Pseudocode for the new implementation of BFS using an adjacency matrix:
```
BFS(adjacency_matrix, start_node):
Create a queue and enqueue the start_node
Create a visited array and mark the start_node as visited
While the queue is not empty:
Dequeue a node from the queue
Process the node
For each adjacent node in the adjacency matrix:
If the adjacent node is not visited:
Mark the adjacent node as visited
Enqueue the adjacent node
```
The time complexity of this new version of BFS using an adjacency matrix is O(V^2), where V is the number of vertices. This is because we need to iterate over each element in the adjacency matrix to check the connections between nodes. In the worst case, we may need to visit every entry in the matrix, resulting in a quadratic time complexity.
In comparison, the version of BFS seen in class using an adjacency list has a time complexity of O(V + E), where V is the number of vertices and E is the number of edges. This version is more efficient because it only visits the nodes and edges that are present in the graph, rather than iterating over all possible connections as in the adjacency matrix implementation.
The two versions are equally efficient when the graph is dense and the number of edges approaches the maximum possible value of V^2. In this scenario, the time complexity of both implementations becomes similar, as the number of iterations required in the adjacency matrix version is comparable to the number of edges in the adjacency list version. However, in most practical cases, where the graph is sparse (fewer edges compared to the total possible connections), the adjacency list version is more efficient.
For more such answers on Pseudocode
https://brainly.com/question/24953880
#SPJ8
