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Different Shapes and Characteristics of Trees

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Different Shapes and Characteristics of Trees

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Different Shapes and Characteristics of Trees

Different Shapes and Characteristics of Trees

Different Shapes and Characteristics of Trees

Different Shapes and Characteristics of Trees

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.

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