Images from Codex Seraphinianus by Serafini

The title of this assignment pays homage to Luigi Serafini, author of a book called the Codex Seraphinianus. The codex is filled with pseudo-scientific writing and figures like the above images, all of which are believed to be purely the product of Serafini's imagination. Two hallmarks of Serafini's work are morphings—many objects in the codex change from one to another—and random writing.

As such, this assignment consists of two parts (A) Word Ladders, where you find ways to morph one word into another, and (B) Random Writer, where your program stochastically (i.e. randomly) generates text. Each part can be programmed separately, but they should be submitted together. Part (B) is on average more difficult than part (A). Your output should match exactly as much as possible (e.g. randomization for RandomWriter is acceptable, as are different word ladders of the same length as the sample output, assuming they are valid). The starter code for this project is available as a ZIP archive (this contains 2 separate QT projects, one for each part of this assignment):

Starter Code

Due Date: Thurs., April 19th at 12:00pm (noon) PST.

Turn in only the following files:

  1. wordladder.cpp, the C++ code for the Part A Word Ladder program (including a main function)
  2. ngrams.cpp, the C++ code for the Part B N-grams program (including a main function)
  3. myinput.txt, your own unique Part B input file representing text to read in as your program's input

This is a not a pair assignment. You must work on your code alone, although as always you are allowed to talk about the problems with other students, on Piazza, in LaIR, office hours, etc.

YEAH (Your Early Assignment Help) Resources

Slides from the video are available here. The video is available on Canvas here. If you are already logged into Canvas, the video can be viewed directly in the embed below.

Part A: Word Ladder

A word ladder is a bridge from one word to another, formed by changing one letter at a time, with the constraint that at each step the sequence of letters still forms a valid word. For example, here is a word ladder connecting the word "code" to the word "data". Each changed letter is underlined as an illustration:


There are many other word ladders that connect these two words, but this one is the shortest path between them. That is, there might be others of the same length, but none with fewer steps than this one.

In the first part of this assignment, write a program that repeatedly prompts the user for two words and finds a minimum-length ladder linking the words. You must use the Stack and Queue collections from Chapter 5, along with following a particular provided algorithm to find the shortest word ladder.

Example Run:

Here is an example log of interaction between your program and the user (with console input in red):

Welcome to CS 106B Word Ladder.
Please give me two English words, and I will change the
first into the second by changing one letter at a time.

Dictionary file name? dictionary.txt

Word #1 (or Enter to quit): code 
Word #2 (or Enter to quit): data 
A ladder from data back to code: 
data date cate cade code

Word #1 (or Enter to quit):
Have a nice day.

Notice that the word ladder prints out in reverse order, from the second word back to the first. If there are multiple valid word ladders of the same length between a given starting and ending word, your program can choose any of them. In this example, it would be fine for your program to choose any ladder of length 5, as that is the minimum length in this case.

Your code should ignore case; in other words, the user should be able to type uppercase, lowercase, mixed case, etc. words and the ladders should still be found and displayed in lowercase. You should also check for several kinds of user input errors, and not assume that the user will type valid input. Specifically, you should check that both words typed by the user are valid words found in the dictionary, that they are the same length, and that they are not the same word. If you receive invalid input, your program should print an error message and re-prompt the user. See the example output for examples.

Before the program can actually calculate a word ladder, it needs to first read in a dictionary of all english words. At the start, your program should prompt the user to enter a dictionary file name to use as the source of the English words. If the user types a filename that does not exist, reprompt them - see the example output for examples. We provide a file dictionary.txt for you to use, with one word per line (there are also smaller dictionary files included to help with testing). Read the dictionary file just once at the start of your program into a Lexicon. A Lexicon is another Stanford Library collection that can very efficiently store dictionaries of words (the runtime of many common single-word operations is O(W), where W is the length of the word). Please see the Lexicon class reference for details. Once you read in the dictionary of words into the Lexicon, you can use the contains() method to check if a word is in the dictionary. You should not loop over the dictionary as part of solving this problem.


