Question

I’m trying to learn about trees by implementing one from scratch. In this case I’d like to do it in C# Java or C++. (without using built in methods)

So each node will store a character and there will be a maximum of 26 nodes per node.

What data structure would I use to contain the pointers to each of the nodes?

Basically I’m trying to implement a radix tree from scratch.

Thanks,

Answer 1

What you describe isn’t quite a radix tree… in a radix tree, you can have more than one character in a node, and there is no upper bound on the number of child nodes.

What you’re describing sounds more limited by the alphabet… each node can be a-z, and can be followed by another letter, a-z, etc. The distinction is critical to the data structure you choose to hold your next-node pointers.

In the tree you describe, the easiest structure to use might be a simple array of pointers… all you need to do is convert the character (e.g. ‘A’) to its ascii value (’65’), and subtract the starting offset (65) to determine which ‘next node’ you want. Takes up more space, but very fast insert and traversal.

In a true radix tree, you could have 3, 4, 78, or 0 child nodes, and your ‘next node’ list will have the overhead of sorting, inserting, and deleting. Much slower.

I can’t speak to Java, but if I were implementing a custom radix tree in C#, I’d use one of the built-in .NET collections. Writing your own sorted list isn’t really helping you learn the tree concepts, and the built-in optimizations of the .NET collections are tough to beat. Then, your code is simple: Look up your next node; if exists, grab it and go; if not, add it to the next-node collection.

Which collection you use depends on what exactly you’re implementing through the tree… every type of tree involves tradeoffs between insertion time, lookup time, etc. The choices you make depend on what is most important to the application, not the tree.

Make sense?