Height and depth of trees in Data Structures Theory - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the depth of a node in a tree?

The depth of a node is the number of edges from the tree's root node to that node. It tells how far the node is from the root.

beginner

Define the height of a tree.

The height of a tree is the length of the longest path from the root node down to the farthest leaf node. It shows how tall the tree is.

intermediate

How is the height of a node different from the depth of a node?

The depth measures distance from the root to the node, while the height measures the longest distance from the node down to a leaf.

beginner

If the root node has depth 0, what is the depth of its immediate children?

The immediate children of the root node have a depth of 1 because they are one edge away from the root.

intermediate

Why is understanding height and depth important in trees?

Knowing height and depth helps us understand tree structure, optimize searches, and analyze algorithms like traversals and balancing.

What is the depth of the root node in a tree?

A 1

B Height of the tree

C Depends on the tree

D 0

The root node is at depth 0 because it has no edges above it.

The height of a leaf node is always:

A 0

B 1

C Equal to the tree height

D Depends on the depth

Leaf nodes have height 0 because they have no children below them.

If a node has depth 3, how many edges are there from the root to this node?

A 1

B 2

C 3

D 4

Depth counts the number of edges from root to the node, so depth 3 means 3 edges.

Which of the following best describes the height of a tree?

A Number of nodes in the tree

B Longest path from root to any leaf

C Number of children of the root

D Depth of the root node

Height is the length of the longest path from the root to a leaf.

If a tree has height 5, what is the minimum possible depth of a leaf node?

A 1

B 5

C 0

D Cannot be determined

The minimum depth of a leaf node is at least 1 because the root is at depth 0 and leaves are below it.

Explain in your own words the difference between the height and depth of nodes in a tree.

Think about how far a node is from the top versus how far it is from the bottom.

Why is it useful to know the height and depth when working with trees in computer science?

Consider how these measures affect how we navigate or organize data.