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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 {@code compareTo} 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 {@code C} is said to be <i>consistent

 * with equals</i> if and only if {@code e1.compareTo(e2) == 0} has

 * the same boolean value as {@code e1.equals(e2)} for every

 * {@code e1} and {@code e2} of class {@code C}.  Note that {@code null}

 * is not an instance of any class, and {@code e.compareTo(null)} should

 * throw a {@code NullPointerException} even though {@code e.equals(null)}

 * returns {@code false}.<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 {@code equals}

 * method.<p>

 *

 * For example, if one adds two keys {@code a} and {@code b} such that

 * {@code (!a.equals(b) && a.compareTo(b) == 0)} to a sorted

 * set that does not use an explicit comparator, the second {@code add}

 * operation returns false (and the size of the sorted set does not increase)

 * because {@code a} and {@code b} are equivalent from the sorted set's

 * perspective.<p>

 *

 * Virtually all Java core classes that implement {@code Comparable} have natural

 * orderings that are consistent with equals.  One exception is

 * {@code java.math.BigDecimal}, whose natural ordering equates

 * {@code BigDecimal} 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>{@code

 *       {(x, y) such that x.compareTo(y) <= 0}.

 * }</pre> The <i>quotient</i> for this total order is: <pre>{@code

 *       {(x, y) such that x.compareTo(y) == 0}.

 * }</pre>

 *

 * It follows immediately from the contract for {@code compareTo} that the

 * quotient is an <i>equivalence relation</i> on {@code C}, and that the

 * natural ordering is a <i>total order</i> on {@code C}.  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}/java.base/java/util/package-summary.html#CollectionsFramework">

 * Java Collections Framework</a>.

 *

 * @param <T> the type of objects that this object may be compared to

 *

 * @author  Josh Bloch

 * @see java.util.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

     * {@code sgn(x.compareTo(y)) == -sgn(y.compareTo(x))}

     * for all {@code x} and {@code y}.  (This

     * implies that {@code x.compareTo(y)} must throw an exception iff

     * {@code y.compareTo(x)} throws an exception.)

     *

     * <p>The implementor must also ensure that the relation is transitive:

     * {@code (x.compareTo(y) > 0 && y.compareTo(z) > 0)} implies

     * {@code x.compareTo(z) > 0}.

     *

     * <p>Finally, the implementor must ensure that {@code x.compareTo(y)==0}

     * implies that {@code sgn(x.compareTo(z)) == sgn(y.compareTo(z))}, for

     * all {@code z}.

     *

     * <p>It is strongly recommended, but <i>not</i> strictly required that

     * {@code (x.compareTo(y)==0) == (x.equals(y))}.  Generally speaking, any

     * class that implements the {@code 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."

     *

     * <p>In the foregoing description, the notation

     * {@code sgn(}<i>expression</i>{@code )} designates the mathematical

     * <i>signum</i> function, which is defined to return one of {@code -1},

     * {@code 0}, or {@code 1} according to whether the value of

     * <i>expression</i> is negative, zero, or positive, respectively.

     *

     * @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);

}