[SOLVED] Full Binary Tree Question

May 2010
12
0
I'm a little confused on how a full binary tree actually works, here is my question:

Every full binary tree with 53 vertices has ________ leaves.


Thanks a lot guys and gals.
 
Apr 2010
15
2
Answer: 27 leaves

Formula for finding this is: \(\displaystyle (number of vertices+1)/2\)

...look at a smaller examples/full binary trees to see that this works:


Every full binary tree with 7 vertices has 4 leaves.
\(\displaystyle (7+1)/2 = 8/2 = 4\)


Every full binary tree with 15 vertices has 8 leaves.
\(\displaystyle (15+1)/2 = 16/2 = 8\)
 
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Apr 2010
15
2
My replay posted twice for some reason... :/ haha but anyway, I hope that was helpful!