How many times do I need to backtrack? well I would have to unassign Blue from D, but now D has no valid domains, so I have to unassign Green from B, however, B has no domains, so now I have to unassign green from E. Therefore, C has no valid elements in its domain so I need to backtrack. Suppose I assigned the value Blue for A, then Green for E, Green for B, Blue for D, and since I assigned Green for B, I have forced C to have blue, but C CANNOT have blue since D now has Blue. However, you might be wondering, why the order A->E->B->D->C will have 2D backtracking. This means that by assigning C, I have actually pretty much solved the problem moving forward with this ordering which means that the worst case scenario is that there will never be any backtracking since by assigning C, I have constrained all the domains on all of my other nodes, and in fact, this will be true for any sized domain (if it works for 2, it will obviously work for 2+ elements in my domain). Then, when I look at D, since C was assigned Blue, I know D must therefore be assigned value Green as well and in this process so on and so forth. so I choose Blue, then, I can eliminate from B, Blue from its domain, so B must have the value Green.

That means, I choose an x in (Blue, Green) for C. Then, suppose I begin assigning values for this CSP in this order C->B->D->E->A, (Blue, Green) and my constraint, no node can have the same color as the node to the its right. To redefine, suppose I illustrate this problem as a coloring problem with 5 nodes, A, B, C, D, E.Īnd each node can have this set of domains. Looking at the problem, I think I can illustrate how you might arrive at the answers in here.

Definition of backtrack