Question

Are the trie and radix trie data structures the same thing?

If they aren’t the same, then what is the meaning of radix trie (AKA Patricia trie)?

Answer 1

A radix tree is a compressed version of a trie. In a trie, on each edge you write a single letter, while in a PATRICIA tree (or radix tree) you store whole words.

Now, assume you have the words hello, hat and have. To store them in a trie, it would look like:

    e - l - l - o
  /
h - a - t
      \
       v - e

And you need nine nodes. I have placed the letters in the nodes, but in fact they label the edges.

In a radix tree, you will have:

            *
           /
        (ello)
         /
* - h - * -(a) - * - (t) - *
                 \
                 (ve)
                   \
                    *

and you need only five nodes. In the picture above nodes are the asterisks.

So, overall, a radix tree takes less memory, but it is harder to implement. Otherwise the use case of both is pretty much the same.