This article explores the distinction between a full binary tree and a complete binary tree.

A full binary tree, also referred to as a proper binary tree or 2-tree, mandates that each node, excluding leaf nodes, possess two children. Thus, every node in a full binary tree has either zero or two children, making it the most balanced when containing exactly (2^n) – 1 nodes.

Conversely, a complete binary tree contains fully filled levels, except for the last level, and all nodes are positioned as far left as possible. While the last level of a complete binary tree may contain incomplete nodes, all other levels must be entirely filled.

The primary disparity between a full binary tree and a complete binary tree lies in the requirements for child nodes. In the former, every node has either zero or two children, whereas in the latter, nodes are as far left as possible, and all levels are completely filled except for potentially the last level.

Full Binary Tree

A full binary tree is characterized by the requirement that every node has two children, except for leaf nodes, making it the most balanced tree if there are exactly (2^n) – 1 nodes.

This means that each internal node in a full binary tree has exactly two children, and every leaf node is at the same level.

The concept of a full binary tree is also known as a proper binary tree or a 2-tree.

The balanced nature of a full binary tree ensures that the height of the tree is minimized, resulting in efficient operations such as traversal and searching.

By requiring every node to have two children, except for leaf nodes, a full binary tree ensures the optimal distribution of nodes in a balanced manner.

Complete Binary Tree

Complete binary trees have all levels, except possibly the last, filled with nodes and these nodes are positioned as far left as possible.

In a complete binary tree, all levels are completely filled, meaning that every node has two children, except for the leaf nodes in the last level. This property ensures that the tree is as balanced as possible.

The leftmost position of the nodes is achieved by filling the nodes from left to right in each level. However, it is important to note that the last level may not be completely filled, but it is filled from left to right.

This distinguishes a complete binary tree from a full binary tree, where every node has two children, including the leaf nodes.

Complete binary trees are commonly used in data structures such as binary heaps and binary search trees.

Perfect Binary Tree

The perfect binary tree is characterized by having all internal nodes with two children and all leaf nodes at the same level. This means that every non-leaf node in a perfect binary tree has exactly two children.

Additionally, all leaf nodes, which are the nodes with no children, are at the same level.

The perfect binary tree is a type of binary tree that is considered to be perfectly balanced. It has a symmetrical structure where each level is completely filled with nodes. This allows for efficient searching, insertion, and deletion operations.

The perfect binary tree is often used in various data structures and algorithms due to its balanced nature. It provides a predictable and optimal structure for storing and accessing data. However, it should be noted that the number of nodes in a perfect binary tree must be a power of 2, as the tree is fully balanced and every level has double the number of nodes compared to the previous level.