algorithm - How to create a forced matrix

Question

I have this requirement to create a tree like structure. Each parent can have at most 3 children. And the tree grows 15 level deep (total 3^15 members). The thing is, addition of child nodes are done by giving each parent a child. For example

                  1
      2           3             4
   5  8  11     6 9 12       7 10 13

Tree grows like this. 5th child goes under 2, 6th child goes under 3, 7th child goes under 4, 8 again under 2... etc. I am given the root node and member to be added, for example, 1 and 10. How can I programmatically find which position the new child should be added?. An answer with an algorithm would be much helpful

Answer 1

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