Question

Two simple questions and my brain’s not working. I’m using Floyd’s Algorithm and trying to reconstruct the path taken from vertex U to vertex V.
Here’s my code to reconstruct the path.

public List<Integer> findCheapestPath(int u, int v)
{
    if (u >= adjMatrix.length || v >= adjMatrix.length || u < 0 || v < 0)
    {
        throw new IllegalArgumentException("Error--Illegal Arugment Exception: One of the verticies are not valid.");
    }
    int intermediate;

    intermediate = path[u][v];
    if (intermediate == -1)
    {
        pathList.add(u);
        return pathList;
    } else
    {
        findCheapestPath(u, intermediate);
        findCheapestPath(intermediate, v);
    }
    return pathList;
}

For one example, let u = 0 and v = 3, and let the shortest path from 0 to 3 be 0,1,2,3.
However I have two problems. My pathList is an instance variable of the class and:

1. I want the list to return “0,1,2,3” but it only returns “0,1,2”, or if i replace pathList.add(u) with pathList.add(v), then it returns
   only “1,2,3” I could not figure out how to make it return the entire
   path including both end vertices. trying to put pathList.add(other
   vertex) will cause it to duplicate every intermediate vertex.
2. When I call the method again, letting u = 3 and v = 0, and let the shortest path from 3 to 0 be “3,0” (already the shortest path), it
   just adds onto my previous list making it with my error from above
   “0,1,2,3” or “1,2,3,0” when it’s supposed to be just “3,0”

Any help?

Answer 1

Don’t use a class variable, and make a wrapper function.

In more detail, change your function to this signature:

private List<Integer> findCheapestPathInner(int u, int v, pathList)

(obviously also changing the recursive call inside it to fit the new signature), and create another function:

public List<Integer> findCheapestPath(int u, int v) {
  List<Integer> pathList = new ArrayList<Integer>();
  pathList.add(u);
  return findCheapestPathInner(u, v, pathList);
}