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Understanding Dijkstra's Algorithm: A Step-by-Step Example

This guide explains Dijkstra's Algorithm through a detailed example. Dijkstra's method is used for finding the shortest paths from a starting node to all other nodes in a weighted graph. The process involves initializing nodes, selecting the node with the minimum temporary distance, and updating distances and predecessors. We walk through each step, demonstrating how nodes are selected based on their distance labels and how the predecessor relationships are established. By the end, you'll grasp how to trace the shortest path from the starting node to any other.

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Understanding Dijkstra's Algorithm: A Step-by-Step Example

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  1. 15.082 and 6.855J Dijkstra’s Algorithm

  2. 1 An Example   4 2 4 2 2 0 2 1 3  1 6 4 2 3 3 5   Initialize Select the node with the minimum temporary distance label.

  3. Update Step 2   4 2 4 2 2 0 2 1 3  1 6 4 2 3 3 5   4

  4. Choose Minimum Temporary Label 2  4 2 4 2 2 0 2 1 3  1 6 4 2 3 3 5  4

  5. Update Step 6 2  4 2 4 2 2 0 2 1 3  1 6 4 2 3 3 5  4 4 3 The predecessor of node 3 is now node 2

  6. Choose Minimum Temporary Label 2 6 4 2 4 2 2 0 2 1 3  1 6 4 2 3 3 5 3 4

  7. Update 2 6 4 2 4 2 2 0 2 1 3  1 6 4 2 3 3 5 3 4 d(5) is not changed.

  8. Choose Minimum Temporary Label 2 6 4 2 4 2 2 0 2 1 3  1 6 4 2 3 3 5 3 4

  9. Update 2 6 4 2 4 2 2 0 6 2 1 3  1 6 4 2 3 3 5 3 4 d(4) is not changed

  10. Choose Minimum Temporary Label 2 6 4 2 4 2 2 0 2 1 3 6 1 6 4 2 3 3 5 3 4

  11. Update 2 6 4 2 4 2 2 0 2 1 3 6 1 6 4 2 3 3 5 3 4 d(6) is not updated

  12. Choose Minimum Temporary Label 2 6 4 2 4 2 2 0 2 1 3 6 1 6 4 2 3 3 5 3 4 There is nothing to update

  13. End of Algorithm 2 6 4 2 4 2 2 0 2 1 3 6 1 6 4 2 3 3 5 3 4 All nodes are now permanent The predecessors form a tree The shortest path from node 1 to node 6 can be found by tracing back predecessors

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