CS111 Spring 2003 Problem Set 7

CS111, Wellesley College, Spring 2003

Problem Set 7

Due on Tuesday, April 1 (No fooling!)

Reading

Diagramming List Recursions
IntList Contract
StringList Contract
String Contract
Study the code in the file IntListOps.java within the lec15_intlists folder.
Study the code in the file StringListOps.java within the ps7_programs/Unjumbler folder.
Study the code in the file Lab8Ops.java within the ps7_programs/Unjumbler folder.

About this Problem Set

The purpose of this problem set is to give you a better understanding of lists via drawing box-and-pointer diagrams and writing recursive list methods. Task 1 is a pencil-and-paper problem in which you will draw an invocation tree for a recursive function that manipulates integer lists. In Task 2, you will write several methods that manipulate lists of strings as part of implementing an "unjumbling assistant" that will help you solve "word jumble" problems. The code for Task 2 is available in the ps7_programs folder in the cs111 download directory.

How to turn in this Problem Set

You are required to turn in both a hardcopy and a softcopy. For general guidelines on problem set submission, including how to submit a softcopy and how to check if you softcopy submission was successful, click here. Please make sure to keep a copy of your work, either on a zip disk, or in your private directory (or, to play it safe, both).

Hardcopy Submission

Your hardcopy packet should consist of:

The cover page;
Your invocation tree and box-and-pointer diagram from Task 1;
Your modified Unjumbler.java file from Task 2.

Staple these together, and slide the packet under the door of Elena's office (E127, in minifocus).

Softcopy Submission

Save the modified Unjumbler.java files in the Unjumbler folder of ps7_programs. Submit your final Unjumbler folder to your drop folder on the cs111 server. Submit only your Unjumbler folder. Do not submit the dicts folder or the UnjumblerTest folder. (These folders are very big and will eat up your disk quota.)

Task 1: Box-and-Pointer Diagrams

Be sure to read the notes on Diagramming List Recursions before attempting this problem.

Suppose that the following methods are defined in a subclass of the IntList class:

public static IntList F (IntList L) {
  return tail(G(0, L));
}
    
public static IntList G (int n, IntList L) {
     if (isEmpty(L)) {
       return prepend(0, L);
  } else {
    IntList subResult = G(n + head(L), tail(L));
    return prepend(head(L) + head(subResult),
                    prepend(head(L) * (n + head(subResult)),
                            tail(subResult)));
  }
}

Suppose that L2 is an integer list whose printed representation is [1,2,3,4]. Draw a combined invocation tree/box-and-pointer diagram that illustrates the invocation F(L2). In your diagram, follow the notational conventions used in the reverse() and appendTails() examples in the notes on Diagramming List Recursions. In your invocation tree, you only need to show invocation nodes for the F and G methods. In your box-and-pointer diagram, you should show all the list nodes of the given list L2, as well as any new list nodes that are created during the execution of F(L2).

Task 2: Word Unjumbler

Overview

Word Jumble is a popular game that appears in many newspapers. There is now even an on-line version of Word Jumble. You may want to play this game a few times before continuing with the assignment.

The game involves "unjumbling" English words whose letters have been reordered. For instance, the jumbled word ytikt can be unjumbled to kitty. The game can be challenging; even relatively short jumbles can be tricky to unjumble. For instance, here are the words that appeared on the March 26, 2003, version of the on-line game; can you unjumble them?:

sweny, puter, nylarx, caupte, nseuaxec

(The last string unjumbles into two words.)

In this problem, you will create a Java program that acts as an "unjumbling assistant". Given a string, your program will first generate all possible reorderings of the letters in the string. Such reorderings are called permutations. For example, there are six reorderings of the letters in the string tra:

[tra,rta,rat,tar,atr,art]

In general, a string with n distinct letters has n! (pronounced "n factorial") permutations. For instance, a 4-letter string has 4! = 24 permutations, a 5-letter string has 5! = 120 permutations, a 6-letter string has 6! = 720 permutations, and so on.

Next, the assistant will determine which of the permutations is an English word by looking them up in a "dictionary". You do not have to worry about how to construct such a dictionary; this has been done for you. Notes on how to use the dictionary as a "black box" can be found later in this problem description. In the case of "tra", filtering out the English words leaves:

[rat,tar,art]

When the string you are unjumbling contains duplicate letters, it turns out that a simple permutations generator will yield some duplicate permutations. For instance, the permutations of "dda" will generate the 3! = 6 permutations:

[dda,dda,dad,dad,add,add]

Filtering out the English words yields:

[dad,dad,add,add]

In such cases, the unjumbling assistant should also filter out duplicates to yield the final list:

[dad,add]

To get a feel for what the unjumbling assistant does, you should experiment with the working unjumbler test program in the folder UnjumblerTest within the ps7_programs folder. You can use the program to help you solve the on-line Word Jumble puzzles!

Your Task

Your task is to create your own unjumbler program, mostly from scratch. To do this, "all" you need to do is to write definitions for the nine class methods specified below.

