I have a couple of questions concerning specification of constraints. I
want to know if there is a shorthand way to specify the relationship
between the solutions in the variables. In the first case, I want to
specify a greater than or equal relation. In the second case, I want to
specify a distinct relationship. I can do this painstakingly by drawing
out the complete relationships. I'd just like to know if there is a
shorter way to do it.
1). If I have a list of constraint variables, is there a shorter way to
define that the variables involve a decreasing value? In project euler
problem #240, there are five 6-sided dice (sides numbered 1 to 6) that
can be rolled so that the top three sum to 15. (I've already solved
problem #240, it just gets to be long when we have twenty 12-sided dice).
proc {TopDiceFiveSix ?Sol}
D01|D02|D03|D04|D05|nil = Sol
in
D01::1#6 D02::1#6 D03::1#6 D04::1#6 D05::1#6
D01 + D02 + D03 =: 15
% This is the relations what I want to describe in shorthand???
D01>=:D02
D01>=:D03 D02>=:D03
D01>=:D04 D02>=:D04 D03>=:D04
D01>=:D05 D02>=:D05 D03>=:D05 D04>=:D05
{FD.distribute split Sol}
end
2). If I have a list of constraint variables, is it possible to define
that not of the values can be equal? In project euler problem #68, we
have the following "magic" 3-gon ring, filled with the numbers 1 to 6,
and each line adding to nine. (I've also already solved problem #68,
but it too gets to be long when dealing with a five-gon).
proc {ThreeGonRing ?Sol}
XA#RA#RB # XB#RB#RC # XC#RC#RA = Sol
in
RA::1#6 RB::1#6 RC::1#6
XA::1#6 XB::1#6 XC::1#6
% none of the nodes is equal (should be a shorthand for this???)
RA\=:RB RB\=:RC RC\=:XA XA\=:XB XB\=:XC
RA\=:RC RB\=:XA RC\=:XB XA\=:XC
RA\=:XA RB\=:XB RC\=:XC
RA\=:XB RB\=:XC
RA\=:XC
% each line adds to n
XA + RA + RB =: XB + RB + RC
XB + RB + RC =: XC + RC + RA
% Working clockwise, starting from the group of three with the
numerically lowest external node
XA <: XB
XA <: XC
{FD.distribute split Sol}
end
Thanks,
Chris Rathman
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