Description
This program focuses on recursive backtracking. Turn in a file named Anagrams.java from the Homework section of
the course web site. You will need support files AnagramMain.java and various dictionary text files from the
Homework section of the course web site; place them in the same folder as your class.
Anagrams:
An anagram is a word or phrase made by rearranging the letters of another word or phrase. For example, the words
“midterm” and “trimmed” are anagrams. If you ignore spaces and capitalization and allow multiple words, a multi-word
phrase can be an anagram of some other word or phrase. For example, the phrases “Clint Eastwood” and “old west
action” are anagrams.
In this assignment, you will create a class called Anagrams that uses a dictionary to find all anagram phrases that match a
given word or phrase. You are provided with a client program AnagramMain that prompts the user for phrases and then
passes those phrases to your Anagrams object. It asks your object to print all anagrams for those phrases. Below is a
sample log of execution, wrapped into two columns (user input is underlined):
Welcome to the CSE 143 anagram solver.
Using dictionary file dict1.txt.
Phrase to scramble (Enter to quit)? barbara bush
All words found in “barbara bush”:
[abash, aura, bar, barb, brush, bus, hub, rub, shrub, sub]
Max words to include (Enter for no max)?
[abash, bar, rub]
[abash, rub, bar]
[bar, abash, rub]
[bar, rub, abash]
[rub, abash, bar]
[rub, bar, abash]
Phrase to scramble (Enter to quit)? john kerry
All words found in “john kerry”:
[he, her]
Max words to include (Enter for no max)?
Phrase to scramble (Enter to quit)? hairbrush
All words found in “hairbrush”:
[bar, briar, brush, bus, hub, huh, hush, rub, shrub, sir, sub]
Max words to include (Enter for no max)? 2
[briar, hush]
[hush, briar]
Phrase to scramble (Enter to quit)? george bush
All words found in “george bush”:
[bee, beg, bog, bogus, bough, brush, bug, bugs, bus, egg, ego,
erg, go, goes, gorge, gosh, grub, gush, he, her, here, hog,
hose, hub, hug, rub, she, shrub, shrug, sub, surge]
Max words to include (Enter for no max)? 0
[bee, go, shrug]
(continued on right)
[bee, shrug, go]
[bog, he, surge]
[bog, surge, he]
[bogus, erg, he]
[bogus, he, erg]
[bug, erg, hose]
[bug, goes, her]
[bug, her, goes]
[bug, hose, erg]
[bugs, ego, her]
[bugs, go, here]
[bugs, her, ego]
[bugs, here, go]
[bus, erg, go, he]
[bus, erg, he, go]
[bus, go, erg, he]
[bus, go, he, erg]
[bus, gorge, he]
[bus, he, erg, go]
[bus, he, go, erg]
[bus, he, gorge]
[egg, hose, rub]
[egg, rub, hose]
[ego, bugs, her]
[ego, grub, she]
[ego, her, bugs]
[ego, she, grub]
[erg, bogus, he]
[erg, bug, hose]
[erg, bus, go, he]
[erg, bus, he, go]
[erg, go, bus, he]
[erg, go, he, bus]
[erg, go, he, sub]
[erg, go, sub, he]
[erg, goes, hub]
[erg, he, bogus]
[erg, he, bus, go]
[erg, he, go, bus]
[erg, he, go, sub]
[erg, he, sub, go]
[erg, hose, bug]
[erg, hub, goes]
… (full output is on web site)
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Implementation Details:
Your Anagrams class must have the following public constructor and methods:
public Anagrams(Set dictionary)
In this constructor you should initialize a new anagram solver over the given dictionary of words. You may assume that
the words in the set are in alphabetical order. Do not modify the set passed to your constructor.
You should throw an IllegalArgumentException if the set passed is null.
public Set getWords(String phrase)
In this method you should return a set containing all words from the dictionary that can be made using some or all of the
letters in the given phrase, in alphabetical order. For example, if your anagram solver is using the dictionary
corresponding to dict1.txt and you are passed the phrase “Barbara Bush”, you should return a set containing the
elements [abash, aura, bar, barb, brush, bus, hub, rub, shrub, sub].
You should throw an IllegalArgumentException if the string is null.
public void print(String phrase)
In this method you should use recursive backtracking to find and print all anagrams that can be formed using all of the
letters of the given phrase, in the same order and format as in the example log on the previous page. For example, if your
anagram solver is using the dictionary corresponding to dict1.txt and you are passed the phrase “hairbrush”, your
method should produce the following output:
[bar, huh, sir]
[bar, sir, huh]
[briar, hush]
[huh, bar, sir]
[huh, sir, bar]
[hush, briar]
[sir, bar, huh]
[sir, huh, bar]
You should throw an IllegalArgumentException if the string is null. An empty string generates no output.
public void print(String phrase, int max)
In this method you should use recursive backtracking to find and print all anagrams that can be formed using all of the
letters of the given phrase and that include at most max words total, in the same order and format as in the example log on
the previous page. For example, if your anagram solver is using the dictionary corresponding to dict1.txt and this
method is passed a phrase of “hairbrush” and a max of 2, your method should produce the following output:
[briar, hush]
[hush, briar]
If max is 0, print all anagrams regardless of how many words they contain. For example, if using the same dictionary and
passed a phrase of “hairbrush” and a max of 0, the output is the same as that shown earlier on this page with no max.
You should throw an IllegalArgumentException if the string is null or if the max is less than 0. An empty string
generates no output.
The provided AnagramMain program calls your methods in a 1-to-1 relationship, calling getWords every time before
calling print. But you should not assume any particular order of calls by the client. Your code should still work if the
methods are called in any order, any number of times.
