Complete Data Structures in JavaScript

[dayton-outar]

Source code and explanation needed to fully explain the following,

• [ ] Hashing
• [ ] Heap
• [ ] Binary Tree
• [ ] Splay
• [ ] Trie

[dayton-outar]

An AVL tree and a splay tree are both types of self-balancing binary search trees, but they differ significantly in how they achieve balance and handle operations.

AVL Tree:

• Strict balancing: An AVL tree maintains a balance factor (the difference in height between the left and right subtrees) for each node, ensuring that the tree remains balanced at all times. After every insertion or deletion, the tree may perform one or more rotations to maintain this balance.
• Performance: Because it enforces stricter balance, the AVL tree guarantees (O(\log n)) time complexity for all basic operations (search, insert, delete).
• Best use case: AVL trees are often preferred in applications where search performance is critical, as they tend to have smaller heights compared to other trees.

Splay Tree:

• No strict balancing: A splay tree uses a more relaxed balancing method known as "splaying." After accessing a node (for search, insert, or delete), it brings that node to the root through a series of rotations (zig, zig-zag, or zig-zig operations). Over time, frequently accessed nodes move closer to the root.
• Performance: Splay trees have amortized (O(\log n)) time complexity, meaning that while individual operations might take longer in the worst case (up to (O(n))), the average time per operation over a sequence of operations is (O(\log n)). This makes them efficient in applications with non-uniform access patterns, where some elements are accessed more frequently than others.
• Best use case: Splay trees are well-suited for applications where access patterns exhibit locality (i.e., recently or frequently accessed nodes are more likely to be accessed again soon).

Key Differences:

• Balancing method: AVL trees use strict balancing with a height balance factor, while splay trees use splaying to bring frequently accessed elements near the root.
• Operation time complexity: AVL trees guarantee (O(\log n)) worst-case time complexity, while splay trees guarantee (O(\log n)) amortized time complexity.
• Application scenarios: AVL trees excel in uniformly accessed datasets, whereas splay trees are better for non-uniform access patterns.

In summary, while both are self-balancing trees, AVL trees prioritize maintaining balance strictly for guaranteed efficiency, and splay trees optimize for access patterns by moving frequently used elements closer to the root.