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Revati S Misra

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Aryan Kumar

Aryan Kumar

21-Nov-2023

Dijkstra's algorithm is a widely used algorithm in computer science for finding the shortest path between nodes in a graph, especially in scenarios where all edge weights are non-negative. The algorithm maintains a set of vertices whose shortest distance from the source is known. It repeatedly selects the vertex with the smallest tentative distance, updates its neighbors' distances, and marks the selected vertex as "visited." This process continues until the algorithm has visited all vertices or reached the destination vertex.

Steps of Dijkstra's Algorithm:

Initialization:

  • Assign a tentative distance value to every node. Set the source node's distance to 0 and all other nodes' distances to infinity. Mark all nodes as unvisited.

Start from the Source:

  • Set the current node to the source node (A in this case).

Visit Neighbors:

  • Visit each unvisited neighbor of the current node and calculate their tentative distances through the current node. If the newly calculated tentative distance is less than the current assigned value, update the distance.

Mark Current Node as Visited:

  • Mark the current node as visited.

Select the Next Node:

  • Choose the unvisited node with the smallest tentative distance as the next current node. In this case, it's D with a tentative distance of 2.

Repeat Steps 3-5:

  • Repeat steps 3-5 until all nodes are visited.

Shortest Path:

  • The final distances represent the shortest path from the source node (A) to all other nodes.

Final Shortest Paths:

  • Shortest path from A to B: A -> D -> C -> B (Total distance: 0 + 2 + 4 + 3 = 9)
  • Shortest path from A to C: A -> D -> C (Total distance: 0 + 2 + 4 = 6)
  • Shortest path from A to D: A -> D (Total distance: 0 + 2 = 2)

In summary, Dijkstra's algorithm efficiently finds the shortest path from a source node to all other nodes in a weighted graph, ensuring that the sum of edge weights along the path is minimized.

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