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Recursive Algorithm:
Generate all anagrams of a phrase using recursive backtracking. Many backtracking algorithms involve examining all
combinations of a set of choices. In this problem, the choices are the words that can be formed from the phrase. A
“decision” involves choosing a word for part of the phrase and recursively choosing words for the rest of the phrase. If
you find a collection of words that use up all of the letters in the phrase, it should be printed as output.
Part of your grade will be based on efficiency. One way to implement this program would be to consider every word in
the dictionary as a possible “choice.” However, this would lead to a massive decision tree with lots of useless paths and a
slow program. Therefore for full credit, to improve efficiency when generating anagrams for a given phrase, you must
first find the collection of words contained in that phrase and consider only those words as “choices” in your decision tree.
You should also implement the second print method so that it backtracks immediately once it exceeds the max.
The following diagram shows a partial decision tree for generating anagrams of the phrase “barbara bush”. Notice
that some paths of the recursion lead to dead ends. For example, if the recursion chooses “aura” and “barb”, the letters
remaining to use are [bhs], and no choice available uses these letters, so it is not possible to generate any anagrams
beginning with those two choices. In such a case, your code should backtrack and try the next path.
One difference between this algorithm and other backtracking algorithms is that the same word can appear more than once
in an anagram. For example, from “barbara bush” you might extract the word “bar” twice.
print(“barbara bush”);
…
choices:
[abash, aura, bar,
barb, brush, bus,
hub, rub, shrub, sub]
chosen:
[]
letters to use:
[aaabbbhrrsu]
choices:
[abash, aura, bar,
barb, brush, bus,
hub, rub, shrub, sub]
chosen:
[abash]
letters to use:
[abbrru]
choices:
[abash, aura, bar,
barb, brush, bus,
hub, rub, shrub, sub]
chosen:
[aura]
letters to use:
[abbbhrs]
…
choices:
[abash, aura, bar,
barb, brush, bus,
hub, rub, shrub, sub]
chosen:
[abash, bar]
letters to use:
[bru]
choices:
[abash, aura, bar,
barb, brush, bus, hub,
rub, shrub, sub]
chosen:
[abash, barb]
letters to use:
[ru]
choices:
[abash, aura, bar,
barb, brush, bus,
hub, rub, shrub, sub]
chosen:
[abash, bar, rub]
letters to use:
[]
Output:
[abash, bar, rub]
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LetterInventory Class:
An important aspect of simplifying the solution to many backtracking problems is the separation of recursive code from
code that manages low-level details of the problem. We have seen this in several of our backtracking examples, such as 8
queens (recursive code in Queens.java, low-level code in Board.java). You are required to follow a similar strategy
in this assignment. The low-level details for anagrams involve keeping track of letters and figuring out when one group of
letters can be formed from another. We are providing you a class called LetterInventory to help with this task.
A LetterInventory object represents the count of each letter from A-Z found in a given string (ignoring whitespace,
capitalization, or non-alphabetic characters). For example, a LetterInventory for the string “Hello there” would
keep count of 3 Es, 2 Hs, 2 Ls, 1 O, 1 R, and 1 T. The toString of this inventory would be “[eeehhllort]”.
You can add and subtract phrases from a LetterInventory and ask whether an inventory contains a phrase. For
example, adding “hi ho!” to the above inventory would produce “[eeehhhhilloort]”. Subtracting “he he he”
from this would produce “[hilloort]”. If we asked whether this inventory .contains(“tool”), the result is true.
Constructor/Method Description
public LetterInventory(String s) constructs a letter inventory for the given string
public void add(LetterInventory li)
public void add(String s)
adds the letters of the given string/inventory to this one
public boolean contains(LetterInventory li)
public boolean contains(String s)
returns true if this inventory contains all letters at least as
many times as they appear in the given string/inventory
public boolean isEmpty() returns true if the inventory contains no letters
public int size() returns the total number of letters in the inventory
public void subtract(LetterInventory li)
public void subtract(String s)
removes letters of the given string/inventory from this one;
throws IllegalArgumentException if not contained
public String toString() string version of inventory, such as “[eehhllort]”
Development Strategy and Hints:
Your print method must produce the anagrams in the same format as in the log. The easiest way to do this is to build up
your answer in a list, stack, or other collection. Then you can println the collection and it will have the right format.
The provided AnagramMain program can read its input from different dictionary files. It is initially set to use a very
small dictionary dict1.txt to make testing easier. But once your code works with this dictionary, you should test it
with larger dictionaries such as the provided dict2.txt and dict3.txt. You can find other larger dictionaries here:
• http://www.puzzlers.org/dokuwiki/doku.php?id=solving:wordlists:start
One difficult part of this program is the second version of print that limits the number of words that can appear in the
anagrams. We suggest you do this part last, initially printing all anagrams regardless of the number of words.
Style Guidelines and Grading:
Part of your grade will come from appropriately utilizing recursive backtracking to implement your algorithm as
described previously. We will also grade on the elegance of your recursive algorithm; don’t create special cases in your
recursive code if they are not necessary or repeat cases already handled. Redundancy is another major grading focus;
some methods are similar in behavior or based off of each other’s behavior. You should avoid repeated logic as much as
possible. Your class may have other methods besides those specified, but any other methods you add should be private.
You should follow good general style guidelines such as: making fields private and avoiding unnecessary fields;
declaring collection variables using interface types; appropriately using control structures like loops and if/else;
properly using indentation, good variable names and types; and not having any lines of code longer than 100 characters.
Comment your code descriptively in your own words at the top of your class, each method, and on complex sections of
your code. Comments should explain each method’s behavior, parameters, return, pre/post-conditions, and exceptions.
For reference, our solution is around 85 lines long including comments and blank lines (36 “substantive” lines).
