The set() in Python is implemented internally using a hash table data structure. This implementation allows for efficient average time complexity for operations such as membership checks, additions, and deletions, typically $$O(1)$$ on average.
Hash Table Mechanism
A hash table stores elements in a way that makes it very fast to determine if a specific element is present in the set. Each element is passed through a hash function, which computes an index in an internal array where the element is stored. The choice of a hash function is crucial as it affects the efficiency of the data structure. The hash function aims to distribute elements uniformly across the array to minimize collisions—situations where different elements are assigned the same index.
Handling Collisions
When collisions occur (i.e., two elements are assigned the same index), Python handles them using a method called open addressing (specifically, quadratic probing in CPython). If a collision occurs, the set implementation probes alternative locations in the array (determined by the quadratic function) until an empty slot is found.
Dynamic Resizing
The underlying array of a hash table is dynamically resized to maintain efficient operations as elements are added or removed. When the load factor (the ratio of the number of elements to the capacity of the hash table) reaches a certain threshold, the array is resized. Typically, the size is doubled. This resizing operation involves rehashing all existing elements in the set, which is a costly operation but happens infrequently enough that the amortized cost of insertions and deletions remains $$O(1)$$.
Dummy Values
Internally, Python's sets are implemented similarly to dictionaries,...
