In Dijkstra's algorithm, what condition must be met for a vertex to be added to

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Question: In Dijkstra\'s algorithm, what condition must be met for a vertex to be added to the set of visited vertices?

Options:

Correct Answer: It must have the smallest edge weight

Solution:

In Dijkstra\'s algorithm, a vertex is added to the set of visited vertices when it has the smallest tentative distance from the source vertex.

In Dijkstra's algorithm, what condition must be met for a vertex to be added to the set of visited vertices?

In Dijkstra's algorithm, what condition must be met for a vertex to be added to the set of visited vertices?

Step 1: Start with a source vertex and set its tentative distance to 0.
Step 2: Set the tentative distances of all other vertices to infinity.
Step 3: Look at all the vertices that have not been visited yet.
Step 4: Find the vertex with the smallest tentative distance among the unvisited vertices.
Step 5: Add this vertex to the set of visited vertices.
Step 6: Update the tentative distances of its neighboring vertices based on the distance to the current vertex.
Step 7: Repeat steps 3 to 6 until all vertices have been visited.

Dijkstra's Algorithm – An algorithm used for finding the shortest paths between nodes in a graph, particularly for weighted graphs.
Tentative Distance – The current shortest known distance from the source vertex to a vertex that has not yet been visited.
Visited Vertices – Vertices that have been finalized in terms of their shortest path from the source vertex.