Boggle How-To

A Good IWordOnBoardFinder Implementation

The screenshot below shows a game in which the word "mountain" is highlighted on the board -- the highlighting is done because a class GoodWordOnBoardFinder correctly finds where a given word is on the board.

You're given a JUnit test program TestWordFinder for testing your word-finding code. Hopefully passing the unit tests will be enough for your code to work in the Boggle game -- you can simply change BoggleMain to use the good word-finding implementation and the game should work properly.

board screenshot

Backtracking Code

To find whether a String/word occurs on a board the method cellsForWord which you must write will call a recursive, helper method that does most of the work. The helper method will search for the string/word beginning at a specified (row,column) cell on the board -- the code in method in cellsForWord calls the helper method with every possible (row,column) as a starting point as follows:

 public List<BoardCell> cellsForWord(BoggleBoard board, String word) {

       List<BoardCell> list = new ArrayList<BoardCell>();
       for(int r=0; r < board.size(); r++){
           for(int c=0; c < board.size(); c++){
               if (helper(board,r,c,list, ....)){ 

       // not shown

You're free to write the helper method any way you want to, here's a suggestion.

The helper method can have an int parameter which is an index indicating which character in the string is the one being tentatively matched to the (row,column) board cell. By convention, BoardCell indices start with 0, where (0, 0) is the upper-left cell: The first time the helper method is called this parameter has the value zero indicating the first character of the string should be matched. There are several cases to track in the helper method:

The helper method also maintains some record of the board cells that have been matched so far. This record (could be a list or a set) serves two purposes: it will ultimately be returned by the method cellsForWord if the word is found on the board by the helper method. The record will also help you write code to ensure that the same board cell isn't used more than once in finding the word being searched for.

Although you can make eight recursive calls using eight different statements you can also use a loop like the one below to make the recursive calls:

  int[] rdelta = {-1,-1,-1, 0, 0, 1, 1, 1};
  int[] cdelta = {-1, 0, 1,-1, 1,-1, 0, 1};
  for(int k=0; k < rdelta.length; k++){
    if (helper(board, row+rdelta[k], col+cdelta[k], ...) return true;

Be careful when finding a "Q" in a word since if there's a match the Boggle board cube has two characters and you'll have to adjust parameters in the recursive call to make sure you do the right thing.

When you don't find the word being looked for, you'll have to backtrack and undo the work done so far. As with typical, recursive, backtracking code, this often involves undoing the one step made before the recursive invocation(s). In this case it's likely that the one-step-made is storing a matching BoardCell object.

Different ILexicon Implementations

An inheritance diagram of the classes is given below -- the classes you write must implement the methods of ILexicon and can provide other methods as well if that helps in implementing the required methods. Ignore the CompressedTrieLexicon class in the image below.



Rewrite the wordStatus methods of the
SimpleLexicon class so that it uses the TreeSet.subSet method that returns a subset/subtree of the tree in which all the words are stored --- the subset's first word should be the String whose status is being determined in wordStatus and the subset's last word should be myUpperBound which is a value larger than any element in the lexicon's set of words (see the code). Make sure you check to see if the parameter s is larger than the upper bound since that will cause the TreeSet.subset call to fail. See the SortedSet.subset API for details.


You must write a class named BinarySearchLexicon implementing the ILexicon interface. Store words in a sorted ArrayList (sort the ArrayList after adding all the words to it) and use Collections.binarySearch to search the list.

Read the documentation for binarySearch. Note that when the index value returned is less than zero the value can be used to determine where a word should be in a sorted list. For example, when looking up "ela" the value returned might be -137. This means that "ela" is not in the lexicon, but if it were to be inserted it would be at index 136. This also means that if the word at index 136 does not begin with "ela" then no word in the lexicon has a prefix of "ela". So, any non-negative value returned by binarySearch means the status of a word is LexStatus.WORD. If the value returned is negative, one call of the appropriate String.startsWith() method can determine if LexStatus.PREFIX should be returned (make sure you don't go off the end of the array of words in the lexicon when calling startsWith).


