Venture Into Digital Trees 
The Digital Tree, frequently referred to as a Trie, is a data structure used primarily for predictive text, autocomplete, and spellchecking programs. Its preeminence in these applications is due to the speed of its search, insertion, and deletion capabilities, which significantly exceed that of Binary Trees and rival that of hash tables. Key to its performance, and in contrast to Binary Trees, is its large number of children per node. This is the result of an algorithm which, rather than navigating to the child with a greater or lesser value, navigates to the child with a matching value. Because the choice of children is greater, the Digital Tree has less steps to take before traversing all the way down the tree.
While the widely known Binary Tree is intrinsically limited to two children per node, only the number of possible sets of characters within a string limits the Digital Tree's number of children per node. This is frequently broken down further and each node limited to a single character. As a result a Digital Tree utilizing a string of only single case alphabetic characters would have up to twenty-six children per node.
With only two children per node the Binary Tree's worst case lookup speed is O(log2N) time, where N is the total number of items in the tree. In contrast, the Digital Tree would have a worst case lookup speed in this scenario, of O(log26N). So if we had N = 100,000 items in each tree than the maximum lookup time for a Digital Tree would be O(3.5) while for a Binary Tree it would be O(16.6). Furthermore, if the Digital Tree instead utilized upper and lower case characters of the alphabet resulting in 52 children per node, then the subsequent maximum lookup time for a Digital Tree would be O(2.9).
From these simple calculations we can see that the Digital Tree is clearly faster than the Binary when it comes to traversing the entire tree. It is also apparent that the larger the number of children per node the faster the traversal. In addition, it is noteworthy that the above worst case lookup times for a Digital Tree are still remarkably close to the best case lookup time of a hash table, which is O(1). Furthermore, after taking into account collisions and buckets in a hash table, the gap between the two narrows quickly.