## Word chains (Part 2)

Previously, we laid some groundwork for generating word chains. Rather than arbitrarily returning one word, we might as well get all the words that are one letter different from the first word:

``````prop_next_words_should_be_near() ->
?FORALL({FirstWord, LastWord}, valid_words(),
begin
NextWords = word_chains:next_words(FirstWord),
InvalidWords = lists:filter(fun(W) -> word_chains:get_word_distance(W, FirstWord) =/= 1 end, NextWords),
length(InvalidWords) =:= 0
end).``````

We can calculate the “word distance” using map/reduce:

``````get_word_distance(Word1, Word2) ->
Differences = lists:zipwith(fun(X, Y) -> case X =:= Y of true -> 0; false -> 1 end end, Word1, Word2),
lists:foldl(fun(D, Acc) -> Acc + D end, 0, Differences).``````

For each letter in Word1, we compare it with the same (position) letter in Word2, and assign a 0 if it matches and a 1 if it differs. The sum of these values tells us the difference between the 2 words.

``````2> word_chains:get_word_distance("cat", "cat").
0
3> word_chains:get_word_distance("cat", "cot").
1
4> word_chains:get_word_distance("cat", "cog").
2``````

Using this helper function, we can easily find all the possible next words:

``````next_words(FirstWord) ->
WordList = word_list(),
SameLengthWords = lists:filter(fun(W) -> length(W) =:= length(FirstWord) end, WordList),
WordDistances = lists:map(fun(W) -> {W, get_word_distance(W, FirstWord)} end, SameLengthWords),
lists:map(fun({Word, _}) -> Word end, lists:filter(fun({_, Distance}) -> Distance =:= 1 end, WordDistances)).``````

Almost there! Next time, we will actually start generating some word chains.