Question $2$: Constraint satisfaction problems$-5\backslash \%$

QUESTION $2$a $-2\backslash \%$

Note: The colors in this question are just drawn for better visual representation. In your answers, you can ignore drawing and filling the rows with different colors and simply indicate them with the letters R$,$ G or B$.$

Consider the color mapping problem we covered in the class, where we discussed the map of Australia. We defined our implicit constraint that the adjacent states must have different color:

$(2\backslash \%)$ Draw constraint graph of Australia map coloring problem given the above map and the implicit constraint. Write down at least $5$ implicit constraints for this problem: QUESTION $2$B $-3\backslash \%$

$(2\backslash \%)$ You are asked to make color assignments to a few states, then apply Forward checking after each assignment and rewrite the domain for each of the affected variable $($i$.$e$.,$ the states connected to the one that is assigned the color$).$ As the first step, the calculation is shown below:

NT $=$ green. Apply Forward checking to get the updated domains for each of the variables. The domains should look like below:

NSW $=$ Blue $($while keeping NT $=$ Green$).$ Apply Forward checking to get the updated domains for each of the variables. Show the domains either the list of colors for each variable or insert the table here with colors mentioned as R$,$ G$,$ or B after applying this step:

WA $=$ Red. Apply Forward checking to get the updated domains for each of the variables. Same as above

Do you see any contradiction or issue with the above assignment? If yes, then write maximum of $3$ sentences about the issue: QUESTION $2$C $-1\mathrm{.}5\backslash \%$

$(2\backslash \%)$ Assume we made the assignment NT $=$ Blue. Which of the following Arcs are consistent? For each of the arcs, determine if it is consistent and if not then report for each tail which values should be deleted. You redraw the table for each of the three rows below and either cross the color.