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 returntrue (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 thoughthis 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)}. This interface is a member of the Java Collections Framework. @param < T> the type of objects that may be compared by this comparator @author Josh Bloch @author Neal Gafter @version 1.26, 04/21/06 @see Comparable @see java.io.Serializable @since 1.2
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