Lecture 8

src/main/java/it/unimi/di/prog2/h08/IntSet.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.h08;
+
+import it.unimi.di.prog2.h08.impl.EmptyException;
+
+/**
+ * {@code IntSet}s are mutable, unbounded sets of integers.
+ *
+ * <p>A typical IntSet is \( S = \{x_1, \ldots, x_n \} \).
+ */
+public class IntSet {
+
+  // Constructors
+
+  /**
+   * Initializes this set to be empty.
+   *
+   * <p>Builds the set \( S = \varnothing \).
+   */
+  public IntSet() {}
+
+  // Methods
+
+  /**
+   * Adds the given element to this set.
+   *
+   * <p>This method modifies the object, that is: \( S' = S \cup \{ x \} \).
+   *
+   * @param x the element to be added.
+   */
+  public void insert(int x) {}
+
+  /**
+   * Removes the given element from this set.
+   *
+   * <p>This method modifies the object, that is: \( S' = S \setminus \{ x \} \).
+   *
+   * @param x the element to be removed.
+   */
+  public void remove(int x) {}
+
+  /**
+   * Tells if the given element is in this set.
+   *
+   * <p>Answers the question \( x\in S \).
+   *
+   * @param x the element to look for.
+   * @return whether the given element belongs to this set, or not.
+   */
+  public boolean isIn(int x) {
+    return false;
+  }
+
+  /**
+   * Returns the cardinality of this set.
+   *
+   * <p>Responds with \( |S| \).
+   *
+   * @return the size of this set.
+   */
+  public int size() {
+    return 0;
+  }
+
+  /**
+   * Returns an element from this set.
+   *
+   * @return an arbitrary element from this set.
+   * @throws EmptyException if this set is empty.
+   */
+  public int choose() throws EmptyException {
+    return 0;
+  }
+}

src/main/java/it/unimi/di/prog2/h08/IntSets.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.h08;
+
+import java.util.Objects;
+
+/** A collection of methods for {@link IntSet}s. */
+public class IntSets {
+
+  // See EJ 2.4
+  /** . */
+  private IntSets() {}
+
+  /**
+   * Builds a set from an array of elements.
+   *
+   * @param a and array of integer elements.
+   * @return the set containing an entry for every distinct element of {@code a}.
+   * @throws NullPointerException if {@code a} is {@code null}.
+   */
+  public static IntSet getElements(int[] a) throws NullPointerException {
+    Objects.requireNonNull(a, "L'array non può essere null");
+    IntSet s = new IntSet();
+    for (int i = 0; i < a.length; i++) s.insert(a[i]);
+    return s;
+  }
+}

src/main/java/it/unimi/di/prog2/h08/IntSetsClient.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.h08;
+
+/** A class to test some methods of {@link IntSet}. */
+public class IntSetsClient {
+
+  /** . */
+  private IntSetsClient() {}
+
+  /**
+   * Builds a set from an array of elements.
+   *
+   * @param args the elements of the set.
+   */
+  public static void main(String[] args) {
+    int[] a = new int[args.length];
+    int i = 0;
+    for (String s : args) a[i++] = Integer.parseInt(s);
+    IntSet S = IntSets.getElements(a);
+    System.out.println(S);
+  }
+}

src/main/java/it/unimi/di/prog2/h08/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.h08;
+
+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 {
+
+  // Constructors
+
+  /** Initializes this to be the zero polynomial, that is \( p = 0 \). */
+  public Poly() {}
+
+  /**
+   * 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 {}
+
+  /**
+   * 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 null;
+  }
+
+  // Methods
+
+  /**
+   * 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;
+  }
+
+  /**
+   * 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;
+  }
+
+  /**
+   * 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;
+  }
+
+  /**
+   * 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 {
+    return null;
+  }
+
+  /**
+   * 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 {
+    return null;
+  }
+
+  /**
+   * Returns the negate polynomial.
+   *
+   * <p>If \( p \) is this polynomial, returns \( -p \).
+   *
+   * @return this polynomial multiplied by \( -1 \).
+   */
+  public Poly minus() {
+    return null;
+  }
+}

src/main/java/it/unimi/di/prog2/h08/Polys.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.h08;
+
+/** A collection of methods for {@link Poly}s. */
+public class Polys {
+
+  // See EJ 2.4
+  /** . */
+  private Polys() {}
+
+  /**
+   * Returns the derivative of the given polynomial.
+   *
+   * @param p the polynomial to differentiate.
+   * @return the derivative of {@code p}.
+   * @throws NullPointerException if {@code p} is {@code null}.
+   */
+  public static Poly diff(Poly p) throws NullPointerException {
+    Poly q = new Poly();
+    for (int i = 1; i <= p.degree(); i++) q = q.add(new Poly(p.coeff(i) * i, i - 1));
+    return q;
+  }
+}