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

The problem presented here is : consider you have are looking at a particular element of a hashtable. How costly is it to delete it?

Suppose you have a simple linked list :

v ----> w ----> x ----> y ----> z
                |
            you're here

Now if you remove x, you need to connect w to y to keep your list linked. You need to access w and tell it to point to y (you want to have w ----> y). But you can't access w from x because it's simply linked! Thus you have to go through all your list to find w in O(n) operations, and then tell it to link to y. That's bad.

Then, suppose you're doubly-linked :

v <---> w <---> x <---> y <---> z
                |
            you're here

Cool, you can access w and y from here, so you can connect the two (w <---> y) in O(1) operation!