+ * + * Lists (and arrays) of objects that implement this interface can be sorted + * automatically by {@link Collections#sort(List) Collections.sort} (and + * {@link Arrays#sort(Object[]) Arrays.sort}). Objects that implement this + * interface can be used as keys in a {@linkplain SortedMap sorted map} or as + * elements in a {@linkplain SortedSet sorted set}, without the need to + * specify a {@linkplain Comparator comparator}.
+ * + * The natural ordering for a class C is said to be consistent + * with equals if and only if e1.compareTo(e2) == 0 has + * the same boolean value as e1.equals(e2) for every + * e1 and e2 of class C. Note that null + * is not an instance of any class, and e.compareTo(null) should + * throw a NullPointerException even though e.equals(null) + * returns false.
+ * + * It is strongly recommended (though not required) that natural orderings be + * consistent with equals. This is so because sorted sets (and sorted maps) + * without explicit comparators behave "strangely" when they are used with + * elements (or keys) whose natural ordering is inconsistent with equals. In + * particular, such a sorted set (or sorted map) violates the general contract + * for set (or map), which is defined in terms of the equals + * method.
+ * + * For example, if one adds two keys a and b such that + * (!a.equals(b) && a.compareTo(b) == 0) to a sorted + * set that does not use an explicit comparator, the second add + * operation returns false (and the size of the sorted set does not increase) + * because a and b are equivalent from the sorted set's + * perspective.
+ * + * Virtually all Java core classes that implement Comparable have natural + * orderings that are consistent with equals. One exception is + * java.math.BigDecimal, whose natural ordering equates + * BigDecimal objects with equal values and different precisions + * (such as 4.0 and 4.00).
+ * + * For the mathematically inclined, the relation that defines + * the natural ordering on a given class C is:
+ * {(x, y) such that x.compareTo(y) <= 0}.
+ * The quotient for this total order is:
+ * {(x, y) such that x.compareTo(y) == 0}.
+ *
+ *
+ * It follows immediately from the contract for compareTo that the
+ * quotient is an equivalence relation on C, and that the
+ * natural ordering is a total order on C. When we say that a
+ * class's natural ordering is consistent with equals, we mean that the
+ * quotient for the natural ordering is the equivalence relation defined by
+ * the class's {@link Object#equals(Object) equals(Object)} method:
+ * {(x, y) such that x.equals(y)}.
+ *
+ * This interface is a member of the
+ *
+ * Java Collections Framework.
+ *
+ * @param The implementor must ensure sgn(x.compareTo(y)) ==
+ * -sgn(y.compareTo(x)) for all x and y. (This
+ * implies that x.compareTo(y) must throw an exception iff
+ * y.compareTo(x) throws an exception.)
+ *
+ * The implementor must also ensure that the relation is transitive:
+ * (x.compareTo(y)>0 && y.compareTo(z)>0) implies
+ * x.compareTo(z)>0.
+ *
+ * Finally, the implementor must ensure that x.compareTo(y)==0
+ * implies that sgn(x.compareTo(z)) == sgn(y.compareTo(z)), for
+ * all z.
+ *
+ * It is strongly recommended, but not strictly required that
+ * (x.compareTo(y)==0) == (x.equals(y)). Generally speaking, any
+ * class that implements the Comparable interface and violates
+ * this condition should clearly indicate this fact. The recommended
+ * language is "Note: this class has a natural ordering that is
+ * inconsistent with equals."
+ *
+ * In the foregoing description, the notation
+ * sgn(expression) designates the mathematical
+ * signum function, which is defined to return one of -1,
+ * 0, or 1 according to whether the value of
+ * expression is negative, zero or positive.
+ *
+ * @param o the object to be compared.
+ * @return a negative integer, zero, or a positive integer as this object
+ * is less than, equal to, or greater than the specified object.
+ *
+ * @throws NullPointerException if the specified object is null
+ * @throws ClassCastException if the specified object's type prevents it
+ * from being compared to this object.
+ */
+ public int compareTo(T o);
+}