MiniZinc Assign Different Domain to Each Var in Array

Question

I have an array: array[backpacks] of int: capacity specifying the capacity of each backpack.

Now I want to create an array of variables which the constraint solver will have to satisfy. I want each variable to take values in domain 1..capacity where capacity corresponds to the one specified in the above array.

Would something like this work: array[backpacks] of var capacity: bagcaps ?

Or do I have to do something like: array[backpacks] of var 1..MAX: bagcaps

and then add constraints: constraint forall(i in backpacks) bagcaps[i] <= capacity[i] ?

Thank you.

Answer 1

There is no short cut to restrict the domain of specific element in the array declaration. The traditional version is the one you wrote last:

constraint forall(i in backpacks) bagcaps[i] <= capacity[i]);

However, you can make this as an predicate (and place it in a separate file which is then imported into the model with include). E.g. some thing like this:

set of int: backpacks = 1..6;
array[backpacks] of int: capacity = [10,4,3,7,5,3];
array[backpacks] of var 1..max(capacity): bagcaps;

solve satisfy;

predicate restrict_domains(array[int] of var int: x, array[int] of int: d) =
        forall(i in index_set(x)) ( x[i] <= d[i] );

constraint
     % forall(i in backpacks) ( bagcaps[i] <= capacity[i] ) % original
     restrict_domains(bagcaps,capacity)
;

% output [];

Note that you must still use restrict_domains as a constraint. And I recommend that you always restrict the domain in the declaration as much as possible, i.e. use the declaration using var 1..max(capacity) instead of var int.