Hi guys: Can any one please tell me what does this means? Thanks
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The second matrix is simply the symmetric version of the first.
This
1 2 3 4 5 6 7
1 0 2 3 x 2 4 x
2 2 3 11 2 3 5
3 3 9 2 3 5
4 3 9 3 5
5 9 3 4
6 8 4
7 8
is simply the running of Dijkstra's algorithm
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1st Matrix
1 2 3 4 5 6 7
1 x 2 3 x 2 4 x
2 x 2 9 x 1 3
3 x x 2 2 2
4 x 7 x 9
5 x 2 x
6 x 1
7 x
2nd Matrix
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1 2 3 4 5 6 7
1 x 2 3 x 2 4 x
2 2 x 2 9 x 1 3
3 3 2 x x 2 2 2
4 x 9 x x 7 x 4
5 2 x 2 7 x 2 x
6 4 1 2 x 2 x 1
7 x 3 2 4 x 1 x
Based on the information provided, it seems that the second matrix is a symmetric version of the first matrix. To understand what this means, let's break it down step by step.
First, let's look at the first matrix:
1 2 3 4 5 6 7
1 x 2 3 x 2 4 x
2 x 2 9 x 1 3
3 x x 2 2 2
4 x 7 x 9
5 x 2 x
6 x 1
7 x
In this matrix, the numbers in each cell represent the weights of the edges between each pair of vertices. The x's represent that there is no edge between those vertices.
Now, let's move on to the second matrix:
1 2 3 4 5 6 7
1 x 2 3 x 2 4 x
2 2 x 2 9 x 1 3
3 3 2 x x 2 2 2
4 x 9 x x 7 x 4
5 2 x 2 7 x 2 x
6 4 1 2 x 2 x 1
7 x 3 2 4 x 1 x
In this matrix, you'll notice that it is very similar to the first matrix, but it has been modified to be symmetric. In other words, for every non-diagonal value (excluding the x's), the value from the first matrix has been copied to the corresponding position in the second matrix.
For example, in the first matrix, the weight between vertices 2 and 4 is 9. In the second matrix, we copied that weight to the position representing the weight between vertices 4 and 2.
This process has been done to ensure that the matrix is symmetric, which is a property required in certain algorithms, such as Dijkstra's algorithm.
Speaking of Dijkstra's algorithm, it is mentioned in the given information that the second matrix represents the running of Dijkstra's algorithm. Dijkstra's algorithm is a graph search algorithm used to find the shortest path between two vertices in a weighted graph. The second matrix was most likely generated as part of the process of running Dijkstra's algorithm on the graph represented by the first matrix.
In summary, the second matrix is the symmetric version of the first matrix, and it represents the running of Dijkstra's algorithm on the graph represented by the first matrix.