Convert recursive binary tree traversal to iterative

Question

I was asked to write the iterative version, but I wrote the recursive version i.e.

void inorderTraverse(BinaryTree root)
{
    if(root==NULL)
        printf("%d",root->id);
    else
    {
        inorderTraverse(root->left);
        printf("%d",root->id);
        inorderTraverse(root->right);
    }
}

I'm not looking for the code, I want to understand how this can be done. Had it been just the last recursive call, I would have done

void inorderTraverse(BinaryTree root)
{
    while(root!=NULL)
    {
        printf("%d",root->id);
        root=root->right;
    }
}

But how do I convert to an iterative program when there are two recursive calls?

Here are the type definitions.

struct element{
    struct element* parent;
    int id;
    char* name;
    struct element* left;
    struct element* right;
};
typedef element* BinaryTree;

This is what I thought of, am I on the right track?

temp=root;
while(1)
{
    while(temp!=NULL)
    {
     push(s,temp);
     temp=temp->left;
     continue;
    }

    temp=pop(s);
    if(temp==NULL)
    return;
    printf("%d\t",temp->data);
    temp=temp->right;
}

Answer 1

The problem you're seeing is that you need to "remember" the last place you were iterating at.
When doing recursion, the program internally uses "the stack" to remember where to go back to.
But when doing iteration, it doesn't.

Although... does that give you an idea?