Random sort demonstration

[Dar Scott]

This script demonstrates what is going on with random sorts of short lists using this:

      sort items of myVar by random( the number of items of myVar)

This is a button script on a stack with a wide field with a scrollbar.

local lineAssignments

on mouseUp
   set the cursor to watch
   put empty into field 1
   put "a,b,c" into original
   put 0 into numFirstSame
   put 100 into trials
   repeat trials times
      put original into myVar
      put empty into lineAssignments
      sort items of myVar by randomLog( the number of items of myVar, each)
      delete char -1 of lineAssignments
      put "(" & original & ") is assigned (" & lineAssignments & ") and sorted as (" & myVar & ") where the" after field 1
      if  (item 1 of original) is (item 1 of myVar) then
         put " first is same" after field 1
         add 1 to numFirstSame
      else
         put " first is different" after field 1
      end if
      put return after field 1
   end repeat
   put round( (numFirstSame/trials) * 100) into percentSame
   put "The first was the same " & percentSame & "% of the time" after field 1
   set the scroll  of field 1 to 999999
end mouseUp

function randomLog pRange, pEach
   get random(pRange)
   put pEach & "->" & it & comma after lineAssignments
   return it
end randomLog

Note that this uses function randomLog() instead of random() so the assignments can be gleamed.

These are the last few lines of a typical output:

(a,b,c) is assigned (a->3,b->2,c->2) and sorted as (b,c,a) where the first is different
(a,b,c) is assigned (a->1,b->2,c->2) and sorted as (a,b,c) where the first is same
(a,b,c) is assigned (a->1,b->2,c->1) and sorted as (a,c,b) where the first is same
(a,b,c) is assigned (a->2,b->2,c->3) and sorted as (a,b,c) where the first is same
The first was the same 53% of the time

I got percentages in the range 45% to 60%.  My theory (other email) predicted 52 percent.  You can try upping the number of trials and commenting out the per-sort lines, and see what you get.

The problem is equality in the sort.  It keeps the same order in comparison of pairs of items.  For example, the items sorted in the last case above as though they were 2,2,3.  The first item is still first.  

So...

Use large values for the argument to random() in random sorts.

Dar