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Language/Type: C# Dictionary collections
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Write a method named Rarest that accepts a SortedDictionary from strings to strings as a parameter and returns the value that occurs least frequently in the dictionary. If there is a tie, return the value that comes earlier in ABC order. For example, if a variable called dict containing the following elements:

{{"Alyssa", "Harding"}, {"Char", "Smith"}, {"Dan", "Smith"}, {"Jeff", "Jones"}, {"Kasey", "Jones"},
 {"Kim", "Smith"}, {"Morgan", "Jones"}, {"Ryan", "Smith"}, {"Stef", "Harding"}}

Then a call of Rarest(dict) would return "Harding" because that value occurs 2 times, fewer than any other. Note that we are examining the values in the dictionary, not the keys. If the dictionary passed is empty, throw an ArgumentException.

Constraints: Obey the following restrictions in your solution.

  • You may create one additional data structure (stack, queue, set, dictionary, etc.) as auxiliary storage. (You can have as many simple variables as you like.)
  • You should not modify the contents of the dictionary passed to your method.
    Declare your method in such a way that any caller can be sure that this will not happen.
  • Your solution should run in no worse than O(N log N) time, where N is the number of pairs in the dictionary.
Method: Write a C# method as described, not a complete program or class.

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