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29 * A comparison function, which imposes a <i>total ordering</i> on some
30 * collection of objects. Comparators can be passed to a sort method (such
31 * as {@link Collections#sort(List,Comparator) Collections.sort} or {@link
32 * Arrays#sort(Object[],Comparator) Arrays.sort}) to allow precise control
33 * over the sort order. Comparators can also be used to control the order of
34 * certain data structures (such as {@link SortedSet sorted sets} or {@link
35 * SortedMap sorted maps}), or to provide an ordering for collections of
36 * objects that don't have a {@link Comparable natural ordering}.<p>
38 * The ordering imposed by a comparator <tt>c</tt> on a set of elements
39 * <tt>S</tt> is said to be <i>consistent with equals</i> if and only if
40 * <tt>c.compare(e1, e2)==0</tt> has the same boolean value as
41 * <tt>e1.equals(e2)</tt> for every <tt>e1</tt> and <tt>e2</tt> in
44 * Caution should be exercised when using a comparator capable of imposing an
45 * ordering inconsistent with equals to order a sorted set (or sorted map).
46 * Suppose a sorted set (or sorted map) with an explicit comparator <tt>c</tt>
47 * is used with elements (or keys) drawn from a set <tt>S</tt>. If the
48 * ordering imposed by <tt>c</tt> on <tt>S</tt> is inconsistent with equals,
49 * the sorted set (or sorted map) will behave "strangely." In particular the
50 * sorted set (or sorted map) will violate the general contract for set (or
51 * map), which is defined in terms of <tt>equals</tt>.<p>
53 * For example, suppose one adds two elements {@code a} and {@code b} such that
54 * {@code (a.equals(b) && c.compare(a, b) != 0)}
55 * to an empty {@code TreeSet} with comparator {@code c}.
56 * The second {@code add} operation will return
57 * true (and the size of the tree set will increase) because {@code a} and
58 * {@code b} are not equivalent from the tree set's perspective, even though
59 * this is contrary to the specification of the
60 * {@link Set#add Set.add} method.<p>
62 * Note: It is generally a good idea for comparators to also implement
63 * <tt>java.io.Serializable</tt>, as they may be used as ordering methods in
64 * serializable data structures (like {@link TreeSet}, {@link TreeMap}). In
65 * order for the data structure to serialize successfully, the comparator (if
66 * provided) must implement <tt>Serializable</tt>.<p>
68 * For the mathematically inclined, the <i>relation</i> that defines the
69 * <i>imposed ordering</i> that a given comparator <tt>c</tt> imposes on a
70 * given set of objects <tt>S</tt> is:<pre>
71 * {(x, y) such that c.compare(x, y) <= 0}.
72 * </pre> The <i>quotient</i> for this total order is:<pre>
73 * {(x, y) such that c.compare(x, y) == 0}.
76 * It follows immediately from the contract for <tt>compare</tt> that the
77 * quotient is an <i>equivalence relation</i> on <tt>S</tt>, and that the
78 * imposed ordering is a <i>total order</i> on <tt>S</tt>. When we say that
79 * the ordering imposed by <tt>c</tt> on <tt>S</tt> is <i>consistent with
80 * equals</i>, we mean that the quotient for the ordering is the equivalence
81 * relation defined by the objects' {@link Object#equals(Object)
82 * equals(Object)} method(s):<pre>
83 * {(x, y) such that x.equals(y)}. </pre>
85 * <p>Unlike {@code Comparable}, a comparator may optionally permit
86 * comparison of null arguments, while maintaining the requirements for
87 * an equivalence relation.
89 * <p>This interface is a member of the
90 * <a href="{@docRoot}/../technotes/guides/collections/index.html">
91 * Java Collections Framework</a>.
93 * @param <T> the type of objects that may be compared by this comparator
98 * @see java.io.Serializable
102 public interface Comparator<T> {
104 * Compares its two arguments for order. Returns a negative integer,
105 * zero, or a positive integer as the first argument is less than, equal
106 * to, or greater than the second.<p>
108 * In the foregoing description, the notation
109 * <tt>sgn(</tt><i>expression</i><tt>)</tt> designates the mathematical
110 * <i>signum</i> function, which is defined to return one of <tt>-1</tt>,
111 * <tt>0</tt>, or <tt>1</tt> according to whether the value of
112 * <i>expression</i> is negative, zero or positive.<p>
114 * The implementor must ensure that <tt>sgn(compare(x, y)) ==
115 * -sgn(compare(y, x))</tt> for all <tt>x</tt> and <tt>y</tt>. (This
116 * implies that <tt>compare(x, y)</tt> must throw an exception if and only
117 * if <tt>compare(y, x)</tt> throws an exception.)<p>
119 * The implementor must also ensure that the relation is transitive:
120 * <tt>((compare(x, y)>0) && (compare(y, z)>0))</tt> implies
121 * <tt>compare(x, z)>0</tt>.<p>
123 * Finally, the implementor must ensure that <tt>compare(x, y)==0</tt>
124 * implies that <tt>sgn(compare(x, z))==sgn(compare(y, z))</tt> for all
127 * It is generally the case, but <i>not</i> strictly required that
128 * <tt>(compare(x, y)==0) == (x.equals(y))</tt>. Generally speaking,
129 * any comparator that violates this condition should clearly indicate
130 * this fact. The recommended language is "Note: this comparator
131 * imposes orderings that are inconsistent with equals."
133 * @param o1 the first object to be compared.
134 * @param o2 the second object to be compared.
135 * @return a negative integer, zero, or a positive integer as the
136 * first argument is less than, equal to, or greater than the
138 * @throws NullPointerException if an argument is null and this
139 * comparator does not permit null arguments
140 * @throws ClassCastException if the arguments' types prevent them from
141 * being compared by this comparator.
143 int compare(T o1, T o2);
146 * Indicates whether some other object is "equal to" this
147 * comparator. This method must obey the general contract of
148 * {@link Object#equals(Object)}. Additionally, this method can return
149 * <tt>true</tt> <i>only</i> if the specified object is also a comparator
150 * and it imposes the same ordering as this comparator. Thus,
151 * <code>comp1.equals(comp2)</code> implies that <tt>sgn(comp1.compare(o1,
152 * o2))==sgn(comp2.compare(o1, o2))</tt> for every object reference
153 * <tt>o1</tt> and <tt>o2</tt>.<p>
155 * Note that it is <i>always</i> safe <i>not</i> to override
156 * <tt>Object.equals(Object)</tt>. However, overriding this method may,
157 * in some cases, improve performance by allowing programs to determine
158 * that two distinct comparators impose the same order.
160 * @param obj the reference object with which to compare.
161 * @return <code>true</code> only if the specified object is also
162 * a comparator and it imposes the same ordering as this
164 * @see Object#equals(Object)
165 * @see Object#hashCode()
167 boolean equals(Object obj);