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I was wondering if there is a name for the construct described below:

Given $N$ integers $n_0, ..., n_{N-1}$ we construct a tree of height $N$ levels such that:

  • each node of level $0$ (i.e the root) has $n_0$ children.
  • each node of level $1$ has $n_1$ children.
  • ...
  • each node of level $N-1$ has $n_{N-1}$ children

also, this is a sum tree, which means that:

  • an integer is associated with each node
  • we arbitrarily set the associated integer for each leaf node
  • the integer associated with each parent is set to be the sum of the integers associated with its children

Is there a name for that?

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  • $\begingroup$ What will you do with a name? How will you use it? Usually it's better to ask about the actual problem you're trying to solve: we might be able to help with that. There are lots of concepts with no standard "name"; there are far more interesting concepts than "names", so it's usually not so useful to ask for a "name" of something. In this sort of situation, if you're writing a paper, just introduce your own term/name, define it, and use it consistently throughout the paper, and you're good. $\endgroup$ – D.W. May 10 '16 at 23:06
  • $\begingroup$ I am programming this data structure and usually other software engineers like concise names. I guess I could just name it whatever, but it also has to be characteristic of what it is and what it does and ideally has already been named by someone else which helps communication. Maybe I could settle for perfect sum tree... $\endgroup$ – burnedWood May 11 '16 at 18:14

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