Université de Bordeaux

public interface Point2D {
  double getAbscisse();

  void setAbscisse(double x);

  double getOrdonnee();

  void setOrdonnee(double y);

  double getModule();

  void setModule(double m);

  double getArgument();

  void setArgument(double a);

  Point2D clone();

  boolean equals(Point2D o);

  String toString();

  Point2D translation(double dx , double dy);

  Point2D homothetie(double rapport);

  Point2D rotation(double angle);
}

public interface ShapeStack {

    public boolean isEmpty();
    public void pop();
    public void push(Shape s);
    public Shape top();

    public boolean equals(ShapeStack s);
    ShapeStack clone();
    public String toString(); 
}

public class Relation {
  public Relation(boolean[][] tRelation) {
    int n = tRelation.length;
    relation = new boolean[n][n];
    for (int i = 0; i < n; ++i)
      for (int j = 0; j < n; ++j)
        relation[i][j] = tRelation[i][j];
  }

  public boolean inRelation(int i, int j) {
    return relation[i][j];
  }

  public boolean isReflexive() {
    for (int i = 0; i < relation.length; ++i)
      if (!inRelation(i, i))
        return false;
    return true;
  }

  public boolean isSymetrique() {
    for (int i = 1; i < relation.length; ++i)
      for (int j = 0; j < i; ++j)
        if (inRelation(i, j) != inRelation(j, i))
          return false;
    return true;
  }

  public boolean isTransitive() {
    int n = relation.length;
    for (int i = 0; i < n; ++i)
      for (int j = 0; j < n; ++j)
        if (inRelation(i, j))
          for (int k = 0; k < n; ++k)
            if (inRelation(j, k) && !inRelation(i, k))
              return false;
    return true;
  }

  public static Relation composed(Relation r1, Relation r2) {
    int n = r1.relation.length;
    boolean[][] composed = new boolean[n][n];
    for (int i = 0; i < n; ++i)
      for (int j = 0; j < n; ++j)
        if (r1.inRelation(i, j))
          for (int k = 0; k < n; ++k)
            if (r2.inRelation(j, k))
              composed[i][k] = true;
    return new Relation(composed);
  }

  public int[] image(int i) {
    // on determine la taille de l’image
    int taille = 0;
    int n = relation.length;
    for (int j = 0; j < n; ++j)
      if (inRelation(i, j))
        taille++;
    int tableImage[] = new int[taille];
    for (int j = 0, k = 0; j < n; ++j)
      if (inRelation(i, j))
        tableImage[k++] = j;
    return tableImage;
  }

  private boolean[][] relation;
}