case_study_word_play.md

Case study: word play

This chapter presents the second case study, which involves solving word puzzles by searching for words that have certain properties. For example, we’ll find the longest palindromes in English and search for words whose letters appear in alphabetical order. And I will present another program development plan: reduction to a previously solved problem.

Reading word lists

For the exercises in this chapter we need a list of English words. There are lots of word lists available on the Web, but the one most suitable for our purpose is one of the word lists collected and contributed to the public domain by Grady Ward as part of the Moby lexicon project (see https://wikipedia.org/wiki/Moby_Project). It is a list of 113,809 official crosswords; that is, words that are considered valid in crossword puzzles and other word games. In the Moby collection, the filename is 113809of.fic; you can download a copy from https://www.gutenberg.org/files/3201/files/CROSSWD.TXT. For this chapter, the file is renamed as words.txt and DOS style line endings have been converted to UNIX style (use dos2unix command if available or use: sed 's/\r$//').

This file is in plain text, so you can open it with a text editor, but you can also read it from Ruby. The File class method open takes the name of the file as a parameter and returns a File object you can use to read the file.

>> fin = File.open('words.txt')
=> #<File:words.txt>

fin is a common name for a file object used for input. The file object provides several methods for reading, including readline, which reads characters from the file until it gets to a newline and returns the result as a string:

>> fin.readline
=> "aa\n"

The first word in this particular list is “aa”, which is a kind of lava. The sequence \n represents the newline character that separates this word from the next.

The file object keeps track of where it is in the file, so if you call readline again, you get the next word:

>> fin.readline
=> "aah\n"

The next word is “aah”, which is a perfectly legitimate word, so stop looking at me like that. Or, if it’s the newline character that’s bothering you, we can get rid of it with the string method strip:

>> line = fin.readline
=> "aahed\n"
>> word = line.strip
=> "aahed"

You can also use a file object as part of a for loop. This program reads words.txt and prints each word, one per line:

fin = File.open('words.txt')
for line in fin
  word = line.strip
  puts word
end

Exercises

There are solutions to these exercises in the next section. You should at least attempt each one before you read the solutions.

Exercise 1
Write a program that reads words.txt and prints only the words with more than 20 characters (not counting whitespace).

Exercise 2
In 1939 Ernest Vincent Wright published a 50,000 word novel called Gadsby that does not contain the letter “e”. Since “e” is the most common letter in English, that’s not easy to do.

In fact, it is difficult to construct a solitary thought without using that most common symbol. It is slow going at first, but with caution and hours of training you can gradually gain facility.

All right, I’ll stop now.

Write a method called no_e? that returns true if the given word doesn’t have the letter “e” in it.

Modify your program from the previous section to print only the words that have no “e” and compute the percentage of the words in the list that have no “e”.

Exercise 3
Write a method named avoids? that takes a word and a string of forbidden letters, and that returns true if the word doesn’t use any of the forbidden letters.

Modify your program to prompt the user to enter a string of forbidden letters and then print the number of words that don’t contain any of them. Can you find a combination of 5 forbidden letters that excludes the smallest number of words?

Exercise 4
Write a method named uses_only? that takes a word and a string of letters, and that returns true if the word contains only letters in the list. Can you make a sentence using only the letters acefhlo? Other than “Hoe alfalfa?”

Exercise 5
Write a method named uses_all? that takes a word and a string of required letters, and that returns true if the word uses all the required letters at least once. How many words are there that use all the vowels aeiou? How about aeiouy?

Exercise 6
Write a method called abecedarian? that returns true if the letters in a word appear in alphabetical order (double letters are ok). How many abecedarian words are there?

Search

All of the exercises in the previous section have something in common; they can be solved with the search pattern we saw in Section Searching. The simplest example is:

def no_e?(word)
  for letter in word.chars
    return false if letter == 'e'
  end
  return true
end

The for loop traverses the characters in word. If we find the letter “e”, we can immediately return false; otherwise we have to go to the next letter. If we exit the loop normally, that means we didn’t find an “e”, so we return true.

You could write this method more concisely using the include? method, but I started with this version because it demonstrates the logic of the search pattern.

avoids? is a more general version of no_e? but it has the same structure:

def avoids?(word, forbidden)
  for letter in word.chars
    return false if forbidden.include?(letter)
  end
  return true
end

We can return false as soon as we find a forbidden letter; if we get to the end of the loop, we return true.

uses_only? is similar except that the sense of the condition is reversed:

def uses_only?(word, available)
  for letter in word.chars
    return false if !available.include?(letter)
  end
  return true
end

Instead of a list of forbidden letters, we have a list of available letters. If we find a letter in word that is not in available, we can return false.

uses_all? is similar except that we reverse the role of the word and the string of letters:

def uses_all?(word, required)
  for letter in required.chars
    return false if !word.include?(letter)
  end
  return true
end

Instead of traversing the letters in word, the loop traverses the required letters. If any of the required letters do not appear in the word, we can return false.

If you were really thinking like a computer scientist, you would have recognized that uses_all? was an instance of a previously solved problem, and you would have written:

def uses_all?(word, required)
  return uses_only?(required, word)
end

This is an example of a program development plan called reduction to a previously solved problem, which means that you recognize the problem you are working on as an instance of a solved problem and apply an existing solution.

