Find maximum element in hashtable with doubly linked list in each slot

Question

There is a hash table, slots in an array, each slot has a doubly linked list, unsorted.

Total element count is n , slot count is m .

What is the time complexity to:

• Find the maximum element in whole hashtable.
• Find the successor element for a given element x.

They should be both O(n) , right? Because you have to iterate every element.

But, in the book <The algorithm design manual 2nd> , page 90 , it says it's O(n+m) , but I don't get it.

Anyone, help to tell which is right? And, why.

Thanks.

Answer 1

Slots can be empty (have no elements in the list). You have to iterate all the slots to find all the non-empty lists, so that's O(m) work. Then you have to search all the lists, which is O(n) work. Total work: O(n + m).