Travelling salesman dynamic programming implementation

Question

So I was implementing a travelling salesman algorithm in C# using the dynamic programming approach, but after studying the well-known pseudocode I learned quite nothing. At least I think so. Nevertheless, here's a glimpse of my code, I would be glad if someone would help me in explaining that C(S,k) function. I think I get what it does, but I'm not quite sure if mine version does what it needs to do.

Pseudocode (slides 25 and 26):

class TSP
{
   public int cols;
   public int[,] matrix;
   public ArrayList solution;
   (...)

}

public int C(ArrayList S, int k)
{
   int min = int.MaxValue;

   if (S.Count == 2)
      min = matrix[0, k];
   else
   {
      foreach (int m in S)
      {
         S.RemoveAt(k);
         if (C(S, m) + matrix[m, k] < min)
            min = C(S, m) + matrix[m, k];
      }
   }
   return min;
}

Yes, I think it should fill an arraylist with solution rather than returning a value...

I have modified it (thanks for the advice) and it looks like:

public int MinimumRouteCostThroughNode(ArrayList RestNodes, int Node)
{
   int RouteCost = int.MaxValue;

   if (RestNodes.Count == 2)
   {
       RouteCost = matrix[0, Node];
   }
   else
   {
       RestNodes.Remove(Node);
       ArrayList CopyOfRestNodes = new ArrayList(RestNodes);          
       foreach (int AnotherNode in RestNodes)
       {
           int MinimumCostThroughNodeAndAnotherNode = MinimumRouteCostThroughNode(CopyOfRestNodes, AnotherNode) + matrix[AnotherNode, Node];
           if (MinimumCostThroughNodeAndAnotherNode < RouteCost)
           {
               RouteCost = MinimumCostThroughNodeAndAnotherNode;
           }
       }
   }
   return RouteCost;
}

When I debug the program it seems to be doing fine, however the RouteCost is each time being over-written and I don't know how can I get a variable (that would stay the same in every recursive? If not then does it mean that I need to make a global variable or pass it in the definition of a function? Or is there another way?

Answer 1

I think its the double recursion that is going on. First in the if statement - if (C(S, m)... then again right below it. min = C(S, m)... that should be called once, tested for min, then set min.

If your foreach loop is changed like this:

  foreach (int m in S)
  {
     S.RemoveAt(k);
     var recurse = C(S, m) + matrix[m, k];
     if (recurse < min)
        min = recurse;
  }