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29 * This interface imposes a total ordering on the objects of each class that
30 * implements it. This ordering is referred to as the class's <i>natural
31 * ordering</i>, and the class's <tt>compareTo</tt> method is referred to as
32 * its <i>natural comparison method</i>.<p>
34 * Lists (and arrays) of objects that implement this interface can be sorted
35 * automatically by {@link Collections#sort(List) Collections.sort} (and
36 * {@link Arrays#sort(Object[]) Arrays.sort}). Objects that implement this
37 * interface can be used as keys in a {@linkplain SortedMap sorted map} or as
38 * elements in a {@linkplain SortedSet sorted set}, without the need to
39 * specify a {@linkplain Comparator comparator}.<p>
41 * The natural ordering for a class <tt>C</tt> is said to be <i>consistent
42 * with equals</i> if and only if <tt>e1.compareTo(e2) == 0</tt> has
43 * the same boolean value as <tt>e1.equals(e2)</tt> for every
44 * <tt>e1</tt> and <tt>e2</tt> of class <tt>C</tt>. Note that <tt>null</tt>
45 * is not an instance of any class, and <tt>e.compareTo(null)</tt> should
46 * throw a <tt>NullPointerException</tt> even though <tt>e.equals(null)</tt>
47 * returns <tt>false</tt>.<p>
49 * It is strongly recommended (though not required) that natural orderings be
50 * consistent with equals. This is so because sorted sets (and sorted maps)
51 * without explicit comparators behave "strangely" when they are used with
52 * elements (or keys) whose natural ordering is inconsistent with equals. In
53 * particular, such a sorted set (or sorted map) violates the general contract
54 * for set (or map), which is defined in terms of the <tt>equals</tt>
57 * For example, if one adds two keys <tt>a</tt> and <tt>b</tt> such that
58 * <tt>(!a.equals(b) && a.compareTo(b) == 0)</tt> to a sorted
59 * set that does not use an explicit comparator, the second <tt>add</tt>
60 * operation returns false (and the size of the sorted set does not increase)
61 * because <tt>a</tt> and <tt>b</tt> are equivalent from the sorted set's
64 * Virtually all Java core classes that implement <tt>Comparable</tt> have natural
65 * orderings that are consistent with equals. One exception is
66 * <tt>java.math.BigDecimal</tt>, whose natural ordering equates
67 * <tt>BigDecimal</tt> objects with equal values and different precisions
68 * (such as 4.0 and 4.00).<p>
70 * For the mathematically inclined, the <i>relation</i> that defines
71 * the natural ordering on a given class C is:<pre>
72 * {(x, y) such that x.compareTo(y) <= 0}.
73 * </pre> The <i>quotient</i> for this total order is: <pre>
74 * {(x, y) such that x.compareTo(y) == 0}.
77 * It follows immediately from the contract for <tt>compareTo</tt> that the
78 * quotient is an <i>equivalence relation</i> on <tt>C</tt>, and that the
79 * natural ordering is a <i>total order</i> on <tt>C</tt>. When we say that a
80 * class's natural ordering is <i>consistent with equals</i>, we mean that the
81 * quotient for the natural ordering is the equivalence relation defined by
82 * the class's {@link Object#equals(Object) equals(Object)} method:<pre>
83 * {(x, y) such that x.equals(y)}. </pre><p>
85 * This interface is a member of the
86 * <a href="{@docRoot}/../technotes/guides/collections/index.html">
87 * Java Collections Framework</a>.
89 * @param <T> the type of objects that this object may be compared to
92 * @see java.util.Comparator
96 public interface Comparable<T> {
98 * Compares this object with the specified object for order. Returns a
99 * negative integer, zero, or a positive integer as this object is less
100 * than, equal to, or greater than the specified object.
102 * <p>The implementor must ensure <tt>sgn(x.compareTo(y)) ==
103 * -sgn(y.compareTo(x))</tt> for all <tt>x</tt> and <tt>y</tt>. (This
104 * implies that <tt>x.compareTo(y)</tt> must throw an exception iff
105 * <tt>y.compareTo(x)</tt> throws an exception.)
107 * <p>The implementor must also ensure that the relation is transitive:
108 * <tt>(x.compareTo(y)>0 && y.compareTo(z)>0)</tt> implies
109 * <tt>x.compareTo(z)>0</tt>.
111 * <p>Finally, the implementor must ensure that <tt>x.compareTo(y)==0</tt>
112 * implies that <tt>sgn(x.compareTo(z)) == sgn(y.compareTo(z))</tt>, for
115 * <p>It is strongly recommended, but <i>not</i> strictly required that
116 * <tt>(x.compareTo(y)==0) == (x.equals(y))</tt>. Generally speaking, any
117 * class that implements the <tt>Comparable</tt> interface and violates
118 * this condition should clearly indicate this fact. The recommended
119 * language is "Note: this class has a natural ordering that is
120 * inconsistent with equals."
122 * <p>In the foregoing description, the notation
123 * <tt>sgn(</tt><i>expression</i><tt>)</tt> designates the mathematical
124 * <i>signum</i> function, which is defined to return one of <tt>-1</tt>,
125 * <tt>0</tt>, or <tt>1</tt> according to whether the value of
126 * <i>expression</i> is negative, zero or positive.
128 * @param o the object to be compared.
129 * @return a negative integer, zero, or a positive integer as this object
130 * is less than, equal to, or greater than the specified object.
132 * @throws NullPointerException if the specified object is null
133 * @throws ClassCastException if the specified object's type prevents it
134 * from being compared to this object.
136 public int compareTo(T o);