How is a full binary tree characterized?

A full binary tree is characterized by all nodes having either zero or two children.

A full binary tree, also known as a proper or plane binary tree, is a specific type of binary tree in which every node in the tree has either zero or two children. That is, no node in the tree has only one child. This characteristic makes full binary trees particularly interesting and useful in certain types of computer science problems and algorithms.

In a full binary tree, all the leaf nodes (those with zero children) are typically at the same level, or one level difference in case of an incomplete binary tree. This uniformity of structure can simplify certain operations and algorithms that work with such trees. For example, in a full binary tree, the number of leaf nodes is always one more than the number of nodes with two children.

Another important characteristic of a full binary tree is its relationship between the number of nodes and the height of the tree. The height of a full binary tree with 'n' nodes is log(n+1) base 2. This logarithmic relationship means that full binary trees are height-balanced, which is an important property for many algorithms, such as search algorithms, that depend on the tree's height for their performance.

Full binary trees are widely used in computer science. They form the basis for heaps, which are used in heap sort, a common sorting algorithm. They are also used in binary search trees, which are a fundamental data structure for many search algorithms. Understanding the properties and characteristics of full binary trees is therefore crucial for any student of computer science.