Finding a word ladder is a specific instance of what is known as a shortest-path problem: a problem in which we try to find the shortest possible route from a given start to a given end point. Shortest-path problems come up in routing Internet packets, comparing gene mutations, Google Maps, and many other domains. The strategy we will use for finding the shortest path between our start and end words is called breadth-first search ("BFS"). This is a search process that gradually expands the set of paths among which we search “outwards:” BFS first considers all possible paths that are one step away from the starting point, then all possible paths two steps away, and so on, until a path is found connecting the start and end point. A step can be understood as one unit of measurement—depending on the problem, this could be a millisecond, a minute, a mile, a subway stop, and so on. By exploring all possible paths of a given length before incrementing to the next length, BFS guarantees that the first solution you find will be the shortest possible.

For word ladders, start by examining ladders that contain only words that are one “step” away from the starting word—i.e., words in which only one letter has been changed. If you find your ending word among these one-step-away ladders, congratulations—you’re done! If not, look for your target word in all ladders containing words that are two steps away, i.e., ladders in which two letters have been changed. Then check three letters, four, etc., until your target word is located. We implement the breadth-first algorithm using a Queue that stores partial ladders, each of which represents a possibility that we will examine in turn to see if it is a complete path between our start and ends words. Each partial ladder is represented as a Stack, which means that your overall collection will be a Queue of Stacks.

Here is a partial pseudocode description of the algorithm to solve the word-ladder problem. Note: some students complain at this point that we have given you too much information and that they want to figure the problem out on their own — if so, great! Don’t look at the pseudocode below if you want to try it on your own!

Finding a word ladder between words w1 and w2:
	Create an empty queue of stacks.

	Create/add a stack containing {w1} to the queue. 
	While the queue is not empty:

		Dequeue the partial-ladder stack from the front of the queue.

		For each valid English "neighbor" word (differs by 1 letter) 
		of the word on top of the stack:
			If that neighbor word has not already been used
			in a ladder before:
				If the neighbor word is w2:
					Hooray! we have found a solution (and it is the stack
					you are working on in the queue).
					Create a copy of the current partial-ladder stack.
					Put the neighbor word on top of the copy stack. 
					Add the copy stack to the end of the queue.

Some of the pseudo-code corresponds almost one-to-one with actual C++ code. Other parts are more abstract, such as the instruction to examine each "neighbor" of a given word. A neighbor of a given word w is a word of the same length as w that differs by exactly 1 letter from w. For example, “date” and “data” are neighbors; “dog” and “bog” are neighbors.

Your solution is not allowed to look for neighbors by looping over the dictionary every time; this is much too inefficient. To find all neighbors of a given word, use two nested loops: one that goes through each character index in the word, and one that loops through the letters of the alphabet from a-z, replacing the character in that index position with each of the 26 letters in turn. For example, when examining neighbors of “date”, you'd try:

  • aate,bate,cate,...,zateall possible neighbors where only the 1st letter is changed.
  • date,dbte,dcte,...,dzteall possible neighbors where only the 2nd letter is changed.
  • ...
  • data,datb,datc,...,datzall possible neighbors where only the 4th letter is changed.

Note that many of the possible letter combinations along the way (aate, dbte, datz, etc.) are not valid English words. Your algorithm has access to an English dictionary, and each time you generate a word using this looping process, you should look it up in the dictionary to make sure that it is actually a legal English word. Only valid English words should be included in your group of neighbors.

Another way of visualizing the search for neighboring words is to think of each letter index in the word as being a "spinner" that you can spin up and down to try all values A-Z for that letter. The diagram below tries to depict this:

Another subtle issue is that you should not reuse words that have been included in a previous, shorter ladder. For example, suppose that you have the partial ladder cat → cot → cog in your queue. Later on, if your code is processing the ladder cat → cot → con, one neighbor of con is cog, so you might want to examine cat → cot → con → cog. But doing so is unnecessary. If there is a word ladder that begins with these four words, then there must be a shorter one that, in effect, cuts out the middleman by eliminating the unnecessary word con. As soon as you've enqueued a ladder ending with a specific word, you've found a minimum-length path from the starting word to the end word in that ladder, so you never have to enqueue that end word again.

