Explanation of Dijkstra's Algorithm for Finding the Shortest Path in a Graph (video - 5 minutes)
Vinsloev Academy discusses Dijkstra's algorithm in their video, demonstrating how it can be used to find the shortest path in a graph. Using the example of travel between cities, where the nodes represent cities and edges are roads with weights corresponding to distances in kilometers, the author illustrates practical applications of the algorithm. Starting from node A and aiming to reach goal node F, Vinsloev Academy prepares viewers for a step-by-step exploration through the graph to calculate the shortest paths considering the weights connected to each edge.
In the initial steps of the algorithm, the author updates the distance list, starting from A with a value of 0, while setting the rest of the nodes to infinity. The focus then shifts to finding the nearest node with the shortest distance — in this case, node B, which is updated to a distance of 1. As the author navigates through other nodes, they continuously update the distance whenever a shorter path is discovered, treating the graph methodically.
As the author moves through nodes, they reflect on their progress, noting which nodes have been visited and the current distances to each target node. Ultimately, reaching node F reveals that the shortest path from A to F is A → B → D → F, effectively illustrating how Dijkstra's algorithm can calculate the shortest path even in complex graphs with diverse weights.
In conclusion, Vinsloev Academy emphasizes the significance of Dijkstra's algorithm in real-world applications like computer networking and transportation. With accurate visualizations and approachable explanations, viewers can grasp how to apply this algorithm in their projects. The encouragement to like and subscribe further supports their channel's growth. At the time of writing, the video has garnered 14,459 views and 154 likes, which speaks to its popularity among programming enthusiasts.
This article showcases how Vinsloev Academy effectively presents Dijkstra's algorithm, making it accessible to anyone looking to delve deeper into topics related to graphs and shortest paths. The presentation is not only educational but also inspiring for future programmers enhancing their skills in this domain.
Toggle timeline summary
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Introduction to Dijkstra's algorithm and its application in finding shortest paths in graphs.
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Real-world application examples, including travel applications where nodes are cities and edges are roads.
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Finding the shortest path between cities based on distances.
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Networking example emphasizing the need for the fastest route for message delivery.
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Beginning the example from node A to goal F.
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Updating the distances for nodes starting from A.
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Initial distance set to infinity for undiscovered nodes.
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Calculating and updating distances for node B.
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Updating distance for node C.
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Marking node A as visited.
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Moving to node B and evaluating distances to G and D.
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Crossing out node B after visiting and updating distances.
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Calculating distance from node C to F.
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Marking node C as visited.
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Evaluating node G and its connection to D.
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Finding the distance from D to F and updating the shortest path.
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Completion of the algorithm with node F as the goal.
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Conclusion on the shortest path discovered using Dijkstra's algorithm.
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Summary of how Dijkstra's algorithm works.
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Encouragement to like and subscribe for more content.
Transcription
Hello and welcome to Vinslov Academy. In this video we are going to explain the Dijkstra's algorithm and how you can use it to find a shortest path in a graph. So for example we have this graph right here and if we should take a real world application that we could use this in, it could for example be in a travel application where the nodes are cities and the edges between them are roads and the weight of these edges is the distance in kilometers. So if you want to go from one city to another you can find the shortest path by looking at the distance between the cities. Another example could be for example in networking when you are communicating from one computer to another over network you want to use the fastest route to ensure that your message will be delivered in the shortest time span. So in this example we will start at node A because this is our start node and our goal is going to be F so we want to travel from A to F. So we will write goal and the first thing that we are going to do is to update the list right here. So as we are starting at A we will write 0 here because there is no weight for us to start at A and then the rest of these will be updated to infinity because we have not yet discovered these. So then we start by our list here so we have A so first off we will take the nearest node that has the shortest weight distance so this is B so we will say 0 plus 1 is 1 so we write 1 right here. And since 1 is less than infinity we will update this and say the value 1 and then we will say the next node we can reach is C so we will say 0 plus 3 and that is 3 and again we update this one right here. And now we have visited every node that we could reach from A so we will cross out A here and say we have visited A. So next we move on to the node that has the shortest distance and that was B so we look at B and then we say the shortest node here is G because 4 and 6 so we say 1 plus 4 and that is 5 and 5 is less than infinity so we update this with a 5. Then we say D because that is the next node we can reach so we say 1 plus 6 and that is 7 so we can update this here and say 7 and now we have visited every node that we could in B so we will cross out B. Then the next node that has the shortest value is C so we will say from C to F so 3 plus 8 and that is 11 so we will just write 11 here. I am writing both the value under the node and here for a clear overview so we will cross out infinity and write 11 and since there are no other nodes than F that we can visit from C we can now cross out C. Then the next node that we are to visit is G so we say from G to D because this is the only node we have 5 plus 5 and that is 10 but that is not less than 7 so we will not update this and therefore we will not update it over here. Now we have visited G because it only has this one node that we have unvisited from G so we say G here and cross that out. The next node that we are going to visit is D so we say from D to F because that is the only one we can reach that we haven't visited yet so we say D to F and that is 7 plus 3 and that is 10 which is actually less than 11 so we can cross out 11 and write 10 here and we can cross out 11 here and write 10. And now we have visited D and all we have left is F which is our goal node. So now we have seen that we can find the shortest path with 10 so it is shorter to travel from A to B to D and down to F even though there are more nodes than the more direct path of A, C and F. But this is shorter due to the weight in between them and that is basically what Dijkstra's algorithm is doing. It is calculating the shortest path from one node to another in a graph with weighted edges. Remember to like and subscribe and then I will see you next time here on Vinslove Academy.