Programming Logic - D Heaps

I am writting a code that should do the following for a d-heap:
1. deleteMin( and percolate down)
2. insert
3. buildHeap

I have code that was given to us and is similar to this code:

I know how to do a d-heap by hand and how it works, but when it comes to putting it in code I over think the problem and I get stuck. What is the relationship between the parent and child nodes and how would this change the code to take an inputed value of d from the user? Thanks for the help.
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