3.6 Dijkstra Algorithm - Single Source Shortest Path - Greedy Method

Dijkstra Algorithm for Single Source Shortest Path
Procedure
Examples
Time Complexity
Drawbacks
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This is just for my reference sorry i don't know a better way: 4:36 start of the example 5:13 repeating steps start 5:28 performing relaxation 6:11 next vertex (3) selected 6:51 vertex 4 selected 7:18 making chart of shortest distances 7:48 time complexity of the algorithm 9:26 text book example begins 13:34 drawback of the algorithm

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Mr. @Abdul Bari, thank you so much for your lucid explanation, I've enjoyed it very much. One quick suggestion regarding runtime complexity analysis: since in actual implementation of Dijkstra algorithm, priority queue data structure is used to get the next node with minimum d[v] and to update d[v], and as a result, runtime comes to big-oh of O(E*log(V)), I think it'll be nice if you could make a video specifically on priority queue and how its use in different algorithms can result in better runtime. Thanks and hope to watch a video on this topic soon :)

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[@PratikShah123]

Thanks for one more great video !! Btw, This is my understanding of Time complexity: 1. *Initialization:* - Setting the initial distance to each vertex: O(V) 2. *Main Loop:* - The main loop of Dijkstra's algorithm runs for each vertex in the graph, processing each vertex once. - Within each iteration of the loop, we extract the minimum distance vertex from the priority queue, which takes O(log V) time in a binary heap. Since this operation is performed for each vertex, the total time for this step is O(V * log V). 3. *Relaxation:* - For each vertex, we iterate through its adjacent vertices and relax the distances if a shorter path is found. - In the worst case, each edge is considered once, leading to O(E) relaxation operations. - Each relaxation operation involves updating the distance of a vertex in the priority queue, which takes O(log V) time in a binary heap. - So, the total time for relaxation is O(E * log V). 4. *Total Time Complexity:* - Combining the time complexities of initialization, the main loop, and relaxation, the overall time complexity of Dijkstra's algorithm using a binary heap for the priority queue is O((V + E) * log V). In summary, using a binary heap for the priority queue in Dijkstra's algorithm results in a time complexity of O((V + E) * log V), where V is the number of vertices and E is the number of edges in the graph. PS: Thanks to ChatGPT !!

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