The map-coloring problem consists of nding an assignment of k> 1 different colors to the regions of a given map, in such a way that no pair of neighboring regions (whose borders do not consist of a single point) are given the same color. it is known that a solution with k = 4 exists for any map. a) Formulate the map-coloring problem, for k= 4 colours, as a search problem, by precisely defining the state space, the initial state, the goal test, the set of possible actions and the path cost. b) What is the branching factor of the search tree? con The map-coloring problem consists of nding an assignment of k> 1 different colors to the regions of a given map, in such a way that no pair of neighboring regions (whose borders do not consist of a single point) are given the same color. it is known that a solution with k = 4 exists for any map. a) Formulate the map-coloring problem, for k= 4 colours, as a search problem, by precisely defining the state space, the initial state, the goal test, the set of possible actions and the path cost. b) What is the branching factor of the search tree? con