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Lesson: Algorithms

The polymorphic algorithms described in this section are pieces of reusable functionality provided by the JDK. All of them come from the Collectionsclass. All take the form of static methods whose first argument is the collection on which the operation is to be performed. The great majority of the algorithms provided by the Java platform operate on Listobjects, but a couple of them (min and max) operate on arbitrary Collectionobjects. The algorithms are described below.

Sorting

The sort algorithm reorders a List so that its elements are ascending order according to some ordering relation. Two forms of the operation are provided. The simple form just takes a List and sorts it according to its elements' natural ordering. If you're unfamiliar with the concept of natural ordering, now would be a good time to read the Object Ordering section.

The sort operation uses a slightly optimized merge sort algorithm. If you don't know what this means but you do care, see any basic textbook on algorithms. The important things to know about this algorithm are that it is:

• Fast: This algorithm is guaranteed to run in n log(n) time, and runs substantially faster on nearly sorted lists. Empirical studies showed it to be as fast as a highly optimized quicksort. Quicksort is generally regarded to be faster than merge sort, but isn't stable, and doesn't guarantee n log(n) performance.
• Stable: That is to say, it doesn't reorder equal elements. This is important if you sort the same list repeatedly on different attributes. If a user of a mail program sorts his in-box by mailing date, and then sorts it by sender, the user naturally expects that the now-contiguous list of messages from a given sender will (still) be sorted by mailing date. This is only guaranteed if the second sort was stable.

Here's a trivial little program that prints out its arguments in lexicographic (alphabetical) order.

import java.util.*;

public class Sort {
    public static void main(String args[]) {
        List l = Arrays.asList(args);
        Collections.sort(l);
        System.out.println(l);
    }
}

Let's run the program:

% java Sort i walk the line

[i, line, the, walk]

The program was included only to show you that I have nothing up my sleeve: The algorithms really are as easy to use as they appear to be. I won't insult your intelligence by including any more silly examples.

The second form of sort takes a Comparatorin addition to a List and sorts the elements with the Comparator. Remember the permutation group example at the end of the Map section? It printed out the permutation groups in no particular order. Suppose you wanted to print them out in reverse order of size, largest permutation group first. The following example below shows you how to achieve this with the help of the second form of the sort method.

Recall that the permutation groups are stored as values in a Map, in the form of List objects. The revised printing code iterates through the Map's values-view, putting every List that passes the minimum-size test into a List of Lists. Then, the code sorts this List using a Comparator that expects List objects, and implements reverse-size ordering. Finally, the code iterates through the now-sorted List, printing its elements (the permutation groups). This code replaces the printing code at the end of Perm's main method:

// Make a List of all permutation groups above size threshold
List winners = new ArrayList();
for (Iterator i = m.values().iterator(); i.hasNext(); ) {
    List l = (List) i.next();
    if (l.size() >= minGroupSize)
	winners.add(l);
}

// Sort permutation groups according to size
Collections.sort(winners, new Comparator() {
    public int compare(Object o1, Object o2) {
	return ((List)o2).size() - ((List)o1).size();
    }
});

// Print permutation groups
for (Iterator i=winners.iterator(); i.hasNext(); ) {
    List l = (List) i.next();
    System.out.println(l.size() + ": " + l);
}

Running this program on the same dictionary in the Map section, with the same minimum permutation group size (eight) produces the following output:

% java Perm2 dictionary.txt 8

12: [apers, apres, asper, pares, parse, pears, prase, presa, rapes,
     reaps, spare, spear]
11: [alerts, alters, artels, estral, laster, ratels, salter, slater,
     staler, stelar, talers]
10: [least, setal, slate, stale, steal, stela, taels, tales, teals,
     tesla]
 9: [estrin, inerts, insert, inters, niters, nitres, sinter, triens,
     trines]
 9: [capers, crapes, escarp, pacers, parsec, recaps, scrape, secpar,
     spacer]
 9: [anestri, antsier, nastier, ratines, retains, retinas, retsina,
     stainer, stearin]
 9: [palest, palets, pastel, petals, plates, pleats, septal, staple,
     tepals]
 8: [carets, cartes, caster, caters, crates, reacts, recast, traces]
 8: [ates, east, eats, etas, sate, seat, seta, teas]
 8: [arles, earls, lares, laser, lears, rales, reals, seral]
 8: [lapse, leaps, pales, peals, pleas, salep, sepal, spale]
 8: [aspers, parses, passer, prases, repass, spares, sparse, spears]
 8: [earings, erasing, gainers, reagins, regains, reginas, searing,
     seringa]
 8: [enters, nester, renest, rentes, resent, tenser, ternes, treens]
 8: [peris, piers, pries, prise, ripes, speir, spier, spire]

Shuffling

The shuffle algorithm does the opposite of what sort does: it destroys any trace of order that may have been present in a List. That is to say, it reorders the List, based on input from a source of randomness, such that all possible permutations occur with equal likelihood (assuming a fair source of randomness). This algorithm is useful in implementing games of chance. For example, it could be used to shuffle a List of Card objects representing a deck. Also, it's useful for generating test cases.

There are two forms of this operation. The first just takes a List and uses a default source of randomness. The second requires the caller to provide a Randomobject to use as a source of randomness. The actual code for this algorithm is used as an example in the List section.

Routine Data Manipulation

The Collections class provides three algorithms for doing routine data manipulation on List objects. All of these algorithms are pretty straightforward:

• reverse: Reverses the order of the elements in a List.

• fill: Overwrites every element in a List with the specified value. This operation is useful for re-initializing a List.

• copy: Takes two arguments, a destination List and a source List, and copies the elements of the source into the destination, overwriting its contents. The destination List must be at least as long as the source. If it is longer, the remaining elements in the destination List are unaffected.

Searching

The binarySearch algorithm searches for a specified element in a sorted List using the binary search algorithm. There are two forms of this algorithm. The first takes a List and an element to search for (the "search key"). This form assumes that the List is sorted into ascending order according to the natural ordering of its elements. The second form of the call takes a Comparator in addition to the List and the search key, and assumes that the List is sorted into ascending order according to the specified Comparator. The sort algorithm (described above) can be used to sort the List prior to calling binarySearch.

The return value is the same for both forms: if the List contains the search key, its index is returned. If not, the return value is (-(insertion point) - 1), where the insertion point is defined as the point at which the value would be inserted into the List: the index of the first element greater than the value, or list.size() if all elements in the List are less than the specified value. This admittedly ugly formula was chosen to guarantee that the return value will be >= 0 if and only if the search key is found. It's basically a hack to combine a boolean ("found") and an integer ("index") into a single int return value.

The following idiom, usable with both forms of the binarySearch operation, looks for the specified search key, and inserts it at the appropriate position if it's not already present:

    int pos = Collections.binarySearch(l, key);
    if (pos < 0)
        l.add(-pos-1, key);

Finding Extreme Values

The min and max algorithms return, respectively, the minimum and maximum element contained in a specified Collection. Both of these operations come in two forms. The simple form takes only a Collection, and returns the minimum (or maximum) element according to the elements' natural ordering. The second form takes a Comparator in addition to the Collection and returns the minimum (or maximum) element according to the specified Comparator.

These are the only algorithms provided by the Java platform that work on arbitrary Collection objects, as opposed to List objects. Like the fill algorithm above, these algorithms are quite straightforward to implement. They are included in the Java platform solely as a convenience to programmers.

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