Hash Tables

A hash table uses hash functions to compute an integer value for data. This integer value can then be used as an index into an array, giving us a constant time access to the requested data. However, using separate chaining, we won't always achieve the best and average case efficiency of O(1) . If we have too small a hash table for the data set size and/or a bad hash function, elements can start to build in one index in the array. Theoretically, all n element could end up in the same linked list. Therefore, to do a search in the worst case is equivalent to looking up a data element in a linked list, something we already know to be O(n) time. However, with a good hash function and a well created hash table, the chances of this happening are, for all intents and purposes, ignorable.

Wasted memory space

Create a hash table where the elements of the array are pointers to linked list objects. You have your linked list as normal, but when you add an element to the linked list, you also add a pointer to that element from the correct place in the hash table specified by the hash value of the data in the new linked list element.

Create a hash table of all the words in the dictionary. When you encounter a word, whose spelling you want to check, just hash it and see if it exists in the table. If it does, then you've spelled it correctly. If not, then you haven't. This allows you to look up a word in O(1) time rather than O(n) time, which, in a dictionary on the order of 800,000 words, is a big time saver.

O(1) . Lookup is O(1) and deleting from a linked list is O(1) , so the total efficiency is O(1) .