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Language/Type: Java TreeMap collections
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Write a method named rarest that accepts a TreeMap from strings to strings as a parameter and returns the value that occurs least frequently in the map. If there is a tie, return the value that comes earlier in ABC order. For example, if a variable called map 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(map) would return "Harding" because that value occurs 2 times, fewer than any other. Note that we are examining the values in the map, not the keys. If the map passed is empty, throw an IllegalArgumentException.

Constraints: Obey the following restrictions in your solution.

  • You may create one additional data structure (stack, queue, set, map, etc.) as auxiliary storage. (You can have as many simple variables as you like.)
  • You should not modify the contents of the map 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 map.
Method: Write a Java method as described, not a complete program or class.

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