What is the time complexity of inserting an element at the beginning of a data set?

The time complexity of inserting an element at the beginning of a data set depends on the data structure used to store the set.

• If the set is implemented as a linked list (e.g., singly linked list), insertion at the beginning will have a complexity of O(1), as it is enough to change the pointer to the new element.
• If the set is implemented as an array or dynamic array (e.g., ArrayList), inserting at the beginning requires shifting all elements, which gives a complexity of O(n).
• In standard set data structures (e.g., HashSet in Swift or Set in iOS), there is no concept of "beginning" as the set is unordered. Insertion of an element usually occurs in amortized O(1).

Thus, if we are talking specifically about a set, then inserting an element does not have a "beginning" concept and occurs in O(1). If it is an ordered collection, then inserting at the beginning can be O(1) or O(n) depending on the implementation.