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

While going through the textbook, I also got confused on the same topic(whether "x" is a pointer to an element or the element itself) and then eventually landed upon this question. But after going through the above discussion and referring textbook again, I think in the book "x" is implicitly assumed to be a "node" and its possible attributes are "key", "next".

Some lines form the textbook..

1)CHAINED-HASH-INSERT(T,x) insert x at the head of list T[h(x.key)]

2)If the lists were only singly linked, then to delete element x, we would first have to find x in the list T[h(x.key)] so that we could update the next attribute of x’s predecessor.

Hence we can assume that the pointer to the element is given and I think Fezvez has given a good explanation for the asked question.