Does anyone know how I should approach this algorithm? It needs to have $O(n^3)$ complexity and I can only come up with an algorithm that has $O(n^4)$ complexity (of doing a n^2 min path from each vertex to $n-1$ other vertexes, and since I need to do this n times, it will be $n^4$ or so I think...

Input: Array $A[1...n][1...n]$ such that $A[i][j]$ gives length of edge(distance) between two points or $-1$ if there isn't and edge.

Output: a vertex $v$, such that distances(total lengths) to all other vertexes are minimized.

Can someone explain in pseudocode or in words how to do this?

  • 1
    $\begingroup$ compute all pair shortest path distances, and update the distance matrix. This operation takes $O(n^3)$ using Floyd Warshall algorithm. Now with the updated distance matrix, sum the values along each column (row) and then choose the index with the least sum. $\endgroup$ Dec 4 '17 at 3:00
  • $\begingroup$ We're happy to help you understand the concepts but just solving exercises for you is unlikely to achieve that. You might find this page helpful in improving your question. $\endgroup$
    – D.W.
    Dec 4 '17 at 3:37

you can use Floyd Warshall algorithm to find distance of every pair and then just use a simple for to find the sum of distance of any of vertices and print the minimum of them


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