Question

Computer Science

Posted 6 months ago

```
Dijkstra's shortest path algorithm is run on the graph, starting at vertex A. When a vertex is
dequeued, 0 or more adjacent vertices' distances are updated.
For each iteration of the while loop in Dijkstra's algorithm, find the vertex dequeued and the adjacent
vertices updated. Enter updated vertices as A, B, C or "none" if no adjacent vertices are updated.
5
E
C
Iteration
Vertex dequeued
Adjacent vertices updated
1
Ex: C
Ex: A, B, C or none
1
2
6
2
B
A
9
3
3
4
8
5
D
```

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Answer from Sia

Posted 6 months ago

Explanation

Dijkstra's algorithm is used to find the shortest path from a starting vertex to all other vertices in a weighted graph.

Step-by-step Instruction

▪

Choose to return a string because Hello World contains multiple characters

▪

Define concrete use cases and testing cases for the function: when user calls function_name(), it should return "Hello World"

```
To solve the problem of identifying the vertex dequeued and the adjacent vertices updated for each iteration of Dijkstra's algorithm, follow these steps:
1.
```

```
- Start at vertex A.
- Set the initial distances to all vertices as infinity, except for the starting vertex A, which is set to 0.
- Use a priority queue to keep track of the vertices to be processed.
2.
```

```
- Dequeue the vertex with the smallest distance from the priority queue.
- For each adjacent vertex, calculate the potential new distance.
- If the new distance is smaller than the current known distance, update the distance and enqueue the adjacent vertex.
3.
```

```
- For each iteration, record the vertex dequeued and the adjacent vertices whose distances were updated.
Here is a Python implementation of Dijkstra's algorithm with comments explaining each step:
```

python

Time Complexity

The time complexity of Dijkstra's algorithm using a priority queue (min-heap) is $O((V + E) \log V)$, where $V$ is the number of vertices and $E$ is the number of edges.

Space Complexity

The space complexity is $O(V + E)$ due to the storage of the graph, distances, and priority queue.

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