This should have been my first post in the Graph Theory series but nevertheless I got time to discuss this now. Every one must have heard the famous problem of Seven Bridges of Königsberg. If not, then please take some time to read about the problem either on the Wikipedia or right down below:
The city of Konigsberb is located on both the banks of the river Pregel(Kaliningrad, Russia - former Prussia). The city also included two big islands and these islands were connected to each other and the main land by the means of seven bridges. Something like below:
The problem is to devise a...

Read More
# Data Structures

This category contains all the posts related to data structures. For e.g.: Hash Tables, Linked Lists, Trees, Graphs, Heaps, Tries etc..

## Graph Theory Applications – The Instant Insanity Puzzle

[nextpage title="Applications of Graph Theory"]
Graph Theory is used in modelling and solving a lot of real world problems, games and puzzles. Here we discuss a very famous puzzle " The Instant Insanity " problem.
The goal of this post is to demonstrate that such complicated problem statements can be so easily modeled and solved using Graph Theory. Also I would like to build some more interest into Graph Theory. If you want to feel more comfortable with the basics of Graph Theory, here is a list of primers you might like to read once.
Problem Definition - The Instant Insanity Puzzle
The...

Read More
## Priority Queues

Introduction
You have N distinct jobs to process, and you are given the responsibility to schedule them on the only available job processor.
New jobs keeps on getting added into the set of available jobs. Not all the jobs are to be executed as they come.
There might be few which needs to be executed immediately and few can be postponed for some time.
You have an efficiently algorithm to decide the priority of an incoming job. The task at hand is as follows:
To schedule available jobs based on the priority assigned to them.
Add new jobs to the set after assigning a priority to it.
...

Read More
## Understanding Heap Sort

[nextpage title="Introduction"]
Heap Sort is one of the efficient sorting algorithms with a guaranteed worst case running time of O(NlogN). This is an in place sorting algorithm but it does not offer stable sorting.
In place Sorting: A sorting algorithm which sorts the input using very small or no extra space. It means that the input data is overwritten by the resulting output data.
Stable Sorting: A stable sorting algorithm is one, in which the relative order of equal keys is preserved. It means if there are non unique keys in the input data, then their relative order of occurrence in ...

Read More
## Operations on a Heap

Introduction
In this post, we will try to put together all the leanings from the previous posts and define the basic operations on a heap. Also, we will try and derive the running time of each such operation and write code for the same.
Also, we will discuss an interesting problem statement which can be easily solved using the heap property.
Basic Operations on Heap
The heap can support the following basic operations as any other data structure
IncreaseKey - Changes the key value of a given node to a new value. It is assumed that the new value is at least as big as the current value....

Read More
## Building Heaps from an array of keys

[nextpage title="Introduction"]
In the last post we learnt the basics of the heap data structure, its array and tree representations. We also learnt about the heap property and its significance.
In the process of learning we understood that a given node can be disturbed and the heap property needs to be restored using the Heapify operation.
Here in this post, we will try building heaps from an array of keys.
Building Heaps
Let us think about the easiest way to build a heap. Assume we are given the below array A:
This clearly is not satisfying the max heap property because the root ...

Read More
## Understanding the Heap Datastructure

Introduction
Heap(specifically binary heap) is a special data structure which can be viewed as a nearly complete binary tree. This post is mostly focused on understanding the heap datastructure
The first few impressions about heap after reading the above line:
The height of the binary tree would be minimum. For e.g.: if the tree has N nodes, the height would be logN.
The tree can also be stored in an array, in fact it would be easier to store this tree in an array (because it is complete).
This makes it an awesome data structure because the minimum height guarantees logN running ti...

Read More