word search algorithm matlab

Question

I am looking for an efficient word search algorithm. If you can help me come up with it it would be even better

a h c k 
x r j i
b v t l
c y q s

and I want to find 'arts' . If 'stra' was also a valid word I want that to be found as well. (vertical, horizontal, diagonal and reverse). I came up with a few algorithms but thy don't seem efficient and consume long coding. First one included using find() to get the first letter and look at that column or rows.

This is an university assignment, right? Two of your colleagues have been here before. First read [here](http://stackoverflow.com/questions/20406257/does-matlab-have-a-function-similar-to-strfind/20406898#20406898), then [here](http://stackoverflow.com/questions/20380587/is-it-possible-to-rotate-a-matrix-by-45-degrees-in-matlab/20381889#20381889) and finally [here](http://stackoverflow.com/questions/20334461/wordsearch-algorithm-in-matlab). If you still have questions, tell us exactly where you got stuck. — thewaywewalk, Dec 13 '13 at 12:50
I am not stuck on horizontal or vertical search. I am stuck on diagonal as I said on my problem example. I was wondering if I have to extract the whole diagonal and use strfind or is there a more efficient way. — Arijoon, Dec 13 '13 at 12:57
First show those few algorithms that you have and how much time they consume, otherwise it will be hard to indicate improvements. Keep in mind that there are only (N+M-1)*2 diagonals that need to be evaluated in both directions. I can't imagine them being that hard to extract. — Dennis Jaheruddin, Dec 13 '13 at 13:18
possible duplicate of [Using strfind in Matlab for different diagonal directions in a Matrix](http://stackoverflow.com/questions/20551661/using-strfind-in-matlab-for-different-diagonal-directions-in-a-matrix) — Daniel, Dec 13 '13 at 16:11
possible duplicate of [Searching for a word in a grid](http://stackoverflow.com/questions/20530946/searching-for-a-word-in-a-grid) — chappjc, Dec 13 '13 at 18:03

Rody Oldenhuis · Accepted Answer · 2013-12-13T13:42:49.430

Here's one way:

%// Example word grid
C = [
    'a' 'h' 'c' 'k' 'r'
    'x' 'r' 'j' 'i' 'p'
    'b' 'v' 't' 'l' 'q'
    'a' 'y' 'q' 's' 'o'];

%// Your search term
target = 'arts';

%// Optionally, do some obvious checks here. 
%//  - length of the search string may exceeds the grid's dimensions
%//  - there are no matches for the first letter
%//  - and similar

%// Form single cellstring containing all search directions
allDirections = [
    %{
    // horizontal, horizontal-reversed
    %}
    cellstr([C ; C(:,end:-1:1)])
    %{
    // vertical, vertical-reversed
    %}
    cellstr([C'; C(:,end:-1:1)']) 
    %{
    // Diagonal, top-left to bottom-right, and reversed
    %}
    arrayfun(@(ii){diag(C,ii)'}, -size(C,1)+2:size(C,2)-2)';
    arrayfun(@(ii){diag(C(end:-1:1,end:-1:1),ii)'}, -size(C,1)+2:size(C,2)-2)';
    %{
    // Diagonal, top-right to bottom-left, and reversed
    %}
    arrayfun(@(ii){diag(C(:,end:-1:1),ii)'}, -size(C,1)+2:size(C,2)-2)';
    arrayfun(@(ii){diag(C(end:-1:1,:),ii)'}, -size(C,1)+2:size(C,2)-2)';
];

%// And now just find the string
strfind(allDirections , target)

Of course, you could to improve (memory) efficiency by

doing the strfind on all the directions separately
doing 2 × strfind on the same direction, but with the target inverted
etc.

But aside from these relatively minor optimizations, I don't think you can do much better in MATLAB in practice.

A theoretically more efficient recursive, branch-and-bound type search roughly goes like this:

find all occurrences of the first letter
eliminate all of those occurrences that cannot satisfy the length of the target based on the dimensions of the grid
Search the neighborhoods of all hits for occurrences of the second letter
Eliminate occurrences based on length, etc.

(Don't forget to filter on direction after the second letter, as the hits for the second letter fixes the search directions)

As far as I can see, this would need a lot less reads and comparisons than my version. However, my guess would be that using canned routines (as I did) is going to be faster and less complicated than using (nested) loops. But I could be wrong.

Try. Profile. Learn. Smile. Correct me :)

nice approach! but it's probably hard to tell where exactly the word started in the initial matrix, isn't it? And as far as I know from the similar questions, it's possible that one word appears several times. And also, as you just concatenate everything what happens if there is a "invalid" word over two lines like: C = [ a r ; t s]; it would get detetected by your algorithm, but is incorrect. Am I right? — thewaywewalk, Dec 13 '13 at 13:36
@thewaywewalk: (a) that's true, although it's fairly easy to derive where the hit(s) occurred, since you have knowledge of which row in `allDirections` corresponds to which row/col/direction. (b) No. I'm concatenating whole rows of characters, not individual characters. Just print the `allDirections` to see what I mean. Each entry in that `cell` is a valid string abiding to the OP's rules. — Rody Oldenhuis, Dec 13 '13 at 13:41

word search algorithm matlab

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