Hashing

Part 1:

Hashing is the last topic of all these data structure blogs I have been writing about. I will try to sum up hashing from the basics, but in easier languages and as usual with algorithms and full programs. This post will be also a long and ever increasing post. So, keep close and keep studying.

Introduction:

Let me say that you are coding a database for a coaching institute and want to create a system for looking up each student's result. Now, here the main requirement is to have a high lookup speed. First thought which will come to your mind is the balanced binary tree. In this binary tree, it is guaranteed to have log(n) timed search, updating and balancing operation. But, although log(n) is not high, it can soon go up to higher numbers pretty soon. So, we, in this post, will discuss a much better approach. 

What is hashing? 

Hashing is a technique of creating a array where the entry of the array and the index are related by a certain function, enabling the search of the items in that array makes faster. 

The technique is specifically achieved by Hashing functions. Hashing functions are functions, which take a data as input, and create a index out of it. Because of the computational barriers, hashing functions are required to have

(1) easy and fast computability

(2) uniform (in case of crytographic functions, independent) distribution of the keys among the data.

This second point can be harder to understand. This second point kind of means, that it is sometimes desired of the hashing function that if you can find a pattern or distribution or probability distribution out of the keys, this distribution should be not dependent or biased to the distribution of the data from which the keys are produced. If you do not currently understand it, its not a big deal; a big chunk of the following content does not use it. 

Hash table: 

In the above description, we have referred to a array which stores the data or a reference to data. This array itself is called hash table. Hash table either stores each data with its calculated index, or it stores a link to the list of data with same key. From this, we come to the first block in our road. 

Collision problem:

The problem arrives with a "bad" hashing function. Actually hashing functions can not always guarantee to let all the points of the data to have different key. So, it happens that number of them may end up having the same key. Now, the same key can be avoided in two ways. 

I will talk about the two ways, (1) chain creation and (2) open addressing

Chain creation

Let us assume that the collision happens as there are many elements with the same key. The easiest way to deal with is to create a table with the possible keys as indices. Then, for each key, we create one chain of (implemented as linked list) elements with the same key. Therefore, our ultimate structure is an array of linked lists. If you have read about graphs, this is a analogous structure with the adjacency list. 

Next , I will present a program to create a hashing table with chain creation.