* * 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 {@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.
* * 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 {@link TreeSet}, {@link 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' {@link Object#equals(Object)
* equals(Object)} method(s):
* {(x, y) such that x.equals(y)}.
*
* Unlike {@code 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.
*
* @param
*
* 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."
*
* @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 NullPointerException if an argument is null and this
* comparator does not permit null arguments
* @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
* {@link 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,
*
*
* 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.
*
* @param obj the reference object with which to compare.
* @return comp1.equals(comp2) implies that sgn(comp1.compare(o1,
* o2))==sgn(comp2.compare(o1, o2)) for every object reference
* o1 and o2.true 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);
}