- * - * 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);
-}