The space complexity of a hash table is generally $$ O(n) $$, where $$ n $$ is the number of key-value pairs stored in the hash table. This complexity arises because each key-value pair occupies a certain amount of space, and the total space required grows linearly with the number of elements stored in the hash table[2][3][4].
In more detail, the space complexity can vary slightly depending on the implementation of the hash table, particularly in how it handles collisions and whether it uses open addressing or closed addressing (chaining):
Open Addressing: In open addressing, all elements are stored directly in the hash table array itself. The space complexity remains $$ O(n) $$ because each element occupies one slot in the array, and the size of the array is proportional to the number of elements to avoid excessive collisions[2].
Closed Addressing (Chaining): In closed addressing, each slot of the hash table array can store multiple elements usi...