Here are some things you need to know:

Unlike in previous assignments, you are not given skeleton method declarations that you will flesh out. Instead, you must write all of your method declarations from scratch. Write all of your definitions within the Unjumbler class in the file Unjumbler.java within the folder Unjumbler of the ps7_programs folder. Carefully read the comments at the top of the Unjumbler.java; these tell you which class methods you can use in the file without an explicit class name as a prefix.
Unlike most previous programming assignments, which were Java applets, this assignment is a Java application. Code that you want to be executed when you run the program must be in the main method of Unjumbler.java. On a Mac, you must be sure to quit out of any previous MRJ applications before attempting to run your program again.
Unlike in previous assignments, you are not provided with test cases for your methods. You are required to write your own testing code for this assignment. You should test each of your methods by adding appropriate testing code to the main method of the Unjumbler class, just as you did in Lab 8. Recall that the fromString class method for the StringList is a very convenient way to generate a string list. For instance fromString("[I,am,Sam]") yields a three element list containing the strings "I", "am", and "Sam".
In many cases below, you will need a working version of one or more of the earlier methods to write a later method. In order to remove the dependency between the different methods, we have provided you with a class named UnjumblerAnswers that contains working versions of each of the nine methods. If you don't have a working method meth1, but need meth1 to define meth2, you can use UnjumblerAnswers.meth1 within your definition of meth2. This allows you to work on the nine methods below in any order, while still being able to test each method along the way.

public static StringList remove (String s, StringList L)
Returns a new list in which all occurrences of s in L have been removed. The other strings in the list should have the same relative order in the resulting list as in the given list.
Examples:
remove("I", fromString("[I,know,that,I,said,that,I,did]")))
      returns the string list [know,that,said,that,did].

remove("that", fromString("[I,know,that,I,said,that,I,did]"))
      returns the string list [I,know,I,said,I,did].

remove("said", fromString("[I,know,that,I,said,that,I,did]"))
      returns the string list [I,know,that,I,that,I,did].

remove("you", fromString("[I,know,that,I,said,that,I,did]"))
      returns the string list [I,know,that,I,said,that,I,did].

Note: Use the equals instance method from the String class to compare two strings. For instance, "cat".equals("cat") returns true but "cat".equals("dog") returns false. You should not use == to compare two strings because it may not return what you expect. For instance, while "cat" == "dog" is guaranteed to return false, "cat" == "cat" and "cat" == ("c" + "at") are not guaranteed to return true. They may return true in some implementations and some circumstances, but you cannot rely on this behavior.
public static StringList removeDuplicates (StringList L)
Returns a list containing each string in L exactly once. The order of the elements in the returned list should be the relative order of the first occurrence of each element in L.
Examples:
removeDuplicates(fromString("[I,know,that,I,said,that,I,did]"))
      returns the string list [I,know,that,said,did].

removeDuplicates(fromString("[you,say,what,you,mean,and,mean,what,you,say]"))
      returns the string list [you,say,what,mean,and].

removeDuplicates(fromString("[lists,are,cool]"))
      returns the string list [lists,are,cool].

Note: The remove method from above is helpful here!
public static StringList mapConcat (String s, StringList L)
Given a list L with n strings, returns a new list with n strings in which the ith string of the resulting list is the result of concatenating s to the ith element of L.
Examples:
mapConcat("com", fromString("[puter,plain,municate,pile]"))
returns the string list [computer,complain,communicate,compile].

mapConcat("I ", fromString("[came,saw,conquered]"))
returns the string list [I came,I saw,I conquered].
public static StringList insertions (String s1, String s2)
Given two strings s1 and s2, where s2 has n characters, returns a list of n + 1 strings that result from inserting s1 at all possible positions within s2, from left to right.
Examples:
insertions("*", "split")
      returns the string list [*split,s*plit,sp*lit,spl*it,spli*t,split*]

insertions("a", "bcd")
      returns the string list [abcd,bacd,bcad,bcda]

insertions("com", "[pile]")
      returns the string list [compile,pcomile,picomle,pilcome,pilecom]

insertions("abc", "")
      returns the string list [abc]

Note: The Lab8Ops class contains two helper methods that are useful for defining insertions:
1. public static String first (String s)
  Returns a string consisting of the first character of s. For example, first("computer") returns the string "c".
2. public static String butFirst (String s)
  Returns a string consisting of all but the first character of s. For example, butFirst("computer") returns the string "omputer".
public static StringList insertionsList (String s, StringList L)
Returns a list that contains all the strings that result from inserting s at all possible positions in all the strings of L.
Examples:
insertionsList("a", fromString("[bc,cb]"))
      returns the string list [abc,bac,bca,acb,cab,cba]

insertionsList("*", fromString"[I,am,Sam]"])
      returns the string list [*I,I*,*am,a*m,am*,*Sam,S*am,Sa*m,Sam*]

insertionsList("abc", fromString("[]"))
      returns the string list []

