Height of a tree with only one node

Question

According to Wikipedia,

The height of a tree is the length of the path from the root to the deepest node in the tree. A (rooted) tree with only one node (the root) has a height of zero (or one).

I dont get it-is it zero or one (or both)?

Answer 1

Depends on convention. There isn't a "right" answer here. I was taught it's 1. But zero is just as correct.

Answer 2

It just an assuption you make for the recursive description of the height of a binary tree. You can consider a tree composed by just a node either with 0 height or with 1 height.

If you really want to think about it somehow you can think that

• it's 0 if you consider the height as a edge count (so that a single node doesn't have any edge, hence 0)
• it's 1 if you consider the height as a node count (so that a single node counts as 1)

This is just to describe how much height the smallest tree has, then in any case whenever you add a descending node you will add also a related edge so it will increase accordingly.

In the example provided in wikipedia:

This tree can have height 4 (nodes) or 3 (edges). It depends if you are counting it by edges or by nodes.

Answer 3

depends how you want to interpret the height of a tree. in some applications, a tree with one node is interpreted as having height of one and others consider it as having height of zero.

Answer 4

One advantage of using a node count rather than an edge count is that it distinguishes the empty case (zero nodes, and node level) from the minimal case (one node, and a node level of one). In some cases, an empty tree will not be meaningful, but in other cases an empty try will be perfectly legitimate.