# What does every root is at the same level mean

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?

• Are you sure it doesn't say every leaf is at the same level? May 1, 2015 at 6:49
• 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. May 1, 2015 at 6:53
• 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. May 1, 2015 at 7:09
• 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. May 1, 2015 at 7:29
• 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. :) May 1, 2015 at 10:14