To implement this strategy, keep track of the set of words that have already been used in any ladder. Ignore those words if they come up again. Keeping track of which words you've used also eliminates the possibility of getting trapped in an infinite loop by building a circular ladder, such as cat → cot → cog → bog → bag → bat → cat.

A final tip: it may be helpful to test your program on smaller dictionary files first to find bugs or issues related to your dictionary or to word searching.

Part B: Random Writer

In the second part of this assignment, you will write a program that takes in a text file and then (randomly) generates new text in the same style. In effect, your program will automate an exercise that writers have used for centuries to improve their style: imitating another writer. Benjamin Franklin, for example, wrote in his autobiography that he taught himself to write elegantly by trying to re-write passages from The Spectator (a popular 18th-century magazine) in the same style. In the 20th century, the writer Raymond Queneau featured the practice of trying to imitate the voice of other writers prominently among his famous "Exercises in Style.". A more recent computational style imitator is the postmodern essay generator, created in 1996; hit refresh a few times to see what it can do.

Your program will accomplish the task of imitating a text’s style by building and relying on a large data structure of word groups called "N-grams." A collection of N-grams will serve as the basis for your program to randomly generate new text that sounds like it came from the same author as your input file; your program will also use the Map and Vector collections from Chapter 5.

Below is an example log of interaction between your program and the user (console input in red).

Welcome to CS 106B Random Writer ('N-Grams').
This program makes random text based on a document. 
Give me an input file and an 'N' value for groups 
of words, and I'll create random text for you.

Input file name? hamlet.txt 
Value of N? 3

# of random words to generate (0 to quit)? 40
... chapel. Ham. Do not believe his tenders, as you 
go to this fellow. Whose grave's this, sirrah? 
Clown. Mine, sir. [Sings] O, a pit of clay for to 
the King that's dead. Mar. Thou art a scholar; speak 
to it. ...

# of random words to generate (0 to quit)? 20
... a foul disease, To keep itself from noyance; but 
much more handsome than fine. One speech in't I 
chiefly lov'd. ...

# of random words to generate (0 to quit)? 0 

Key Idea: N-Grams

But what, you may ask, is an N-gram? The "Infinite Monkey Theorem" states that an infinite number of monkeys typing random keys forever would eventually produce the works of William Shakespeare. (See here.) That's silly, but could a monkey randomly produce a new work that sounded like Shakespeare's works, with similar vocabulary, sentence structure, punctuation, etc.? What if we chose words at random, instead of individual letters? Suppose that rather than each word having an equal probability of being chosen, we weighted the probability based on how often that word appeared in Shakespeare's works?

Picking random words would likely produce gibberish, but let's look at chains of two words in a row. For example, perhaps Shakespeare uses the word "to" 10 times total, and 7 of those occurrences are followed by "be", 1 time by "go", and 2 times by "eat". We can use those ratios when choosing the next word. If the last word we chose is "to", randomly choose "be" next 7/10 of the time, "go" 1/10 of the time, and "eat" 2/10 of the time. We never choose any other word to follow "to". We call a chain of two words like this, such as "to be", a 2-gram. Here’s an example sentence produced by linking together a sequence of 2-grams:

Go, get you have seen, and now he makes as itself? (2-gram)

A sentence of 2-grams tends to not make any sense (or even be grammatically correct), so let’s consider chains of 3 words (3-grams). If we chose the words "to be", what word should follow? If we had a collection of all sequences of 3 words-in-a-row, together with their probabilities, we could make a weighted random choice. If Shakespeare uses "to be" 22 times and follows them with "or" 5 times, "in" 3 times, "with" 10 times, and "alone" 4 times, we could use these weights to randomly choose the next word. So now the algorithm would pick the third word based on the first two, and the fourth based on the second+third, and so on. Here’s a sample sentence produced by linking 3-grams together:

One woe doth tread upon another's heel, so fast they follow. (3-gram)

We can generalize this idea from 2- or 3-grams to N-grams for any integer N. If you make a collection of all groups of N-1 words along with their possible following words, you can use this to select an Nth word given the preceding N-1 words. The higher your choice of N, the more similar the new random text will be to the original data source. Here is a random sentence generated from 5-grams of Hamlet:

I cannot live to hear the news from England, But I do prophesy th'election lights on Fortinbras. (5-gram)

As you can see, the text is now starting to sound a lot like the original. Each particular piece of text randomly generated in this way is also called a Markov chain. Markov chains are very useful in computer science and elsewhere, such as artificial intelligence, machine learning, economics, and statistics.

