Question

I was wondering how (or maybe even if it’s possible) to implement recursion without a separate function that calls itself.
So far all algorithms implementing recursion I’ve seen use a separate function. I thought a lot and came up with the idea that a goto statement with some variable mutation can do the job but I’m really unsure about that.
I made a mini research and found info about this Structured programming theorem which proves that every algorithm can be implemented with only three data structures, so such a recursion implementation must be posible but I still cannot assemble everything into consistent knowledge and understanding for the whole would-be approach.

Answer 1

What you are looking for is basically expressing a recursive function into an iterative form.
This can easily be done by using a Stack. Here’s a very simple example in C#:

int NodeCount(Node n)
{
      if (n.Visited) return 0; // This node was visited through another node, discard
      n.Visited = true;
      int res = 1;
      foreach (Node ni in n.Children) // Recurse on each node
      {
            res += NodeCount(ni); // Add the number of sub node for each node
      }
      return res;           
}

Here’s the exact same function in iterative form:

int NodeCount(Node root)
{
    int res = 0;
    Stack<int> stk = new Stack<int>();
    stk.Push(root) // We start with the root node
    while( stk.Count > 0) // While we still have nodes to visit
    {
          Node current = stk.Pop(); // Get the node on top of the stack
          current.Visited = true;  // Mark it as visited
          res ++; // Add one to the count
          foreach (Node ni in n.Children) // Push all non visited children to the stack
          {     
                if (ni.Visited == false) 
                        stk.Push(ni);
          }

    }
    return res;
}