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/**
* 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>Unlike {@code Comparable}, a comparator may optionally permit
* comparison of null arguments, while maintaining the requirements for
* an equivalence relation.
*
* <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.<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 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.
*/
/**
* 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()
*/
}