/frames 10 def 

%include /u/rs/book3/pslib/tools.ps
%include /u/rs/book3/pslib/example.ps

/hsortA
 { /incr exch def 
   0 1 incr 1 sub
   {
     incr add incr N 1 sub 
      { /lll exch def  
        lll incr neg incr { /xxx exch def 
                 xxx incr sub xxx compare { exit } if 
                 xxx xxx incr sub compareswap 
                 /xxx xxx incr sub def
                 } for 
        xxx lll SUBFILEx 
      } for
   nextframe
   } for 
} def

/SUBFILEx
 {
  /rr exch def /ll exch def 
  LL 1 RR
    {
      dup dup dup
      ll incr sub le exch rr gt or exch rr exch sub incr mod 0 ne or { SqGrL }{ SqWhL } ifelse
      exch PT
    } for
  nextframe
  } def

/hsortB
 { /incr exch def 
   incr 1 N 1 sub 
    { /lll exch def  
      lll incr neg incr { /xxx exch def 
                 xxx incr sub xxx compare { exit } if 
                 xxx xxx incr sub compareswap 
                 /xxx xxx incr sub def
               } for 
      xxx lll SUBFILEx 
    } 
  for } def

4 hsortB

----------------------------
T 20pc Interleaving 4-sorts.

One way to 4-sort a file \itpc{top} is to first insertion-sort the
subfile at positions 1, 5, 9, $\ldots$ , then insertion-sort the subfile at
positions 2, 6, 10, $\ldots$ , then insertion-sort the subfile at
positions 3, 7, 11, $\ldots$ , then insertion-sort the subfile at
positions 4, 8, 12, $\ldots$.  But the three subfiles are independent, so
the same result can be achieved by inserting each element into position into
its subfile, going back four at a time \itpc{bottom}.  Taking the rows
in the bottom diagram in the order 1 5 9 2 6 10 3 7 11 4 8 gives the
top diagram.