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  package java.lang;
  import java.util.*;
  
  /**
   * This interface imposes a total ordering on the objects of each class that
   * implements it.  This ordering is referred to as the class's <i>natural
   * ordering</i>, and the class's <tt>compareTo</tt> method is referred to as
   * its <i>natural comparison method</i>.<p>
   *
   * 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}.<p>
   *
   * The natural ordering for a class <tt>C</tt> is said to be <i>consistent
   * with equals</i> if and only if <tt>e1.compareTo(e2) == 0</tt> has
   * the same boolean value as <tt>e1.equals(e2)</tt> for every
   * <tt>e1</tt> and <tt>e2</tt> of class <tt>C</tt>.  Note that <tt>null</tt>
   * is not an instance of any class, and <tt>e.compareTo(null)</tt> should
   * throw a <tt>NullPointerException</tt> even though <tt>e.equals(null)</tt>
   * returns <tt>false</tt>.<p>
   *
   * 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 <tt>equals</tt>
   * method.<p>
   *
   * For example, if one adds two keys <tt>a</tt> and <tt>b</tt> such that
   * {@code (!a.equals(b) && a.compareTo(b) == 0)} to a sorted
   * set that does not use an explicit comparator, the second <tt>add</tt>
   * operation returns false (and the size of the sorted set does not increase)
   * because <tt>a</tt> and <tt>b</tt> are equivalent from the sorted set's
   * perspective.<p>
   *
   * Virtually all Java core classes that implement <tt>Comparable</tt> have natural
   * orderings that are consistent with equals.  One exception is
   * <tt>java.math.BigDecimal</tt>, whose natural ordering equates
   * <tt>BigDecimal</tt> objects with equal values and different precisions
   * (such as 4.0 and 4.00).<p>
   *
   * For the mathematically inclined, the <i>relation</i> that defines
   * the natural ordering on a given class C is:<pre>
   *       {(x, y) such that x.compareTo(y) &lt;= 0}.
   * </pre> The <i>quotient</i> for this total order is: <pre>
   *       {(x, y) such that x.compareTo(y) == 0}.
   * </pre>
   *
   * It follows immediately from the contract for <tt>compareTo</tt> that the
   * quotient is an <i>equivalence relation</i> on <tt>C</tt>, and that the
   * natural ordering is a <i>total order</i> on <tt>C</tt>.  When we say that a
   * class's natural ordering is <i>consistent with equals</i>, 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:<pre>
   *     {(x, y) such that x.equals(y)}. </pre><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 this object may be compared to
   *
   * @author  Josh Bloch
   * @see Comparator
   * @since 1.2
   */
  public interface Comparable<T> {
      /**
       * Compares this object with the specified object for order.  Returns a
       * negative integer, zero, or a positive integer as this object is less
       * than, equal to, or greater than the specified object.
       *
       * <p>The implementor must ensure <tt>sgn(x.compareTo(y)) ==
       * -sgn(y.compareTo(x))</tt> for all <tt>x</tt> and <tt>y</tt>.  (This
       * implies that <tt>x.compareTo(y)</tt> must throw an exception iff
       * <tt>y.compareTo(x)</tt> throws an exception.)
       *
       * <p>The implementor must also ensure that the relation is transitive:
       * <tt>(x.compareTo(y)&gt;0 &amp;&amp; y.compareTo(z)&gt;0)</tt> implies
       * <tt>x.compareTo(z)&gt;0</tt>.
       *
       * <p>Finally, the implementor must ensure that <tt>x.compareTo(y)==0</tt>
       * implies that <tt>sgn(x.compareTo(z)) == sgn(y.compareTo(z))</tt>, for
       * all <tt>z</tt>.
       *
       * <p>It is strongly recommended, but <i>not</i> strictly required that
       * <tt>(x.compareTo(y)==0) == (x.equals(y))</tt>.  Generally speaking, any
       * class that implements the <tt>Comparable</tt> 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."
       *
       * <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.
       *
       * @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);
  }
  