[gecode-users] Problem to formulate a constraint

[Uwe Nowak]

Hi!

Thank you for your answer. As I stated, I am a beginner to gecode and constraint programming at all. I did not 
try reification, but by this keyword I managed to solve the problem.



However, I still think, that I am formulating my constraint in a bad way. I managed to reduce my 
(sub)problem to the following:

I have an one-dimensional array
#############

Furthermore, I have patterns such as
Pattern 1 = aa#a
Pattern 2 = b#b#b
where the hash means an empty field. 

I want to place these patterns on the array, i.e. possible placements are 
Placement 1: aa#a###b#b#b#
Placement 2: aabab#b######

No I want to store the position (i.e. the column) of each pattern in an IntVarArray c, i.e. in Placement 1 it 
is c=(0; 7) in Placement 2 it is c=(0; 2). However I do not know, how to formulate the non-overlapping.


I have three possible Ideas:
1. For each pattern I have an BoolVarArray to indicate if the pattern is placed there
For Placement 1 I have two arrays (for pattern 1 = 1101000000000) and (for Pattern 2 = 0000000101010)
Then I have constraints
c_a=j <==> x_{j+0} = x_{j+1} = x_{j+3} = 1
c_b=j <==> y_{j+0} = y_{j+2} = y_{j+4} = 1


2. I have one IntVarArray that stores the pattern placed at this field.
For Placement 1 this is 1101000202020
Then I have constraints
c_a=j <==> x_{j+0} = x_{j+1} = x_{j+3} = 1
c_b=j <==> x_{j+0} = x_{j+2} = x_{j+4} = 2


3. I assign different numbers to each point of the the pattern, I.e. pattern 1 = 12#3 and Pattern 2=4#5#6
For Placement 1 this is 1203000405060
Then I have constraints
c_a=j <==> x_{j+0} = 1 
c_a=j <==> x_{j+1} = 2 
c_a=j <==> x_{j+3} = 3
c_b=j <==> x_{j+0} = 4 
c_b=j <==> x_{j+2} = 5 
c_b=j <==> x_{j+4} = 6

However I am somehow lost, how to formulate such constraints efficiently. 
Although this seems a little bit similar to the Pentomino example, with my current gecode-skills I am not 
able to transfer the Ideas.

Best Regards,
Uwe
 
 
----------------ursprüngliche Nachricht-----------------
Von: "Christian Schulte" cschulte at kth.se 
An: "'Uwe Nowak'" uwe.nowak at itwm.fraunhofer.de , users at gecode.org 
Datum: Thu, 23 May 2013 17:49:07 +0200
-------------------------------------------------
 
 
> Hi,
> 
> Did you try reification? While not great, it should not be too hard to pull
> this off. Or am I missing something here?
> 
> Best
> Christian
> 
> --
> Christian Schulte, Professor of Computer Science, KTH,
> www.ict.kth.se/~cschulte/
> 
> 
> -----Original Message-----
> From: users-bounces at gecode.org [mailto:users-bounces at gecode.org ] On 
> Behalf
> Of Uwe Nowak
> Sent: Thursday, May 23, 2013 3:40 PM
> To: users at gecode.org 
> Subject: [gecode-users] Problem to formulate a constraint
> 
> I am a beginner with gecode and have a problem to formulate a constraint.
> I was looking through all channel constraints, however they do not seem to
> fit my needs, or I am unable to formulate my needs in the language of the
> channel constraints.
> 
> I have the following variables
> *an IntVar c with a finite set of values {A_1,...,A_n} *an IntVarArray p
> 
> I have the following fixed parameters
> For each value A_t I have a finite set of fixed indexed values I_t (e.g, an
> std::set<int>)
> A constant B
> 
> Now I want to formulate the following constraints for(t = 1...n){
> 	c=A_t ==> for all I in I_t: p[i]=B
> }
> 
> 
> I thought to create an IntVarArgs of the subset of p with the indices I_t
> However, than I have tor formulated for an IntVarArgs q_t:
> for(t = 1...n){
> 	c=A_t ==> For all elements q_t[i]=B
> }
> 
> However, I do not find the right expressions to formulate this in gecode...
> 
> 
> 
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