If binary search and search tree operate in the same time, why do both exist and when should each be used?

Although binary search and search trees can have the same asymptotic time complexity (O(log n)), they are used in different scenarios due to the characteristics of data structures and operations.

• Binary search works on sorted arrays or lists and is efficient for searching elements. However, inserting and deleting in an array require shifting elements and have a complexity of O(n).

• Search trees (e.g., balanced binary trees) support dynamic operations: insertion, deletion, and search in O(log n). This is convenient when data changes frequently.

When to use:

• If data is static and many fast searches are needed — binary search on an array.
• If data is dynamic, with frequent additions or deletions — search tree.

Thus, both tools complement each other depending on the requirements for data structure and operations.