Minizinc: set enumerated set of options based on array position, as opposed to set of options for all array positions

Question

I am familiar with such approaches as

set of int: RANGE = 1..5;
enum OPTS = {A,B,C};
array[RANGE] of var OPTS = result;

but what about when I would like to specify the OPTS for each position in RANGE? Something that looks like

[{A,B,C},{A,B},{A,B,C,D},{B,D},{A}]

then generate result[n] so that it picks one of the available options at n.

I've tried with the following model but a model inconsistency is detected.

set of int: RANGE = 1..5;
enum OPTS = {A,B,C,D};
array[RANGE] of set of OPTS: t = [{A,B,C},{A,B},{A,B,C,D},{B,D},{A}];
array[RANGE] of var OPTS: result;
constraint forall(i in RANGE)(
  forall(j in t[i])(
    result[i] = j
  )
);

output [show(result)]

with a possible result being [B,A,B,D,A] - the last position result[5] cannot be anything other than A.

I try to use the Minizinc manuals but I cannot decipher how to use examples within the specifications eg https://www.minizinc.org/doc-2.4.3/en/spec.html#set-operations, which presuppose other knowledge (e.g. how to interpret the syntax) that I could spend countless hours trying to hunt down an explanation for on my level, since searching this stuff seems to be really unfruitful.

Thanks!

Answer 1

If I understand you correctly you can use set of OPTS to construct the array of OPTS, here called t (you cannot call it output since it's a reserved word). Note that as you presented the problem, it's not a var but a constant array so you don't need the var keyword when you construct the array.

set of int: RANGE = 1..5;
enum OPTS = {A,B,C,D};
array[RANGE] of set of OPTS: t = [{A,B,C},{A,B},{A,B,C,D},{B,D},{A}];

Update

Here's a model for the updated question. The trick here is that t[i] defines the valid domain of result[i], and you can simply use in for this.

set of int: RANGE = 1..5;
enum OPTS = {A,B,C,D};
array[RANGE] of set of OPTS: t = [{A,B,C},{A,B},{A,B,C,D},{B,D},{A}];
array[RANGE] of var OPTS: result;

constraint 
  forall(i in RANGE) (
     % ensure that result[i] only takes the values in t[i]
     result[i] in t[i]
  )
;

output [show(result)]

There are 48 solutions to this problem, such as:

[A, A, A, B, A]
----------
[B, A, A, B, A]
----------
[C, A, A, B, A]
----------
[A, B, A, B, A]
----------
[B, B, A, B, A]
----------
[C, B, A, B, A]
----------
[A, A, B, B, A]
----------
...