# What Is Height and Depth of Tree in Data Structure?

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Larry Thompson

In data structure, a tree is a hierarchical data structure consisting of nodes connected by edges. Each node can have zero or more child nodes, and there is always one node called the root that has no parent. Trees are widely used in various applications, such as file systems, database management systems, and hierarchical representations of data.

## Height of a Tree

The height of a tree is defined as the maximum number of edges between the root and any leaf node in the tree. It represents the length of the longest path from the root to a leaf node. The height of a tree is often used to measure its efficiency and performance.

Example:

• Tree 1:
• Root
• Node A
• Node B
• Tree 2:
• Root
• Node A
• Node B
• Node C
• Node D
• Node E (Leaf Node)
• Tree 3:

In the above example, Tree 1 has a height of 2, Tree 2 has a height of 4, and Tree 3 has a height of 0 (as it only contains the root node).

## Depth of a Tree

The depth of a node in a tree is defined as the number of edges between the root and that particular node. It represents the level or position of the node within the tree hierarchy.

Example:

• Tree:
• Root (Depth: 0)
• Node A (Depth: 1)
• Node B (Depth: 2)
• Node C (Depth: 3)
• Node D (Depth: 4)
• Node E (Leaf Node) (Depth: 5)
• Another Example:

In the above example, each node is labeled with its corresponding depth value.

Understanding the height and depth of a tree is essential for analyzing and designing efficient algorithms. It helps in determining the time complexity of tree-based operations and optimizing their performance.