Note: The StringListOps class contains a helper method append that is useful for defining insertionsList:
public static StringList append (StringList L1, StringList L2)
Returns a new string list containing all the elements of L1 followed by all of the elements of L2. For example,
- append(fromString("[I,do]"), fromString("[not,like,green,eggs]")) returns [I,do,not,like,green,eggs]
- append(fromString("[I,do]"), fromString("[]")) returns [I,do]
- append(fromString("[]"), fromString("[not,like,green,eggs]")) returns [not,like,green,eggs]
public static StringList permutations (String s)
Returns a list of all permutations of the string s. A permutation of a string s is any string that is formed by reordering the letters in the string s (without duplicating or deleting any letters). For a string with n distinct characters, there are exactly n! (i.e., "n factorial") permutations. If some characters in s are repeated, there are still n! permutations, but the permutations contain duplicates. The elements in the list returned by permutations may be in any order.
Examples:
permutations("a") returns the string list [a].

permutations("ab") returns the string list [ab,ba] or the string list [ba,ab].

permutations("abc") returns (any permutation of) the string list [abc,bac,bca,acb,cab,cba].

permutations("abcd") returns (any permutation of) the string list
```
      [abcd,bacd,bcad,bcda,
       acbd,cabd,cbad,cbda,
       acdb,cadb,cdab,cdba
       abdc,badc,bdac,bdca,
       adbc,dabc,dbac,dbca,
       adcb,dacb,dcab,dcba].
```
permutations("121") returns (any permutation of) the string list [121,211,211,112,112,121]. Note that when the given string contains duplicate characters, the permutation list will contain duplicates.

permutations("1231") returns (any permutation of) the string list
```
      [1231,2131,2311,2311,
       1321,3121,3211,3211,
       1312,3112,3112,3121,
       1213,2113,2113,2131,
       1123,1123,1213,1231,
       1132,1132,1312,1321].
```
Note: There are many ways to define the permutations method, but a particularly elegant way uses the first, butFirst, and insertionsList methods from above. Be very careful in defining your base case!
public static StringList filterWords (StringList L)
Returns a list of all strings in L that are English words. The resulting strings should be in the same relative order as in L.
Examples:
filterWords(fromString("[the,dog,barked,at,the,cat]")) returns the string list [the,dog,barked,at,the,cat].

filterWords(fromString("[the,dog,barkd,ate,hte,cat]")) returns the string list [the,dog,ate,cat].

filterWords(fromString("[tra,rta,rat,tar,atr,art]")) returns the string list [rat,tar,art].

Note: To determine if a string is an English word, you should use the class method isWord that is already defined for you in the Unjumbler class:
public static boolean isWord (String s)
Returns true if s is a word in the default English dictionary, and false otherwise.

The default dictionary (which can be changed within the Unjumbler class) contains 22641 English words (all lower case, no proper nouns) of up to 8 characters in length. It is not a "perfect" dictionary: there are some perfectly acceptable English words that are not in the dictionary.
You can change the default dictionary to one that contains 45425 English words without a length restriction, but this takes longer to load. For details on how to do this, see the comments near the end of Unjumbler.java.
public static StringList unjumble (String s)
Returns a list of all the permutations of s that are English words (as determined by the default dictionary). The order of elements in the resulting list does not matter, but each word in the resulting list should listed only once.
Examples:
unjumble("tra") returns the string list [rat,tar,art].

unjumble("tras") returns the string list [rats,arts,star]
(the default dictionary doesn't recognize tars or tsar as words).

unjumble("argle") returns the string list [glare,large,lager,regal].

unjumble("sbso") returns the string list [sobs,boss].

unjumble("xzzy") returns the string list [].

Note: You should only remove duplicates after performing filterWords. It turns out that performing removeDuplicates on a large lists (such as the output of permutations) can take a very long time. (To understand why this is so, take CS230!)
public static void unjumbleInteractively()
Launches an interactive session in the Java Console that repeatedly prompts the user for a string and displays the list of unjumbled English words for that string. The interactive session ends when the user enters the empty string.
Example: Below is a sample session of unjumbleInteractively(). The text typed by the program is in italics, while the text typed by the user is in bold:
Enter a string to unjumble and press Return (enter the empty string to quit): argle Constructing dictionary from file ../dicts/dict8.txt. This may take a little while... Done! Dictionary constructed with 22641 words. [glare,large,lager,regal] Enter a string to unjumble and press Return (enter the empty string to quit): eshou [house] Enter a string to unjumble and press Return (enter the empty string to quit): sbos [boss,sobs] Enter a string to unjumble and press Return (enter the empty string to quit): Thank you for using the unjumbler!

Notes:
- To read input from the Java Console, use the following class method from the Stdin class:
  public static String readLine (String s)
  Displays the prompt s in the Java Console window, and waits for the user to type a line of text. When the user presses the return key, returns the line of text that has been typed as a string.
- In the above example, the following text is automatically displayed when the dictionary is loaded, which automatically happens when the isWord method is invoked for the first time.
  Constructing dictionary from file ../dicts/dict8.txt. This may take a little while... Done! Dictionary constructed with 22641 words.