/*
 * @(#)Comparator.java	1.11 01/11/29
 *
 * Copyright 2002 Sun Microsystems, Inc. All rights reserved.
 * SUN PROPRIETARY/CONFIDENTIAL. Use is subject to license terms.
 */

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
 * <tt>Collections.sort</tt>) to allow precise control over the sort order.
 * Comparators can also be used to control the order of certain data
 * structures (such as <tt>TreeSet</tt> or <tt>TreeMap</tt>).<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>(compare((Object)e1, (Object)e2)==0)</tt> has the same boolean value as
 * <tt>e1.equals((Object)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, if one adds two keys <tt>a</tt> and <tt>b</tt> such that
 * <tt>(a.equals((Object)b) && c.compare((Object)a, (Object)b) != 0)</tt> to a
 * sorted set with comparator <tt>c</tt>, the second <tt>add</tt> operation
 * will return false (and the size of the sorted set will not increase)
 * because <tt>a</tt> and <tt>b</tt> are equivalent from the sorted set's
 * perspective.<p>
 *
 * Note: It is generally a good idea for comparators to implement
 * <tt>java.io.Serializable</tt>, as they may be used as ordering methods in
 * serializable data structures (like <tt>TreeSet</tt>, <tt>TreeMap</tt>).  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>total order</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((Object)x, (Object)y) <= 0}.
 * </pre> The <i>quotient</i> for this total order is:<pre>
 *       {(x, y) such that x.compareTo((Object)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
 * natural 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 natural ordering is the
 * equivalence relation defined by the objects' <tt>equals(Object)</tt>
 * method(s):<pre>
 *       {(x, y) such that x.equals((Object)y)}.
 * </pre>
 *
 * @author  Josh Bloch
 * @version 1.11 11/29/01
 * @see Comparable
 * @see Arrays#sort(Object[], Comparator)
 * @see TreeMap
 * @see TreeSet
 * @see SortedMap
 * @see SortedSet
 * @see java.io.Serializable
 * @since JDK1.2
 */

public interface Comparator {
    /**
     * 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>
     *
     * 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 implementer 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."
     * 
     * @return a negative integer, zero, or a positive integer as the
     * 	       first argument is less than, equal to, or greater than the
     *	       second. 
     * @throws ClassCastException if the arguments' types prevent them from
     * 	       being compared by this Comparator.
     */
    int compare(Object o1, Object o2);

    /**
     * 
     * Indicates whether some other object is "equal to" this
     * Comparator.  This method must obey the general contract of
     * <tt>Object.equals(Object)</tt>.  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     java.lang.Object#equals(java.lang.Object)
     * @see java.lang.Object#hashCode()
     */
    boolean equals(Object obj);
}