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The module describes comparator objects for determining a binary order and builds a generalized priority queue with it.

Order relation

When comparing two objects, there are two ways to look at the comparison behavior, which creates a notion of ordering between the two objects:

  1. Each object knows how to compare itself -- Comparison is considered intrinsic to the object and is part of its behavior.
  2. Comparison is done by an external object -- A third object is introduced that contains the ability to compare two objects.

These two different outlooks on binary object ordering will be explored below in terms of the two Java interfaces that are used to model them.


There are many computing tasks that require performing some sort of comparison between data objects. A few data types are endowed with a "natural" ordering of their values. The integers have a natural ordering "less or equal to", labeled "<=", defined as follows.

n<= m iff m = n + k, for some non-negative integer k
( Note : a rigorous mathematical definition of the set of non-negative integers is beyond the scope of this lecture).

The above natural order of the integers is a concrete instance of an abstract concept called an order relation. An order relation on a set S is a boolean function R on S x S that is

  • reflexive: R(x, x) is true for all x in S,
  • anti-symmetric: R(x,y) and R(y,x) implies x = y, for all x, y in S, and
  • transitive: R(x, y) and R(y, z) implies R(x, z), for all x, y, z in S.

To model order relations that are naturally endowed in certain types of data objects, Java provides an interface called Comparable , which has exactly one method called

int compareTo(Object rhs) , defined abstractly as

  • x.compareTo(y)<0 means x is "less than" y ,
  • x.compareTo(y) == 0 means x is "equal to" y , and
  • x.compareTo(y)>0 means y is "less than" x .

For example, the Integer class implements the Comparable interface as follows. If x and y are Integer objects then,

  • x.compareTo(y)<0 means x<y ,
  • x.compareTo(y) == 0 means x == y , and
  • x.compareTo(y)>0 means y<x .

Common data types that have a natural ordering among their values, such as Double , String , Character , all implement Comparable .

    Advantages and disadvantages

  • Advantages
    • Objects carry their ability to be compared with them and thus can be involved in comparison operations anywhere.
    • The comparison operation is invariant and thus consistent in all situations.
  • Disadvantages
    • Comparison operation cannot be changed to match different situations.


Most of the time, the ordering among the data objects is an extrinsic operation imposed on the object by the user of the objects. For example, the Pizza objects in homework 2 have no concepts of comparing among themselves, however, the user can impose an ordering on them by comparing their price/area ratios or their profits. To model extrinsic ordering relation, Java provides an interface in the java.util package called Comparator , which has exactly two methods:

  • int compare(Object x, Object y) , to model the ordering
    • compare(x, y)<0 means x is "less than" y ,
    • compare(x, y) == 0 means x is "equal to" y , and
    • compare(x, y)>0 means yis "less than" x , and
  • boolean equals(Object x) , to model equality of Comparators . Unlike the equals method of most objects, equality of Comparator s also requires that their comparison behavior be identical.

Questions & Answers

How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
How can I make nanorobot?
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
how can I make nanorobot?
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
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Source:  OpenStax, Principles of object-oriented programming. OpenStax CNX. May 10, 2013 Download for free at http://legacy.cnx.org/content/col10213/1.37
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