How is the time complexity of inserting an element into a data structure of type set determined?

In data structures like a set (for example, Set in Swift or HashSet in other languages), the insertion operation typically has an amortized time complexity of O(1). This is achieved through the use of hash tables, where an element is placed into a bucket based on its hash.

However, in the worst case, if there are many hash collisions, the complexity can degrade to O(n), where n is the number of elements in the set. But in practice, such cases are rare, and insertion is considered efficient.