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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# Data Structures

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

## 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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## Inorder Predecessor of node in Binary Tree Using Parent Pointer

Introduction
This is the seventh article in the Tree Traversals - Online Classes.
This article presents ways to find out inorder predecessor of node in binary tree. As we have already read about the Inorder Successor it wont take much effort to understand the predecessor.
Definition - Inorder Predecessor of node in Binary Tree
If a node K is called the inorder predecessor of node N then N must be visited immediately after K in a inorder traversal of the tree.
Below is a more formal definition of Inorder Predecessor:
If the node has a left sub-tree, then inorder predecessor is the ...

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## Inorder Successor of node in Binary Tree Using Parent Pointer

Introduction
This is the sixth article in the Tree Traversals - Online Classes.
This article presents ways to find out inorder successor of node in binary tree. Before we jump into the code it would be good to correctly define the meaning of the problem.
Definition - Inorder Successor of node in Binary Tree
If a node K is called the inorder successor of node N then K must be visited immediately after N in a inorder traversal of the tree.
Below is a more formal definition of Inorder Successor:
If the node has a right sub-tree, then inorder successor is the left most node of the rig...

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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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