Phrase Finder Word Search

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Mensa Daily Puzzlers

For over 15 years Mensa Page-A-Day calendars have provided several puzzles a year for my programming pleasure.  Coding "solvers" is most fun, but many programs also allow user solving, convenient for "fill in the blanks" type.  Below are Amazon  links to the two most recent years.

Mensa 365 Puzzlers  Calendar 2017

Mensa 365 Puzzlers Calendar 2018

(Hint: If you can wait, current year calendars are usually on sale in January.)


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Problem Description

PhraseFinder searches for set of valid words which can be formed from a given set of letters.  The user specifies the smallest and largest word lengths and the number of words in the output phrase.  Words are validated against one of several available dictionaries, again specified by the user.    

Background & Techniques

This program was motivated by a recent puzzle in the Mensa Puzzle-A-Day calendar.  The twenty-four letters  ABCDEEFHIKLLLLOOOORRTWWY are an analog of a "famous movie direction".  What is it phrase?  The answer, which I didn't get,  is "Follow the yellow brick road".  But that led me to wonder if I could have found it with a program.  The answer turns out to be, "probably not" - it is the 29,275th solution and takes about 45 minutes to find on my older laptop, even though "solutions" are found  at  the rate of about 10 per second.  And this is only up to the "B's"!

But it is much faster and more capable than the older "Unscramble" program previously published as part of our Wordstuff program.   It does work great for finding anagram phrases from grandkids full names.  

A dictionary file, "general.dic", is included with the downloadable zip file and contains about 17,000 words. Additional larger and smaller dictionaries may also be downloaded.  You may  provide your own word  lists as text files, one word per line.

Non-programmers are welcome to read on, but may want to skip to the bottom of this page to download executable version of the program.

Notes for Programmers 

The original unscramble program found phrases by permuting subsets of letters and checking them against a dictionary - a slow process.  This version treats letter groups as "multisets'., sets of elements which may have repeated elements.  The common data structure used to represent multisets is an array of integers, each integer representing the count of elements corresponding to the index of that  set element.  In our case, working with letters, our TMSetRec type is an array of 26 integers  representing the number of occurrences of the letters 'A' through 'Z'.   

Three primary functions handle the multisets: MakeMSet takes a string of letters and returns a TMSetrec.  IsSubset takes two multisets and returns true if the second is a subset of the first..  And SetDiff subtracts one multiset from another.   

Rather than pass all possible permutations of word candidates against the dictionary, in this version, we make a sorted string list of all dictionary words which are within the given length range and whose multiset representation is a subset of the master set of letters.   The recursive Findwords procedure passes through this list looking for words which are subsets of the remaining unused letters.  When one is found, it is subtracted from the remaining letters and a recursive call is made to find the next word.  After the final word is found, if the remaining letters set is empty, we have found a solution.

 Running/Exploring the Program 

bulletDownload source
bulletDownload  executable
bulletDownload additional dictionaries 

Suggestions for Further Explorations

If only our dictionary identified parts of speech, additional filtering could reduce the number of solutions displayed (must have at least one verb and one adjective,  can't be all nouns. etc.) 


Original Date: October 1, 2005

Modified: July 29, 2017

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