Before I get started, if you need some background on what a heap is:
https://en.wikipedia.org/wiki/Heap_(data_structure)
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You might want to look at my code. It is in C#, but I have a generic heap, and all you need to make a heap is a compare function. You don't need two values when you add to a heap. You can have multiple heaps of the same type but they can use different priority algorithms based on the delegate you pass in on construction.
github.com/ZacharyPatten/Towel
This was a student of mine's homework project. His professor's specifications required the Heap to store Node objects with key-values on them. I understand that you can do this many different ways, but thank you for the clarification. I like the idea of initializing with a different delegate to indicate algorithm changes :)
If you have to store keys and values, all you do is (in C# using my example) this:
Heap<(KeyType, ValueType)>
So there should only ever be one generic type, even if you need to store multiple values, you just pass in a type with multiple values.
Just wanted to clarify that. Let me know if that doesn't make sense and I will gladly elaborate.
But yeah. Hope the student had fun figuring out the algorithms of a heap. :)
Yeah, your template looks a lot like the templating stuff I'd use in C++ and Java (I don't know C# but I understand it is similar enough).
We both had fun working through the methods :D It is definitely good practice.