Some of you might recall me annoying people on #haskell over the New Year about my Latin Squares project. Well, I'm looking at re-doing it from scratch, but the first thing I need to do is find a new way of representing my square. I have been using a list of lists ([[a]]) to represent a matrix. The problem with this data structure is that I need to be able to manipulate matrices as both row-oriented and column-oriented data structures, as I need to examine the values in the columns as well as in the rows. As it stands, I was doing this by transposing the matrix, manipulating it, then transposing it back again. This is a pain, as it takes up about 15% to 20% of the run time. The other problem with using a list of lists is that the only reason I'm sure that the matrix is valid (i.e. all the rows are the same length, etc.) is because I created it that way, not because the data structure requires it. As such, I'd like to know if there's any way of storing a an n-by-n matrix such that the algorithm/function to get either the rows or the columns is less than O(n^2) like transposition is. I did try using an Array, but my (admittedly hurried and naive) usage of them took longer than a list of lists, was more difficult to manipulate, and wasn't required separate inverse functions to row and cols. Also, since I need to look all throughout the list of values, it's still O(n^2), but this time for both rows and columns. I know that when doing something similar to this in Java a few years ago (a primitive Sudoku solver, to be precise), I could represent the rows and columns as to separate 2D arrays, with rows(i,j) pointing to the same object as cols(j,i). Is something like this possible in Haskell? in particular, I will be storing lists of possible values in the cells of the matrix, so the capability to backtrack would be very nice, as I'd be trying each value at a time to see if it is valid. I'd also want to use such a matrix implementation next semester for a project, which I plan on being a quick comparison of various programming languages as to ease of use and efficiency for matrix-based computing problems. -- Ivan Lazar Miljenovic