I’m currently studying data structures and algorithms and often find myself unsure about which data structure to choose for a given problem to optimize performance. I understand the basics of common data structures like arrays, linked lists, stacks, queues, trees, and hash tables, but I struggle with deciding which one is the most appropriate in various scenarios.

Search Operations: When should I prefer a binary search tree over a hash table for search operations, and vice versa? What are the trade-offs in terms of time and space complexity?

Insertion and Deletion: For a scenario that requires frequent insertions and deletions, is there a clear advantage of using linked lists over arrays? Are there any specific cases where one is significantly better than the other?

Graph Representation: In what situations should I use an adjacency matrix over an adjacency list for representing graphs? How do the size of the graph and the density of edges affect this choice?