Which of the following is TRUE about binary trees:
a. Every binary tree is either complete or full. b. Every complete binary tree is also a full binary tree. c. Every full binary tree is also a complete binary tree. d. None of the above.
The one true statement among the options is C that is; Every full binary tree is also a complete binary tree. Since the full binary tree is a binary tree in which each node has either 0 or 2 children. Apart from this, a complete binary tree is a binary tree where every level, except possibly the last one, is completely filled, and all nodes are as far left as possible.
Also, it is known that a full binary tree satisfies the conditions of having either 0 or 2 children for each node, it inherently meets the criteria for being completely filled at each level and having all nodes as far left as possible. Thus, we can conclude that every full binary tree is also a complete binary tree.
Understanding Complete and Full Binary Trees
A binary tree is a data structure in which each node can have at most two children, referred to as the left child and the right child. When it comes to binary trees, two important concepts are complete binary trees and full binary trees.
Complete Binary Tree:
In a complete binary tree, all levels are completely filled except possibly for the last level, which is filled from left to right. This means that all nodes are as far left as possible on each level. Complete binary trees are particularly useful for efficiently storing and searching for data.
Full Binary Tree:
A full binary tree is a type of binary tree in which every node has either 0 or 2 children. This means that no node has only one child. Full binary trees are also known as proper binary trees or 2-tree.
Relationship between Complete and Full Binary Trees:
From the characteristics of these two types of binary trees, we can determine that every full binary tree is also a complete binary tree. Because in a full binary tree, the criteria of having 0 or 2 children for each node inherently results in the tree being completely filled at each level and all nodes being positioned as far left as possible.
In conclusion, the statement "Every full binary tree is also a complete binary tree" is true, showcasing the relationship between the concepts of fullness and completeness in binary tree structures.