[gecode-users] Constraints on "wave" form

[Mikael Zayenz Lagerkvist]

Richard Portelli skrev 12/06/14 10:32:
> Hello Christian,
> I would like to know if there is an easy way to implement a special 
> constraint.
> I have an array with 10 numbers.
> My constraint would be : if you plot the array values in function of 
> the index,  you should have a wave aspect /\.
> For example with 10 numbers
>
> 1 3 5 9 11 7 6 5 4 2 0 (increasing then decreasing) There is no 
> importance at witch index there is the inflexion point.
>
> Would you have an idea how to implement that in a clean way?
>

For reference, this is similar to the inflexion constraint 
(http://www.emn.fr/z-info/sdemasse/gccat/Cinflexion.html) with the 
number of inflexions set to 1 (assuming that valleys are also ok).

The simplest way in my opinion to model this constraint would be the 
following.

   Assume the sequence of numbers is called x and has n entries.
   Define a new boolean array of variables y with n-1 values.
   For each place i in y, add the constraint
     y[i] = (x[i] < y[i])
   (that is, reified ordering).
   On the y variables, add the constraint regular(y, 1*0*)

The ordering constraint and the regular expression can be modified to 
suit your particular needs.

Cheers,
Mikael