1. If the induction proof for the towers of Hanoi problem used a base case of n=5 (instead of n=1), would it still be a valid proof? How would the truth that it aims assert be dierent than the n=1 proof?

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2. The following snippet of code defines the Recor der interface. The recorder ADT is used to keep of various objects it is a method of tagging. For example, one might need to keep track of which instant messages (objects) have been displayed to the usr This could be represented by adding items to a Recorder, with the Recorder offering additional functionality to check if a messages was displayed (contained), or undo adding the last element (e.g., win dow clo sed before read by user). public inteface Recorder Item> { void add (Item item boolean contains (Item item) //is item in the colle ction? void undo ); //add an item //removes the last item adde d Give an implementation of Recor der that allows the addition of elements in O(1), query of elements in O(n) time, and removing elements in O(1) time. 6 points 2. The following snippet of code defines the Recor der interface. The recorder ADT is used to keep of various objects it is a method of tagging. For example, one might need to keep track of which instant messages (objects) have been displayed to the usr This could be represented by adding items to a Recorder, with the Recorder offering additional functionality to check if a messages was displayed (contained), or undo adding the last element (e.g., win dow clo sed before read by user). public inteface Recorder Item> { void add (Item item boolean contains (Item item) //is item in the colle ction? void undo ); //add an item //removes the last item adde d Give an implementation of Recor der that allows the addition of elements in O(1), query of elements in O(n) time, and removing elements in O(1) time. 6 points