For the problem below, two ”high level” greedy strategy is given. One of the strategies gives a correct solutions, and the other sometimes gives an incorrect solutions. Decide which greedy strategy...

For the problem below, two ”high level” greedy strategy is given. One of the strategies gives
a correct solutions, and the other sometimes gives an incorrect solutions. Decide which greedy strategy
produces optimal solutions, and give a proof that it is correct and a counter-example showing the other
strategy is incorrect.( show proof  and counter example)

You are given a list of classes C and a list of classrooms R. Each class c has a positive enrollment E(c)
and each room r has a positive integer size S(r) which denotes its capacity. You want to assign each
class a room in a way that minimizes the total sizes of rooms used. However, the capacity of the room
assigned to a class must be at least the enrollment of the class. You cannot assign two classes to the
same room.

Greedy strategy A: Repeat until all classes are assigned, or a class cannot be included in any unassigned
room. Assign the largest unassigned class to the smallest unassigned room larger than or equal to its
enrollment.

Greedy Strategy B: Repeat until all classes are assigned or a class cannot be included in any unassigned
room: Assign the largest unassigned room to the largest unassigned class smaller than or equal to its
capacity.