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public class TestBinaryTree { static public void main(String[] args) { BinaryTree<String> e = new BinaryTree<String>("E"); BinaryTree<String> g = new BinaryTree<String>("G"); BinaryTree<String> h = new BinaryTree<String>("H"); BinaryTree<String> i = new BinaryTree<String>("I"); BinaryTree<String> d = new BinaryTree<String>("D", null, g); BinaryTree<String> f = new BinaryTree<String>("F", h, i); BinaryTree<String> b = new BinaryTree<String>("B", d, e); BinaryTree<String> c = new BinaryTree<String>("C", f, null); BinaryTree<String> tree = new BinaryTree<String>("A", b, c); System.out.printf("tree: %s", tree); } }

The output is:

Each individual entity of an entity type (think of an instance of a class) will be characterized by a set of attribute values Attributes are the adjectives or descriptors of the entities the database will store For instance, extending the example from two paragraphs above, a particular student could have the attributes Bill Smith, Akron, OH, Fisher Dorm, 323, Computer Science, Professor Findley, etc The structure of a database is described by its schema As we will see later, in order to convert the data model to a relational database schema, each entity instance of an entity type must be unique Something in the set of attributes must make each entity different from all other entities of the same type.

tree: [A, B, D, G, E, C, F, H, I]

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The program creates the binary tree shown in Figure 11.21 and then indirectly invokes its toString() method that it inherits from the AbstractCollections class. Figure 11.21 shows two views of the same tree. The larger view shows all the details, representing each object reference with an arrow.

Returning to the example in the previous paragraph, we expect only one Bill Smith, and if there are two or more, we will find a way to make the different Bill Smith entities unique We will assign a key to each entity of the student entity type such that we can distinguish each student Having selected the entity types to include in the database, the data modeler then specifies the relationships among the entities For instance, we mentioned previously the advisor/advisee relationship between professors and students One of the important decisions to make is whether the relationship will be 1:1 (one-to-one), 1:N (one-to-many), or N:M (many-to-many) These ratios are called cardinality ratios In the case of the advisor/advisee relationship, the designer might decide the relationship is 1:N, with 1 advisor advising N students.

CHAP. 11]

On the other hand, if the school assigns multiple advisors to each student (for instance, one for the student s major field and one for student life questions), the relationship could be defined as N:M, multiple advisors for each student, and multiple students for each advisor Another pair of decisions related to the cardinality ratio of a relationship is the specification of minimum cardinalities Must a student have an advisor If so, then the minimum cardinality on the professor side of the advisor/advisee relationship must be 1 If not, then the minimum cardinality on the professor side of the relationship will be 0; a student entity may exist who is not associated with any advisor Likewise, must every professor be an advisor If so, then the minimum cardinality on the student side of the advisor/advisee relationship must be 1.

By extending the AbstractCollection class, the BinaryTree class automatically inherits these methods that are defined by using the iterator() and size() methods:

isEmpty() contains(Object object) toArray() toArray(Object[] objects) toString() add(Object object) addAll(Collection collection) clear() containsAll(Collection collection) remove(Object object) removeAll(Collection collection) retainAll(Collection collection) However, the mutating methods will throw an UnsupportedOperationException because they invoke other methods that are not implemented, namely the add() and the Iterator.remove() methods. public public public public public public public public public public public public boolean boolean Object[] Object[] String boolean boolean void boolean boolean boolean boolean

If not, then the minimum cardinality on the student side will be 0; a professor entity can exist with no associated advisees Other relationships might be 1:1 Imagine an entity type called Parking Permit, and that the policy is to allow each student one and only one parking permit The relationship between student and parking permit could be called parks/permit-to-park, and the relationship is 1:1 The minimum cardinality on the student side would probably be 1, since otherwise it would mean the database tracks parking permits that are not issued to anyone The minimum cardinality on the parking permit side would probably be 0, since some students probably will not have cars to park A many-to-many, N:M, relationship would exist between students and courses We could call this relationship takes/is-taken-by Each student will take many courses, and many students will take each course.

This example builds the same tree as the one in Example 11.21 and then tests the contains() method on it and its subtrees:

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