Introduction
For those who are not familiar with the snakes and ladders game. Here is a link for introduction. So the fastest reach in snakes and ladders, is a modified version of the game. So, you are playing the game called snakes and ladders and you have an enchanted dice. You are the master of the dice and you can command it to get any number between 1 and 6 both inclusive. This means that when you throw the dice, the number on the upper face is totally controlled by you. If you ask for a 5, you get a 5 and so on.
Problem Statement - Fastest Reach in Snakes and Ladders
The problem in ha...

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# graph theory

## Further Reading for Minimum Spanning Tree

Introduction
This is a supplement to the posts for Minimum Spanning Tree and their Analysis. Check out the other related articles in the following section.
Further Reading for Minimum Spanning Tree
This section is meant to be read in conjunction to the post Minimum Spanning Tree - Prim's Algorithm
The minimum spanning tree of a Graph is the union of minimum spanning trees of its connected components.
This is a very important observation and it must be discussed in length and breadth because this will help us design our algorithm for MST in a
better way.
Why is it so important to underst...

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## Depth First Traversal

Introduction
This is the second post in the Graph Traversals – Online Classes.
I Recommend you to look at the first post Breadth First Traversal as it contains more explanation and details and I will keep this post smaller just around the depth first concept.
Depth First Traversal
The Idea
In this traversal, we choose a start vertex and keep moving forward along the length of the graph until there is no undiscovered vertex in that path. Once reaching a dead end, we back track to all the visited vertices and check if we have any vertex which has an adjacent undiscovered vertex.
We kee...

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## Breadth First Traversal

Introduction
This is the first article in the Graph Traversals – Online Classes.
Dear Readers, these set of posts under Graph Traversals will make more sense if you have read the Graph Theory. Here is a quick brush up for the same. However, if you are familiar with Graph Theory and have a basic knowledge of what graphs are and how they are stored, you can dive into the traversals.
Later in the series we will discover that the Graph Traversals are widely used in various application. Let me point out a couple of real world examples here:
How can we conduct matches between teams in a C...

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## Complex Graph Operations

Introduction
This is the fourth article in the Graph Theory - Online Classes.
After learning the basic graph operations, its time to dive deeper and have some understanding about the complex operations which we can be done over a graph or a set of graphs. To learn about the basics you can always visit Graph Theory Basics.
Complex Graph Operations
Union of Graphs
The union of two graphs G(VG, EG) and H(VH, EH) is the union of their vertex sets and their edge families. Which means G ∪ H = (VG ∪ VH, EG ∪ EH).
The below image shows a union of graph G and graph H. Make sure that all the v...

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## Graph Operations

Introduction
This is the third article in the Graph Theory - Online Classes.
With some basic concepts we learnt in the previous two articles listed here in Graph Theory, now we have enough tools to discuss some operations on any graph. In this article we will try to define some basic operations on the Graph.
Graph Operations - Extracting sub graphs
In this section we will discuss about various types of sub graphs we can extract from a given Graph.
Sub graph
Getting a sub graph out of a graph is an interesting operation. A sub graph of a graph G(V,E) can be obtained by the following...

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## Special Graphs

Introduction
This is the second article in the Graph Theory - Online Classes.
Dear readers, I assume that you have already finished reading the first post, if not I would advise you to please go through the first article in the series Introduction to Graph Theory, as this post will require some basic knowledge which we discussed in the previous post.
Few Special Graphs
The Null Graph
The first graph we will discuss is the Null Graph. By definition, this graph has a V(G) which is non-empty and a E(G) which is empty. In simple words a graph which only has vertices and no edges is a Null...

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