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How to form a k-nary tree with x leaf nodes.
By noob_master, history, 6 years ago, In English

How to form a k-nary tree with x leaf nodes.
Is there any way to find whether a k-nary tree(every node has either k child or it is a leaf node) which have x leaf nodes exists or not. If exits then how to find it.

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6 years ago, hide # |
 
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Unless I’m missing something, you can make an arbitrary k-ary tree with any number of nodes.

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6 years ago, hide # |
 
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Work through a few small examples and look for a pattern that can be generalized.

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    6 years ago, hide # ^ |
     
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    I asked the question after trying. Nevertheless, I will try again.

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      6 years ago, hide # ^ |
       
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      Let’s walk through some examples together.

      For any k, we can start with a k-ary tree of 1 node. Each time we want to go from a k-ary tree of a certain size to the one of the next smallest possible size, we will choose a leaf node and make it an internal node with k children (which are leaves).

      k=2
      k=3
      k=11

      ...

      Result
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