(Solved): You are designing a menu for a special event. There are several choices, each represented as a vari ...

You are designing a menu for a special event. There are several choices, each represented as a variable: (A)ppetizer, (B)everage, main (C)ourse, and (D)essert. The domains of the variables are as follows: A: (v)eggies, (e)scargot B: (w)ater, (s)oda, (m)ilk $$C:$$ (f)ish, (b)eef, (p)asta D: (a)pple pie, (i)ce cream, (ch)eese Because all of your guests get the same menu, it must obey the following dietary constraints: 1. Vegetarian options: The appetizer must be veggies or the main course must be pasta or fish (c) both). 2. Total budget: If you serve the escargot, you cannot afford any beverage other than water. 3 alcium reguirement: You must serve at least one of milk, ice cream, or cheese. The constraint graph over the variables $$A,B,C$$, and $$D$$ is given below: a. [3 pts] Show the initial domains for each variable b. [4 pts] Imagine we first assign $$A=$$ e. Cross out eliminated values to show the domains of the variables after forward checking. c. [4 pts] Again imagine we first assign $$A=e$$. Cross out eliminated values to show the domains of the variables after arc consistency has been enforced. [ 1 pt.] Give a solution for this CSP or state that none exists. [3 pts.]What is worst-case time complexity of Arc-Consistency (AC-3) algorithm?