See the sample output files for more examples.

Step 1: Building Map of N-Grams

Your program will read the input file one word at a time and build a specific kind of compound collection, namely, a map from each (N-1)-gram in your input text to all of the words that occur directly after it in the input. For example, if you are building sentences out of 3-grams, that is, N-grams for N=3, then your code should examine each sequence of 2 words and keep track of which third word directly follows it each time it occurs. So if you are using 3-grams and the pair of words "to be" is followed by "or" twice and "just" once, your collection should map the key {to, be} to the value {or, just, or}. We might think of these (N-1)-grams as “prefixes” and the words that follow them as various possible “suffixes.” Using this terminology, your map should be built so that it connects a collection of each prefix sequence (of N-1 words) to another collection of all possible suffixes (all Nth words that follow the prefix in the original text).

The following figure illustrates the map you should build from the input file. As this figure shows, when reading the input file, you should keep track of a window of N-1 words at all times. As you read each word from the file, you should insert the previous window as a key in your collection of prefixes, with the newly-read word, the current suffix, as one of its corresponding values. (Remember that your collection of suffixes must be able to contain multiple occurrences of the same word—such as "or" occurring twice after the prefix {to, be}—otherwise, your collection will not have the word-frequency information needed to weight your probabilities.) Then, discard the first word from the window, append the new word to the window, and repeat. The map is thus built over time as you read each new word:

File Location Data
to be | or not to be just ...
map    = {}
window = {to, be}
to be or | not to be just ...
map    = { {to, be} : {or} }
window = {be, or}
to be or not | to be just ...
map    = { {to, be} : {or},
		   {be, or} : {not} }
window = {or, not}
to be or not to | be just ...
map    = { {to, be} : {or},
		   {be, or} : {not},
		   {or, not} : {to} }
window = {not, to}
to be or not to be | just ...
map    = { {to, be} : {or},
		   {be, or} : {not},
		   {or, not} : {to},
		   {not, to} : {be} }
window = {to, be}
to be or not to be just | ...
map    = { {to, be} : {or, just},
		   {be, or} : {not},
		   {or, not} : {to},
		   {not, to} : {be} }
window = {be, just}
to be or not to be just
be who you want to be
or not okay you want okay|
map    = { {to, be} : {or, just, or},
		   {be, or} : {not, not}, 
		   {or, not} : {to, okay},
		   {not, to} : {be}, 
		   {be, just} : {be}, 
		   {just, be} : {who}, 
		   {be, who} : {you}, 
		   {who, you} : {want}, 
		   {you, want} : {to, okay}, 
		   {want, to} : {be}, 
		   {not, okay} : {you}, 
		   {okay, you} : {want}, 
		   {want, okay} : {to},
		   {okay, to} : {be} }

Note that the order of sequences matters: for example, the prefix {you, are} is different from the prefix {are, you}. Also notice that the map wraps around. For example, if you are computing 3-grams like in the above example, perform 2 more iterations to connect the last 2 prefixes at the end of the file to the first 2 words at the start of the file. In our example above, this leads to {want, okay} connecting to "to" and {okay, to} connecting to "be". If we were doing 5-grams, we would perform 4 more iterations and connect the last 4 prefixes to the first 4 words in the file, and so on. This will be very useful for your algorithm later on in the program.

Note that you should not change case or strip punctuation of words as you read them. The casing and punctuation turns out to help the sentences start and end in a more authentic way. Just store the words in the map as you read them.

