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The SortedSet Interface

A SortedSetis a Setthat maintains its elements in ascending order, sorted according to the elements' natural order, or according to a Comparator provided at SortedSet creation time. (Natural order and Comparators are discussed in the previous section, on Object Ordering.) In addition to the normal Set operations, the Set interface provides operations for:

• Range-view: Performs arbitrary range operations on the sorted set.
• Endpoints: Returns the first or last element in the sorted set.
• Comparator access: Returns the Comparator used to sort the set (if any).

The SortedSet interface is shown below:

public interface SortedSet extends Set {
    // Range-view
    SortedSet subSet(Object fromElement, Object toElement);
    SortedSet headSet(Object toElement);
    SortedSet tailSet(Object fromElement);

    // Endpoints
    Object first();
    Object last();

    // Comparator access
    Comparator comparator();
}

Set Operations

The operations that SortedSet inherits from Set behave identically on sorted sets and normal sets with two exceptions:

• The Iterator returned by the iterator operation traverses the sorted set in order.
• The array returned by toArray contains the sorted set's elements in order.

Although the interface doesn't guarantee it, the toString method of the JDK's SortedSet implementations returns a string containing all the elements of the sorted set, in order.

By convention, all Collection implementations provide a standard constructor that takes a Collection, and SortedSet implementations are no exception. This constructor creates a SortedSet object that orders its elements according to their natural order. Additionally, by convention, SortedSet implementations provide two other standard constructors:

• One that takes a Comparator and returns a new (empty) SortedSet sorted according to the specified Comparator.
• One that takes a SortedSet and returns a new SortedSet containing the same elements as the given SortedSet, and sorted according to the same Comparator (or using the elements' natural ordering, if the specified SortedSet did too). Note that the compile-time type of the argument determines whether this constructor is invoked in preference to the ordinary Set constructor, and not the runtime type!

The first of these standard constructors is the normal way to create an empty SortedSet with an explicit Comparator. The second is similar in spirit to the standard Collection constructor: it creates a copy of a SortedSet with the same ordering, but with a programmer-specified implementation type.

Range-view Operations

The Range-view operations are somewhat analogous to those provided by the List interface, but there is one big difference. Range-views of a sorted set remain valid even if the backing sorted set is modified directly. This is feasible because the endpoints of a range view of a sorted set are absolute points in the element-space, rather than specific elements in the backing collection (as is the case for lists). A range-view of a sorted set is really just a window onto whatever portion of the set lies in the designated part of the element-space. Changes to the range-view write back to the backing sorted set and vice-versa. Thus, it's OK to use range-views on sorted sets for long periods of time (unlike range-views on lists).

Sorted sets provide three range-view operations. The first, subSet takes two endpoints (like subList). Rather than indices, the endpoints are objects. They must be comparable to the elements in the sorted set (using the set's Comparator or the natural ordering of its elements, whichever the set uses to order itself). Like subList the range is half-open, including its low endpoint but excluding the high one.

Thus, the following one-liner tells you how many words between "doorbell" and "pickle", including "doorbell" but excluding "pickle", are contained in a SortedSet of strings called dictionary:

int count = dictionary.subSet("doorbell", "pickle").size();

Similarly, the following one-liner removes all of the elements beginning with the letter "f" (a rather heavy-handed approach to censorship?):

dictionary.subSet("f", "g").clear();

A similar trick can be used to print a table telling you how many words begin with each letter:

for (char ch='a'; ch<='z'; ch++) {
    String from = new String(new char[] {ch});
    String to = new String(new char[] {(char)(ch+1)});
    System.out.println(from + ": " +
                       dictionary.subSet(from, to).size());
}

Suppose that you want to view a closed interval (which contains both its endpoints) instead of an open interval. If the element type allows for the calculation of the successor a given value (in the element-space), merely request the subSet from lowEndpoint to successor(highEndpoint) . Although it isn't entirely obvious, the successor of a string s in String's natural ordering is s+"\0" (that is, s with a null character appended).

Thus, the following one-liner tells you how many words between "doorbell" and "pickle," including "doorbell" and "pickle," are contained in a the dictionary:

int count = dictionary.subSet("doorbell", "pickle\0").size();

A similarly technique can be used to view an open interval (which contains neither endpoint). The open interval view from lowEndpoint to highEndpoint is the half-open interval from successor(lowEndpoint) to highEndpoint. To calculate the number of words between "doorbell" and "pickle", excluding both:

int count = dictionary.subSet("doorbell\0", "pickle").size();

The SortedSet interface contains two more range-view operations, headSet and tailSet, both of which take a single Object argument. The former returns a view of the initial portion of the backing SortedSet, up to but not including the specified object. The latter returns a view of the final portion of the the backing SortedSet, beginning with the specified object, and continuing to the end of the backing SortedSet Thus, the following code allows you to view the dictionary as two disjoint "volumes" (a-m and n-z):

SortedSet volume1 = dictionary.headSet("n");
SortedSet volume2 = dictionary.tailSet("n");

Endpoint Operations

The SortedSet interface contains operations to return the first and last elements in the sorted set, called (not surprisingly) first and last. In addition to their obvious uses, last allows a workaround for a deficiency in the SortedSet interface. One thing you'd like to do with a SortedSet is to go into the interior of the set and iterate forwards or backwards. It's easy enough to go forwards from the interior: Just get a tailSet and iterate over it. Unfortunately, there's no easy way to go backwards.

The following idiom obtains the first element in a sorted set that is less than a specified object o in the element-space:

Object predecessor = ss.headSet(o).last();

This is a fine way to go one element backwards from a point in the interior of a sorted set. It could be applied repeatedly to iterate backwards, but unfortunately this is very inefficient, requiring a lookup for each element returned.

Comparator Accessor

The SortedSet interface contains an accessor method called comparator that returns the Comparator used to sort the set, or null if the set is sorted according to the natural order of its elements. This method is provided so that sorted sets can be copied into new sorted sets with the same ordering. It is used by the standard SortedSet constructor, described above.

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