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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

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The denominator of a certain fraction is 9 more than the numerator. If 6 is added to both terms of the fraction, the value of the fraction becomes 2/3. Find the original fraction. 2. The sum of the least and greatest of 3 consecutive integers is 60. What are the valu
1. x + 6 2 -------------- = _ x + 9 + 6 3 x + 6 3 ----------- x -- (cross multiply) x + 15 2 3(x + 6) = 2(x + 15) 3x + 18 = 2x + 30 (-2x from both) x + 18 = 30 (-18 from both) x = 12 Test: 12 + 6 18 2 -------------- = --- = --- 12 + 9 + 6 27 3
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Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 1 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 113?
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Solve for the first variable in one of the equations, then substitute the result into the other equation. Point For: (6111,4111,−411)(6111,4111,-411) Equation Form: x=6111,y=4111,z=−411x=6111,y=4111,z=-411
x=61/11 y=41/11 z=−4/11 x=61/11 y=41/11 z=-4/11
Need help solving this problem (2/7)^-2
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Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
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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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