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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# online classes

## 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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## Graph Theory

Preface
This is the first article in the Graph Theory - Online Classes. To all my readers and friends, you can safely skip the first two paragraphs.
The motivation to write this series
Its been long I have been planning to write this article and now I think is the right time to start a new category & series of articles in the Graph Theory. As a student it was always the most complicated topic for me and I was scared with the topic. I am sure many of you must have faced the same. Of course everyone has their own reason, for me it was the order in which it was taught and definitely it w...

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## Tree Diameter

Introduction
This is the fifth article in the Tree Traversals - Online Classes.
A very interesting problem is to find the diameter of a tree. The challenge is not in coding the algorithm but in understanding the meaning of the problem. We will try to define the problem so that visualizing the solution becomes easy.
Defining the problem - Tree Diameter
Few confusions about the diameter must be avoided before we start.
The tree diameter is always the distance between two leaf nodes
The diameter may or may not pass through the root.
The diameter can also lie on one of the two sides,...

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## Spiral Traversal

Spiral Traversal or Zigzag Traversal in a Tree.
This is the fourth article in the Tree Traversals - Online Classes.
Recently I wrote an article on Level Order Tree Traversal. Another problem on the same lines is to traverse the tree in a zigzag manner. That is also termed as spiral traversal. This question has been asked in many companies during the interview process.
Although it is not very specific problem, if you understand the idea behind traversing a tree in breadth first manner, then you can easily solve this. Please read further for more understanding.
Defining the problem
L...

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