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.

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- May 12th 2010, 04:13 PMMathHelp12345[SOLVED] Full Binary Tree Question
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. - May 12th 2010, 05:16 PMlozts
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:

http://www.ad.ntust.edu.tw/course/ad...pics/tree1.jpg

Every full binary tree with 7 vertices has 4 leaves.

$\displaystyle (7+1)/2 = 8/2 = 4$

http://www.gamedev.net/reference/pro...FullBinary.jpg

Every full binary tree with 15 vertices has 8 leaves.

$\displaystyle (15+1)/2 = 16/2 = 8$ - May 12th 2010, 05:17 PMlozts
My replay posted twice for some reason... :/ haha but anyway, I hope that was helpful!

- May 12th 2010, 05:22 PMMathHelp12345
Thanks so much, I was unaware of the formula for this.