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Gilbert and McCarty describe cardinality as the number of objects that participate in an association and whether the participation is optional or mandatory. To determine cardinality, ask the following questions:

  • Which objects collaborate with which other objects?

  • How many objects participate in each collaboration?

  • Is the collaboration optional or mandatory?

For example, let's consider the following example. We are creating an Employee class that inherits from Person, and has relationships with the following classes:

  • Division

  • JobDescription

  • Spouse

  • Child

What do these classes do? Are they optional? How many does an Employee need?

  • Division

    • This object contains the information relating to the division that the employee works for.

    • Each employee must work for a division, so the relationship is mandatory.

    • The employee works for one, and only one, division.

  • JobDescription

    • This object contains a job description, most likely containing information such as salary grade and salary range.

    • Each employee must have a job description, so the relationship is mandatory.

    • The employee can hold various jobs during the tenure at a company. Thus, an employee can have many job descriptions. These descriptions can be kept as a history if an employee changes jobs, or it is possible that an employee might hold two different jobs at one time. For example, a supervisor might take on an employee's responsibilities if the employee quits and a replacement has not yet been hired.

  • Spouse

    • In this simplistic example, the Spouse class contains only the anniversary date.

    • An employee can be married or not married. Thus, a spouse is optional.

    • An employee can have only one spouse.

  • Child

    • In this simple example, the Child class contains only the string FavoriteToy.

    • An employee can have children or not have children.

    • An employee can have no children or an infinite number of children (wow!). You could make a design decision as to the upper limit of the number of children that the system can handle.

To sum up, Table 9.1 represents the cardinality of the associations of the classes we just considered.

Table 9.1. Cardinality of Class Associations
















Cardinality Notation

The notation of 0…1 means that an employee can have either zero or one spouse. The notation of 0…n means that an employee can have any number of children from zero to an unlimited number. The n basically represents infinity.

Figure 9.7 shows the class diagram for this system. Note that in this class diagram, the cardinality is indicated along the association lines. Refer to Table 9.1 to see whether the association is mandatory.

Figure 9.7. Cardinality in a UML diagram.


Multiple Object Associations

How do we represent an association that might contain multiple objects (like 0 to many children) in code? Here is the code for the Employee class:

import java.util.Date;

public class Employee extends Person{

        private String CompanyID;

        private String Title;

        private Date StartDate;

        private Spouse spouse;

        private Child[] child;

        private Division division;

        private JobDescription[] jobDescriptions;

        public String getCompanyID() {return CompanyID;}

        public String getTitle() {return Title;}

        public Date getStartDate() {return StartDate;}

        public void setCompanyID(String CompanyID) {}

        public void setTitle(String Title) {}

        public void setStartDate(int StartDate) {}


Note that the classes that have a one-to-many relationship are represented by arrays in the code:

private Child[] child;

private JobDescription[] jobDescriptions;

Optional Associations

One of the most important issues when dealing with associations is to make sure that your application is designed to check for optional associations. This means that your code must check to see whether the association is null.

Suppose in the previous example, your code assumes that every employee has a spouse. However, if one employee is not married, the code will have a problem (see Figure 9.8). If your code does indeed expect a spouse to exist, it may well fail and leave the system in an unstable state. The bottom line is that the code must check for a null condition, and must handle this as a valid condition.

Figure 9.8. Checking all optional associations.


For example, if no spouse exists, the code must not attempt to invoke a spouse method. This could lead to an application failure. Thus, the code must be able to process an Employee object that has no spouse.

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