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Can someone explain running times (constant, linear, nlogn) and Heaps?

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I'm trying to understand my homework which is to illustrate a linear time heap constructor as well as a nlogn heap constructor. I understand that linear is faster and more efficient than nlogn, I just don't understand how to come up with their constructors by having that information

My professor wants us to illustrate both in a diagram and in javacode, but I have no idea where to begin. All he gave us was a list of numbers to use.

Another part of the homework is to create a delete min that has a log(n) running time, I have no idea what this means. I believe I understand what heaps are, but I'm not sure how to do the java coding at all. None of the youtube videos I am looking at are helping me either, it's quite frustrating.

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