How are the height and depth of a tree related?
Height and depth of a tree are related but oppositely directed characteristics.
Depth
Measured downward from the root. Shows how far a specific node is from the root.
javascript
depth(node) = number of edges from the root to this nodeHeight
Measured upward from a leaf. Shows how many edges lie between a node and the deepest leaf.
javascript
height(node) = length of the longest path from this node to a leafRelationship
- The root's depth = 0, the tree's height = the root's height.
- The depth of the deepest node = the tree's height.
Example
javascript
A
/ \
B C
/ \
D E- Depth of
A= 0,B= 1,D= 2 - Tree height = 2 The maximum depth of a tree equals its height.
Summary
Depth is the path down to a node, height is the path up from a node. Maximum depth = the height of the whole tree.
Short Answer
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