one.
+   * @return the product among this and the given polynomial.
+   * @throws NullPointerException if {@code q} is {@code null}.
+   */
+  public Poly mul(Poly q) throws NullPointerException {
+    if (q == null) throw new NullPointerException();
+    if ((q.deg == 0 && q.terms[0] == 0) || (deg == 0 && terms[0] == 0)) return new Poly();
+    Poly r = new Poly(deg + q.deg);
+    for (int i = 0; i <= deg; i++)
+      for (int j = 0; j <= q.deg; j++) r.terms[i + j] = r.terms[i + j] + terms[i] * q.terms[j];
+    return r;
+  }
+
+  /**
+   * Performs polynomial subtraction.
+   *
+   * <p>If \( p \) is this polynomial, returns \( p - q \).
+   *
+   * @param q the polynomial to subtract from this one.
+   * @return the subtraction among this and the given polynomial.
+   * @throws NullPointerException if {@code q} is {@code null}.
+   */
+  public Poly sub(Poly q) throws NullPointerException {
+    if (q == null) throw new NullPointerException();
+    return add(q.minus());
+  }
+
+  /**
+   * Returns the negate polynomial.
+   *
+   * <p>If \( p \) is this polynomial, returns \( -p \).
+   *
+   * @return this polynomial multiplied by \( -1 \).
+   */
+  public Poly minus() {
+    Poly r = new Poly(deg);
+    for (int i = 0; i <= deg; i++) r.terms[i] = -terms[i];
+    return r;
+  }
+}

src/main/java/it/unimi/di/prog2/e09/PolyClient.java

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+/*
+
+Copyright 2024 Massimo Santini
+
+This file is part of "Programmazione 2 @ UniMI" teaching material.
+
+This is free software: you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation, either version 3 of the License, or
+(at your option) any later version.
+
+This material is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this file.  If not, see <https://www.gnu.org/licenses/>.
+
+*/
+
+package it.unimi.di.prog2.e09;
+
+/** A class to test some methods of {@link Poly}. */
+public class PolyClient {
+
+  /** . */
+  private PolyClient() {}
+
+  /**
+   * Tests some methods of {@link Poly}.
+   *
+   * <p>Starting from term \( t_0 = x + 1 \) reads a list of \( t_i \) of terms from the standard
+   * input, given as a (coefficient, degree) pairs, and computes the polynomial \( t_0 \cdot t_1
+   * \cdot t_2 \cdots \), emitting in the standard output the pairs "coefficient degree" for every
+   * term in the result (in increasing order of degree).
+   *
+   * @param args not used.
+   */
+
+  /*- Uncomment the main method once you have implemented the add method in Poly class
+
+  public static void main(String[] args) {
+    Poly result = null;
+    Poly xp1 = new Poly(1, 1).add(new Poly(-1, 0));
+    try (Scanner s = new Scanner(System.in)) {
+      while (s.hasNextInt()) {
+        Poly term = new Poly(s.nextInt(), s.nextInt());
+        if (result == null) result = term;
+        else result = result.mul(xp1).add(term);
+      }
+      for (int d = 0; d <= result.degree(); d++) System.out.println(result.coeff(d) + " " + d);
+    }
+  }
+  */
+}

src/main/java/it/unimi/di/prog2/e09/SparsePoly.java

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+/*
+
+Copyright 2024 Massimo Santini
+
+This file is part of "Programmazione 2 @ UniMI" teaching material.
+
+This is free software: you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation, either version 3 of the License, or
+(at your option) any later version.
+
+This material is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this file.  If not, see <https://www.gnu.org/licenses/>.
+
+*/
+
+package it.unimi.di.prog2.e09;
+
+import it.unimi.di.prog2.h08.impl.NegativeExponentException;
+import java.util.List;
+
+/**
+ * {@code SparsePoly}s are immutable polynomials with integer coefficients such that the number of
+ * nonzero coefficient is small with respect to the degree.
+ *
+ * <p>A typical {@code Poly} is \( p = c_0 + c_1 x + c_2 x^2 + \cdots + c_n x^n \).
+ */
+public class SparsePoly {
+
+  /**
+   * A record holding a term of the polynomial.
+   *
+   * @param coeff the coefficient.
+   * @param degree the degree.
+   */
+  public record Term(int coeff, int degree) {
+    /**
+     * Builds a term.
+     *
+     * @throws NegativeExponentException if if {@code degree} &lt; 0.
+     */
+    public Term { // using the compact constructor
+      if (degree < 0)
+        throw new NegativeExponentException("A term cannot have a negative exponent.");
+    }
+  }
+
+  /** The array of terms (in increasing non-zero degree). */
+  private final List<Term> terms;
+
+  /** Initializes this to be the zero polynomial, that is \( p = 0 \). */
+  public SparsePoly() {
+    terms = null; // replace this with the actual implementation
+  }
+
+  /**
+   * Initializes this to be the polynomial \(p = cx^n\).
+   *
+   * @param c the coefficient.
+   * @param n the degree.
+   * @throws NegativeExponentException if {@code n} &lt; 0.
+   */
+  public SparsePoly(int c, int n) throws NegativeExponentException {
+    terms = null; // replace this with the actual implementation
+  }
+
+  /**
+   * Returns the coefficient of the term of given exponent.
+   *
+   * @param d the exponent of the term to consider.
+   * @return the coefficient of the considered term.
+   */
+  public int coeff(int d) {
+    return 0; // replace this with the actual implementation
+  }
+
+  /**
+   * Returns the degree of this polynomial.
+   *
+   * @return the largest exponent with a non-zero coefficient; returns 0 if this is the zero {@code
+   *     Poly}.
+   */
+  public int degree() {
+    return 0; // replace this with the actual implementation
+  }
+
+  /**
+   * Performs polynomial addition.
+   *
+   * <p>If \( p \) is this polynomial, returns \( p + q \).
+   *
+   * @param q the polynomial to add to this one.
+   * @return the sum among this and the given polynomial.
+   * @throws NullPointerException if {@code q} is {@code null}.
+   */
+  public SparsePoly add(SparsePoly q) throws NullPointerException {
+    return null; // replace this with the actual implementation
+  }
+
+  /**
+   * Performs polynomial multiplication.
+   *
+   * <p>If \( p \) is this polynomial, returns \( p q \).
+   *
+   * @param q the polynomial to multiply by this one.
+   * @return the product among this and the given polynomial.
+   * @throws NullPointerException if {@code q} is {@code null}.
+   */
+  public SparsePoly mul(SparsePoly q) throws NullPointerException {
+    return null; // replace this with the actual implementation
+  }
+
+  /**
+   * Performs polynomial subtraction.
+   *
+   * <p>If \( p \) is this polynomial, returns \( p - q \).
+   *
+   * @param q the polynomial to subtract from this one.
+   * @return the subtraction among this and the given polynomial.
+   * @throws NullPointerException if {@code q} is {@code null}.
+   */
+  public SparsePoly sub(SparsePoly q) throws NullPointerException {
+    return null; // replace this with the actual implementation
+  }
+
+  /**
+   * Returns the negate polynomial.
+   *
+   * <p>If \( p \) is this polynomial, returns \( -p \).
+   *
+   * @return this polynomial multiplied by \( -1 \).
+   */
+  public SparsePoly minus() {
+    return null; // replace this with the actual implementation
+  }
+}