Converting Recursive Tarjan to Iterative to find SCCs

Question

So I've successfully implemented a recursive tarjan's that provides me the SCC of a graph

My recursive implementation is as follows:

public void DFSRecursive(long currentNode){
    low[currentNode] = preCount++;
    visited[currentNode] = true;
    stack.Push(currentNode);                                                                                                                 
    long minimum = low[currentNode];    
    foreach(long successorNode in SuccessorMap[currentNode])
    {
        if(!visited[successorNode])
        {
            DFSRecursive(successorNode);                 
        }
        if(low[successorNode] < minimum)
        {
        minimum = low[successorNode];
        }
    }
    if(minimum < low[currentNode])
    {
        low[currentNode] = minimum;
        return;
    }
    List<long> component = new List<long>();
    long stackTop;
    do
    {
        stackTop = stack.Pop();
        component.Add(stackTop);
    } 
    while(stackTop != currentNode);
    SCComponent.Add(component);
}

Now I need to convert this to an iterative solution. I have already checked a lot of resources to help me out including a very similar SO question (Non-recursive version of Tarjan's algorithm). I can't use an enumerator since I have to deal with long values and the successor indices of the current state have been stored in a Dictionary(SuccessorMap[]) (need to deal with graphs with # of Nodes > 5 billion).

I have followed the general guidelines available to convert a recursive solution to an iterative one:

Replaced the recursive call with push to the local stack
Replaced "returns" with pop from local stack

Set the variables at the start of the loop and popped from the local stack

public void DFSIterative(long currentNode)
{
    var internalStack = new Stack<long>();
    low[currentNode] = preCount++;          
    stack.Push(currentNode);
    long minimum = low[currentNode];
    internalStack.Push(currentNode);

    while(!(internalStack.Count == 0))
    {
      currentNode = internalStack.Pop();
      visited[currentNode] = true;
      foreach(long successorNode in SuccessorMap[currentNode])
      {
        if(!visited[successorNode])
        {
          internalStack.Push(successorNode); 
        }
        if(low[successorNode] < minimum)
        { 
          minimum = low[successorNode];
        }
      }
      if(minimum < low[currentNode])
      {
        low[currentNode] = minimum;
        return;
      }
   }
   List<long> component = new List<long>();
   long stackTop;
   do
   {
     stackTop = stack.Pop();
 component.Add(w);
   }
   while(stackTop != currentNode);

   SCComponent.Add(component);
   }

I recognize that the do-while loop in the iterative method will always throw a InvalidOperationException(stack empty), but i haven't been figure out implement the recursive do-while iteratively.

Would really appreciate any sort of help to assist me.

Converting Recursive Tarjan to Iterative to find SCCs

0 Answers0