20 Jul 2016

This post is one in a series about stuff formally trained programmers know – the rest of the series can be found here.

Binary Tree

In the previous post we looked at the tree pattern, which is a theoretical way of structuring data with many advantages. A tree is just a theory though, so what does an actual implementation of it look like? A common data structure implementation is a binary tree.

The name binary tree gives us a hint to how it is structured, each node can have at most 2 child nodes.

Example of annotated binary tree

Classifications

As a binary tree has some flexibility in it, a number classifications have come up to have a consistent way to discuss a binary tree. Common classifications are: - Full binary tree: Each node in a binary tree can have zero, one or two child nodes. In a full binary tree each node can only have zero or two child nodes. - Perfect binary tree: This is a full binary tree with the additional condition that all leaf nodes (i.e. nodes with no children) are at the same level/depth. - Complete binary tree: The complete binary tree is where each leaf node is as far left as possible. - Balanced binary tree: A balanced binary tree is a tree where the height of the tree is as small a number as possible.

Implementations

While a binary tree is more than just a pattern, there are no out of the box implementations in C#, Java or JavaScript for it. The reason is that it is a very simple data structure and so if you need just the data structure you could implement it yourself but more importantly, you likely want more than the simple structure - you want a structure that optimises for traversal or data management.

References

Wikipedia: Binary Tree

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