Looping with indices

I wrote the methods in the previous section with for loops because I only needed the characters in the strings; I didn’t have to do anything with the indices.

For abecedarian? we have to compare adjacent letters, which is a little tricky with a for loop:

def abecedarian?(word)
  previous = word[0]
  for c in word.chars
    return false if c < previous
    previous = c
  end
  return true
end

An alternative is to use recursion:

def abecedarian?(word)
  return true if word.length <= 1
  return false if word[0] > word[1]
  return abecedarian?(word[1..-1])
end

Another option is to use a while loop:

def abecedarian?(word)
  i = 0
  while i < word.length-1
    return false if word[i+1] < word[i]
    i = i+1
  end
  return true
end

The loop starts at i=0 and ends when i=word.length-1. Each time through the loop, it compares the ith character (which you can think of as the current character) to the i+1th character (which you can think of as the next).

If the next character is less than (alphabetically before) the current one, then we have discovered a break in the abecedarian trend, and we return false.

If we get to the end of the loop without finding a fault, then the word passes the test. To convince yourself that the loop ends correctly, consider an example like 'flossy'. The length of the word is 6, so the last time the loop runs is when i is 4, which is the index of the second-to-last character. On the last iteration, it compares the second-to-last character to the last, which is what we want.

Here is a version of palindrome? (see Exercises from Fruitful methods chapter) that uses two indices; one starts at the beginning and goes up; the other starts at the end and goes down.

def palindrome?(word)
  i = 0
  j = word.length-1

  while i < j
    return false if word[i] != word[j]
    i = i+1
    j = j-1
  end

  return true
end

Or we could reduce to a previously solved problem and write:

def palindrome?(word)
  return reverse?(word, word)
end

Using reverse? from Section Debugging of Strings chapter.

Debugging

Testing programs is hard. The methods in this chapter are relatively easy to test because you can check the results by hand. Even so, it is somewhere between difficult and impossible to choose a set of words that test for all possible errors.

Taking no_e? as an example, there are two obvious cases to check: words that have an ‘e’ should return false, and words that don’t should return true. You should have no trouble coming up with one of each.

Within each case, there are some less obvious subcases. Among the words that have an “e”, you should test words with an “e” at the beginning, the end, and somewhere in the middle. You should test long words, short words, and very short words, like the empty string. The empty string is an example of a special case, which is one of the non-obvious cases where errors often lurk.

In addition to the test cases you generate, you can also test your program with a word list like words.txt. By scanning the output, you might be able to catch errors, but be careful: you might catch one kind of error (words that should not be included, but are) and not another (words that should be included, but aren’t).

In general, testing can help you find bugs, but it is not easy to generate a good set of test cases, and even if you do, you can’t be sure your program is correct. According to a legendary computer scientist:

Program testing can be used to show the presence of bugs, but never to show their absence!

— Edsger W. Dijkstra

Glossary

• file object:
  A value that represents an open file.

• reduction to a previously solved problem:
  A way of solving a problem by expressing it as an instance of a previously solved problem.

• special case:
  A test case that is atypical or non-obvious (and less likely to be handled correctly).

Exercises

Exercise 7
This question is based on a Puzzler that was broadcast on the radio program Car Talk (https://www.cartalk.com/puzzler/browse):

Give me a word with three consecutive double letters. I’ll give you a couple of words that almost qualify, but don’t. For example, the word committee, c-o-m-m-i-t-t-e-e. It would be great except for the ‘i’ that sneaks in there. Or Mississippi: M-i-s-s-i-s-s-i-p-p-i. If you could take out those i’s it would work. But there is a word that has three consecutive pairs of letters and to the best of my knowledge this may be the only word. Of course there are probably 500 more but I can only think of one. What is the word?

Write a program to find it.

Exercise 8
Here’s another Car Talk Puzzler (https://www.cartalk.com/puzzler/browse):

“I was driving on the highway the other day and I happened to notice my odometer. Like most odometers, it shows six digits, in whole miles only. So, if my car had 300,000 miles, for example, I’d see 3-0-0-0-0-0.

“Now, what I saw that day was very interesting. I noticed that the last 4 digits were palindromic; that is, they read the same forward as backward. For example, 5-4-4-5 is a palindrome, so my odometer could have read 3-1-5-4-4-5.

“One mile later, the last 5 numbers were palindromic. For example, it could have read 3-6-5-4-5-6. One mile after that, the middle 4 out of 6 numbers were palindromic. And you ready for this? One mile later, all 6 were palindromic!

“The question is, what was on the odometer when I first looked?”

Write a Ruby program that tests all the six-digit numbers and prints any numbers that satisfy these requirements.

Exercise 9
Here’s another Car Talk Puzzler you can solve with a search (https://www.cartalk.com/puzzler/browse):

“Recently I had a visit with my mom and we realized that the two digits that make up my age when reversed resulted in her age. For example, if she’s 73, I’m 37. We wondered how often this has happened over the years but we got sidetracked with other topics and we never came up with an answer.

“When I got home I figured out that the digits of our ages have been reversible six times so far. I also figured out that if we’re lucky it would happen again in a few years, and if we’re really lucky it would happen one more time after that. In other words, it would have happened 8 times over all. So the question is, how old am I now?”

Write a Ruby program that searches for solutions to this Puzzler. Hint: you might find the string method rjust useful.