How does a hash table work?

Question

I\'m looking for an explanation of how a hash table works - in plain English for a simpleton like me!

For example, I know it takes the key, calculates the hash (I a

Answer 1

A hash table totally works on the fact that practical computation follows random access machine model i.e. value at any address in memory can be accessed in O(1) time or constant time.

So, if I have a universe of keys (set of all possible keys that I can use in a application, e.g. roll no. for student, if it's 4 digit then this universe is a set of numbers from 1 to 9999), and a way to map them to a finite set of numbers of size I can allocate memory in my system, theoretically my hash table is ready.

Generally, in applications the size of universe of keys is very large than number of elements I want to add to the hash table(I don't wanna waste a 1 GB memory to hash ,say, 10000 or 100000 integer values because they are 32 bit long in binary reprsentaion). So, we use this hashing. It's sort of a mixing kind of "mathematical" operation, which maps my large universe to a small set of values that I can accomodate in memory. In practical cases, often space of a hash table is of the same "order"(big-O) as the (number of elements *size of each element), So, we don't waste much memory.

Now, a large set mapped to a small set, mapping must be many-to-one. So, different keys will be alloted the same space(?? not fair). There are a few ways to handle this, I just know the popular two of them:

• Use the space that was to be allocated to the value as a reference to a linked list. This linked list will store one or more values, that come to reside in same slot in many to one mapping. The linked list also contains keys to help someone who comes searching. It's like many people in same apartment, when a delivery-man comes, he goes to the room and asks specifically for the guy.
• Use a double hash function in an array which gives the same sequence of values every time rather than a single value. When I go to store a value, I see whether the required memory location is free or occupied. If it's free, I can store my value there, if it's occupied I take next value from the sequence and so on until I find a free location and I store my value there. When searching or retreiving the value, I go back on same path as given by the sequence and at each location ask for the vaue if it's there until I find it or search all possible locations in the array.

Introduction to Algorithms by CLRS provides a very good insight on the topic.