The main advantages of Tries over Binary Search Trees (BSTs) are as follows:
1. Time Complexity
Search, Insert, and Delete Operations: Tries offer a time complexity of $$O(L)$$ for search, insert, and delete operations, where $$L$$ is the length of the key. This is independent of the number of keys stored in the Trie, making it particularly efficient for operations on large datasets[1][2][3][4][5]. In contrast, BSTs have a time complexity of $$O(L \log n)$$ in the average case and $$O(n)$$ in the worst case, where $$n$$ is the number of nodes in the tree[1][11][14].
2. Prefix-Based Searching
Prefix Search and Autocomplete: Tries are inherently designed to support prefix-based searching, which is essential for applications like autocomplete and spell-checking. This is because Tries store keys by their prefixes, allowing for efficient retrieval of all keys that share a common prefix[1][2][4][6]. BSTs do not naturally support prefix-based operations and would require additional logic to implement such features[1][4].
3. Memory Efficiency with Common Prefixes
Common Prefix Sharing: Tries can be more memory-efficient when dealing with datasets that have many common prefixes. They store only the unique prefixes once, reducing redundancy and saving space[3][5][6]. BSTs, on the other hand, do not inherently share common prefixes, which can lead to higher memory usage for similar datasets[1][4].
4. No Collisions
Collision-Free: Unlike hash tables, which can suffer from collisions and require collision resolution strategies, Tries do not have this issue. Each character in a key is stored in a separate node, ensuring unique paths for different keys[1][2][6]. BSTs do not have collision issues either, but they do not offer the same level of efficiency for string operations as Tries[1][4].
5. Alphabetical Order
Ordered Iteration: Tries naturally support ordered iteration of keys, which allows for easy retrieval of keys in lexicographical order. This is useful for applications that require sorted data[1][4][6]. BSTs can also support ordered iteration, but it is not as straightforward as in Tries[1][4].
6. Dynamic Operations
Efficient Dynamic Operations: Tries support efficient dynamic operations suc...
