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I have variables x y and z, and I have the values that they can be assigned to, I.E. x can be assigned 1,2, or 3, y can be 1, and z can be 2. The problem is a constraint that says once a value has been taken by a variable, no other variables can have that value.

The issue that I am running into is if I start with x, how can I efficiently tell that it's value should be 3?

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  • $\begingroup$ Is the set of possible values can contain an infinite number of elements? $\endgroup$ – user3563894 Sep 3 '18 at 16:06
  • $\begingroup$ Also, how the set of possible values is represented by? $\endgroup$ – user3563894 Sep 3 '18 at 16:09
  • $\begingroup$ Set of values is finite, and I am not sure I understand your second question. $\endgroup$ – Crispies Sep 3 '18 at 16:14
  • $\begingroup$ Can we assume that the set of values is represented by a set $S=\{v_1,v_2,\ldots,v_n \}$? $\endgroup$ – user3563894 Sep 3 '18 at 16:16
  • $\begingroup$ And is there a single constraint as described above, or there are multiple constraints, and one of them is that "once a value has been taken by a variable, no other variables can have that value"? $\endgroup$ – user3563894 Sep 3 '18 at 16:19
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The problem you are describing amounts to constraint programming and the specific constraint you are talking about is the alldifferent constraint. I'm not offering a purely algorithmic solution, but reading a bit on constraint programming could give you some ideas on how to construct a search tree where you make a decision (i.e., assign a value to a variable) at each node, and how to backtrack to a feasible node when you reach an infeasible node.

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