Method for determining transposition when comparing two numeric v alues (more information)

[Chris Sharman]

>As some of you have pointed out when one value is subtracted from another
>and the result is evenly divisible by 9 (no remainder) this may indicate
>transposition.  But not all differences evenly divisible by 9 indicate
>transposition.  I've thought if there is a way of counting the number of
>ones, twos, threes etc. in the two values I am trying to compare and
>determining if each value has the same number of ones, twos, threes etc.,
>and then using this along with the evenly-divisible-by-nine technique, that
>this would be a reliable indicator of transposition.  Just don't know of a
>way to get Quiz to count the number of ones, two, threes in each value.  Any
>one have any ideas on how to deal with this?

The reason transpositions have a difference of 9*K is as follows:
Consider ...ab... and ...ba... (two numbers identical except for adjacent
digits a&b).

The difference is 10^X * [(10*a + b) - (10*b + a)]
		= 10^X * 9 * (a - b)
(all the other identical digits cancel out).

def dif int*9 = absolute(ss1 - ss2)

; Divide by 9 should give an integer. More usefully, it should give
; 10^X * absolute(a - b).
; absolute(a-b) is a digit 1-9.
; the length of this number will give the position of the transposition

def lenr = size(ascii(floor(dif/9))) - 1

; lenr is the length of the matching rhs of the numbers.

def asc-ss1 char*9 = ascii(ss1,9)

def transposed-ss1 char*9 = &
	asc-ss1[1:7 - lenr] + &; before the transposition
	reverse(asc-ss1[8 - lenr:2]) + &; the transposition
	asc-ss1[10 - lenr: lenr]    ; after the transposition

select if (transposed-ss1 = ascii(ss2,9))

This should select just simple transpositions ... probably quite slowly !

Chris
_______________________________________________________________________
Chris.Sharman@CCAgroup.co.uk		http://www.ccagroup.co.uk/
CCA Stationery Ltd, Eastway, Fulwood, Preston, Lancashire, PR2 9WS.
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