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package java.util;
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.
Author: Josh Bloch, Neal Gafter Type parameters: - <T> – the type of objects that may be compared by this comparator
See Also: Since: 1.2
/**
* A comparison function, which imposes a <i>total ordering</i> on some
* collection of objects. Comparators can be passed to a sort method (such
* as {@link Collections#sort(List,Comparator) Collections.sort} or {@link
* Arrays#sort(Object[],Comparator) 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 {@link SortedSet sorted sets} or {@link
* SortedMap sorted maps}), or to provide an ordering for collections of
* objects that don't have a {@link Comparable natural ordering}.<p>
*
* The ordering imposed by a comparator <tt>c</tt> on a set of elements
* <tt>S</tt> is said to be <i>consistent with equals</i> if and only if
* <tt>c.compare(e1, e2)==0</tt> has the same boolean value as
* <tt>e1.equals(e2)</tt> for every <tt>e1</tt> and <tt>e2</tt> in
* <tt>S</tt>.<p>
*
* 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 <tt>c</tt>
* is used with elements (or keys) drawn from a set <tt>S</tt>. If the
* ordering imposed by <tt>c</tt> on <tt>S</tt> 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 <tt>equals</tt>.<p>
*
* For example, suppose one adds two elements {@code a} and {@code b} such that
* {@code (a.equals(b) && c.compare(a, b) != 0)}
* to an empty {@code TreeSet} with comparator {@code c}.
* The second {@code add} operation will return
* true (and the size of the tree set will increase) because {@code a} and
* {@code b} are not equivalent from the tree set's perspective, even though
* this is contrary to the specification of the
* {@link Set#add Set.add} method.<p>
*
* Note: It is generally a good idea for comparators to also implement
* <tt>java.io.Serializable</tt>, as they may be used as ordering methods in
* serializable data structures (like {@link TreeSet}, {@link TreeMap}). In
* order for the data structure to serialize successfully, the comparator (if
* provided) must implement <tt>Serializable</tt>.<p>
*
* For the mathematically inclined, the <i>relation</i> that defines the
* <i>imposed ordering</i> that a given comparator <tt>c</tt> imposes on a
* given set of objects <tt>S</tt> is:<pre>
* {(x, y) such that c.compare(x, y) <= 0}.
* </pre> The <i>quotient</i> for this total order is:<pre>
* {(x, y) such that c.compare(x, y) == 0}.
* </pre>
*
* It follows immediately from the contract for <tt>compare</tt> that the
* quotient is an <i>equivalence relation</i> on <tt>S</tt>, and that the
* imposed ordering is a <i>total order</i> on <tt>S</tt>. When we say that
* the ordering imposed by <tt>c</tt> on <tt>S</tt> is <i>consistent with
* equals</i>, we mean that the quotient for the ordering is the equivalence
* relation defined by the objects' {@link Object#equals(Object)
* equals(Object)} method(s):<pre>
* {(x, y) such that x.equals(y)}. </pre><p>
*
* This interface is a member of the
* <a href="{@docRoot}/../technotes/guides/collections/index.html">
* Java Collections Framework</a>.
*
* @param <T> the type of objects that may be compared by this comparator
*
* @author Josh Bloch
* @author Neal Gafter
* @see Comparable
* @see java.io.Serializable
* @since 1.2
*/
public interface Comparator<T> {
Compares its two arguments for order. Returns a negative integer,
zero, or a positive integer as the first argument is less than, equal
to, or greater than the second.
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."
Params: - o1 – the first object to be compared.
- o2 – the second object to be compared.
Throws: - ClassCastException – if the arguments' types prevent them from
being compared by this comparator.
Returns: a negative integer, zero, or a positive integer as the
first argument is less than, equal to, or greater than the
second.
/**
* Compares its two arguments for order. Returns a negative integer,
* zero, or a positive integer as the first argument is less than, equal
* to, or greater than the second.<p>
*
* In the foregoing description, the notation
* <tt>sgn(</tt><i>expression</i><tt>)</tt> designates the mathematical
* <i>signum</i> function, which is defined to return one of <tt>-1</tt>,
* <tt>0</tt>, or <tt>1</tt> according to whether the value of
* <i>expression</i> is negative, zero or positive.<p>
*
* The implementor must ensure that <tt>sgn(compare(x, y)) ==
* -sgn(compare(y, x))</tt> for all <tt>x</tt> and <tt>y</tt>. (This
* implies that <tt>compare(x, y)</tt> must throw an exception if and only
* if <tt>compare(y, x)</tt> throws an exception.)<p>
*
* The implementor must also ensure that the relation is transitive:
* <tt>((compare(x, y)>0) && (compare(y, z)>0))</tt> implies
* <tt>compare(x, z)>0</tt>.<p>
*
* Finally, the implementor must ensure that <tt>compare(x, y)==0</tt>
* implies that <tt>sgn(compare(x, z))==sgn(compare(y, z))</tt> for all
* <tt>z</tt>.<p>
*
* It is generally the case, but <i>not</i> strictly required that
* <tt>(compare(x, y)==0) == (x.equals(y))</tt>. 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."
*
* @param o1 the first object to be compared.
* @param o2 the second object to be compared.
* @return a negative integer, zero, or a positive integer as the
* first argument is less than, equal to, or greater than the
* second.
* @throws ClassCastException if the arguments' types prevent them from
* being compared by this comparator.
*/
int compare(T o1, T o2);
Indicates whether some other object is "equal to" this comparator. This method must obey the general contract of 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.
Params: - obj – the reference object with which to compare.
See Also: Returns: true only if the specified object is also
a comparator and it imposes the same ordering as this
comparator.
/**
* Indicates whether some other object is "equal to" this
* comparator. This method must obey the general contract of
* {@link Object#equals(Object)}. Additionally, this method can return
* <tt>true</tt> <i>only</i> if the specified object is also a comparator
* and it imposes the same ordering as this comparator. Thus,
* <code>comp1.equals(comp2)</code> implies that <tt>sgn(comp1.compare(o1,
* o2))==sgn(comp2.compare(o1, o2))</tt> for every object reference
* <tt>o1</tt> and <tt>o2</tt>.<p>
*
* Note that it is <i>always</i> safe <i>not</i> to override
* <tt>Object.equals(Object)</tt>. However, overriding this method may,
* in some cases, improve performance by allowing programs to determine
* that two distinct comparators impose the same order.
*
* @param obj the reference object with which to compare.
* @return <code>true</code> only if the specified object is also
* a comparator and it imposes the same ordering as this
* comparator.
* @see Object#equals(Object)
* @see Object#hashCode()
*/
boolean equals(Object obj);
}