3. Constraints Satisfaction Problems (25 pts): In the map-coloring problem shown below, each variable in (A, B, C, D, E, P has the same domain [red, green, blue]. We use the backtracking algorithm with the forward checking to solve the problem. Recall that when a value is assigned to a variable V, forward checking eliminates inconsistent values in the variables adjacent to V in the constraint graph. Use these heuristics, in this order to select the next variable to assign: (i) most constrained variable (aka, minimum remaining values), (ii) most constraining variable (aka, degree heuristic), (ii) least constraining value. Whern several variables tie, select the first in alphabetic order. When several values tie, select them in the following order: red, green, blue a. Draw the constraint graph for this problem: a graph with a node for each variable and an arc between two variables if there is a constraint between them Which variable will be selected first by the algorithm? Why? Which value will be assigned to this variable? Why? Which values of which variable domains does the forward-checking operation then remove? Which variable will be selected next? Why? Which value will be assigned to this variable? Why? Which values of which variable domains does the forward-checking operation then remove? Use your answers to the above questions to count the number of complete valid assignments for this problem. Tell us how you proceed to do the counting. b. C. d. e. f