Why deletion of elements of hash table using doubly-linked list is O(1)?

Question

On CLRS\'s textbook \"Introduction to Algorithm\", there\'s such paragraph on pg. 258.

We can delete an element in O(1) time if the lists are doubly linked. (Note th

Answer 1

In general you are correct - the algorithm you posted takes an element itself as input though and not just its key:

Note that CHAINED-HASH-DELETE takes as input an element x and not its key k, so that we don't have to search for x first.

You have the element x - since it is a double linked list you have pointers to predecessor and successor, so you can fix those elements in O(1) - with a single linked list only the successor would be available, so you would have to search for the predecessor in O(n).