You are planning the seating arrangement for a wedding. You are given the list of guests, V , and a lookup-table T where T [v] for v V is a list of guests that v knows. If u knows v, then v also knows u. You are required to arrange the seating such that any guest at a dining table knows every other guest sitting at the same dining table either directly or through some other guests sitting at the same dining table. For example, if x knows y and y knows z and z knows w, then x, y, z, w can sit at the same dining table. Describe an efficient algorithm that takes as input the set V and lookup-table T and returns the minimum number of dining tables needed to achieve a valid seating. You can assume a check in the lookup-table is an O(1) operation.

You are planning the seating arrangement for a wedding. You are given the list of guests, V, and a lookup-table T where T[v] for vV is a list of guests that v knows. If u knows v, then v also knows u. You are required to arrange the seating such that any guest at a dining table knows every other guest sitting at the same dining table either directly or through some other guests sitting at the same dining table. For example, if x knows y and y knows z and z knows w, then x,y,z,w can sit at the same dining table. Describe an efficient algorithm that takes as input the set V and lookup-table T and returns the minimum number of dining tables needed to achieve a valid seating. You can assume a check in the lookup-table is an O(1) operation. Note 1: Please provide a detailed description of your solution in plain English or in pseudocode. Also, explain the time complexity and correctness of the prescribed algorithm. Note 2: You are also allowed to use BFS and DFS as blackbox algorithms (you do not need to explain how it works if you use it) so long as you detail the inputs and outputs to the algorithms as well as any modifications you make