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You want to be able to access the largest element in a stack.

You've already implemented this Stack class:

class Stack # Initializes an empty stack. def initialize @items = [] end # Pushes a new item onto the stack. def push(item) @items << item end # Removes and returns the last item. # # If the stack is empty, returns nil. (It would also be # reasonable to throw an exception.) def pop if @items.empty? nil else @items.pop end end # Returns the last item without removing it. def peek if @items.empty? nil else @items[-1] end end end

Use your Stack class to implement a new class MaxStack with a method get_max that returns the largest element in the stack. get_max should not remove the item.

Your stacks will contain only integers.

What if we push several items in increasing numeric order (like 1, 2, 3, 4...), so that there is a new max after each push? What if we then pop each of these items off, so that there is a new max after each pop? Your algorithm shouldn't pay a steep cost in these edge cases.

You should be able to get a runtime of for push, pop, and get_max.

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time for push, pop, and get_max. additional space, where m is the number of operations performed on the stack.

Our solution requires additional space for the second stack. But do we really need it?

Can you come up with a solution that requires additional space? (It's tricky!)

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