To read in a file word by word (instead of line by line, as getline does), you can use the following syntax:

ifstream stream;
... // initialize stream somehow
string word;
while (stream >> word) {
	// each time through this loop, word is the next word in the file

You can also read in a single word using the following syntax:

ifstream stream;
... // initialize stream somehow
string word;
stream >> word;

Step 2: Generating Random Text

To generate random text from your map of N-grams, first choose a random starting point for the document. To do this, randomly chose a key from your map - you can use the map's keys() member function, which returns a Vector containing all of the keys in the map. (For randomness in general, #include "random.h" and call the global function randomInteger(min, max). where min and max are inclusive). Remember that each key is prefix, a collection of N-1 words. Those N-1 words will form the start of your random text, and will be the first sequence in your sliding "window" as you create your text.

For all subsequent words, use your map to look up all possible prefixes that can follow the current N-1 words, and randomly choose one according to their appropriately-weighted probabilities. If you have built your map the way we described above, as a map from {prefix} → {suffixes}, this simply amounts to choosing one of the possible suffix words at random. Once you have chose your random suffix word, slide your current window of N-1 words by discarding the first word in the window and appending the new suffix, and repeat the process.

Since your random text is unlikely to start and end at the proper beginning or end of a sentence, just preface and conclude your random text with "..." to indicate this. Here is another partial log of execution:

Input file? tiny.txt
Value of N? 3
# of random words to generate (0 to quit)? 16
... who you want okay to be who you want to be or not to be or ...

Your code should check for several kinds of user input errors, and not assume that the user will type valid input. Specifically, re-prompt the user if they type the name of a file that does not exist. Also re-prompt the user if they type a value for N that is not an integer, or is an integer less than 2 (a 2-gram has prefixes of length 1; but a 1-gram is essentially just choosing random words from the file and is uninteresting for our purposes). When prompting the user for the number of words to randomly generate, re-prompt them if the number of random words to generate is not at least N. You may assume that the value the user types for N is not greater than the number of words found in the file. See the sample output files for examples of proper program output for various cases.

Creative Aspect: myinput.txt

Along with your program, submit a file myinput.txt that contains text that can be used as input for Part B. This can be anything you want, as long as it is non-empty and is something you gathered yourself (not just a copy of an existing input file). For example, if you like a particular band, you could paste several of their songs into a text file, which leads to funny new songs when you run your N-grams program on this data. Or gather the text of a book you really like, or poems, or anything you want. This is meant to give you a chance to play around with the creative power of your program, and is worth a small part of your grade on the assignment.

Development Strategy and Hints

This program can be tricky if you don't develop and debug it step-by-step. Don't try to write everything all at once. Make sure to test each part of the algorithm before you move on.

  1. Think about exactly what types of collections to use for each part. Are duplicates allowed? Does order matter? Do you need random access? Where will you add/remove elements? Etc. Note that some parts of each program require you to make compound collections, that is, a collection of collections.
  2. Refer to the Stanford Library Documentation! This page documents all methods on Stanford Library collections.
  3. Test each function with a very small input first. For example, use input file tiny.txt with a small number of words; this will let you print your entire map and examine its contents for debugging purposes.
  4. Recall that you can print the contents of any collection to cout and examine its contents for debugging.
  5. Remember that when you assign one collection to another using the = operator, it makes a full copy of the entire contents of the collection. This could be useful if you want to copy a collection.
  6. You can loop over the elements of a vector or set using a for-each loop. A for-each also works on a map, iterating over the keys in the map. You can look up each associated value based on the key in the loop.
  7. Don't forget to test your input on unusual inputs, like large and small values of N, large /small # of words to generate, large and small input files, and so on. It's hard to verify random input, but you can look in smallish input files to verify that a given word really does follow a given prefix from your map.

Possible Extra Features

That's all! You are done. Consider adding extra features to one or both of these programs. Note that since we use automated testing for part of our grading process, it is important that you submit a program that conforms to the preceding assignment spec, even if you do extra features. You should submit two versions of your program for extensions: the provided one without any extra features added, and a second one with extra features. Please distinguish them by explaining which is which in the comment header. In the comment header, please also list all extra features that you worked on and where in the code they can be found (what functions, lines, etc. so that the grader can look at their code easily).