Differences Between Strictly Binary Trees and Full Binary Trees

Often, the terms strictly binary tree and full binary tree are interchanged or used interchangeably, leading to confusion. However, these terms represent distinct properties of binary trees. This article will delve into the definitions, characteristics, and distinctions between strictly binary trees and full binary trees to provide clarity.

What is a Binary Tree?

A binary tree is a type of tree data structure where each node can have at most two children. We will henceforth refer to it simply as a tree for short.

In the diagram below, the aqua-colored node is the root node, while the pink, green, yellow, and violet nodes are child nodes. The green and yellow nodes are termed left child nodes, and the pink and violet nodes are right child nodes. A newly generated node that stems from another node can also be called a parent node, even if it later becomes a child node itself. Nodes that have the same parent are referred to as sibling nodes.

Strictly Binary Trees

A strictly binary tree, also known as a proper binary tree, is characterized by the following properties:

Each internal node (a node with one or more children) must have exactly two children. Hence, every internal node has zero or two children. Internal nodes that have children are required to have precisely two children, ensuring the binary nature is not violated.

The strictly binary tree emphasizes the requirement that every internal node must possess exactly two children, hence the term "proper."

Full Binary Trees

A full binary tree has a similar structure to a strictly binary tree, characterized by the following:

Each node has zero or two children. The term "full" can be somewhat broader and may apply to trees where every node is either a leaf (with zero children) or an internal node with two children. This means a full binary tree can be seen as a subset of strictly binary trees, but not all strictly binary trees are full binary trees.

The key difference is that a strictly binary tree requires every internal node to have exactly two children, whereas a full binary tree allows for nodes to have zero or two children, but not one.

Key Differences and Examples

To illustrate, consider the following images:

Image A

Image B

Image C

Image D

Image E

Quiz Time

Let's test your understanding with a few questions. Consider the following tree structures and determine if they are full, strictly binary, or complete:

Is Image A a full tree? Is Image A complete? Is Image B a full tree? Is Image B complete? Is Image C a full tree? Is Image C complete? Is Image D a full tree? Is Image D complete? Is Image E a full tree? Is Image E complete?

Summary and Further Reading

In summary, while the definitions can overlap, the term strictly binary tree emphasizes the condition that every internal node must have exactly two children, while a full binary tree may simply refer to the same structure without emphasizing this strict condition.

Further reading on binary tree types and properties can provide a deeper understanding of how these trees are utilized in computer science and data structures. Understanding the differences is crucial for building and optimizing algorithms that rely on these tree structures.

To wrap up, we have explained the nuances and differences between strictly binary trees and full binary trees. The distinctions are subtle but significant, especially when crafting efficient algorithms and data models in computer science.