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In the map-coloring problem shown to the right, each variable (A, B, C, D, E, and F) has the domain r, g, b). To solve this problem, use the simple backtracking algorithm with the forward-checking operation. Recall that when a value is assigned to a certain variable V, forward checking eliminates inconsistent values in the variables adjacent to V in the constraint graph. To select the next variable to assign, use these heuristics in this order: Most-constrained variable (aka, minimum remaining values), Most constraining variable (aka, degree heuristic). Least constraining value. When several variables tie, select the first in alphabetic order. When several values tie, select them in the following order:r,g, b. a) Draw the constraint graph for this problem. b) 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? d) Which variable will be selected next? Why? Which value will be assigned to this variable? In the map-coloring problem shown to the right, each variable (A, B, C, D, E, and F) has the domain r, g, b). To solve this problem, use the simple backtracking algorithm with the forward-checking operation. Recall that when a value is assigned to a certain variable V, forward checking eliminates inconsistent values in the variables adjacent to V in the constraint graph. To select the next variable to assign, use these heuristics in this order: Most-constrained variable (aka, minimum remaining values), Most constraining variable (aka, degree heuristic). Least constraining value. When several variables tie, select the first in alphabetic order. When several values tie, select them in the following order:r,g, b. a) Draw the constraint graph for this problem. b) 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? d) Which variable will be selected next? Why? Which value will be assigned to this variable