You do not have to implement CompressedTrieLexicon, but you may complete it for extra credit. The compressed trie trades space for time. It is slightly slower than a trie, but it requires less space/storage.

We provide a mostly complete TrieLexicon implementation that we discussed in lab and which is explained in some detail below. You'll also want to look at the code to understand how the lexicon works. For extra credit you must implement a new subclass of TrieLexicon; the subclass should be named CompressedTrieLexicon. In implementing the class you'll write code to remove nodes with only one child as described below. A chain of nodes pointed to by one link can be compressed into a node storing a suffix rather than a single character. The picture below shows the result of compressing such nodes in a trie.

You'll need to create a new method compress to perform this one-child compression, you'll call this method in the load method you override as below:

public class CompressedTrieLexicon extends TrieLexicon { // some code not shown @Override public void load(ArrayList<String> list) { super.load(list); compress(); } // more code not shown }

In a trie, determining whether a string is a word or a prefix is an O(W) operation where W is the length of the string -- note: this is independent of N the number of entries stored in the trie/lexicon. A picture of a trie storing the words "do", "dog", "dot", "doting", "drag", "drastic", "to", "top", "torn", and "trap" is shown below on the left. The compressed version of this trie is shown on the right.

TrieLexicon CompressedTrieLexicon
triepicture compressed trie

The red dots in the diagram indicate that the path from the root to the node represents a word. You can see how this works be examining the code in the TrieLexicon class. In particular, note that when a node has nothing below it, the path to that node represents a word that isn't a prefix of another word. Because of how the TrieLexicon is constructed, determining if a sequence of characters is a word or a prefix is fairly straightforward.

If a path hits a null pointerm then the path cannot represent either a prefix or a word since any pointer out of a node ultimately reaches a leaf that represents a word that isn't a prefix of another word. For example, in the tries shown above the string "toaster" would result in the code following the "t" link, then the "o" link from that, then would fail since there's no "a" link from the "o" node.

To compress the trie you'll write code that finds every leaf. From each leaf you'll write code that follows the parent pointers back up the trie until either a node representing a word is found or a node that has more than one child is found.

The second case is illustrated in the diagram by the strings "drastic", "torn", and "trap". In each case the sequence of nodes with single pointers is replaced by one node with a suffix stored that represents the eliminated nodes, e.g., "stic", "rn", and "rap" in the diagram. Note that the number of nodes eliminated is one less than the length of the suffix stored --- we need one node to store the suffix.

The first case described is represented by the string "doting". We can't replace "ting" by a node with that suffix because we'd have to differentiate between "dot" and "doting" and that's hard with one node. Instead we leave "dot" and only compress "ing" below it.

The suffix of the single-node-pointing-path is stored after the parent pointers are followed. Since the trie nodes store a string, they can certainly store a suffix. You'll need to code a new version of wordStatus in the CompressedTrie class to recognize when a suffix-node is reached.

You should benchmark your CompressedTrieLexicon class by determining how many nodes are stored/saved compared to the non-compressed trie and determining how much more time the new, compressed version takes. Two methods in the TrieLexicon class for counting nodes are provided, they may prove useful in benchmarking your class. These methods are nodeCount and oneWayCount.

Lexicon Testing and Benchmarking

We provide a JUnit testing class TestLexicon to use as you develop your ILexicon implementations. To test different implementations simply change the code in the method makeLexicon to return the implementation you want to test and run the JUnit tests (see the howto for JUnit assistance.)

We also provide a benchmarking class LexiconBenchmark that facilitates evaluating the efficiency of different implementations as well as correctness. Confidence in an implementation's correctness is increased if it returns the same results as other implementations.

Autoplayer Classes

You'll write two classes that let the computer find all valid words on a Boggle board. Each class will extend AbstractAutoPlayer and thus implement the IAutoPlayer interface. When you implement method findAllValidWords you should first set the autoplayer's score to zero and then clear any words already stored -- you do this by calling the inherited method clear(). Remember that since you inherit all the classes from AbstractAutoPlayer you can call them in the classes you write. If you choose to override an inherited method you should use the @Override annotation, but for the auto-player classes you likely don't need to override any methods, you simply need to implement findAllValidWords. You may find it useful to implement helper methods as well.

