# Binary Trees

• May 28th 2009, 12:55 AM
kurac
Binary Trees
Hi,

How do i find out the number of leaves, number on internal vertices and the height on tree T .

All we know is T has 2148 vertices.

I think the tree height is 11? Can someone confirm that for me?

How do i find out number leaves and internal vertices? Thanks.
• May 28th 2009, 01:49 AM
Isomorphism
Quote:

Originally Posted by kurac
Hi,

How do i find out the number of leaves, number on internal vertices and the height on tree T .

All we know is T has 2148 vertices.

I think the tree height is 11? Can someone confirm that for me?

How do i find out number leaves and internal vertices? Thanks.

If we know the tree is complete, then you can show by induction that for a height 'n' tree, there will be \$\displaystyle 2^n - 1\$ vertices, \$\displaystyle 2^{n-1}\$ leaf vertices... of course remaining are internal vertices (Wink)
• May 28th 2009, 02:38 AM
kurac
thanks for that.

I have a tree t with 2148 vertices.
Assume t is full.
So i have calculated a tree height of 11.

number of leaves = 2047
number of internal vertices = 1124.

Can you please check that for me? your help is so much appreciated.