A comparison function, which imposes a
total ordering on some
collection of objects. Comparators can be passed to a sort method (such
as
Collections.sort or
Arrays.sort) to allow precise control
over the sort order. Comparators can also be used to control the order of
certain data structures (such as
sorted sets or
sorted maps), or to provide an ordering for collections of
objects that don't have a
natural ordering.
The ordering imposed by a comparator c on a set of elements
S is said to be consistent with equals if and only if
c.compare(e1, e2)==0 has the same boolean value as
e1.equals(e2) for every e1 and e2 in
S.
Caution should be exercised when using a comparator capable of imposing an
ordering inconsistent with equals to order a sorted set (or sorted map).
Suppose a sorted set (or sorted map) with an explicit comparator c
is used with elements (or keys) drawn from a set S. If the
ordering imposed by c on S is inconsistent with equals,
the sorted set (or sorted map) will behave "strangely." In particular the
sorted set (or sorted map) will violate the general contract for set (or
map), which is defined in terms of equals.
For example, suppose one adds two elements a and b such that
(a.equals(b) && c.compare(a, b) != 0)
to an empty TreeSet with comparator c.
The second add operation will return
true (and the size of the tree set will increase) because a and
b are not equivalent from the tree set's perspective, even though
this is contrary to the specification of the
Set.add method.
Note: It is generally a good idea for comparators to also implement
java.io.Serializable, as they may be used as ordering methods in
serializable data structures (like TreeSet, TreeMap). In
order for the data structure to serialize successfully, the comparator (if
provided) must implement Serializable.
For the mathematically inclined, the relation that defines the
imposed ordering that a given comparator c imposes on a
given set of objects S is:
{(x, y) such that c.compare(x, y) <= 0}.
The
quotient for this total order is:
{(x, y) such that c.compare(x, y) == 0}.
It follows immediately from the contract for
compare that the
quotient is an
equivalence relation on
S, and that the
imposed ordering is a
total order on
S. When we say that
the ordering imposed by
c on
S is
consistent with
equals, we mean that the quotient for the ordering is the equivalence
relation defined by the objects'
equals(Object) method(s):
{(x, y) such that x.equals(y)}.
This interface is a member of the
Java Collections Framework.
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A comparison function, which imposes a total ordering on some
collection of objects.
