So there is no misunderstanding, the trial positioning would be
applicable to all levels, not just the first. In other words, solving
for each of the remaining Queens in turn is the same as for the first
Queen, except for the eighth Queen where no lower level positioning
need be considered,
On Apr 13, 2005, at 1:04 PM, Lee Cullens wrote:
John
The type of problem you mention and the extent of positioning you go
to could result in an incomplete solution. In very general terms one
would need to place the first Queen then find an appropriate position
for the second, and each of the remaining Queens in turn until either
there are no appropriate positions to be found or all eight Queens
have been positioned. If all eight Queens can not be positioned, then
the first Queen would be moved and the remaining Queen positioning
worked through again.
This is a "made for recursion" type of problem, but could be done with
nested loops.
The "Trying everything" approach can , of course, be a very lengthy
process. I seem to remember a more sophisticated model for this type
of problem (I think somehow related to linear algebra) but can't
recall the specifics at the moment. Maybe one of the more academic
(an younger) members of this list can point you in such a direction.
Lee C
On Apr 13, 2005, at 12:15 PM, [EMAIL PROTECTED] wrote:
I read through Magnus Hetland's book and noticed the Eight Queens
problem, which I had solved some time ago using Visual Basic.
This time, I wanted to use a non-recursive solution. I randomly place
each queen on board coordinates running from 0,0(top left hand corner
of board) to 7,7(lower right hand corner of board)
Here's the interesting part: I can only get eight queens safely on
the board perhaps every one in 20 runs. At least 12 or 13 of those
times, I can place seven queens, while five or six times, I can only
place six queens or even five!
Once a queen is safely placed, I establish her "territory". Once this
is done, when I try to place a subsequent queen, I check for all
placed queen's territories. Once I place six or seven queens, I have
to give the program a lot more tries to try to find a safe square.
And it can't always be done.
Does this sound right? Does trying to place each queen randomly cause
this anomaly?
I can post my code(beginner code!) if anyone is interested in seeing
it.
Best,
John
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