Multiway trie properties

The structure of a multiway trie depends only on the keys in it, not on the order in which they were inserted

Multiway tries have a strong key ordering property: At a node X, all keys in X’s leftmost subtree are smaller than keys in X’s nexttoleftmost subtree, etc. (according to lexicographic ordering)

So, a preorder traversal of a multiway trie visits keys in sorted order

Also, after following a sequence of digits to get to a node X, all keys in the trie that have that sequence as prefix are in the subtree rooted at X

Suppose there are r bits per digit (so radix R = 2
r
), and keys contain at most B bits. Then:

The worst case height of a Rary trie containing N keys is B/r

Compare: worst case height in a regular BST containing N keys is N, which with Bbit keys can be as much as 2
B

When N is large and B is comparable to log
R
N, DST’s give worstcase time cost guarantees better than balanced BST’s, and are much easier to implement

However there is a space cost disadvantage of multiway trees: Each node must store R child pointers, and for a typical tree many of these will be null

This problem can be addressed with ternary tries
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