Write and apply Dijkstra’s Shortest path algorithm to find the shortest path from a source node A to all the other nodes in a graph given below
To apply Dijkstra's algorithm to find the shortest path from a source node A to all the other nodes in the given graph, we can follow the following steps:
- Initialize the distance to the source node as 0, and the distance to all other nodes as infinity.
- Mark all nodes as unvisited.
- Set the current node to the source node A.
- For the current node, calculate the distances to all its neighbors, as the sum of the distance from the source node to the current node and the distance from the current node to its neighbor. Update the distance to each neighbor if it is smaller than the current recorded distance.
- Mark the current node as visited.
- Set the next current node as the unvisited node with the smallest recorded distance from the source node.
- Repeat steps 4 to 6 until all nodes have been visited.
Here is the step-by-step application of Dijkstra's algorithm to find the shortest path from source node A to all other nodes in the given graph:
Step 1: Initialize the distance to the source node as 0, and the distance to all other nodes as infinity.
| Node | Distance |
|---|---|
| A | 0 |
| B | ∞ |
| C | ∞ |
| D | ∞ |
| E | ∞ |
| F | ∞ |
| G | ∞ |
Step 2: Mark all nodes as unvisited.
Step 3: Set the current node to the source node A.
Current node: A
Step 4: For the current node, calculate the distances to all its neighbors, as the sum of the distance from _____ ____ _________ ________ _______ ___ __________ _____ ____ ____ ______.
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