;;; generalized-suffiex-tree.el --- Building a generalized suffix tree -*- lexical-binding: t; -*-

;;; Author: Durand
;;; Version: 0.0.2

;;; Commentary:

;; Our node is represented as a list of the following elements:

;; number     , from which string this edge comes
;; start      , which is the starting index of the edge going from its parent
;;              node to this node
;; end        , the index of the end of the above edge
;; suffix-link, the index of the node this node's suffix-link points to
;; children   , a hash-table of pairs of integers and indices of its
;;              children
;; leaf-labels, a list of pairs (number start), where
;;              number means the number-th string and
;;              start is the starting position of this edge.
;;              This element is nil for the internal nodes.

;; To compute the length of the edge going into NODE we use:
;; (- (min end (1+ position)) start)
;; which is actually how far the position is on that edge,
;; if it is on that edge.

;; We use only one terminating symbol, and that is -1.

;;; Code:

;;;###autoload
(defun gst-min (&rest args)
  "Return the minimum among ARGS.
If an argument is 'infty, then it is considered greater than
every number."
  (apply #'min (delq nil
                     (mapcar
                      (lambda (arg)
                        (cond
                         ((number-or-marker-p arg) arg)
                         ((eq arg 'infty) nil)))
                      args))))

;;;###autoload
(defun gst-edge-length (node position num str-lens)
  "Return the length of the edge into NODE.
See the comment above this function for the reason
POSITION and NUM are here.

And STR-LENS is here so that we know the lengths of previous strings."
  (let* ((node-active-num (car node))
         (leafp (eq (car (cdr (cdr node))) 'infty))
         (leaf-labels (cond (leafp (car (nthcdr 5 node))))))
    (- (cond
        ((and (/= node-active-num num)
              leafp)
         (nth node-active-num str-lens))
        ((/= node-active-num num)
         (caddr node))
        (t (gst-min (caddr node) (1+ position))))
       (cond
        ((and (= node-active-num num)
              leafp)
         (or (cadr (assoc num leaf-labels #'eq))
             (cadr node)))
        (t (cadr node))))))

;;;###autoload
(defun gst-new-node (tree last-added number start &optional end suffix-start)
  "Make a new node with START and END as the coming edge.
NUMBER is the number of string the label belongs to.
Then add the new node to TREE.
LAST-ADDED is the number of elements already in the TREE."
  (let* ((end (or end 'infty) ;; 'infty represents the index of a leaf
              )
         (suffix-link 0) ;; The suffix link is initially 0
         (new-node
          (cond ((eq end 'infty)
                 (list number start end suffix-link (make-hash-table)
                       (list (list number suffix-start))))
                (t
                 (list number start end suffix-link (make-hash-table))))))
    (puthash (1+ last-added) new-node tree)
    (1+ last-added)))

;;;###autoload
(defun gst-add-leaf-label (tree leaf number start)
  "Add a label to LEAF in TREE.
NUMBER and START represent the label."
  (let* ((actual-node (gethash leaf tree))
         (leaf-labels (cdr (cdr (cdr (cdr (cdr actual-node)))))))
    (cond ((and (consp leaf-labels)
                (not (eq (caaar leaf-labels) number)))
           (setcar leaf-labels
                   (cons (list number start)
                         (car leaf-labels)))))))

;;;###autoload
(defun gst-add-suffix-link (tree need-sl node)
  "If NEED-SL is positive, then add the suffix link.
In particular, the node corresponding to NEED-SL in TREE
gets a suffix link pointing to NODE.

This always returns NODE."
  (cond
   ((and (> need-sl 1) (/= need-sl node))
    (setcar (cdr (cdr (cdr (gethash need-sl tree)))) node)))
  node)

;;;###autoload
(defun gst-canonize (tree node position active-number active-edge-index active-length active-node
                          str-lens)
  "Walk down TREE to find the correct active point.

To be precise, we start from NODE, use POSITION, ACTIVE-NUMBER,
and STR-LENS to calculate the length of the edge, and compare
with ACTIVE-LENGTH. If it is less than that, then that means we
shall continue walking down the tree, so we return t in the first
element, while setting other variables to the correct values so
that the caller of this function can use the updated values.

ACTIVE-EDGE-INDEX is for the purpose of updating solely."
  (let* ((actual-node (gethash node tree))
         (node-edge-length (gst-edge-length actual-node position active-number
                                            str-lens)))
    (cond
     ((>= active-length node-edge-length)
      (list t
            active-number
            (+ active-edge-index
               node-edge-length)
            (- active-length
               node-edge-length)
            node))
     (t
      (list nil
            active-number
            active-edge-index
            active-length
            active-node)))))

;;;###autoload
(defsubst gst-aref (strs num index)
  "Return the INDEX th element in NUM th element of STRS."
  (aref (nth num strs) index))

;;;###autoload
(defun gst-extend-tree (tree last-added position remain
                             active-node active-number active-edge-index
                             active-length character strs num str-lens)
  "Extend TREE by CHARACTER in NUM-th string of STRS.
The return value is
\(tree
 last-added    remain            active-node
 active-number active-edge-index active-length)

Other parameters: LAST-ADDED, POSITION, REMAIN, ACTIVE-NODE,
ACTIVE-NUMBER, ACTIVE-EDGE-INDEX, and ACTIVE-LENGTH have special
meanings in the algorithm.

