This repository contains Donald Knuth's GraphBase list of five-letter words, as well as scripts to run various combinatoric experiments, graph algorithms, and other algorithms to explore the relationships among these words.
The list of words comes from [1] and is in the public domain.
A Python program that contains a method for getting all of the five letter words from a file, and that's about it.
Exercises 26-37 of Knuth's Volume 4 Fascile 0 are intended as a warm up to get to know the SGB five letter word list. Solutions to these exercises are listed below.
distinct.py- computes the number of SGB words containing exactly k distinct letters.
diff_by_one_fixed.py - (fixed 2019-03-09) computes the number of words in the SGB
that are off by a single letter in each position. An example is rover and spuds.
Each corresponding letter is only different by one: r -> s, o->p, and so on.
This uses recursive backtracking to generate possible matches for each word, and
uses a hash table to check for their existence in the original word set.
There are 38 such pairs in the SGB.
Also see Five Letter Words on the charlesreid1.com wiki.
diff_by_n_fixed.py - (added 2019-03-10.) using the corrected approach (above) to
computing differences by 1, this generalizes the calculation to words that are different
by a distance d for each letter position.
Also see Five Letter Words: Part 4: Revisiting Diff by One (blog post) on charlesreid1.github.io.
euclidean_distance.py - computes the euclidean distance between two words. This uses
the traditional Euclidean distance definition but reinterprets distance to mean edit distance.
lexico.py - find words that are sorted by lexicographic order (front to back, a-z).
palindromes.py - look for five letter words that are either a palindrome, or a palindrome pair.
diff_by_n.py - computes words in SGB that have an edit distance of n.
reverse_lexico.py - variation on lexico.py that finds words whose letters are in
reverse lexicographic order.
letter_coverage.py - computes coverage of the alphabet (minimum number of words required
to provide X letters of the alphabet)
Knuth mentions, in the text, a couple of facts about how many words cover how much of the alphabet. We authored a dynamic program to compute precisely this - given a number of letters N from the alphabet, this program computes the minimum number of words it takes to cover all N letters.
Also see Letter Coverage page on the charlesreid1.com wiki.
- Knuth, Donald. The Stanford GraphBase: A Platform for Combinatorial Computing. New York: ACM Press, 1994. <http://www-cs-faculty.stanford.edu/~knuth/sgb.html>
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