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Stacks and Queues in Java

I have been working on some Java code recently that required both a stack and a queue. The choices to use aren’t immediately obvious. There is a Queue interface, but no clear concrete implementation to use. There is also a Stack class, but the javadocs point out that other classes “should be used in preference to this class”. So, what implementation do you use for stacks and queues in Java?

I found my quick rule of thumb to be that you can use the ArrayDeque class for both Stack and Queues, but some more details are below.
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