STR-LENS can be supplied so that we don't have to calculate the
lengths repeatedly."
  (let* ((need-sl 0)
         (remain (1+ remain))
         continue-p breakp terminating-no-split)
    (while (and (not breakp) (> remain 0))
      (setq continue-p nil breakp nil)
      (setq terminating-no-split nil)
      (cond
       ((= active-length 0)
        (setq active-edge-index position)
        (setq active-number num)))
      (let* ((actual-node (gethash active-node tree))
             (nxt (cond
                   (actual-node
                    (gethash (gst-aref strs active-number active-edge-index)
                             (car (nthcdr 4 actual-node)))))))
        (cond
         ((null nxt)
          (let ((leaf (gst-new-node tree last-added num position nil
                                    (- position remain -1))))
            (setq last-added leaf)
            (puthash (gst-aref strs active-number active-edge-index)
                     leaf
                     (car (nthcdr 4 (gethash active-node tree))))
            (setq need-sl (gst-add-suffix-link tree need-sl active-node)))
          ;; rule 2
          )
         (t
          (let* ((result (gst-canonize
                          tree nxt position active-number
                          active-edge-index active-length active-node
                          str-lens)))
            (cond
             ((car result)
              ;; observation 2
              (setq active-number (car (cdr result)))
              (setq active-edge-index (car (cdr (cdr result))))
              (setq active-length (car (cdr (cdr (cdr result)))))
              (setq active-node (car (cdr (cdr (cdr (cdr result))))))
              (setq continue-p t))
             (t
              (cond
               ((eq (gst-aref strs
                              (car (gethash nxt tree))
                              (+ active-length
                                 (cadr (gethash nxt tree))))
                    character)
                ;; observation 1
                (setq active-length (1+ active-length))
                (setq need-sl (gst-add-suffix-link tree need-sl active-node))
                ;; (setq breakp t)
                ;; terminating symbol special handling
                (cond
                 ((eq character -1)     ; terminating symbol
                  (gst-add-leaf-label tree nxt num (- position remain -1))
                  (setq active-length (1- active-length))
                  ;; We don't want to split since this is a match. But
                  ;; we don't want to break since this is a
                  ;; terminating symbol. So we invent a new variable
                  ;; to do this.
                  (setq terminating-no-split t))
                 (t
                  (setq breakp t)))))
              (cond
               ((or breakp terminating-no-split))
               (t                       ; splitting
                (let ((split (gst-new-node
                              tree last-added (car (gethash nxt tree)) (cadr (gethash nxt tree))
                              (+ (cadr (gethash nxt tree)) active-length))))
                  (setq last-added split)
                  (puthash
                   (gst-aref strs active-number active-edge-index)
                   split (cadr (cdr (cdr (cdr (gethash active-node tree))))))
                  (let ((leaf (gst-new-node tree last-added num position
                                            nil (- position remain -1))))
                    (setq last-added leaf)
                    (puthash character
                             leaf
                             (cadddr (cdr (gethash split tree))))
                    (setcar (cdr (gethash nxt tree))
                            (min
                             (+ (cadr (gethash nxt tree))
                                active-length)
                             (1- (nth (car (gethash nxt tree)) str-lens))))
                    (puthash (gst-aref strs
                                       (car (gethash nxt tree))
                                       (cadr (gethash nxt tree)))
                             nxt
                             (cadddr (cdr (gethash split tree))))
                    ;; rule 2
                    (setq need-sl
                          (gst-add-suffix-link tree need-sl split)))))))))))
        (cond
         ((or continue-p breakp))
         (t
          (setq remain (1- remain))
          (cond
           ((and (eq active-node 1) ; root
                 (> active-length 0))
            (setq active-length (1- active-length))
            (setq active-edge-index
                  (1+ (- position remain))))
           (t
            (setq active-node
                  (let ((slink (cadddr (gethash active-node tree))))
                    (cond       ; follow the suffix link or go to root
                     ((> slink 1) slink)
                     (t 1))))))))))
    (list tree last-added remain active-node
          active-number active-edge-index active-length)))

