Is this a possibly new algorithm using C++ to provide an inorder iterator for Binary Search Trees?

I did not study details of the algorithm, but why do you think that you have O(1)? You are using the while loop to traverse to the left. You are using rescursion (which is actually a hidden loop and hidden stack -- only using other means). And you are using a stack explicitly. It clearly show at least O(log n).

@pepr, You are correct about 0(Log n). Nonetheless, I just modified the algorithm to be O(1) constant space. Please see below and attached file. Could you comment on this change? Thank you.

#include "stdio.h"
using namespace std;
#include <stack>

 
// BST Node
struct Node
{
    int key;
    struct Node *left;
    struct Node *right;
};

// A utility function to create a new BST node
Node *newNode(int item)
{
    Node *temp =  new Node;
    temp->key = item;
    temp->left = temp->right = NULL;
    return temp;
}
 
/* A utility function to insert a new node with given key in BST */
Node* insert(Node* node, int key)
{
    if (node == NULL) return newNode(key);
    if (key < node->key)
        node->left  = insert(node->left, key);
    else
        node->right = insert(node->right, key);
    return node;
}

class Iterator
{

private:
      Node* thisRoot;
      Node* thisCurr;
      Node* thisMaximum;
      stack<Node*> cards;

      void InOrder(Node* root, Node*& succ, int key)
      {
            // Base case
            if (root == NULL)  return ;
 
            // If key is present at root
             if (root->key == key)
            {
                  // the minimum value in right subtree is successor
                  if (root->right != NULL)
                  {
                        Node* tmp = root->right ;
                        while (tmp->left)
                        {
                                      printf("TEMP %d\n",tmp->key);
                                cards.push(tmp);
                              tmp = tmp->left;
                        }
                        succ = tmp ;
                  }
                   return ;
            }
 
            // If key is smaller than root's key, go to left subtree
            if (root->key > key)
            {
                  succ = root;
                  InOrder(root->left, succ, key) ;
            }
                else
            {
                  if (key == thisMaximum->key)
                  {
                      return;
                  }
                    if (cards.size() > 0)
                  {
                               
                              succ = cards.top();
                          if (succ != NULL && key < thisMaximum->key)
                        {
                                        if (cards.size() > 1)   // This is my latest change for 0(1) space requirement.
                              {
                                              cards.pop();
                              }
                              InOrder(
                                 root->right,
                                 succ,
                                 key) ;
                        }
                  }
            }
      }

      Node* HelperGoLeft(Node* where)
      {
            if (where == NULL)
            {
                  return NULL;
            }
            if (where->left == NULL & where->right ==  NULL)
            {
                  return where;
            }
            return HelperGoLeft(where->left);
      }

      Node* HelperGoRight(Node* where)
      {
            if (where == NULL)
            {
                  return NULL;
            }
            if (where->left == NULL & where->right ==  NULL)
            {
                  return where;
            }
            return HelperGoRight(where->right);
      }

public:

      Iterator(Node* theTree)
      {
            thisRoot =  theTree;
            thisCurr =  HelperGoLeft(thisRoot);
            thisMaximum = HelperGoRight(thisRoot);
      }

      int next()
      {
            struct Node* successor(NULL);
            InOrder(thisRoot, thisCurr, thisCurr->key);
            return thisCurr->key;
      }
      bool HasNext()
      {
            return thisRoot != NULL && thisCurr->key < thisMaximum->key;
      }
};

int main(int argc, char* argv[])
{
    /* Let us create following BST
              50
           /     \
          30      70
         /  \    /  \
       20   40  60   80 */
    Node *root = NULL;
    root = insert(root, 50);
    insert(root, 30);
    insert(root, 20);
    insert(root, 40);
    insert(root, 70);
    insert(root, 60);
    insert(root, 80);
    insert(root, 100);
    insert(root, 90);
    insert(root, 110);
 

     Iterator* test = new Iterator(root);
     while( test->HasNext())
     {      
       printf("%d\n", test->next());
     }      
    return 1;
}
Iterator.cpp

@d-glitch,
                  May I ask you to look at my comment on 2/21/2016 in response to your answer to my Experts Exchange question?  "Using computational imaging and CMOS imaging sensor chips to filter a specific visible light wavelength"?
                 Today , I will test the algorithm on some large, randomly generated binary trees as you recommended.
                Thank you.

I would lke to thank @pepr and @d-glitch for having solved this problem.