Every Full Binary Tree is Also a Complete Binary Tree

Which statement is true about binary trees?

The one true statement among the given options is C. Every full binary tree is also a complete binary tree.

Understanding Binary Trees

Binary trees are hierarchical data structures in which each node has at most two children, referred to as the left child and the right child. They are commonly used in computer science for various applications, such as searching and sorting algorithms.

Full Binary Trees

A full binary tree is a type of binary tree in which every node has either 0 or 2 children. This means that every internal node has exactly two children. This property distinguishes full binary trees from other types of binary trees.

Complete Binary Trees

A complete binary tree is a binary tree in which every level, except possibly the last one, is fully filled, and all nodes are as far left as possible. In other words, a complete binary tree is filled from left to right across each row, with no gaps.

Relationship Between Full and Complete Binary Trees

Since a full binary tree ensures that every node has either 0 or 2 children, it naturally satisfies the criteria of being completely filled at each level (except possibly the last one) and having all nodes positioned as far left as possible. Therefore, it can be deduced that every full binary tree is also a complete binary tree.

Understanding the distinctions between full and complete binary trees is essential in designing efficient algorithms and data structures. By recognizing the characteristics of each type of binary tree, developers can optimize their solutions for various computational problems.

If you're interested in exploring more about binary trees and their applications, you can delve deeper into the topic by visiting resources like textbooks, online tutorials, and educational platforms.