data structures and algorithm

Shortest Path using Dijkstra’s Algorithm

Introduction This is the third post in the Graph Traversals – Online Classes. After learning how to move through a graph, we might be interested in learning more. One interesting problem is determining the shortest path between two vertices of a graph. The problem can be extended and defined in many other forms. I prefer to call it "minimizing the cost". For e.g. When we measure the cost in terms of the distances between vertices, it can be called as the Shortest Path. When we measure the cost in terms of the money spent between vertices, it can be called as the Cheapest Path. Whe...
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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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