Here's a diagram of some of the classes and interfaces in the player hierarchy. You'll implement the two classes at the bottom of the diagram: BoardFirstAutoPlayer and LexiconFirstAutoPlayer.

*player classes*


Once you've implemented GoodWordOnBoardFinder to find where a word occurs on a board you'll be able write/implement class named LexiconFirstAutoPlayer in a straightforward way. This new class extends AbstractAutoPlayer. To find all the words on a board simply iterate over every value in a lexicon checking to see if the word is on the board by calling the cellsForWord method you wrote earlier. This means you'll need to construct the LexiconFirstAutoPlayer with an ILexicon and an IWordOnBoardFinder to work with. These could be passed to the constructor or could be fields that are initialized in the constructor. For analyzing different lexicons you'll want to be able to change which kind of ILexicon is used by the LexiconFirstAutoPlayer, so parameterizing the constructor makes some sense.


Rather than iterating over every every word in the dictionary you can use the board to generate potential words. For example, in the board shown in the screen shot below on the right the following words can be formed starting the "L" in the upper-left corner: "LORE", "LOSE", "LOST", "LOT". From the output it's clear that "LOSER" isn't in the lexicon being used when the screen shot was taken since it is on the board, but isn't shown in the output.

Starting at the cell "R" at [1,3] (recall the first row has index zero) we can form "REST" and "RESORT". Starting at the cell "R" at [0,2] we can form "ROLL" and "ROSE" as well as "REST".

Since no word begins with "GT", "GP", "GS", no search will proceed from the "G" in the lower-right after looking at more than two cubes since these two-character prefixes aren't found in the lexicon.

You'll write a recursive helper method for this class to find all the words starting at a specified [row,column]. The basic idea is to pass to this helper method at least the following:

The code you write will be very similar to the code you wrote in GoodWordOnBoardFinder.cellsForWord with its helper method.

When first called, the string built from the search so far is the empty string: "". The current cube/cell on the board, if legal and not used in the search so far, is added to the end of the string built so far. If the string is a word, the word is added to the collection of found words by calling the inherited add(..) method. (See the code in AbstractPlayer for how the words found are stored via this method.)

If the string is either a word or the prefix of a word in the lexicon then the search is continued by calling the helper method for each adjacent cube with the string built so far. If the string is not a prefix (or a word) then the search is cut-off at this point and the recursion will unwind/backtrack (essentially to the point where the last possible word/prefix was formed).

As with all flood-fill/backtracking code you must make sure your code doesn't re-use a board-cell/cube once it has been used in the current search. This means that each board-cell/cube that contributed to the string built from the search so far can't be re-used in extending the string. But the cell/cube can be re-used when searching for different strings/starting from or continuing from different cubes. You can use in instance variable/field to store the BoardCell objects used in the current word being formed, but other approaches work as well (e.g., using a parameter) --- note that BoardCell implements Comparable. But, since you're backtracking, be sure to undo the marking of a board cell both in the string being built and in the structure storing which board cells contributed to the string.

Using JUnit

See the Markov Assignment Howto for information on using JUnit.

Random Numbers

Boggle boards are generated by the BoggleBoardFactory class when its getBoard method is called. This method generates a board by calling an IBoardMaker implementation makeBoard method. You'll likely use the StandardBoardMaker implementation supplied and created in the factory class. This factory uses a random number generator without a specific seed so that when you start a sequene of Boggle games different boards are generated.

You can ensure that some reproduceable sequence of boards is generated by using the setRandom method of the BoggleBoardFactory class with a java.util.Random object created without a specific seed, e.g.,

  BoggleBoardFactory.setRandom(new Random(12345));

When debugging you may want to do this to ensure that you have repeatable behavior. In your game-playing program you'll probably want users to have a different sequence of boards every time, but in debugging and statistic generation you want a reproduceable sequence. For example, the supplied BoggleStats class sets the seed to ensure that comparisons across different implementations of lexicons and autoplayers are valid.

Last modified: Thu Mar 24 15:26:06 EDT 2011