Consider the problem of coloring the six regions (numbered 1..6 ) in the following map using three colors: R, G, and B, so that no adjacent regions have the same color. Two regions are adjacent if they share part of an edge(note: they are NOT adjacent if they only share a corner), (i) [2 points] If initially every variable has all three possible values except region 1 has known value R(1=R) and region 2 has known value G(2=G), what is the result of the Forward Checking algorithm for this step? Final Domains: (ii) [2 points] Assume the initial domains of the regions in the map above are given as 1={R,G,B},2={R,G},3={R,G,B},4={R},5={R,G,B}, and 6={R}. What is the result of applying the Arc Consistency algorithm, AC3 ? Final Domains: (iii) [2 points] Assume no variables have been assigned yet, solve the CSP using backtracking with forward checking. Final Assignments