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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

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
Do somebody tell me a best nano engineering book for beginners?
s. Reply
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?
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
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what is the function of carbon nanotubes?
I'm interested in nanotube
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Ramkumar Reply
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Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
I'm interested in Nanotube
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how did you get the value of 2000N.What calculations are needed to arrive at it
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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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