Understanding Full and Complete Binary Trees

What is the difference between a full binary tree and a complete binary tree?

In binary trees, a full binary tree is a tree where each node has either 0 or 2 children while a complete binary tree has all levels, except possibly the last, fully filled and all nodes are as left as possible. So which statement is correct?

c. every full binary tree is also a complete binary tree

The answer to your question lies in understanding the definitions of a full binary tree and a complete binary tree in relation to each other. For starters, a full binary tree is a special type of binary tree in which all nodes have either 0 or 2 children. In contrast, a complete binary tree is a binary tree in which every level, except possibly the last, is fully filled and all nodes are as left as possible. Consequently, it is possible for a full binary tree to also be a complete binary tree, and vice versa, under specific circumstances.

However, not every full binary tree is a complete binary tree, and not every complete binary tree is a full binary tree. Therefore, the correct statement from your options is: c. every full binary tree is also a complete binary tree, but this is only true if all levels of the tree are fully filled.

To dive deeper into the concept of binary trees and their variations, it is essential to grasp the key distinctions between a full binary tree and a complete binary tree. Understanding these differences will not only enhance your knowledge of binary trees but also help you in designing and analyzing tree structures more effectively.