public abstract interface

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

{(x, y) such that c.compare(x, y) == 0}.It follows immediately from the contract for

`Object.equals(Object)`

method(s):{(x, y) such that x.equals(y)}.

Unlike ` Comparable`

, a comparator may optionally permit
comparison of null arguments, while maintaining the requirements for
an equivalence relation.

This interface is a member of the Java Collections Framework.

`<T>` | the type of objects that may be compared by this comparator |

Comparable, java.io.Serializable