+
+
+;;; This is currently O(kn^2) to merge n lists of length k.
+;;; You could do it in O(knlogn), but we have a small n, and the
+;;; overhead of the other approach is probably greater.
+(defun nnvirtual-merge-sorted-lists (&rest lists)
+ "Merge many sorted lists of numbers."
+ (if (null (cdr lists))
+ (car lists)
+ (sort (apply 'nconc lists) '<)))
+
+
+;;; We map between virtual articles and real articles in a manner
+;;; which keeps the size of the virtual active list the same as the
+;;; sum of the component active lists.
+
+;;; To achieve fair mixing of the groups, the last article in each of
+;;; N component groups will be in the last N articles in the virtual
+;;; group.
+
+;;; If you have 3 components A, B and C, with articles 1-8, 1-5, and
+;;; 6-7 respectively, then the virtual article numbers look like:
+;;;
+;;; 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
+;;; A1 A2 A3 A4 B1 A5 B2 A6 B3 A7 B4 C6 A8 B5 C7
+
+;;; To compute these mappings we generate a couple tables and then
+;;; do some fast operations on them. Tables for the example above:
+;;;
+;;; Offsets - [(A 0) (B -3) (C -1)]
+;;;
+;;; a b c d e
+;;; Mapping - ([ 3 0 1 3 0 ]
+;;; [ 6 3 2 9 3 ]
+;;; [ 8 6 3 15 9 ])
+;;;
+;;; (note column 'e' is different in real algorithm, which is slightly
+;;; different than described here, but this gives you the methodology.)
+;;;
+;;; The basic idea is this, when going from component->virtual, apply
+;;; the appropriate offset to the article number. Then search the first
+;;; column of the table for a row where 'a' is less than or equal to the
+;;; modified number. You can see that only group A can therefore go to
+;;; the first row, groups A and B to the second, and all to the last.
+;;; The third column of the table is telling us the number of groups
+;;; which might be able to reach that row (it might increase by more than
+;;; 1 if several groups have the same size).
+;;; Then column 'b' provides an additional offset you apply when you have
+;;; found the correct row. You then multiply by 'c' and add on the groups
+;;; _position_ in the offset table. The basic idea here is that on
+;;; any given row we are going to map back and forth using X'=X*c+Y and
+;;; X=(X'/c), Y=(X' mod c). Then once you've done this transformation,
+;;; you apply a final offset from column 'e' to give the virtual article.
+;;;
+;;; Going the other direction, you instead search on column 'd' instead
+;;; of 'a', and apply everything in reverse order.
+
+;;; Convert component -> virtual:
+;;; set num = num - Offset(group)
+;;; find first row in Mapping where num <= 'a'
+;;; num = (num-'b')*c + Position(group) + 'e'
+
+;;; Convert virtual -> component:
+;;; find first row in Mapping where num <= 'd'
+;;; num = num - 'e'
+;;; group_pos = num mod 'c'
+;;; num = (num / 'c') + 'b' + Offset(group_pos)
+
+;;; Easy no? :)
+;;;
+;;; Well actually, you need to keep column e offset smaller by the 'c'
+;;; column for that line, and always add 1 more when going from
+;;; component -> virtual. Otherwise you run into a problem with
+;;; unique reverse mapping.
+
+(defun nnvirtual-map-article (article)
+ "Return a cons of the component group and article corresponding to the given virtual ARTICLE."
+ (let ((table nnvirtual-mapping-table)
+ entry group-pos)
+ (while (and table
+ (> article (aref (car table) 3)))
+ (setq table (cdr table)))
+ (when (and table
+ (> article 0))
+ (setq entry (car table))
+ (setq article (- article (aref entry 4) 1))
+ (setq group-pos (mod article (aref entry 2)))
+ (cons (car (aref nnvirtual-mapping-offsets group-pos))
+ (+ (/ article (aref entry 2))
+ (aref entry 1)
+ (cdr (aref nnvirtual-mapping-offsets group-pos)))
+ ))
+ ))
+
+
+
+(defun nnvirtual-reverse-map-article (group article)
+ "Return the virtual article number corresponding to the given component GROUP and ARTICLE."
+ (when (numberp article)
+ (let ((table nnvirtual-mapping-table)
+ (group-pos 0)
+ entry)
+ (while (not (string= group (car (aref nnvirtual-mapping-offsets
+ group-pos))))
+ (setq group-pos (1+ group-pos)))
+ (setq article (- article (cdr (aref nnvirtual-mapping-offsets
+ group-pos))))
+ (while (and table
+ (> article (aref (car table) 0)))
+ (setq table (cdr table)))
+ (setq entry (car table))
+ (when (and entry
+ (> article 0)
+ (< group-pos (aref entry 2))) ; article not out of range below
+ (+ (aref entry 4)
+ group-pos
+ (* (- article (aref entry 1))
+ (aref entry 2))
+ 1))
+ )))
+
+
+(defsubst nnvirtual-reverse-map-sequence (group articles)
+ "Return list of virtual article numbers for all ARTICLES in GROUP.
+The ARTICLES should be sorted, and can be a compressed sequence.
+If any of the article numbers has no corresponding virtual article,
+then it is left out of the result."
+ (when (numberp (cdr-safe articles))
+ (setq articles (list articles)))
+ (let (result a i j new-a)
+ (while (setq a (pop articles))
+ (if (atom a)
+ (setq i a
+ j a)
+ (setq i (car a)
+ j (cdr a)))
+ (while (<= i j)
+ ;; If this is slow, you can optimize by moving article checking
+ ;; into here. You don't have to recompute the group-pos,
+ ;; nor scan the table every time.
+ (when (setq new-a (nnvirtual-reverse-map-article group i))
+ (push new-a result))
+ (setq i (1+ i))))
+ (nreverse result)))
+
+
+(defun nnvirtual-partition-sequence (articles)
+ "Return an association list of component article numbers.
+These are indexed by elements of nnvirtual-component-groups, based on
+the sequence ARTICLES of virtual article numbers. ARTICLES should be
+sorted, and can be a compressed sequence. If any of the article
+numbers has no corresponding component article, then it is left out of
+the result."
+ (when (numberp (cdr-safe articles))
+ (setq articles (list articles)))
+ (let ((carticles (mapcar 'list nnvirtual-component-groups))
+ a i j article entry)
+ (while (setq a (pop articles))
+ (if (atom a)
+ (setq i a
+ j a)
+ (setq i (car a)
+ j (cdr a)))
+ (while (<= i j)
+ (when (setq article (nnvirtual-map-article i))
+ (setq entry (assoc (car article) carticles))
+ (setcdr entry (cons (cdr article) (cdr entry))))
+ (setq i (1+ i))))
+ (mapc (lambda (x) (setcdr x (nreverse (cdr x))))
+ carticles)
+ carticles))
+