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Contents

Introduction to Trees

Different Shapes and Characteristics of Trees

Terms

Problems

Like real trees, tree data structures exhibit branching. This carries a number of implications.

First, one must consider the degree of a tree. This refers to the maximum number of children that a node can have. The most common form of tree in computer science is a binary tree, in which each node can have up to 2 children. There are however, ternary trees, with up to 3 children, quaternary trees with up to four children, and so forth.

The next element to consider is the overall size of the tree. There are a number of ways to quantify tree size. One is the longest path from the root node to a leaf node. This is called the depth. If you imagine a tree as having layers, the depth is the number of layers.

When describing a tree, it is often convenient to be able to describe its form in detail. There are several terms which describe the form of trees. A balanced tree is one where all of the leaves of the tree are within one layer of one of each other. For example:

Figure %: Balanced Tree

is a balanced tree, whereas the following is not:

Figure %: Unbalanced Tree

A complete tree is a type of balanced tree, except that it has one more additional constraint. In a balanced tree, all leaves are of depth n or n + 1. In a complete tree, all of the leaves of depth n + 1 are further to the left than the leaves of depth n. Furthermore, in a complete tree, all branch nodes (except those at depth n) must have the maximum number of children.

Figure %: Complete Tree

A perfect tree is even more particular. It requires that all of the leaves be of the same depth and that every branching node has the maximum number of children.

Figure %: Perfect Tree

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