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You are planning the seating arrangements for a wedding reception. There will be n guests at...

You are planning the seating arrangements for a wedding reception. There will be n guests at the reception, numbered 1 through n.

Certain pairs of guests are mortal enemies and must not be seated at the same table. The set E contains pairs of guests who are mortal enemies. For example, if guests 1 and 3 are mortal enemies, and guests 2 and 7 are mortal enemies, we would have E = {(1,3), (2,7)}.

Other pairs of guests are best friends and must be seated at the same table. The set F contains pairs of guests who are best friends.

Let m = |E| + |F| be the total number of enemy/friend constraints. You are to design an algorithm that will determine whether or not it will be possible to seat all of the guests. You can use as many tables as necessary, and the tables can be arbitrarily large. The time complexity of your algorithm must be O(n + m log* n). If you do not achieve this complexity, you will receive no credit.

Briefly explain the algorithm and the time complexity.

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