About bubble sort vs merge sort

It’s a trick question. If you just want the maximum, (or indeed, the kth value for any k, which includes finding the median), there’s a perfectly good O(n) algorithm. Sorting is a waste of time. That’s what they want to hear.

As you say, the algorithm for maximum is really trivial. To ace a question like this, you should have the quick-select algorithm ready, and also be able to suggest a heap datastructure in case you need to be able to mutate the list of values and always be able to produce the maximum rapidly.

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