Tries and Hash Tables are both efficient data structures used for storing and retrieving data, but they have distinct advantages that make Tries particularly useful in certain scenarios over Hash Tables. Here are some main advantages of Tries over Hash Tables:
Predictable Lookup Time: Tries offer a predictable $$O(n)$$ lookup time where $$n$$ is the size of the key. This predictability is beneficial for latency-critical tasks, as the lookup time does not vary with the number of elements in the data structure, unlike Hash Tables which can have lookup times deteriorating to $$O(n)$$ in worst-case scenarios due to collisions[1].
Efficiency with Small Keys: For small keys, such as integers or pointers, Tries can be more efficient than Hash Tables. This is because Tries remove the overhead associated with complex hash functions required by Hash Tables, making them particularly suitable for scenarios where keys are small[1].
Ordered Iteration: Unlike Hash Tables, which produce a pseudorandom order when iterated over, Tries inherently maintain the order of keys. This makes Tries suitable for applications requiring sorted output, such as dictionaries, where one might need to print all words in alphabetical order[1][7].
Longest-Prefix Matching: Tries excel in identifying the longest common prefix, which is indispensable for tasks like text auto-completion or network routing. This feature allows for efficient prefix searches and auto-complete functionalities, which are not directly supported by Hash Tables[1].
No Need for Hash Functions: Tries do not require a hash function to map keys to values, which eliminates the potential for hash collisions—a common issue in Hash Tables that can affect performance and complexity. This also means there's no need for collision handling algorithms, simplifying the data structure's implementation.
Support for Dynamic Insertion and Deletion: Tries allow for dyna...
