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package java.util;

/**

 * 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)&gt;0) &amp;&amp; (compare(y, z)&gt;0))</tt> implies

     * <tt>compare(x, z)&gt;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.

     */

    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

     * <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);

}