Exercise 15.20 [dbn-elimination-exercise]

Consider applying the variable elimination algorithm to the umbrella DBN unrolled for three slices, where the query is ${\textbf{P}}(R_3|u_1,u_2,u_3)$. Show that the space complexity of the algorithm—the size of the largest factor—is the same, regardless of whether the rain variables are eliminated in forward or backward order.