CODEWITHSUNDEEP
syntax-errorminizincsatisfiability
Kuba
Kuba

Reputation: 291

Minizinc "var set of int: x" instead of "set of int: x"

I have an array of set in the Golfers problem (in each week there should be formed groups, such that no two players play together more than once, and everybody plays exactly one time each week):

int: gr; %number of groups
set of int: G=1..gr;
int: sz; %size of groups
set of int: S=1..sz;
int: n=gr*sz; %number of players
set of int: P=1..n;
int: we; % number of weeks
set of int: W=1..we;

include "globals.mzn";

array[G,W] of var set of P: X; %X[g,w] is the set of people that form group g in week w

My constraints are as follow (I'm not sure if everything works correctly yet):

constraint forall (g in G, w in W) (card (X[g,w]) = sz); %Each group should have size sz

constraint forall (w in W, g,h in G where g > h) (disjoint(X[g,w], X[h,w])); % Nobody plays twice in one week

constraint forall (w,u in W where w > u) (forall (g,h in G) (card(X[g,w] intersect X[h,u]) <= 1 )); % Two players never meet more than once

constraint forall (w in 2..we) (w+sz-1 in X[1,w] /\ 1 in X[1,w]); %Symmetries breaking: week permutations

constraint forall (w in W, g in 1..gr-1) ( min(X[g,w]) < min(X[g+1,w]) ); %Symmetries breaking: group permutations

constraint forall (g in G, s in S) ( s+sz*(g-1) in X[g,1]);

solve satisfy;

output [ show(X[i,j]) ++ if j == we then "\n" else " " endif | i in 1..gr, j in 1..we ];

My problem lies in constraint number 5. I cannot use min on "var set of int: x", I should use it on "set of int: x". Unfortunately, I do not understand the difference between those two (from what I've read this may be connected to defining the size of each set, but I'm not sure).

Could someone explain the problem to me and propose a solution? I would be very very grateful. Thanks!

Upvotes: 0

Views: 828

Answers (2)

Kuba
Kuba

Reputation: 291

I have found out the solution - we should make an array of elements of the set to make the max function possible in this case.

constraint forall (w in 2..we) ( max([i | i in X[1,w-1]]) < max([i | i in X[1,w]])); %Symmetries breaking: week permutations

constraint forall (w in W, g in 1..gr-1) ( min([i | i in X[g,w]]) < min([i | i in X[g+1,w]]));% Symmetries breaking: group permutations (I have been trying to speed up the constraint above, but it does not work with var set of int..)

Upvotes: 0

Kobbe
Kobbe

Reputation: 845

First of all: A var is a decision variable. The goal of all Minizinc programs are to decide the the value of all decision variables. You don't know what the values are and you are trying to find the values. Anything that is not a var is simply a known number. (disregarding the use of sets)

Doing min(X[g,w]) of a decision variable (var) is simply not implemented in Minizinc. The reason would be that using X[g,w] < X[g+1,w] without the min makes more sense. Why only constrain the lowest number in both sets insted of all numbers. I.e {1,3,5} < {1,4} insted of 1 < 1

(I hope MiniZinc has < on sets so I don't lie, I am not sure)

Upvotes: 0

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