What is the minimum height height of a full binary tree?

Question

What is the minimum height of a full binary tree T which has nodes n(T) = 2^k-1 for k= 1, 2, ... ?

Answer 1

The minimum height would occur when when the tree is symmetrical. That is when the left and right subtrees off the root are identical.

 

n(1) = 0     only node is the root;  h(1)=0

n(2) = 3     root and "first" subtree;  h(2)=1

n(3) = 7     each of the two "leaves" then gets two branches giving 4 more nodes; h(3) = 2

 

 

so for n(T) = 2^k-1 what is h(T)?

 

If still can't get it comment back.

 

Marianne,

 

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