/frames 8 def 

%include /u/rs/book3/pslib/tools.ps
/dx 6 def /dy 6 def /ox 0 def /oy 3 def 
/myscale
 {dy mul oy add exch dx mul ox add exch} def

%include /u/rs/book3/pslib/points.ps

[ 49 { 0 } repeat ] /A exch def 
A length /N exch def /LL 0 def /RR N 1 sub def

/frame frames 1 sub def
/nextframe {/frame frame 1 sub def} def
/lastframe {/frame frame 1 add def} def

/ptChar 1 string def 
/PT { /II exch def ptChar 0 A II get 64 add put 
      ptChar exch II 1 add frame pt } def

/ptNum 2 string def 
/PTnum { /II exch def A II get ptNum cvs 
      exch II 1 add frame pt } def

/INITFILE
 { [ 49 { 0 } repeat ] /A exch def } def

/MARKFILE
 {
  /incr exch def /offs exch def
  LL 1 RR
    {
      /xxx exch def
      RR xxx sub offs sub dup 0 gt exch incr mod 0 eq and 
                                     { A xxx 1 put }{} ifelse
    } for
  } def

/DRAWFILE
 {
  LL 1 RR
    { CellWh exch PT } for
  LL 1 RR
    { dup A exch get 0 eq { CellWh }{ CellGr } ifelse exch PT } for
  CellGr RR PT
  nextframe
  } def

/LABELS
 {
  INITFILE
  A RR 4 sub 4 put 
  A RR 8 sub 8 put 
  A RR 13 sub 13 put 
  A RR 26 sub 26 put 
  A RR 39 sub 39 put 
  LL 1 RR
    { dup A exch get 0 ne { 3 exch PTnum }{ pop } ifelse } for
  nextframe
 } def

 0 4 MARKFILE DRAWFILE INITFILE
 9 4 MARKFILE DRAWFILE INITFILE
22 4 MARKFILE DRAWFILE INITFILE
35 4 MARKFILE DRAWFILE INITFILE nextframe
 0 4 MARKFILE
 9 4 MARKFILE
22 4 MARKFILE
35 4 MARKFILE DRAWFILE

nextframe LABELS

----------------------------
Med 4pc A 4- and 13- ordered file.

The bottom row depicts an array with shaded boxes depicting those items
that must be smaller than or equal to the item at the far right, if the
array is both 4- and 13-ordered. The four rows at top depict the origin of
the pattern.  If the item at right is at array position $i$, then 4-ordering
means that items at array positions 
$i-4$, $i-8$, $i-12$, $\ldots$ are
smaller or equal \itpc{top}; 
13-ordering means that the item at $i-13$, 
and therefore, because of 4-ordering, 
the items at $i-17$, $i-21$, $i-25$, $\ldots$ are
smaller or equal \itpc{second from top}; 
also the item at $i-26$, 
and therefore, because of 4-ordering, 
the items at $i-30$, $i-34$, $i-38$, $\ldots$ are
smaller or equal \itpc{third from top}; and so forth.
The white squares left are those than could be larger than the item at left;
there are at most 18 such items.  Thus there are at most $18N$ comparisons
required to insertionsort a 13-ordered and 4-ordered file of size $N$.