The algorithm for solving tree$-$structured CSPs starts by picking a root variable. We can pick any variable for this. For this exercise, we will pick A$.$ There are

several linearizations consistent with A as the root; we will use the one shown below.

In this step we start with the right$-$most node $($E$),$ enforce arc$-$consistency for its parent $($B$),$ then do the same for the second$-$to$-$right$-$most node $($C$)$ and its parent

$($B$),$ and so on$.$ Execute this process, and then mark the remaining values for each variable below.

Node B: Red

Node B: Green

Node B: Blue

Node C: Red

$$ Node D: Red

$$ Node D: Blue

Dode E: Green

Node E: Blue

QUESTION $7$

$[$Continued from the above problem$]$

Step $2$: Assign Forward

Now that all domains have been pruned, we can find the solution in a single forward pass $($i$.$e$.$ no need for backtracking$).$ This is done by starting at the left$-$most

node $($A$),$ picking any value remaining in its domain, then going to the next variable $($B$),$ picking any value in its domain that is consistent with its parent, and

If at any given nod, always picking a value consistent with its parent's assignment.

blue.

What is the solution found by running the

$$ Node A: Red

Node A: Green

Node A: Blue

Node B: Red

$$ Node B: Green

Node B: Blue

Node C: Red

Node C: Green

Node C: Blue

Node D: Red

$\frac{?}{{?}_{\frac{?}{?}}}$ Node D: Green

Node D: Blue

Node E: Red

Node E: Green

Node E: Blue