T
 the type of objects that may be compared by this comparatorpublic interface Comparator<T>
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.
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)}.
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
Modifier and Type  Method and Description 

int 
compare(T o1,
T o2)
Compares its two arguments for order.

boolean 
equals(Object obj)
Indicates whether some other object is "equal to" this comparator.

int compare(T o1, T o2)
In the foregoing description, the notation sgn(
expression )
designates
the mathematical signum function, which is defined to return one of 1
,
0
, or 1
according to whether the value of expression is negative, zero
or positive.
The implementor must ensure that sgn(compare(x, y)) ==
sgn(compare(y, x))
for all x
and y
. (This implies that
compare(x, y)
must throw an exception if and only if compare(y, x)
throws an
exception.)
The implementor must also ensure that the relation is transitive:
((compare(x, y)>0) && (compare(y, z)>0))
implies
compare(x, z)>0
.
Finally, the implementor must ensure that compare(x, y)==0
implies that
sgn(compare(x, z))==sgn(compare(y, z))
for all z
.
It is generally the case, but not strictly required that
(compare(x, y)==0) == (x.equals(y))
. Generally speaking, any comparator that violates
this condition should clearly indicate this fact. The recommended language is "Note: this
comparator imposes orderings that are inconsistent with equals."
o1
 the first object to be compared.o2
 the second object to be compared.NullPointerException
 if an argument is null and this comparator does not permit null argumentsClassCastException
 if the arguments' types prevent them from being compared by this comparator.boolean equals(@Nullable Object obj)
Object.equals(Object)
. Additionally, this method can return
true
only if the specified object is also a comparator and it imposes the same
ordering as this comparator. Thus, comp1.equals(comp2)
implies that
sgn(comp1.compare(o1,
o2))==sgn(comp2.compare(o1, o2))
for every object reference o1
and o2
.
Note that it is always safe not to override Object.equals(Object)
.
However, overriding this method may, in some cases, improve performance by allowing programs to
determine that two distinct comparators impose the same order.
equals
in class Object
obj
 the reference object with which to compare.true
only if the specified object is also a comparator and it imposes the
same ordering as this comparator.Object.equals(Object)
,
Object.hashCode()