调整时间复杂度 - 使用动态数组进行链式哈希

Question

we built a hash table that is a dynamic array and each element in it is a linked list(chain hashing).

if each time we resize the hash table to be twice its original size, we obviously need to move all existing nodes in the chains, to the newly sized hash table, my question is: if we go through each linked list(the chains) -even the empty ones- does this change the complexity of amortized O(1)? if yes is going through the none empty linked lists a good solution(amortized time complexity of O(1))?

Answer 1

Assuming you maintain a load factor of x < 1 (A good default is keeping 0.25 < x < 0.5 , where x is the load factor), and you calculate it based on the number of elements in the hash table, you are fine.

You are going to iterate the table, which will take linear time (<4*n iterations), and this will take place after at least 1/4*n operations - which means your amortized time is at worst ~4*n / (1/4*n) = 16 , which is still constant (This accounts for iterating over empty cells as well).