find-latins.clj

(fn find-latins 
  [vectors] 
  (let [height (count vectors)
        width (->> vectors (map count) (apply max))
        spaces (for [line vectors]
                 (-> (- width (count line))
                     inc
                     range))
        alignments (reduce #(for [cur % up %2]
                              (conj cur up)) 
                           (->>  spaces first (map vector))
                           (next spaces))
        alignments (for [alignment alignments]
                (for [[ofs-left line] (map vector alignment vectors)
                      :let [ofs-right (- width ofs-left (count line))]]
                  (concat
                    (repeatedly ofs-left #(identity nil))
                    line
                    (repeatedly ofs-right #(identity nil)))))
        submatrices (for [alignment alignments
                          n (-> (min width height) inc range)
                          :when (> n 1)
                          x (range (- width n -1))
                          y (range (- height n -1))
                          :let [subm (->> alignment
                                          (drop y)
                                          (take n)
                                          (map #(->> % (drop x) (take n))))]
                          :when (not (some nil? (apply concat subm)))]
                      subm)
        latins (for [subm submatrices
                     :let [n (count subm)
                           latin-row? #(->> % distinct count (= n))]
                     :when (and (->> subm 
                                     (apply concat)
                                     latin-row?)
                                (every? latin-row? subm)
                                (every? latin-row? (apply (partial map vector) subm)))]
                 subm)]
    (->> latins
         distinct
         (group-by count)
         (map (fn [[order latins]] 
                 (vector order (count latins)))))))