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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) &lt;= 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 &quot;equal to&quot; 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);
}
