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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);
}