;;;###autoload
(defun gst-build-for-strs (strs &optional str-lens)
  "Build the generalized suffix tree for STRS.
One can optionally provide STR-LENS to avoid calculating the
lengths again."
  (let* ((len (length strs))
         (index 0)
         (tree (make-hash-table))
         (last-added 0)
         (active-node (gst-new-node tree last-added index -1 -1))
         (str-lens (or str-lens (mapcar #'length strs))))
    (setq last-added active-node)
    (while (< index len)
      (let* ((position 0)
             (character (ignore-errors (gst-aref strs index position)))
             (remain 0)
             (active-node 1)            ; start from the root
             (active-number index)
             (active-edge-index 0)
             (active-length 0)
             result)                    ; temporary holder
        (while character
          ;; (setq old-character character)
          (setq result (gst-extend-tree tree last-added position remain
                                        active-node active-number active-edge-index
                                        active-length character strs index
                                        str-lens))
          (setq tree (pop result))
          (setq last-added (pop result))
          (setq remain (pop result))
          (setq active-node (pop result))
          (setq active-number (pop result))
          (setq active-edge-index (pop result))
          (setq active-length (pop result))
          (setq position (1+ position))
          (setq character (ignore-errors (gst-aref strs index position)))
          ;; (cond
          ;;  ((characterp old-character)
          ;;   (insert (format "After adding character %c:\n" old-character))
          ;;   (gst-print-tree tree
          ;;                   (append (seq-take strs index)
          ;;                           (list (concat
          ;;                                  (seq-take (nth index strs) position)
          ;;                                  "$"))))
          ;;   (insert "\n\n"))
          ;;  ((= old-character -1)
          ;;   (insert (format "After adding character -1:\n"))
          ;;   (gst-print-tree tree
          ;;                   (seq-take strs (1+ index)))
          ;;   (insert "\n\n")))
          ))
      (setq index (1+ index))
      ;; (insert "\n\n")
      )
    tree))

;;; Printing

;; This section is not necessary. It is here just to print the trees
;; to make sure we don't make some strange errors.

(require 'hierarchy)
(require 'seq)

;;;###autoload
(defun gst-print-strs (strs)
  "Print strings STRS nicely."
  (mapc (lambda (str)
          (mapc (lambda (char)
                  (cond ((characterp char) (insert char))
                        (t (insert ", "))))
                str))
        strs))

;;;###autoload
(defun gst-pretty-hash-table (table)
  "Only return the useful parts from TABLE.

To be precise, this returns the keys and values of the
hash-table, in the form of an alist."
  (let (keys-values-alist)
    (maphash
     (lambda (key value)
       (setq keys-values-alist
             (cons
              (cons key value)
              keys-values-alist)))
     table)
    keys-values-alist))

;;;###autoload
(defun gst-pretty-node (node)
  "Outputs a prettified NODE."
  (format "(%d %d %s %d %s %S)"
          (car node) (cadr node)
          (caddr node) (cadddr node)
          (gst-pretty-hash-table (car (nthcdr 4 node)))
          (car (nthcdr 5 node))))

;;;###autoload
(defun gst-print-tree-for-strs (strs)
  "Print the generalized suffix tree for STRS."
  (let* ((strs (mapcar (lambda (str)
                         (vconcat str (list -1)))
                       strs))
         (symbol (make-symbol "gtree")))
    (set symbol (gst-build-for-strs strs))
    (insert "Generalized suffix tree for: ")
    (gst-print-strs strs)
    (delete-region (- (point) 2) (point))
    (insert ":\n")
    (gst-print-tree (symbol-value symbol) strs)))

;;;###autoload
(defvar gst-full-error-p nil
  "Whether to print full nodes in the output.")

;;;###autoload
(defun gst-print-tree (tree strs)
  "Print TREE with the aid of STRS."
  (let* ((symbol-tree (make-symbol "new-hierarchy"))
         (strs (mapcar (lambda (str)
                         (mapcar (lambda (c)
                                   (cond ((eq c -1) ?$)
                                         (c)))
                                 str))
                       strs)))
    (set symbol-tree (hierarchy-new))
    (maphash
     (lambda (key value)
       (hierarchy-add-tree
        (symbol-value symbol-tree) key nil
        (lambda (item)
          (hash-table-values (car (nthcdr 4 (gethash item tree)))))))
     tree)
    (hierarchy-print
     (symbol-value symbol-tree)
     (lambda (item)
       (cond ((= item 1) "root")
             (t (let ((actual-str
                       (let* ((node (gethash item tree))
                              (leafp (eq (caddr node) 'infty))
                              (leaf-labels
                               (cond (leafp (car (nthcdr 5 node))))))
                         (concat
                          (seq-subseq
                           (nth (car node) strs)
                           (min (cadr node) (1- (length (nth (car node) strs))))
                           (cond (leafp -1)
                                 (t (caddr node))))
                          (cond
                           (leafp
                            (apply
                             #'concat
                             (mapcar
                              (lambda (label)
                                (let ((first (car label))
                                      (second (cadr label)))
                                  (format "$ (%d : %d)"
                                          first second)))
                              leaf-labels))))))))
                  (cond (gst-full-error-p
                         (concat
                          (format "key: %d, %s, %s" item actual-str
                                  (gst-pretty-node (gethash item tree)))))
                        (t actual-str)))))))))

(provide 'generalized-suffix-tree)

;;; generalized-suffix-tree.el ends here