$\backslash$table$[[$Course$,$Lecture Time,Lab$/$Practical Time$],[$CS$303,$Sun Tue Thu $11,12,$MON WED $10,11,12,1],[$CS$600,$Sun Tue Thu $12,1,$MON WED $11,1,2],[$CS$101,$Sun Tue Thu $10,11,12,1,2,3,$None$],[$CS$202,$Everyday $10,11,$None$]]$

$\backslash$table$[[$Time$,$SUN TUE THU,MON WED$],[10,,],[11,,],[12,,],[1,,],[2,,],[3,,]]$

You also include the following set of constraints:

$(1)$ Each class must be assigned to exactly one timeslot

$(2)$ Each timeslot can be assigned to a maximum of one class

$(3)$ No classes can be scheduled during the reserved timeslots

$(4)$ The Mon Wed selection for CS$2$O$2$ must occur at the same time as the Sun Tue Thu selection.

Use the following abbreviations to facilitate writing your solution

$CS101$ Lecture $L1$

$CS202$ Lecture $L2$

$CS303$ Lecture $L3$

$CS303$ Lab $P3$

$CS600$ Lecture $L6$

$CS600$ Lab $P6$

Sun Tue Thu $1010S$

Sun Tue Thu $1111S$

Mon Wed $1010M$

Mon Wed $1111M$

and so on

A$.$ Which of the following options is preferred to represent this as a CSP$?$ Explain your answer:

using meeting times as variables and courses as the values of in the domains?

using courses as variables and the time slots as values?

B$.$ Now using courses are variables and times as values, list the variable and the initial domain values. L$1$ is done for you As an example, continue with the others

$\backslash$table$[[$Variable$,$Domain$],[$L$1,10$S $11$S $12$S $1$S $2$S $3$S$],[,]]$

C$.$ Update the table by removing the values that are incompatible with the constraint#$3.$

D$.$ Simulate DFS with forward checking only on your variables and the reduced domains in part C above. Show your steps. How many times did you backtrack?

E$.$ Write a python program so solve this CSP using forward$-$checking. The program should output a schedule of the $4$ courses that doesn't violate any of the constraints.