What is the difference between tree depth and height?

Solution 1:

I learned that depth and height are properties of a node:

• The depth of a node is the number of edges from the node to the tree's root node.
  A root node will have a depth of 0.

• The height of a node is the number of edges on the longest path from the node to a leaf.
  A leaf node will have a height of 0.

Properties of a tree:

• The height of a tree would be the height of its root node,
  or equivalently, the depth of its deepest node.

• The diameter (or width) of a tree is the number of nodes on the longest path between any two leaf nodes. The tree below has a diameter of 6 nodes.

Solution 2:

height and depth of a tree is equal...

but height and depth of a node is not equal because...

the height is calculated by traversing from the given node to the deepest possible leaf.

depth is calculated from traversal from root to the given node.....

Solution 3:

According to Cormen et al. Introduction to Algorithms (Appendix B.5.3), the depth of a node X in a tree T is defined as the length of the simple path (number of edges) from the root node of T to X. The height of a node Y is the number of edges on the longest downward simple path from Y to a leaf. The height of a tree is defined as the height of its root node.

Note that a simple path is a path without repeat vertices.

The height of a tree is equal to the max depth of a tree. The depth of a node and the height of a node are not necessarily equal. See Figure B.6 of the 3rd Edition of Cormen et al. for an illustration of these concepts.

I have sometimes seen problems asking one to count nodes (vertices) instead of edges, so ask for clarification if you're not sure you should count nodes or edges during an exam or a job interview.