Displaying Path to a Node in a Binary Search Tree

Question

I'm working on trying to display the path from the root node of a BST to a target node. The function I have works fine for the first two layers, but then messes up after that. For example, the test numbers are 6, 9, 4, 11, 10(inserted in that order). If I search for 6, 9, or 4, it works (ex: "6 9"). But if I try 11 or 10, it displays them both, and out of order. I'm kind of stumped as to why. Any ideas would be awesome!

template <class T>
void BST<T>::displayPath(T searchKey, BST<T> *node)
{
    if (searchKey == node->mData)
    {
        cout << node->mData << " ";
    }

    else if (searchKey < node->mData )
    {
        cout << node->mData << " ";
        displayPath(searchKey, node->mLeft);
    }
    else// (searchKey > node->mData)
    {
        cout << node->mData << " ";
        displayPath(searchKey, node->mRight);
    }
}

This is the insert function. The numbers are inserted in the order above.

template <class T>
void BST<T>::insert(BST<T> *&node, T data)
{
   // If the tree is empty, make a new node and make it 
   // the root of the tree.
   if (node == NULL)
   { 
      node = new BST<T>(data, NULL, NULL);
      return;
   }

   // If num is already in tree: return.
   if (node->mData == data)
      return;

   // The tree is not empty: insert the new node into the
   // left or right subtree.
   if (data < node->mData)
          insert(node->mLeft, data);
   else
      insert(node->mRight, data);
}

Answer 1

Your code confirms my suspicion. Your method is fine - this is the tree you built from inserting 6, 9, 4, 11, 10 in this order:

first (6):

 6

second (9)

 6
  \
   9

3rd (4)

  6
 / \
4   9

4th (11):

   6
  / \
 /   \
4     9
       \
        \
         11

5th (10):

   6
  / \
 /   \
4     9
       \
        \
         11
         /
        /
       10

So searching for 10, will give you the path (6,9,11,10).

Note that the path from root to an element in a BST is NOT guaranteed to be sorted - if that was what you expected. In fact, it will be sorted only if the node is on the path to the rightest leaf in the tree.

---

Another issue in the code: searching for 7 (or any element that does not exist in the tree) will give you some bogus path.

Answer 2

The code will only work if the input value is in the tree. When you search for a value that isn't there, you're looking for a node that isn't in the tree

template <class T>
void BST<T>::displayPath(T searchKey, BST<T> *node)
{
    if (searchKey == node->mData)
    {
    cout << node->mData << " ";
    }

    else if (searchKey < node->mData )
    {
        cout << node->mData << " ";
        if (node->mLeft == NULL) // When trying to access a node that isn't there
            cout << "Not Found\n";
        else
        displayPath(searchKey, node->mLeft);
    }
    else // (searchKey > node->mData)
    {
        cout << node->mData << " ";
        if (node->mRight == NULL)
            cout << "Not Found\n";
        else
            displayPath(searchKey, node->mRight);
    }
}