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My textbook says a "complete binary tree" is a "full binary tree" where every root is at the same level.

My conceptual understanding:

All this time, I was led by my textbook to believe a root is the "top-most vertex" in which all the other vertex are led away from it. So basically I am led to believe there can be only one root in a tree.

Questions:

What does "where every root is at the same level" even mean?

Isn't a root suppose to be at level 0 all the time?

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    $\begingroup$ Are you sure it doesn't say every leaf is at the same level? $\endgroup$
    – Louis
    May 1, 2015 at 6:49
  • $\begingroup$ Nope. The textbook says "The graph representing such a network is a complete binary tree, that is, a full binary tree where every root is at the same level." page 751"Discrete Mathematics and its Application 7th edition written by Kenneth Rosen. I think your statement is referring to "balanced rooted trees" if my memory serves me right. $\endgroup$
    – Nicholas
    May 1, 2015 at 6:53
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    $\begingroup$ It is a typo then. A full binary tree means that every internal node has either 0 or 2 children. A complete one is then a full tree with all the leaves the same distance from the root. $\endgroup$
    – Louis
    May 1, 2015 at 7:09
  • $\begingroup$ Isn't a full binary tree the same thing as a "2-ary tree"? I thought the internal node must have exactly 2 children for full binary tree. My textbook never spoke about internal nodes having 0 children for full binary tree. $\endgroup$
    – Nicholas
    May 1, 2015 at 7:29
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    $\begingroup$ Another point in favor of a typo is "every root". How many roots is a full binary tree supposed to have? If the answer is 1, then the condition is trivially satisfied for any full binary tree. A member of a singleto set shares all its properties with all other members of the same set. :) $\endgroup$
    – babou
    May 1, 2015 at 10:14

1 Answer 1

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It basically is a typo, every leaf at same level may be the correct words

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