Prolog - find words in matrix - prolog

Question

Given an nxn letter matrix and a list of words, the program should find all the appearances of the words in the matrix and their location.
They could appear up-down, right-left and diagonally (over all 8 directions). A word can appear any number of times (including zero) and they can overlap (like the words bad, and adult) and even be a subset of one another (like the words bad and ad).

Answer 1

EDIT Here's a complete code (finds words in diagonals too). One drawback: words from the main diagonals are found twice.
% word(X) iff X is a word
word("foo").
word("bar").
word("baz").
% prefix(?A, +B) iff A is a prefix of B
prefix([], _).
prefix([A|B], [A|C]) :- prefix(B, C).
% sublist(?A, +B) iff A is a sublist of B
sublist(A, B) :- prefix(A, B).
sublist(A, [_|B]) :- sublist(A, B).
% reversed(?A, +B) iff A is reversed B
reversed(A, B) :- reversed(B, [], A).
reversed([A|B], C, D) :- reversed(B, [A|C], D).
reversed([], A, A).
% rowsreversed(?A, +B) iff matrix A is matrix B with reversed rows
rowsreversed([A|B], [C|D]) :- reversed(A, C), rowsreversed(B, D).
rowsreversed([], []).
% transposed(+A, ?B) iff matrix B is transposed matrix A
transposed(A, B) :- transposed(A, [], B).
transposed(M, X, X) :- empty(M), !.
transposed(M, A, X) :- columns(M, Hs, Ts), transposed(Ts, [Hs|A], X).
% empty(+A) iff A is empty list or a list of empty lists
empty([[]|A]) :- empty(A).
empty([]).
% columns(+M, ?Hs, ?Ts) iff Hs is the first column
% of matrix M and Ts is the rest of matrix M
columns([[Rh|Rt]|Rs], [Rh|Hs], [Rt|Ts]) :- columns(Rs, Hs, Ts).
columns([[]], [], []).
columns([], [], []).
% inmatrix(+M, ?W) iff word W is in the matrix M
inmatrix(M, W) :- inrows(M, W).
inmatrix(M, W) :- incolumns(M, W).
inmatrix(M, W) :- inleftdiagonals(M, W).
inmatrix(M, W) :- inrightdiagonals(M, W).
% inrows(+M, ?W) iff W or reversed W is in a row of M
inrows([R|_], W) :- word(W), sublist(W, R).
inrows([R|_], W) :- word(W), reversed(V, W), sublist(V, R).
inrows([_|Rs], W) :- inrows(Rs, W).
% incolumns(+M, ?W) iff W or reversed W is in a column of M
incolumns(M, W) :- transposed(M, N), inrows(N, W).
% inleftdiagonals(+M, ?W) iff W or reversed W is in a left diagonal of M
inleftdiagonals(M, W) :- inupperleftdiagonals(M, W).
inleftdiagonals(M, W) :- transposed(M, N), inupperleftdiagonals(N, W).
% inupperleftdiagonals(+M, ?W) iff W or reversed W is in an upper left diagonal of M
inupperleftdiagonals(M, W) :- upperdiags(M, N), inrows(N, W).
% upperdiags(+M, ?X) iff X is a list of upper diagonals of matrix M
upperdiags(M, X) :- upperdiags(M, [], Y), reversed(Z, Y), transposed(Z, X).
upperdiags([R|Rs], A, X) :- columns(Rs, _, T), upperdiags(T, [R|A], X).
upperdiags([], X, X).
% inrightdiagonals(+M, ?W) iff W or reversed W is in a right diagonal of M
inrightdiagonals(M, W) :- rowsreversed(N, M), inleftdiagonals(N, W).

Answer 2

Here's a partial solution for horizontal and vertical straight and reverse lookup:
count_hits(Word, Matrix, Result):-
atom_chars(Word, Chars),
reverse(Chars, C2),
transpose_matrix(Matrix, M2),
findall(1, find_chars_in_matrix(Chars,Matrix), A),
findall(1, find_chars_in_matrix(Chars,M2), B),
findall(1, find_chars_in_matrix(C2,Matrix), C),
findall(1, find_chars_in_matrix(C2,M2), D),
length(A, X1),
length(B, X2),
length(C, X3),
length(D, X4),
Result is X1 + X2 + X3 + X4.
transpose_matrix([],[]).
transpose_matrix([[ULCorner|Header]|Body], [[ULCorner|NewHeader]|NewBody]) :-
collect_heads_and_tails(Body, NewHeader, Kernel),
collect_heads_and_tails(NewBody, Header, X2),
transpose_matrix(Kernel, X2).
collect_heads_and_tails([], [], []).
collect_heads_and_tails([[H|T]|TT], [H|X], [T|Y]):-collect_heads_and_tails(TT, X, Y).
find_chars_in_matrix(Chars, [H|_]):-
sublist(Chars, H).
find_chars_in_matrix(Chars, [_|T]):-
find_chars_in_matrix(Chars, T).
sublist(L, [_|T]) :- sublist(L, T).
sublist(A, B) :- prefix(A, B).
prefix([H|T], [H|T2]) :- prefix(T, T2).
prefix([], _).
% test data
matrix([[e,t,r,e],
[r,r,t,r],
[t,r,t,t],
[e,e,t,e]]).
go :- matrix(M), count_hits(etre, M, X), write(X).
:-go.
Two weaknesses: (a) palindromic words are found twice, and one-letter words are found four times - mathematically justifiable, but probably unwanted from a common-sense perspective. (b) diagonal matches aren't found at all, for that you need more involved recursion with at least one additional counting argument.
Full disclosure: transpose_matrix/2 was adapted from the beautiful answer to this question. It's amazing, the wealth of code that stackoverflow has accumulated in just two years...