Assignment #3: Recursion Solution

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How to hand in your work

Submit the requested files through the Assignment #3 link on the CSC 115 conneX site. Please ensure you follow all the required steps for submission (including confirming your submission).

Learning outcomes

When you have completed this assignment, you should have become acquainted with:

  • The use of recursion (specifically using a style of programming using recursive backtracking)

  • Using linked-­‐lists to support recursive backtracking.


Problem description

One form of word play is called anagramming. Some English phrase is given, such as:

I love programming!

and the letters in that phrase are jumbled about into different words:

VIM romping galore.

(“vim” is a programming editor used by many programmers.) To be an anagram of a phrase the exact letters (but perhaps with different capitalization) must appear in both phrases. Punctuation is permitted to differ (i.e., spaces, commas, periods, etc.). There are anagram servers on the web that accept a phrase and then, after searching through a dictionary, produce a long list of anagrams—mostly nonsense

combinations of words, but often containing wonderful ones which just require a bit of re-­‐ordering to be clever and funny. The most established website is the Internet Anagram Server (

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Your task for this assignment is to write a program that takes both a phrase and a dictionary of words, and then generates the anagrams for that phrase given the dictionary.

A sample run

Here is one sample run of the finished program:

lu8617ocrj2o tmp 1733b6d68a126915

lu8617ocrj2o tmp 80bfd995394e613a $ java A3driver –dict=files/small.txt –phrase=”Justin Trudeau”

unjust, duet, air

lu8617ocrj2o tmp bfe59201ee4dccb2 duet, unjust, air

unjust, air, duet

lu8617ocrj2o tmp 70e27813b3c7f549 air, unjust, duet

duet, air, unjust

air, duet, unjust

The dictionary of words in files/small.txt is purposely created to provide the anagram for phrase shown above (i.e., small.txt has only four words). Note the six lines of output have the same words but in different permutations. (The Internet

Anagram Server would suppress permutations, but the algorithm you will implement is simpler that the one on that Server.) The order of the permutations does not matter; rather what matters is that all permutations appear. Please note: I’ve chosen “Justin

Trudeau” for an anagram-­‐phrase example as his name is topical and it has lots of vowels, i.e., my choice does not indicate my political persuasion! (provided to you)

When are two phrases anagrams of each other? When their letter-­‐frequencies match. Keeping track of such frequencies can be a bit tedious, however, and you are provided with a class named AlphabetStats. It has the following methods:

  • public AlphabetStats(String phrase): Computes the letter

frequencies for the letters in phrase. It ignores characters that are not part of the alphabet, i.e., ignores whitespace and punctuation.

  • public String toString(): Produces a string representing letter frequencies currently in the instance of AlphabetStats. (This means that an instance of AlphabetStats can be given as an argument to System.out.print.)

  • public boolean contains(AlphabetStats as): Compares the letter frequencies in the instance with those of as. For example, as1.contains(as2) returns true if all the letter frequencies in as1 are greater than or equal to those in as2 and returns false otherwise.

  • public boolean add(AlphabetStats as): Adds all of the letter frequencies in as to the AlphabetStats instance. For example, after as1.add(as2) is performed, all of the letter frequencies in as1 will have been incremented by the letter-­‐frequency values in as2; as2 is unchanged.

boolean subtract(AlphabetStats as) decrements letter-­‐frequency values.

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  • public boolean isEmpty(): Returns false if the AlphabetStats instance has 0 for all letter frequencies.

This class should be used as part of your recursive-­‐backtracking algorithm for finding anagrams.

So to go back to the original question in this subsection, “When are two phrases anagrams of each other?”, an answer is suggested below:

lu8617ocrj2o tmp 31e3afd6da37ddb

lu8617ocrj2o tmp 80bfd995394e613a String phrase1 = “aabbcc”;

String phrase2 = “cba cba”;

lu8617ocrj2o tmp 3caffd7516ced24f AlphabetStats as1 = new AlphabetStats(phrase1); lu8617ocrj2o tmp 3caffd7516ced24f AlphabetStats as2 = new AlphabetStats(phrase2); lu8617ocrj2o tmp 99b9d4404d9c36e as1.subtract(as2);

lu8617ocrj2o tmp a28b1c10122f37a7 System.out.println(“The two phrases are ” + (as1.isEmpty() ? “” : “NOT “) +

“anagrams of each other”

lu8617ocrj2o tmp 2573dd4525e27715 );,,

Your task is to write three classes. WordList and WordListNode will be used to store intermediate results during recursion, and Anagrammer contains the code actually

performing the recursive-­‐backtrack search for a phrase’s anagrams. I will spend some time in lectures explaining how recursive backtracking works (and the text also describes such backtracking for the “eight-­‐queens” problem).

WordList is a ref-­‐based linked list with six methods (other than the constructor):

  • void insertHead(String w): Inserts at the head a node storing w.

  • void removeHead(): removes the node from the head of the list.

  • boolean contains(String w): returns true if a node in the list already contains a string equal to w.

  • boolean isEmpty(): returns true if the list is empty (i.e., its head is equal to


  • int getLength(): returns the length of the list..

  • String retrieve(int index): returns a string from node in the list at position index; if the index is not legal, then null is returned.

  • All test routines for are to appear in the main() method of WordList. (There must be at least eight test cases.)

Anagrammer has at most two public methods (although you a free to add as many private methods as needed) and one private method:

  • Anagrammer(String dictionary[], String phrase, int maxWords): A constructor to which is passed in some already-­‐input

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dictionary in the form of a string array, the phrase string, the maximum length of acceptable anagrams for the phrase.

  • public void generate(): Using the phrase, dictionary, and maximum length of anagrams provided to the constructor, this method generates the anagrams that result from the combination. Note that generate() itself is not recursive, but rather it will call the (private) recursive method you add to the class.

  • private void findAnagram(WordList words, AlphabetStats phraseStats): This method is meant to be recursive. The first parameter is the list of words so far in current anagram search; the second parameter represents the letters from the original phrase which are still left out of the

list of words. One base case for findAnagram is when phraseStats.isEmpty() returns true (i.e., the contents of words is an anagram of the given phrase). There is at least one more base case and of

course there must, of course, be a recursive call to findAnagram. (Some of this will be discussed during lectures and perhaps labs.) For this assignment you must assume that anagrams do not contain repeated words.

  • All test routines for are to appear in the main() method of Anagrammer. (There must be at least eight test cases, and none of these may be one of the provided tests.)

You are provided with which does the work of reading command-­‐

line arguments, opening and reading the contents of the dictionary file, and invoking generate() on an instance of Anagrammer. Do not modify

Three different dictionaries (files/small.txt, files/medium.txt, files/large.txt) are provided to you. You are, of course, welcome to explore the assignment with

additional dictionaries you may find. (Keep it clean, folks!) The content of files/README.txt describes how the three test outputs in files/ were created.

What you are to write

  1. Please keep all code within a single directory. We will take advantage of what is called the default package in Java, i.e., all Java files in the same directory are considered to be in the same package. This will permit you to use package-­‐ private access for the assignment without a complex directory structure.

  1. Write and Ensure has a main() with tests.

  1. Complete using recursive backtracking (as outlined in lectures). Do not delete the redundancy in the output—for example, if four words are found to make up an anagram, you will see that combination printing in 4! (i.e., 24) lines of output. Ensure has a main() with tests.

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  1. Create a file named test_output.txt that describes your approach to testing.

  1. In all of your coding work, please follow the coding conventions posted at conneX (i.e., a document in the “Lectures & stuff” section).

Files to submit (four in total):




  1. test_output.txt

Grading scheme

  • A” grade: An exceptional submission demonstrating creativity and initiative going above and beyond the assignment requirements. The program runs without any problems and implements the required classes and methods in those classes, and uses recursive backtracking. Required methods are tested with output showing tests and their results (i.e., pass or fail). Any extra work appears in class files having the name <file>, and identified within the file (i.e., Class comment) are details of your extension to the assignment demonstrating creativity and initiative.

  • B” grade: A submission completing the requirements of the assignment. The program runs without any problems and implements the required classes and methods in those classes, along with recursive backtracking. Required methods are tested with output showing tests and their results (i.e., pass or fail). Public methods are tested with output showing tests and their results.

  • C” grade: A submission completing most of the requirements of the assignment. The program runs with some problems and uses recursive backtracking but does implement the required classes and methods, and yet might not have the expected output. Required methods are tested with output showing tests and their results (i.e., pass or fail).

  • D” grade: A serious attempt at completing requirements for the assignment. The program runs with major problems, or does not contain implementations of all required classes and methods.

  • F” grade: Either no submission given, the submission does not compile, or submission represents very little work.

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